critical thinking and problem solving skills used in numeracy program ecd

Engaging Maths

Dr catherine attard, promoting creative and critical thinking in mathematics and numeracy.

• by cattard2017
• Posted on June 25, 2017

What is critical and creative thinking, and why is it so important in mathematics and numeracy education?

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies : Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities , one of which is Critical and Creative Thinking – there’s no excuse!

Critical and creative thinking need to be embedded in every mathematics lesson . Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

How and when do we embed critical and creative thinking?

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys  are also very worthwhile tasks. For good mathematical problems go to the nrich website . For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300   (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

Will critical and creative thinking take time away from teaching basic concepts?

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

• higher-level thinking within authentic and meaningful contexts;
• complex problem solving;
• open-ended responses; and
• substantive dialogue and interaction.

Who should be engaging in critical and creative thinking?

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

How will you and your students engage in critical and creative thinking?

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Encouraging Early Numeracy Skills in Your Program

• June 28, 2016

Early numeracy skills, like early literacy, are an important component of school readiness efforts and are an everyday part of even very young children’s lives.

Although definitions of numeracy vary, it is typically understood to mean “the ability to use appropriate mathematical knowledge, …skills,… and experience whenever they are needed in everyday life” (Department of Education of the Arts in Perry, 11). Early numeracy skills, like early literacy, are an important component of school readiness efforts and are an everyday part of even very young children’s lives.

Early mathematical concepts and skills—those which the first-grade mathematics curriculum builds upon—include those listed below (Bowman, B. T., Donovan, M. S., & Burns, M. S., (Eds.), 2001, 76).

• Recognition of size, shape, and patterns
• Ability to count verbally (first forward, then backward)
• Recognition of numerals
• Ability to identify more and less of a quantity
• Mastery of one-to-one correspondence (i.e., matching sets, or knowing which group has four and which has five)

To achieve these skills requires competency in the four keystones of mathematical literacy listed below (Diezmann and Yelland, 2000, pp. 49-52):

• Representation —finding ways to express mathematical concepts with words, diagrams, pictures, symbols and manipulatives (like blocks) Casey (aged 3) was making piles of sunflower seeds. When asked why, he explained: “We need 5 seeds for each kid. I’m helping!”
• Performing Mathematical Manipulations— utilizing the appropriate calculations and procedures, using the information given to answer the question posed Yvette (28 months) and Charlotte (30 months) were standing in the center’s outside play area and crying. When their caregiver, Julia, came over to see why, Yvette explained: “No trikes!” Julia watched several children zooming around on tricycles. “Hmmmm, we need more trikes, you’re right. How many more?” Yvette shouted, “One for me and one for Charlie!” Julia said, “That’s right. We need 2 trikes for you and Charlie. Let’s see if anyone is done riding them yet.”
• Reasoning— assessing a problem using facts, properties and relationships to make and test conjectures, develop logical arguments, and identify a useful answer. Carl (aged 9 months) looked at the toy his early interventionist brought that day. It was a plastic drum with 3 holes in the top. The holes were in the shape of a triangle, a circle and a square. Carl looked at the blocks surrounding him. They, too, were different shapes. Carl picked up a triangular block. He put it in his month, then banged it on the floor. He touched the edges with his fingers. Then he tried to stuff it in each of the holes of the new toy. Surprise! It fell inside the triangle hole! Carl reached for another block, a circular one this time…
• Problem solving— thinking through an issue, using prior knowledge and skills to reach and validate a solution (and realizing more than one solution may exist). Posing one’s own problems. Jennie (aged 18 months) was given a bag of crackers. “Give everybody one,” her caregiver, Teri, said. Jennie gave each child at the table a cracker. But there was one left over. “What should we do with the extra cracker?” asked Teri. Jennie stopped and thought. Then she opened her mouth and popped it in!

Here, numeracy, language and social skills come together. In all of the competencies above, children’s ability to communicate effectively and express their ideas is integral to success with a given mathematical problem—whether it comes up in play (only five children may be in the blocks area at once) or in a more structured setting. Early numeracy experiences provide ample opportunities to develop and extend children’s vocabulary and literacy skills.

Even very young children’s social environments include access to counting systems (how many steps are we walking up?), as well as exposure to principles of one-to-one correspondence (are there enough cookies for each child?) (Bowman, B. T., et al., 2001, p. 201). Prior to entering school, most children develop an innate understanding of addition and subtraction through everyday interactions (Thomas has two shovels; Joseph wants one; after this transaction, Thomas sees that he has one left) (Bowman B. T. et al., 2001, p. 201). This learning occurs at home as well, where parents introduce important numerical concepts through everyday interactions. For example, young children learn that money has a value when they are denied a toy deemed “too expensive.” Family members and other adults support children’s number learning through songs like “One Two, Buckle My Shoe” and stories like “The Three Bears.” This informal foundation in mathematics, forged during very young children’s prior-to-school years, provides a rudimentary conceptual framework from which formal instruction can begin.

The tips below highlight ways that staff members can build upon the natural curiosity of very young children to establish a solid foundation of early numeracy skills. (Note: Most of these tips are designed for older children—ages 2-3. Younger children can be exposed to stories and songs using repetition, rhymes and numbers. Staff, parents and caregivers should also speak to children about mathematical concepts (e.g., “That’s a great big dog! He’s bigger than our cat, isn’t he?”) even though babies don’t yet understand.

Promoting Early Numeracy Skills in Infant/Family Programs

• Help children learn their own address and phone number. Talk with them about how buildings are numbered, how their house or apartment is one of a series, each with its own number.
• Use dress-up time as an opportunity to talk about relative sizes (“the red dress is bigger than the green dress”) as well as to help children begin to think about their own size relative to other objects (“will that policeman’s jacket fit you, do you think?”).
• Home visitors (and center-based staff) can use cooking as a way to introduce mathematical concepts. Even young children can be helped to fill, stir, and pour—through these activities, children learn to count, measure, divide, and estimate.
• Taking a walk gives children many opportunities to compare (“which leaf is bigger?”), assess (“how many leaves does that branch have?”), note similarities and differences (“does the bunny live in the tree? Does the bird?”) and categorize (“see if you can find all the red leaves”).
• Use an hourglass or timer to time activities. This helps children develop a sense of time and to understand that some things take longer than others.
• Point out the different shapes and colors you see during the day. On a walk, you may see a triangle-shaped sign that’s yellow. Inside you may see a rectangle-shaped sign that’s red.
• Sing songs that rhyme, repeat, or have numbers in them. Songs reinforce patterns (which are tools that help in problem-solving because they tell us what to expect next). They also are fun ways to practice language and mathematics.
• Use a calendar. Talk to children about what day it is, what the different days of the week are, and what they can expect the next day.
• Ask for children’s help in distributing items to class members. Requests like “Give one to each child” helps children understand one-to-one correspondence. When you are distributing items, emphasize the number concept: “One for you, one for me, one for Raul.”
• Ask children to sort crayons and markers into containers (or use buttons, pasta, leaves, shells, etc.).
• Provide children with lots of open-ended play with blocks, empty boxes, milk cartons, etc. Stacking and manipulating these toys help children to learn about shapes and the relationships among shapes (e.g., two triangles make a square). Nesting boxes for younger children help them to understand the relationships between different sized objects.
• Give children a cardboard box or tunnel to climb through. This helps them understand their body in space (this is called “spatial relations”).
• Hang pieces of yarn and ask which is the longest and shortest. Have kids arrange the yarn from longest to shortest.
• Pass a shape around and have children look at it and feel it with eyes open and closed.
• Help children practice patterns by stringing beads, making block patterns, or making a pattern with two napkins at snack time.

References:

• Bowman, B. T., Donovan, M. S., & Burns, M. S., (Eds.). (2001).  Eager to learn: Educating our preschoolers.  Washington, DC: National Academy of Sciences.
• Diezmann, C., & Yelland, N. J. (2000). Developing mathematical literacy in the early childhood years. In Yelland, N. J. (Ed.),  Promoting meaningful learning: Innovations in educating early childhood professionals.  (pp.47-58). Washington, DC: National Association for the Education of Young Children.
• Perry, B. (1998/1999).  Early childhood numeracy.  Canberra: Commonwealth of Australia. Available at:  http://www.aamt.edu.au/NUMERACY/PERRY.PDF

Internet Resources:

• www.naeyc.org/resources/eyly/1997/21.htm
• http://members.tripod.com/~Patricia_F/mathscience.html
• www.ed.gov/pubs/EarlyMath/title.html

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MSU Extension Child & Family Development

The importance of critical thinking for young children.

Kylie Rymanowicz, Michigan State University Extension - May 03, 2016

Critical thinking is essential life skill. Learn why it is so important and how you can help children learn and practice these skills.

We use critical thinking skills every day. They help us to make good decisions, understand the consequences of our actions and solve problems. These incredibly important skills are used in everything from putting together puzzles to mapping out the best route to work. It’s the process of using focus and self-control to solve problems and set and follow through on goals. It utilizes other important life skills like making connections , perspective taking and communicating . Basically, critical thinking helps us make good, sound decisions.

Critical thinking

In her book, “Mind in the Making: The seven essential life skills every child needs,” author Ellen Galinsky explains the importance of teaching children critical thinking skills. A child’s natural curiosity helps lay the foundation for critical thinking. Critical thinking requires us to take in information, analyze it and make judgements about it, and that type of active engagement requires imagination and inquisitiveness. As children take in new information, they fill up a library of sorts within their brain. They have to think about how the new information fits in with what they already know, or if it changes any information we already hold to be true.

Supporting the development of critical thinking

Michigan State University Extension has some tips on helping your child learn and practice critical thinking.

• Encourage pursuits of curiosity . The dreaded “why” phase. Help them form and test theories, experiment and try to understand how the world works. Encourage children to explore, ask questions, test their theories, think critically about results and think about changes they could make or things they could do differently.
• Learn from others. Help children think more deeply about things by instilling a love for learning and a desire to understand how things work. Seek out the answers to all of your children’s “why” questions using books, the internet, friends, family or other experts.
• Help children evaluate information. We are often given lots of information at a time, and it is important we evaluate that information to determine if it is true, important and whether or not we should believe it. Help children learn these skills by teaching them to evaluate new information. Have them think about where or who the information is coming from, how it relates to what they already know and why it is or is not important.
• Promote children’s interests. When children are deeply vested in a topic or pursuit, they are more engaged and willing to experiment. The process of expanding their knowledge brings about a lot of opportunities for critical thinking, so to encourage this action helps your child invest in their interests. Whether it is learning about trucks and vehicles or a keen interest in insects, help your child follow their passion.
• Teach problem-solving skills. When dealing with problems or conflicts, it is necessary to use critical thinking skills to understand the problem and come up with possible solutions, so teach them the steps of problem-solving and they will use critical thinking in the process of finding solutions to problems.

For more articles on child development, academic success, parenting and life skill development, please visit the MSU Extension website.

This article was published by Michigan State University Extension . For more information, visit https://extension.msu.edu . To have a digest of information delivered straight to your email inbox, visit https://extension.msu.edu/newsletters . To contact an expert in your area, visit https://extension.msu.edu/experts , or call 888-MSUE4MI (888-678-3464).

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Supporting critical numeracy and maths skills in teaching and learning

In today’s article, Dave Tout, Justine Sakurai and Carly Sawatzki discuss numeracy and its relationship with mathematics, and the importance of real-world contexts. They’ll also share a problem-solving cycle to help students develop their skills and a classroom example of health numeracy, using trampolining as a focus for mathematical investigation .

Over the last couple of years, we have worked collaboratively to help shape and write Victorian senior secondary curricula that better supports the development of critical numeracy and maths skills in our school students. This is the first of two articles where we will share with you some of the research and theory that guided us, our thoughts about the purpose of education, and how these ideas influenced how we wrote those curriculum frameworks.

This first article will describe the background to our approach, and the second article will describe how we have attempted to espouse this in a curriculum document.

But first, what is, or are, our starting points? There are a few key elements behind our approach, including that:

• numeracy is the use and application of mathematical knowledge in context;
• numeracy is a social practice, which means there is always a clear purpose for learning that is connected to the real world;
• there is an implicit numeracy demand within most real-world problems; and,
• underpinning all this is a problem solving approach.

What is numeracy (and its relationships with mathematics)?

From our perspective, numeracy surrounds us in our everyday lives. Numeracy is about using mathematics to make sense of the world and applying mathematics in a context for a social purpose. For most young people and adults, numeracy gives meaning to mathematics, and mathematical knowledge and skills contribute to efficient and critical numeracy.

Students need a range of mathematical knowledge, skills, understandings and dispositions to solve problems in real contexts across personal, further learning, work, and community settings. To become numerate you need to know some mathematics. As Lynn Steen eloquently said:

...numeracy is not the same as mathematics, nor is it an alternative to mathematics. Today's students need both mathematics and numeracy. Whereas mathematics asks students to rise above context, quantitative literacy is anchored in real data that reflect engagement with life's diverse contexts and situations. (Steen, 2001, p.10)

Numeracy is not just about numbers and arithmetic. The mathematical knowledge and skills needed by all students includes number and quantity, measurement, shape, dimensions and directions, data and chance, and mathematical relationships and thinking. It also includes the ability to dip into your toolkit and choose and use the most appropriate analogue tools and digital technologies.

An Australian model of numeracy that we believe illustrates this perspective well is shown in Figure 1 below. This model incorporates four dimensions of contexts, mathematical knowledge, tools, and dispositions that are embedded in a critical orientation to using mathematics.

Why are real-world contexts so important?

Students often report that the mathematics they encounter at school feels disconnected from the real world. They express their frustration via the question, ‘When am I going to use this?’

Curriculum writers certainly intend that teachers bring their curriculum to life through contextualised lessons that connect with students’ real-world experiences. The complex challenges of modern life and work necessitate that schools deliver contextualised learning opportunities – students need higher levels of mathematics and numeracy than ever before and they need practise applying mathematics and numeracy to a range of familiar and unfamiliar authentic problems and issues (AAMT & AiGroup 2014; Binkley et al., 2012; FYA 2017; Gravemeijer et al., 2017).

As students become numerate, they develop the ability to make considered, mathematically-informed decisions, whether they be related to personal financial matters, planning travel arrangements, understanding and interpreting big data such as with the current COVID-19 epidemic, following instructions about a health or medical matter, or understanding the personal and social implications of problematic gambling.

Another of our key underpinning beliefs is that the exploration of real-world issues and problems is more valuable, satisfying and useful for students than the too frequent, often meaningless and repetitive practise of standard mathematical facts, procedures and processes. If students have little experience grappling with the messiness of real-world situations and problems, and if they can only apply mathematical procedures when problems are packaged in very familiar, structured ways (like in traditional maths classrooms and textbooks), then how can we expect them to value, see, use and apply maths in the world outside the classroom?

The AAMT and AiGroup research project referenced above documented this, with one of the teachers involved commenting on this disconnect:

This is one of the most interesting aspects/concepts of this project. The relationship between workplace mathematical skills and school mathematics could be described as ‘distant’ at best. Teacher observation (AAMT & AiGroup, 2014)

Being illiterate is considered an appalling state in modern Australia, yet evidence of significant numbers of students, especially young women, exiting the education system innumerate does not receive the same attention (ABS, 2013; OECD, 2017).

We believe therefore that we, as maths educators, need to support our students to be able to engage with and problem solve when maths is embedded in real-world situations and contexts, and this includes within our maths classrooms, as well as across the curriculum.

An underpinning problem-solving cycle

We believe that students need to develop the skills to problem solve, to investigate and solve a problem where the mathematics is embedded within a real-world context. The contexts should be the starting point, and students need well-planned and guided experiences with a structured problem-solving cycle , so that they know how to move from the real-world context to the mathematical world and apply their mathematical knowledge to find answers and solutions to the problem at hand.

An important aspect of numeracy is the ability to critically reflect on, evaluate and review your outcomes, and finally to be able to communicate and report on what you did and found.

In our curriculum endeavours, our suggested problem-solving cycle is modelled and adapted from the one used in the OECD's Programme for International Student Assessment (PISA) mathematical literacy assessment framework (OECD, 2019). This is consistent with the Figure 1 model. Our model has four distinct components, as represented in Figure 2 below.

The four stages in the problem-solving cycle are:

• Formulate : where you need to identify, select, and interpret the mathematical information embedded in a real-world context and decide and plan what mathematics you need to use and what questions you might ask.
• Act on and use mathematics : in this stage you need to do the maths ­­– perform the mathematical actions and processes so you can complete the task; this includes the use of a range of tools and technologies.
• Evaluate and reflect : here you are expected to check and reflect on both the mathematical processes you used and the reasonableness of your results and outcomes, especially in relation to the real-world context.
• Communicate and repor t: finally, there’s no point to the activity and investigations if you don’t document and report on your outcomes and any results. Here you need to use a combination of informal and formal mathematical representations.

Below is an example of an investigation taken from the context of health and fitness that illustrates the directions that teaching and learning can take when a numeracy problem-solving cycle is used in practice.

A classroom example – health numeracy

Health and safety related contexts provide interesting and useful opportunities to develop numeracy. Mathematical data and evidence can inform an understanding of risks, costs and benefits associated with such things as:

• Health and exercise
• Vaccination
• Prescription medications
• Alcohol and other drugs of addiction
• Medicare and health insurance

When an individual is informed, they are able to make better personal choices. This is not only good for the individual, their family and community, but can limit costs to the economy.

An example of a health and exercise context that might interest young people is trampolining. The backyard trampoline is a great tool in promoting health and fitness, and commercial trampolining centres are popular amongst young people.

The mock media report below includes statistical and numerical representations and language that underpin risk assessment and behaviour choices, and provides a context from which to initially introduce and study the problem. The ability to engage critically with and determine the trustworthiness of health reports presented by politicians, medical experts, journalists and social media influencers is essential.

Students might discuss:

• What is the probability (overall risk) of a spinal or head injury from trampolining?
• Do the benefits of trampolining outweigh the risks?
• What can be done to prevent accidents and injuries?
• What advice should be given to parents and children?

Once they identify the issues, they can mathematise the questions by unpacking the key concepts of probability and statistics using knowledge of fractions and percentages.

Student thinking may be extended by comparing safety figures between commercial centres, or health data from 20 years ago to today. Once students have considered the mathematics, reflecting on their findings should help them situate the problem and decide if the mathematics makes sense in the context.

A lesson may consider both aspects of the trampoline debate; cause of injuries, and building health.

A lesson sequence on trampoline health for younger students might consider asking students to keep a journal over a week or a month – how many times did they jump on their own or a friend’s trampoline? Students could consider how long each jumping session lasted for. They could break it down into ‘guesstimates’ of how much time was doing tricks , and how much time was straight jumps. They could conduct a survey and ask other students too. Their data could be displayed as a visual proportion on a line to aid in student development of estimation and proportional reasoning.

For an investigation, ask your students to estimate how many trampoline jumps would equal a two kilometre run ? How would they work this out? Trampolining provides a real-life context that is relevant and applicable to students’ daily lives, through which they can learn using the problem-solving cycle.

There are many paths that may be taken as you and your students mathematise this problem. They may want to approach this problem using distance as a perspective by converting jumps into lengths? Another method may be for them to time how long it takes to run as opposed to jump? There are no limits to the approaches that may be employed in applying a mathematical lens to the problem. Be as creative and as physically active as you like when carrying out your mathematical investigations.

Once you have completed the mathematical tasking, the results must be looked at and interpreted within the context of the trampolining context. Ask your students to evaluate and reflect on their thinking: Has the question been answered and do the answers make sense in relation to the question? Finish by asking them to write up the results – get them to make a poster or a video.

Whatever angle you choose to take when designing problem-based tasks for your students, remember to keep it real, relatable, and relevant!

Ashby, K., Pointer, S., Eager, D., & Day, L. (2015). Australian trampoline injury patterns and trends. Australian and New Zealand journal of public health , 39 (5), 491-494. https://doi.org/10.1111/1753-6...

Australian Association of Mathematics Teachers (AAMT) & Australian Industry Group (AiGroup). (2014). Tackling the School–Industry Mathematics Divide . Commonwealth of Australia. https://www.chiefscientist.gov... (PDF, 355KB)

Australian Bureau of Statistics. (2013). Programme for the International Assessment of Adult Competencies (Catalogue No. 4228.0). https://www.abs.gov.au/

Binkley, M., Erstad, O., Herman, J., Raizen, S., Ripley, M., Miller-Ricci, M., & Rumble, M. (2012). Defining twenty-first century skills. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and Teaching of 21st Century Skills (pp. 17-66). Springer.

Carbonell, R. (2018, September 15). Double bounced: Why jumpy insurers are hopping out of the trampoline business. ABC News . https://www.abc.net.au/news/2018-09-15/trampoline-boom-loses-its-bounce-with-insurers/10249630

Foundation for Young Australians. (2017). The New Basics: Big data reveals the skills young people need for the New Work Order . FYA. https://www.fya.org.au/wp-content/uploads/2016/04/The-New-Basics_Update_Web.pdf (PDF, 1.5MB)

Geiger, V., Goos, M., & Forgasz, H. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field. ZDM Mathematics Education, 47 (4), 531-548. https://doi.org/10.1007/s11858-015-0708-1

Goos, M., Geiger, V., & Dole, S. (2014). Transforming professional practice in numeracy teaching. In Y. Li, E. Silver, & S. Li (Eds.), Transforming Mathematics Instruction (pp. 81-102). Springer. https://doi.org/10.1007/978-3-319-04993-9_6

Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education , 15 (1), 105-123. https://doi.org/10.1007/s10763-017-9814-6

Michie, F. (2015, September 11). Rise in serious trampoline injuries in children worries trauma specialists, prompts new research. ABC News . https://www.abc.net.au/news/2015-09-11/rise-in-trampoline-injuries-worries-trauma-specialists/6766536

OECD. (2017). Building Skills for All in Australia: Policy Insights from the Survey of Adult Skills. OECD Skills Studies, OECD Publishing. https://doi.org/10.1787/9789264281110-en .

OECD. (2019). PISA 2018 Assessment and Analytical Framework. PISA, OECD Publishing. https://doi.org/10.1787/b25efab8-en .

Sharwood, L. N., Adams, S., Blaszkow, T., & Eager, D. (2018). Increasing injuries as trampoline parks expand within Australia: a call for mandatory standards. Australian and New Zealand Journal of Public Health , 42 (2), 153-156. https://doi.org/10.1111/1753-6405.12783

Steen, L. (2001). Mathematics and Numeracy: Two Literacies, One Language. The Mathematics Educator , (6)1, 10-16.

With a colleague, consider a problem-based task you’ve used in one of your own lessons. Was this problem real, relatable and relevant to your students, their context and experiences? Now, work together to design a new task for an upcoming lesson or topic area that meets these requirements.

Related articles

Developing Critical Numeracy Across the Curriculum

• Critical Numeracy
• Teaching Activities
• Thinking Strategies
• Student Reasoning
• Teacher Experiences
• giving students an opportunity to make sense of the mathematical concepts and make sense of the context before moving to more critical thinking about both.
• giving an opportunity for exploration with others - pairs, groups or whole class discussions where different views are juxtaposed and reconciled.
• giving an opportunity for students to create something using their new knowledge - particularly products which have an audience greater themselves, enabling feedback from a wider community.

Critical Numeracy = understanding + criticality + community + creativity

The Four Resource Model for Critical Numeracy

Critical Numeracy uses a similar model to the Four Resource Model of Critical Literacy (Luke and Freebody ) to build students' capacities to ask questions about the meaning, validity and usefulness of texts containing mathematical concepts or information. By using a similar model to critical literacy students can recruit and build on the visible thinking strategies that they are developing whether in a literacy or numeracy context.

In the process of  applying a critical numeracy lens , students go deeper into the mathematical ideas and deeper into the contexts. They challenge the usefulness of the mathematical ideas in relationship to the context. So rather than just learning the rules of maths they are encouraged to explore and question their application.

The following gives examples of the type of questions you may ask to help students become familiar with the mathematical ideas and the contexts ( De-coding and Meaning-Making ) before applying a more critical lens ( Using and Analysing ). We also give examples of how to help the students creatively use their understandings. We expand on this model in Thinking Strategies where we link to possible Thinking routines that can assist in developing student capacity in each of the quadrants.

Printer friendly version of the Four Resource Model for Critical Numeracy

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ECD Module 3

Unit 4 online study guide, learning unit 4: reflect on the ecd programme.

  After completing this learning unit, you will:

• Have reflected on the ECD programme
• Be able to evaluate the design of activities. 

Reflect on the ECD programme

Reflecting on your ECD programmes is an excellent way to secure that you will always strive towards improvement. Bear in mind that reflections may take place before, during and after implementation of your programme.

Allowing for space, incentive, time, and means for ECD practitioners to reflect on their programmes and practice are all essential for an effective ECD centre. Without feedback and reflection time, ECD practitioners sometimes work mechanically (like they are on auto pilot) and without objectives.

Reflection allows you to build on the strengths of your programme, and to resolve weaknesses and problem areas. This means that the programme is always evolving, strengthening and improving. When you see the positive impact of your programme reflections, you should feel proud and resolve to carry on with renewed energy. Furthermore, the process of self-reflection can also become a vehicle for collaboration.

Make self-reflection a priority, and create space for it. Your own success and that of the ECD depend on your reflection.  

4.1 Obtain feedback from relevant sources on the value and success of the programme

When we want to reflect on the value and success of our EC programme, we have to start by obtaining feedback from relevant stakeholders (the sources of feedback). Let's begin by examining a mind map of who these stakeholders or feedback sources could be. 

a.  Mentors, colleagues and other ECD practitioners Your mentor or your colleagues in the ECD can give you feedback and help you to evaluate how well you are preparing and implementing programmes. You may want to set up regular feedback sessions while you are still building up experience as an ECD practitioner. Later, you could help to mentor or support other new practitioners. A peer feedback group also enables you to obtain relevant feedback from your peers.

b.  ECD principal The ECD centre director or principal will be a highly experienced practitioner, so she will be an excellent feedback source. She will also probably have a bird’s eye view of your playgroup so may see trends and possibilities more easily.

  c.  Parents There are many ways to obtain feedback from parents:

• Informal conversation when dropping or collecting children
• Telephone calls
• Home visits
• Parent meetings
• Questionnaires
• A notebook in the child’s bag that the ECD practitioner and parents use to correspond with each other

Usually, the ECD practitioner will use all of these methods to obtain meaningful feedback, both positive and negative. Remember: you are most likely to receive the best feedback during informal conversations with parents when they are feeling relaxed. Note down relevant suggestions and where appropriate discuss them further at a parent meeting or through a questionnaire.

  e.  Grade R or Foundation Phase teachers Your ECD centre will probably be a feeder centre for one or two local primary schools. Build up a relationship with the Grade R Foundation Phase teachers. They will be in a good position to give feedback on your programme, as they can assess the children’s learning and development when they enter Grade R.

f.  Community members or organisations People outside the immediate ECD centre staff and the children’s families also have an impact on the success of the ECD centre. You can informally ask these individuals for feedback. If what they have to say is really relevant, you may invite them to a parent meeting and ask them to address your colleagues and the children’s parents.  

The feedback book: Have a feedback book on hand at the ECD centre. This can either be your personal feedback book or you can create a book for all the ECD practitioners to use. Write down feedback as you receive it, otherwise you might forget before you have a chance to use a suggestion or share a compliment or complaint with your colleagues. You could also use a comments box or feedback book for those parents who want to remain anonymous. As trust grows, parents will feel more comfortable about speaking directly to you.

  4.1.1 Obtain feedback on the application of the activities

When you conduct evaluations, you collect and examine evidence in order to make judgements about something’s value. An evaluation is basically making value judgements about something by looking at the advantages and disadvantages of that thing. A value judgement is how effective or ineffective, good or bad, successful or unsuccessful something is. When you evaluate something, you want to assess whether it meets its intended goals. So, how does this relate to the evaluation of activities in an ECD playroom? You will have to make value judgements about your activities, their strengths and weaknesses and whether they meet their intended goals.

Why do you need to evaluate the activities you design? Because an evaluation allows you to assess your current teaching practice and improve your future teaching practice. Evaluation gives you the opportunity to:

• Learn from your mistakes
• Identify your areas of strengths and your areas of challenge
• Make sure that you are being effective
• Check how appropriate things are
• Ensure that what you do matches the purpose
• Identify ways in which you can change and grow Evaluation forms an important part of your ongoing professional growth and development as an ECD practitioner.

Evaluations of activities in an ECD playroom have to meet a number of criteria. The evaluations you conduct must:

• Reveal the activities” strengths and weaknesses in relation to their purpose
• Be consistent and systematic
• Draw on feedback, observations and/or reflections
• Assess the contribution of the activities to the ECD”s aims

Let’s look at each one of these in more detail.  

a.  Evaluations must reveal the strengths and weaknesses of activities in relation to their purpose When you design your activities, they always have a purpose which is linked to the developmental outcomes. For example, the purpose might be to develop fine motor skills or to encourage children to share. The purpose is the intended goal of the activity. So, one of the things that you need to evaluate is whether an activity achieved its purpose. You can assess the strengths and weaknesses of an activity in relation to its purpose. The strengths will be successes, the advantages, the effective parts of an activity, what worked. The weaknesses will be the aspects that were not successful, the disadvantages, and the ineffective parts of an activity, what didn’t work.

You can learn from both the strengths and weaknesses of an activity. The strengths of an activity teach you what is effective so that you can use those aspects again. The weaknesses provide you with opportunities to change what didn’t work so you can improve next time you do that activity or when you design another activity.

b.  Evaluations must be consistent and systematic A consistent evaluation is one that always looks at the same criteria. A systematic evaluation is one that is orderly and well planned. So, how can you make your evaluations consistent and systematic? A useful way is to develop a checklist of the criteria that you need to evaluate. Then you can be sure that you are always assessing the same criteria in an orderly way.

The activity plan that you used to describe your activities can form the basis for the checklist of the criteria that you need to evaluate. The table below gives you a checklist based on the Activity Plan:

The comments/evidence column is for comments explaining the rating or evidence to justify the rating. Evidence can be any proof that supports a rating such as a child’s comment, an observation about a resource that broke or the products that the children produce in an activity. The Comments/Evidence column is there to avoid rather meaningless generalisations about activities "going well" or "being a disaster". An evaluation must be specific about how and why an activity is being judged as effective or ineffective.

  c.  Evaluations must draw on observation, reflection or feedback When you conduct an evaluation, you can use three ways to gather information about the value and success of an activity: These three ways are:

• Observation
• Feedback.  

Observation You learned about doing observations when you were evaluating the learning resources you adapted. To recap, observations are about watching the children doing the activity. During an observation you are watching carefully to see whether the purpose of the activity is being achieved and to assess the strengths and weaknesses of the activity. Observation needs to be about what was said and done during the activity. The observation is a good time to complete the checklist. The checklist will help to record the observations and allows space to note down examples to illustrate comments.

Observation is part of an ongoing cycle: you observe the children during the activity, record your observations, evaluate the activity and then you use these evaluation comments to help you to improve your activity and design new activities. Then you implement (do) your improved activity or your new activity and the cycle starts again. In this way, your observation and evaluation inform your practice (that means that your practice is based on your observation and evaluation).  

Feedback Feedback is information about a performance that leads to action to affirm or develop performance. The "performance" in this case is the activity. So, how is feedback different from reflection? Both are based on observation but reflection is usually self-reflection, it is what you think and feel about the activity. Feedback usually comes from other people such as your colleagues, the children in you playgroup and their parents. In a way, you could say that reflection is your own feedback on an activity and feedback is other people’s reflections on an activity.

Feedback gives you the information you need to reinforce the effective things you are doing and to identify areas where you can improve. When you get feedback, it should motivate you to improve yourself as an ECD practitioner. Feedback is an essential part of your own learning. It helps you to maximise your potential, raise your awareness of your strengths and weaknesses, and identify actions you can take to improve your performance. Feedback helps you to plan productively for the next activity.

Feedback can be informal or formal. Informal feedback could be a comment from a child, a parent, or a colleague during or after the activity. For example, a child might say "I don’t like this glue. It doesn’t stick". From that feedback you would know that you need to improve the quality of the glue next time. A parent might say "I don’t know what you did but all of a sudden James can button his shirt. Thank you!" From that feedback you would know that the activities you’ve been doing to develop fine motor skills and putting on clothes are successful. A colleague might say "Your group was so excited at snack time. They couldn’t stop talking about what fun they had in the music ring. You must share that activity with me."

Formal feedback would be a planned event. For example, you might ask a colleague to sit in on an activity and make observations and then give you feedback. Or you could work with parents to address a specific need of their child and have a feedback discussion about whether the activities are helping or not.

Often formal feedback from a colleague is given by using a feedback form. Your colleague will complete the form while she is observing your activity and then use it as the basis to give you feedback afterwards.

The table below gives an example of a feedback form.

  As you can see, this kind of observation is much more open-ended than the checklist you developed for observation. But your colleague can also use the checklist as a guide to the sorts of things for which to look. As with the checklist, your colleague needs to provide evidence and examples in the comments that she writes on the feedback form.

Your colleague will use this feedback form as the basis for the feedback session you will have. Usually colleagues evaluate one another so you will have opportunities to reinforce positive behaviours and strengths as much as looking at areas where improvement can be made. When you are doing a peer observation, you need to give as much attention to the evidence for effective performance as for ineffective performance. You need to give both affirmative and developmental feedback. Affirmative feedback tells your colleague what she did well. Its purpose is to encourage the person and to reinforce their behaviour. Developmental feedback tells your colleague what needs to be done better and how to do it. Its purpose is to help the person see how she could do better next time. The key to successful feedback is to give the person a manageable amount to go away with and put into practice.

When you evaluate an activity you will always use observation and self-reflection but you should also try to use feedback from others as well. This will give you a more balanced way to evaluate your activities. You may be too judgemental of your own activities or you may be unable to see any problems. Another person’s observations and feedback will help you to see the activity from another perspective.

4.2 Reflect to identify strengths and weaknesses of the programme

As an ECD practitioner, you need to know how to evaluate the activities you design. You must know how to reveal the strengths and weaknesses of your activities. The purpose of finding out what works and what doesn’t is so you can improve and extend the activities you have designed. When you evaluate your activities you need to do so in a consistent and systematic way. You need to get feedback from a variety of relevant sources such as your colleagues, the children in your playgroup and their parents. You also need to do self-reflection and record the findings of your evaluation.

  4.2.1 Identify the strengths and weaknesses of the activities

A strengths and weaknesses table is a useful way to organise anecdotal feedback comments (that means, comments based on individual’s stories and comments). Use this table to do revision of your programme. Pay particular attention to recurring feedback, for example when you hear similar suggestions from the parents or from several different stakeholders. You may like to call on your mentor or a group of peers when you do programme revisions, to make sure you retain the strengths of the programme so that children feel safe and secure.

The following table is an example of an ECD”s strengths and weaknesses:  

How does the programme contribute meaningfully to the overall aims of the ECD service?

What are the overall aims of your ECD service? Usually these aims are stated in an ECD centre’s vision and mission. For example, let’s examine the aims of a typical ECD service. The ECD service below lists six main aims. It states that by participating in the ECD learning programme, children will:

• Develop confidence and self-reliance in themselves as learners
• Demonstrate curiosity and enjoy learning
• Develop the ability to focus their attention and complete structured activities
• Develop a level of communicative competence that is personally satisfying
• Acquire social skills and abilities which enable them to relate to other children and to adults
• Remain true to their individual natures, being free to develop to their own potentials.

This is a very useful set of overall aims. For you as an ECD practitioner, a set of aims like this can help you reflect and adjust your learning programme effectively. For example, you could use a rubric to help you check if your learning programme is matching the identified aims.

The following table is an example of a rubric to check how programme matches its stated aims:

4.3 Reflect to identify the extent to which the programme contributes meaningfully to the overall aims of the ECD service

Once you have made or adapted and used a resource, you need to reflect on how effective it was in achieving its purpose and whether any improvements or changes are needed. There are various steps in reflection that we will discuss.

  Why reflect? Reflection is about examining and reviewing a product or process. It is defined as: “ to think, ponder, or meditate”.   We need to reflect on our resources in order to:

• Ensure that the resource supported the activity adequately and did not distract from the planned learning outcomes
• Identify whether it was useful, effective and appropriate for the activity and the developmental needs and interests of the children
• Identify its suitability in terms of an ECD context and learning programme
• Look at possible improvements as regards its safety, durability, bias and ability to meet any special needs of learners

We do not always willingly reflect on our work – we normally only do so when it is required of us and somehow feel that we are on the defensive. Unless we are honest in our reflections, we will never be able to improve on our efforts or the resources we have provided. There is a difference between being overly critical and being reflective. When we reflect we do so because we want to grow and learn.  

As an ECD practitioner, you will need to develop these skills and reflect on your practice so that you can develop yourself and your facilitation skills. You have to challenge yourself to become more creative and to grow. As you grow, so the children in your care will benefit and you will find that dealing with the challenges of each day in a school become easier.

Instead of seeing reflections and evaluations as a burden – see them as an opportunity.

Remember, “ Attitude determines altitude ”.  

4.3.1 Reflect on the extent to which the designed activities contribute meaningfully to the overall aims of the ECD service

As you know, when you reflect on something, you look at it carefully and think about it critically. Reflection is about examining and reviewing. When you are busy facilitating an activity you tend to make quick decisions to deal with any issues that arise. Reflection allows you the luxury of time to examine these decisions at your leisure and make further decisions about how you wish to respond should similar circumstances arise again. These decisions then become part of your activity when you do it again. Observation is done during an activity but reflection is done after an activity.

After doing an activity, it is important to stop and reflect on the activity. This is not so that you can indulge in self-congratulation or regrets, but rather so that you may have a basis for your own learning by reflecting on experience: this activity was unsatisfactory, what could I have done to improve it? Or: this activity was good, what was it exactly that made it good?

When you reflect you can ask yourself: "Did the activity go according to plan?" Although an activity that went according to plan will probably be effective, you also need to ask yourself whether the plan was a good one in the first place. A sensitive and flexible ECD practitioner will plan with different needs in mind and adapt to various changing circumstances such as the needs of the children.

You should try to reflect on an activity as soon after you have done the activity as possible. This is so your ideas and observations are still fresh in your mind. Your reflection notes don’t need to be long but you do need to write your thoughts down. That is why there is a section for reflection at the end of each Activity Plan.

Like observation, reflection is part of an ongoing learning cycle. In this learning cycle, you plan an activity and then you do the activity. After doing the activity you reflect on the activity and use that reflection to again direct your next action. That action could be to improve your activity, try something different or use something similar for a different purpose. Then you are back into planning and the cycle continues.  

4.4 Identify and note ways to improve upon the programme for future plans and programmes

As an ECD practitioner, you need to make sure that you evaluate your programme activities regularly. The best way to do this is to structure evaluation sessions and stick to them! Most effective ECD practitioners use an evaluation schedule like this:

ECD Evaluation schedule  

a.  Daily evaluation Write up feedback comments on Activity Plans and daily programme during the day. At the end of the day, take ten minutes to reflect and make simple adjustments.

b.  Weekly evaluation At the end of the week, take 15 minutes to reflect on the weekly programme. Notice any problem areas you experienced. Also, check the feedback book. Make any revisions to the following week’s programme.

  c.  End of term evaluation Meet with other ECD practitioners. Review the programme together. Check that the learning programme for different playgroups link well together. Ask questions like the ones in the checklist that follows. Discuss and implement improvements strategies.

Making an effort to improve your ECD service How can you ensure that you provide a consistently good quality ECD service? You always have to make efforts to improve the quality of the service you offer. You can do this by identifying the problems and weaknesses in your ECD service. You can also build on your strengths and what you already have in place in your ECD service. Remember to work co-operatively with co-workers, families and the community. These groups know your ECD service well. They will have many ideas for ways to improve. They may also notice problems and weaknesses that you have overlooked.

  Suggested ways to improve the quality of your ECD service

• Do you recognise the individual needs of the child?
• Are you accountable to the community and caregivers?
• Do you provide experiences that challenge children, and are achievable?
• Are problem-solving and critical thinking an integral part of the programme?
• Do you provide opportunities for the child to develop in a holistic way?
• Do you avoid stereotyping and bias?
• Do you encourage integrated learning?
• Are there many opportunities for experiential learning?
• Do you insist on regular assessment and evaluation?
• Do you encourage free play and unguided activities?
• Do you plan in advance?
• Do you spend enough time playing with the children?
• Do you meet regularly as staff to discuss the children’s progress as well as the standard of care and education?

Now take a look at these opportunities:

1. Do you recognise the individual needs of the child? All children are different and need to be treated as special. They acquire knowledge and skills at different developmental stages. As an ECD practitioner, you must take this into consideration when you plan your ECD programme. The mode of learning will not be the same for each child.

2 .  Are you accountable to the community and caregivers? As a practitioner you need to be transparent and available to those who entrust their children to your care. The parent and caregiver community should be kept informed of and involved with what is happening in the playschool.  We can no longer be practitioners in isolation. We need to work with the community and share expertise with colleagues. It is up to you to be well-informed and knowledgeable of ongoing developments in early childhood development.

3.   Do you provide experiences that challenge children and are achievable? As an ECD practitioner you take learners from the known to the unknown. Small children have had varied experiences. Which provide you with a starting point? Try not to under- or over estimate what a young child is capable of learning. Provide a stimulating learning environment where children can be challenged to reach their full potential. If you know your learners well, it will be easier for you to provide an enriching programme.  

4.   Are problem-solving and critical thinking an integral part of the programme? Problem solving is a process of thinking, identifying and finding solutions to everyday situations. This is a life skill that helps children to feel independent and builds their self-esteem. They learn that they have the resources to deal with situations that need answers. This realisation empowers the child to try out possibilities in a supportive environment. It implies that you should avoid stepping in before a child has had the chance to try something for him/herself. You should never interfere to the extent that you stunt (inhibit) their experiential learning.

5.   Do you allow the child to develop in a holistic way? The child should develop emotionally, intellectually, physically, socially, spiritually and creatively. Such holistic development can be achieved through interactive play, storytelling, listening to music, discussing feelings, drama and role play. Children also need to be exposed to an assortment of resources that they explore in a variety of ways.

6. Do you avoid stereotyping and bias? You can encourage children to respect and value all human beings by helping them to understand and celebrate our different cultures, traditions, social customs likes and dislikes. You, as the ECD practitioner, need to have an unbiased approach to gender, race, language, physical ability and children’s special needs. You also need to be aware of other forms of bias that might influence your teaching.

Remember, the children will see you as their role model when they have to deal with their peers.

7.   Do you encourage integrated learning? Children learn best in an integrated environment rather than in isolation. The curriculum should combine all learning areas where possible and avoid fragmentation (breaking up the content into bits and pieces). For example, if "water" is the topic for the week, you could incorporate a story about water (e.g. the water cycle), measuring by using containers of different sizes and shapes, a song about water, uses of water in the home, experiments with water, stories about water the possibilities are endless. Literacy, numeracy and life skills as explained in the NCS documents can be focused on individual skills. However, they are all interrelated and occur throughout the day in the ECD environment.

8.   Are there many opportunities for experiential learning? A hands-on approach is worthwhile and valuable. Children learn best when they do and see, rather than from just being told. Active learning is far more effective than passive rote learning and memorising. You can promote active learning by using different questioning techniques, experimentation and wide variety of different learning materials.  

9. Do you insist on regular assessment and evaluation? Plan your programme to include continuous assessment and evaluation. Ongoing observation and reviewing of the learners” skills and abilities is an integral part of the ECD practitioner’s day. This helps with the learning process and assists the practitioner when planning her or his programme. The concept of continuous assessment and evaluation is one of the philosophical pillars on which outcomes-based education is based. Do keep in mind that testing can be very stressful for young children, and that the results are not always reliable, because children also have good and bad days.

10.   Do you encourage free play and unguided activities? Informal play and games are very important for the child’s development because they promote curiosity, problem solving and co-operative learning skills. Not all activities should be guided. Children should be encouraged to experiment, discover and invent their own activities and rules.

11. Do you spend enough time playing with the children? Play is the most important activity in the lives of children. Sometimes it seems more important than eating and sleeping. This can be easy and fun and also involve trying hard to do something right.

Play is the work, the occupation of childhood.

Why is play important?

• Play is important because it helps children grow strong and healthy
• Play is important because children can learn about the meaning of things in the world
• Play is important because it helps children learn about people
• Play is important because it helps children learn and grow in a way that helps them feel good about themselves
• Play is important because it is practice for being grown-up

You as an ECD practitioner do not work in isolation. Meeting with one another to discuss problems will always improve conditions for the children. This not only supplies support to one another but allows you to help less experienced staff members to deal with issues and to maintain quality.

  4.4.1 Identify and record useful ways to improve upon and extend the activities for further use

If an activity does not work, it doesn’t mean you are a "bad" teacher. You are only a "bad" teacher if you don’t reflect on your activities and make the effort to revise the elements of the activity that did not work. The whole point of doing evaluations is for you to improve and extend your teaching practice. A good evaluation should highlight both the strengths and weaknesses of an activity. There are different ways to use evaluations to improve and extend activities. When you evaluate the strengths of an activity you are asking yourself questions such as "What worked?" "Why did it work?" The point is to learn what you are good at. Perhaps you can use this information to improve something else that didn’t work. Or you can extend that which worked for one activity when you design another activity.

When you evaluate the weaknesses of an activity you are asking yourself questions such as "What problems arose?" "Why did they arise?" "How did I deal with them?" The purpose of this questioning is not to focus on the negative. The point is to learn from what has happened. You can turn problems and weaknesses into opportunities to improve and extend your teaching practice.

A good evaluation probes beneath the surface of issues and does not quickly assume that the source of an issue has been located. This involves a willingness to keep asking "why?" and to consider alternative explanations. For example, was your playgroup "unresponsive" to an activity because they were bored or because it was too difficult or was it the specific time of day and they were too tired? You need to keep digging until you find a reasonable explanation for an issue.

When you discussed doing observations and giving feedback, you were encouraged to be specific. This will help you when you want to make changes to your activities. You can look at an activity and ask yourself questions about each aspect such as:

• What could I have done in my design to avoid problems?
• If I do this activity again, which specific areas need to be improved?
• How can I improve those specific areas?
• What extension activities can I do to help the children with needs and issues that arose from the activity?
• What follow-up activities can I do to consolidate the skills the children developed in this activity?

  A good evaluation will consider alternative approaches, which could be adopted in future activities. Your adoption of these approaches will be firmly based on the evidence from the evaluation of the activity. It will not just be a case of randomly trying something different. Teaching is a profession that requires constant introspection (looking at yourself and your teaching style) for serious growth and development to take place.

When you have decided how to improve and extend your activities, you need to record your decisions. The Activity Plan that you used to describe your activities has a section for evaluation where you can record your decisions. This section will be a summary of all the feedback, observations and reflections that make up your evaluation as well as the decisions you have made to improve and extend your activity based on that evaluation. You need to record these decisions to help you when you want to do the activity again or when you design another activity. You also need to record the decisions to help any other ECD practitioner who wants to use your Activity Plan. Keep your evaluations in the file with your Activity Plans. This file is an important resource to help you grow and develop as an ECD practitioner.

Summative Assessment

You are required to complete a number of summative assessment activities in your Learner Portfolio of Evidence Guide. The Learner Portfolio of Evidence Guide will guide you as to what you are required to do:

• Complete all the required administration documents and submit all the required documentation, such as a certified copy of your ID, a copy of your CV and relevant certificates of achievement:
• Learner personal information form
• Pre-assessment preparation sheet
• Assessment plan document
• Declaration of authenticity form
• Appeals procedure declaration form
• Place your complete learner workbook (with the completed class activities) in the specified place in the learner PoE guide
• Complete the knowledge questions under the guidance of your facilitator:

• Complete the other summative assessment activities in your workplace:

Once you have completed all the summative activities in your Learner PoE guide, complete the assessment activities checklist to ensure that you have submitted all the required evidence for your portfolio, before submitting your portfolio for assessment.

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• Open access
• Published: 11 January 2023

The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1  

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

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• Science, technology and society

Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

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Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

Bensley DA, Spero RA (2014) Improving critical thinking skills and meta-cognitive monitoring through direct infusion. Think Skills Creat 12:55–68. https://doi.org/10.1016/j.tsc.2014.02.001

Article   Google Scholar  

Castle A (2009) Defining and assessing critical thinking skills for student radiographers. Radiography 15(1):70–76. https://doi.org/10.1016/j.radi.2007.10.007

Chen XD (2013) An empirical study on the influence of PBL teaching model on critical thinking ability of non-English majors. J PLA Foreign Lang College 36 (04):68–72

Google Scholar  

Cohen A (1992) Antecedents of organizational commitment across occupational groups: a meta-analysis. J Organ Behav. https://doi.org/10.1002/job.4030130602

Cooper H (2010) Research synthesis and meta-analysis: a step-by-step approach, 4th edn. Sage, London, England

Cindy HS (2004) Problem-based learning: what and how do students learn? Educ Psychol Rev 51(1):31–39

Duch BJ, Gron SD, Allen DE (2001) The power of problem-based learning: a practical “how to” for teaching undergraduate courses in any discipline. Stylus Educ Sci 2:190–198

Ennis RH (1989) Critical thinking and subject specificity: clarification and needed research. Educ Res 18(3):4–10. https://doi.org/10.3102/0013189x018003004

Facione PA (1990) Critical thinking: a statement of expert consensus for purposes of educational assessment and instruction. Research findings and recommendations. Eric document reproduction service. https://eric.ed.gov/?id=ed315423

Facione PA, Facione NC (1992) The California Critical Thinking Dispositions Inventory (CCTDI) and the CCTDI test manual. California Academic Press, Millbrae, CA

Forawi SA (2016) Standard-based science education and critical thinking. Think Skills Creat 20:52–62. https://doi.org/10.1016/j.tsc.2016.02.005

Halpern DF (2001) Assessing the effectiveness of critical thinking instruction. J Gen Educ 50(4):270–286. https://doi.org/10.2307/27797889

Hu WP, Liu J (2015) Cultivation of pupils’ thinking ability: a five-year follow-up study. Psychol Behav Res 13(05):648–654. https://doi.org/10.3969/j.issn.1672-0628.2015.05.010

Huber K (2016) Does college teach critical thinking? A meta-analysis. Rev Educ Res 86(2):431–468. https://doi.org/10.3102/0034654315605917

Kek MYCA, Huijser H (2011) The power of problem-based learning in developing critical thinking skills: preparing students for tomorrow’s digital futures in today’s classrooms. High Educ Res Dev 30(3):329–341. https://doi.org/10.1080/07294360.2010.501074

Kuncel NR (2011) Measurement and meaning of critical thinking (Research report for the NRC 21st Century Skills Workshop). National Research Council, Washington, DC

Kyndt E, Raes E, Lismont B, Timmers F, Cascallar E, Dochy F (2013) A meta-analysis of the effects of face-to-face cooperative learning. Do recent studies falsify or verify earlier findings? Educ Res Rev 10(2):133–149. https://doi.org/10.1016/j.edurev.2013.02.002

Leng J, Lu XX (2020) Is critical thinking really teachable?—A meta-analysis based on 79 experimental or quasi experimental studies. Open Educ Res 26(06):110–118. https://doi.org/10.13966/j.cnki.kfjyyj.2020.06.011

Liang YZ, Zhu K, Zhao CL (2017) An empirical study on the depth of interaction promoted by collaborative problem solving learning activities. J E-educ Res 38(10):87–92. https://doi.org/10.13811/j.cnki.eer.2017.10.014

Lipsey M, Wilson D (2001) Practical meta-analysis. International Educational and Professional, London, pp. 92–160

Liu Z, Wu W, Jiang Q (2020) A study on the influence of problem based learning on college students’ critical thinking-based on a meta-analysis of 31 studies. Explor High Educ 03:43–49

Morris SB (2008) Estimating effect sizes from pretest-posttest-control group designs. Organ Res Methods 11(2):364–386. https://doi.org/10.1177/1094428106291059

Article   ADS   Google Scholar  

Mulnix JW (2012) Thinking critically about critical thinking. Educ Philos Theory 44(5):464–479. https://doi.org/10.1111/j.1469-5812.2010.00673.x

Naber J, Wyatt TH (2014) The effect of reflective writing interventions on the critical thinking skills and dispositions of baccalaureate nursing students. Nurse Educ Today 34(1):67–72. https://doi.org/10.1016/j.nedt.2013.04.002

National Research Council (2012) Education for life and work: developing transferable knowledge and skills in the 21st century. The National Academies Press, Washington, DC

Niu L, Behar HLS, Garvan CW (2013) Do instructional interventions influence college students’ critical thinking skills? A meta-analysis. Educ Res Rev 9(12):114–128. https://doi.org/10.1016/j.edurev.2012.12.002

Peng ZM, Deng L (2017) Towards the core of education reform: cultivating critical thinking skills as the core of skills in the 21st century. Res Educ Dev 24:57–63. https://doi.org/10.14121/j.cnki.1008-3855.2017.24.011

Reiser BJ (2004) Scaffolding complex learning: the mechanisms of structuring and problematizing student work. J Learn Sci 13(3):273–304. https://doi.org/10.1207/s15327809jls1303_2

Ruggiero VR (2012) The art of thinking: a guide to critical and creative thought, 4th edn. Harper Collins College Publishers, New York

Schellens T, Valcke M (2006) Fostering knowledge construction in university students through asynchronous discussion groups. Comput Educ 46(4):349–370. https://doi.org/10.1016/j.compedu.2004.07.010

Sendag S, Odabasi HF (2009) Effects of an online problem based learning course on content knowledge acquisition and critical thinking skills. Comput Educ 53(1):132–141. https://doi.org/10.1016/j.compedu.2009.01.008

Sison R (2008) Investigating Pair Programming in a Software Engineering Course in an Asian Setting. 2008 15th Asia-Pacific Software Engineering Conference, pp. 325–331. https://doi.org/10.1109/APSEC.2008.61

Simpson E, Courtney M (2002) Critical thinking in nursing education: literature review. Mary Courtney 8(2):89–98

Stewart L, Tierney J, Burdett S (2006) Do systematic reviews based on individual patient data offer a means of circumventing biases associated with trial publications? Publication bias in meta-analysis. John Wiley and Sons Inc, New York, pp. 261–286

Tiwari A, Lai P, So M, Yuen K (2010) A comparison of the effects of problem-based learning and lecturing on the development of students’ critical thinking. Med Educ 40(6):547–554. https://doi.org/10.1111/j.1365-2929.2006.02481.x

Wood D, Bruner JS, Ross G (2006) The role of tutoring in problem solving. J Child Psychol Psychiatry 17(2):89–100. https://doi.org/10.1111/j.1469-7610.1976.tb00381.x

Wei T, Hong S (2022) The meaning and realization of teachable critical thinking. Educ Theory Practice 10:51–57

Xu EW, Wang W, Wang QX (2022) A meta-analysis of the effectiveness of programming teaching in promoting K-12 students’ computational thinking. Educ Inf Technol. https://doi.org/10.1007/s10639-022-11445-2

Yang YC, Newby T, Bill R (2008) Facilitating interactions through structured web-based bulletin boards: a quasi-experimental study on promoting learners’ critical thinking skills. Comput Educ 50(4):1572–1585. https://doi.org/10.1016/j.compedu.2007.04.006

Yore LD, Pimm D, Tuan HL (2007) The literacy component of mathematical and scientific literacy. Int J Sci Math Educ 5(4):559–589. https://doi.org/10.1007/s10763-007-9089-4

Zhang T, Zhang S, Gao QQ, Wang JH (2022) Research on the development of learners’ critical thinking in online peer review. Audio Visual Educ Res 6:53–60. https://doi.org/10.13811/j.cnki.eer.2022.06.08

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Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

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Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

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South African Journal of Childhood Education    |    ISSN: 2223-7674 (PRINT)    |    ISSN: 2223-7682 (ONLINE)

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Problem-Solving Skills, Memory Power, and Early Childhood Mathematics: Understanding the Significance of the Early Childhood Mathematics in an Individual’s Life

• Published: 09 January 2024

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Early childhood mathematics is the process of teaching mathematics and learning mathematics in a playful manner to the interests and questions of children. Early childhood mathematics includes counting and the application of counting, which includes mathematical activities such as sorting, matching, and pattern recognition. Deeper understanding of basic math concepts that include number sense, shapes and spatial awareness, measurement, patterns, and basic operations such as addition and subtraction. This study aims to investigate the relationship between children’s mathematical knowledge and skills developed in early stages and their later achievements in mathematics. Research data were collected from 53 children’s parents and 36 experts through telephonic interview questionnaire methods. The data collected was analyzed using SPSS software. The validity and reliability of the variables in the questionnaire have been tested. The results of this study reveal a significant positive correlation between children’s early mathematical knowledge and skills and later achievement in mathematics. Specifically, children who demonstrated higher levels of mathematical competencies during their early years exhibited greater success in later academic performance in mathematics. Additionally, the study identified several factors that influence this relationship, including parental involvement, socioeconomic status, and quality of early mathematics instruction. The novelty of this study is highlighting the importance of early math development; it leads to an understanding of educational practices that improve children’s math learning and promote future success in math. Based on the study findings, it is suggested that educators and policymakers emphasize the importance of early mathematical education and provide targeted interventions and support to enhance children’s mathematical knowledge and skills during their formative years.

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Agoestanto, A., & Kharis, M. (2018). March. Characteristic of critical and creative thinking of students of mathematics education study program. In Journal of Physics: Conference Series, 983 (1), 012076. IOP Publishing.

Aunio, P. (2019). Early numeracy skills learning and learning difficulties—evidence-based assessment and interventions. In Cognitive foundations for improving mathematical learning 195–214. Academic Press.

Bang, H. J., Li, L., & Flynn, K. (2023). Efficacy of an adaptive game-based math learning app to support personalized learning and improve early elementary school students’ learning. Early Childhood Education Journal, 51 (4), 717–732.

Article   Google Scholar  

Björklund, C., van den Heuvel-Panhuizen, M., & Kullberg, A. (2020). Research on early childhood mathematics teaching and learning. ZDM, 52 , 607–619.

Cevikbas, M., & Kaiser, G. (2023). Can flipped classroom pedagogy offer promising perspectives for mathematics education on pandemic-related issues? A systematic literature review. ZDM–Mathematics Education , 55 (1), 177–191.

DiStefano, M., Retanal, F., Bureau, J. F., Hunt, T. E., Lafay, A., Osana, H. P., & Maloney, E. A. (2023). Relations between math achievement, math anxiety, and the quality of parent–child interactions while solving math problems. Education Sciences , 13 (3), 307.

Dolapcioglu, S., & Doğanay, A. (2022). Development of critical thinking in mathematics classes via authentic learning: An action research. International Journal of Mathematical Education in Science and Technology, 53 (6), 1363–1386.

Dowker, A., Cheriton, O., Horton, R., & Mark, W. (2019). Relationships between attitudes and performance in young children’s mathematics. Educational Studies in Mathematics, 100 , 211–230.

Ferres-Forga, N., Halberda, J., Batalla-Ferres, A., & Bonatti, L. L. (2022). Improving mathematics performance in 7-year-old children: Training the mapping from estimated quantities to Arabic digits. Journal of Numerical Cognition, 8 (1), 123–147.

Genc, M., & Erbas, A. K. (2019). Secondary mathematics teachers’ conceptions of mathematical literacy. International Journal of Education in Mathematics, Science and Technology, 7 (3), 222–237.

Google Scholar  

Goldsmith, J. S., & Kurpius, S. E. R. (2018). Fostering the academic success of their children: Voices of Mexican immigrant parents. The Journal of Educational Research, 111 (5), 564–573.

Grimm, D., Bauer, J., Wise, P., Krüger, M., Simonsen, U., Wehland, M., Infanger, M., & Corydon, T. J. (2020), December. The role of SOX family members in solid tumours and metastasis. In Seminars in cancer biology, 67 , 122–153. Academic Press.

Hasibuan, A. M., Saragih, S., & Amry, Z. (2019). Development of learning materials based on realistic mathematics education to improve problem solving ability and student learning independence. International Electronic Journal of Mathematics Education, 14 (1), 243–252.

Hassan, M. N., Abdullah, A. H., Ismail, N., Suhud, S. N. A., & Hamzah, M. H. (2019). Mathematics curriculum framework for early childhood education based on science, technology, engineering and mathematics (STEM). International Electronic Journal of Mathematics Education, 14 (1), 15–31.

Hu, B. Y., Wu, H., Curby, T. W., Wu, Z., & Zhang, X. (2018). Teacher–child interaction quality, attitudes toward reading, and literacy achievement of Chinese preschool children: Mediation and moderation analysis. Learning and Individual Differences, 68 , 1–11.

Huang, M. C. L., Chou, C. Y., Wu, Y. T., Shih, J. L., Yeh, C. Y., Lao, A. C., Fong, H., Lin, Y. F., & Chan, T. W. (2020). Interest-driven video creation for learning mathematics. Journal of Computers in Education, 7 , 395–433.

Huang, X., Zhang, J., & Hudson, L. (2019). Impact of math self-efficacy, math anxiety, and growth mindset on math and science career interest for middle school students: The gender moderating effect. European Journal of Psychology of Education, 34 , 621–640.

Lam, P. C. (2018). Bridging beliefs and practices: A study of Hong Kong kindergarten teachers' perceptions of “learning through play” and the implementation of “play” in their practices (Doctoral dissertation, Northeastern University).

Lange, A. A., Robertson, L., Tian, Q., Nivens, R., & Price, J. (2022). The effects of an early childhood-elementary teacher preparation program in STEM on pre-service teachers. Eurasia Journal of Mathematics, Science and Technology Education , 18 (12), em2197.

Lindmeier, A., Seemann, S., Kuratli-Geeler, S., Wullschleger, A., Dunekacke, S., Leuchter, M., Vogt, F., Opitz, E. M., & Heinze, A. (2020). Modelling early childhood teachers’ mathematics-specific professional competence and its differential growth through professional development–an aspect of structural validity. Research in Mathematics Education, 22 (2), 168–187.

Muller, C. (2018). Parent involvement and academic achievement: An analysis of family resources available to the child. In Parents, their children, and schools 77–114. Routledge.

Mulligan, J., Woolcott, G., Mitchelmore, M., Busatto, S., Lai, J., & Davis, B. (2020). Evaluating the impact of a spatial reasoning mathematics program (SRMP) intervention in the primary school. Mathematics Education Research Journal, 32 , 285–305.

Parker, R., & Thomsen, B. S. (2019). Learning through play at school: A study of playful integrated pedagogies that foster children’s holistic skills development in the primary school classroom.

Passolunghi, M. C., De Vita, C., & Pellizzoni, S. (2020). Math anxiety and math achievement: The effects of emotional and math strategy training. Developmental Science, 23 (6), e12964.

Pourdavood, R., McCarthy, K., & McCafferty, T. (2020). The impact of mental computation on children’s mathematical communication, problem solving, reasoning, and algebraic thinking. Athens Journal of Education, 7 (3), 241–253.

Prabhakar, J., & Ghetti, S. (2020). Connecting the dots between past and future: Constraints in episodic future thinking in early childhood. Child Development, 91 (2), e315–e330.

Raoelison, M., Boissin, E., Borst, G., & De Neys, W. (2021). From slow to fast logic: The development of logical intuitions. Thinking & Reasoning, 27 (4), 599–622.

Rasheed, N. M., & Tashtoush, M. A. (2023). The impact of cognitive training program for children (CTPC) to development the mathematical conceptual and achievement. Journal of Higher Education Theory & Practice , 23 (10).

Roberts, W. M., Newcombe, D. J., & Davids, K. (2019). Application of a constraints-led approach to pedagogy in schools: Embarking on a journey to nurture physical literacy in primary physical education. Physical Education and Sport Pedagogy, 24 (2), 162–175.

Sa’diyah, K., Muchyidin, A., & Izzati, N. (2022). Application of collaborative teamwork learning model and guided note taking model and their influence on students’ ability to understand mathematical concepts. Journal of Mathematics Instruction, Social Research and Opinion, 1 (1), 14–26.

Scammacca, N., Fall, A. M., Capin, P., Roberts, G., & Swanson, E. (2020). Examining factors affecting reading and math growth and achievement gaps in grades 1–5: A cohort-sequential longitudinal approach. Journal of Educational Psychology, 112 (4), 718.

Schaaf, R. L., & Engel, K. (2018). Learning with digital games. Insights for Educators, pp.1–45.Schaaf, R.L. and Engel, K., 2018. Learning with digital games. Insights for Educators , 1–45.

Syafdaningsih, S., & Rukiyah, R. (2020). Educational game tools in early childhood mathematics learning.

Tashtoush, M. A., Wardat, Y., Aloufi, F., & Taani, O. (2022). The effect of a training program based on TIMSS to developing the levels of habits of mind and mathematical reasoning skills among pre-service mathematics teachers. EURASIA Journal of Mathematics, Science and Technology Education , 18 (11), em2182.

Thai, K. P., Bang, H. J., & Li, L. (2022). Accelerating early math learning with research-based personalized learning games: A cluster randomized controlled trial. Journal of Research on Educational Effectiveness, 15 (1), 28–51.

Theiner, G. (2021). The extended mind: a chapter in the history of transhumanism. The mind-technology problem: Investigating minds, selves and 21st Century Artefacts, 275–321.

Vogt, F., Hauser, B., Stebler, R., Rechsteiner, K., & Urech, C. (2020). Learning through play–pedagogy and learning outcomes in early childhood mathematics. In innovative approaches in early childhood mathematics, 127–141. Routledge.

Vrabec, A. N. (2021). Exploring the effects of an adaptive number eBook on parental attitudes toward mathematics (Doctoral dissertation, University of Dayton).

Wahyuningsih, S., Nurjanah, N. E., Rasmani, U. E. E., Hafidah, R., Pudyaningtyas, A. R., & Syamsuddin, M. M. (2020). STEAM learning in early childhood education: A literature review. International Journal of Pedagogy and Teacher Education, 4 (1), 33–44.

Wati, T. P., Naimah, N., Karimullah, S. S., & Anggita, I. S. (2022). Consistency of Balinese family education in forming a love of culture from an early childhood. Devotion Journal of Community Service, 3 (11), 1–126.

Zanabazar, A., Deleg, A., & Ravdan, M. (2023). A study of factors causing math anxiety among undergraduate students. International Journal of Innovative Research and Scientific Studies, 6 (3), 578–585.

Zippert, E. L., & Rittle-Johnson, B. (2020). The home math environment: More than numeracy. Early Childhood Research Quarterly, 50 , 4–15.

Živković, M., Pellizzoni, S., Mammarella, I. C., & Passolunghi, M. C. (2023). The relationship between math anxiety and arithmetic reasoning: The mediating role of working memory and self-competence. Current Psychology, 42 (17), 14506–14516.

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Chen, W. Problem-Solving Skills, Memory Power, and Early Childhood Mathematics: Understanding the Significance of the Early Childhood Mathematics in an Individual’s Life. J Knowl Econ (2024). https://doi.org/10.1007/s13132-023-01557-6

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