modeling with mathematics authentic problem solving in middle school

Book Reviews / mathematics

Authentic Math Modeling in Middle School

by MiddleWeb · Published 11/12/2015 · Updated 11/13/2019

Modeling with Mathematics: Authentic Problem Solving in Middle School By Nancy Butler Wolf (Heinemann, 2015 – Learn more )

Are you left wondering what so many people are talking about when they speak of open ended tasks, Dan Meyer, MARS Tasks, NCTM Illuminations, high low ceilings, and modeling in mathematics? Good news. The author of Modeling with Mathematics, Nancy Butler Wolf, addresses all of these issues and then some in her book.

Wolf has taken many of the top names and topics in mathematics and has applied their work to the Common Core Mathematical Practice Standard “Modeling in Mathematics” (MP4). She also touches on Constructing Viable Arguments and Critiquing the Reasoning of Others.

Wolf’s work could act as a strong extension for teachers who are trying to build steps towards understanding problems and topics presented by Boaler. Wolf touches on engagement with a strong section on helping teachers deal with the dreaded IDK response when students are tasked with open ended problems or problems which, simply put, just involve words.

Wolf also does a good job with her second topic: taking textbook problems and transitioning them into problems that are rich tasks and useful for mathematical modeling.

An example she gives includes a problem with Distance = Rate x Times. She transitions this basic formula problem into a scenario where students design a route with stops using a set of criteria, and where (Distance = Rate x Times) would be helpful and build into a quicker way to come up with a given route for the individual who needed help with his schedule.

The discussion of transitioning textbook problems to rich tasks is Wolf’s extension of ideas that have been spoken of by Dan Meyer, who is currently prominent in K-12 education.

A good resource for new math teachers

The strong points in Wolf’s Modeling with Mathematics include student/teacher discussion examples, problem examples, and some great ideas/examples on using rubrics to grade rich tasks. I was a little frustrated that so many examples were from sources I was already familiar with. These include resources from NCTM Illuminations, Dan Meyer’s 3-Act Math, and MARS Tasks, to name a few. These are all great resources, but the book’s content wasn’t anything “new” per se , at least from my perspective as an active professional learner in the math sphere.

Wolf’s book might be best suited for an audience that may not yet be deeply immersed in math or math coaching, or someone who is trying to wrap their head around the topics above or see them in another light. She excels at offering clear explanations.

Maia Fastabend is a 6th year teacher from Southern Oregon who when not teaching can be found whitewater kayaking or trail running. She has experience teaching 6th-8th grade general math and advanced math, some district coaching/speaking (including NW Math Conference 2014 and the Southern Oregon Tech Conference 2015), and recently has found her niche teaching remedial/support. Musings about her teaching and current topics can be found at http://teachrunlife.blogspot.com/ .

Share this:

Tags: Dan Meyer Heinemann high low ceilings Maia Fastabend MARS Tasks math problems mathematics middle school Nancy Butler Wolf NCTM Illuminations

MiddleWeb is all about the middle grades, with great 4-8 resources, book reviews, and guest posts by educators who support the success of young adolescents. And be sure to subscribe to MiddleWeb SmartBrief for the latest middle grades news & commentary from around the USA.

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Notify me of follow-up comments by email.

Notify me of new posts by email.

This site uses Akismet to reduce spam. Learn how your comment data is processed .

• Popular Posts
• Recent Posts
• Recent Comments

Book Reviews / Teacher Portfolios

Start your Educational Consulting Business

Articles / New Teacher Advice

26 Tips for Beginning Teachers, from A to Z

Articles / Student Research

Use Inquiry Charts to Boost Student Research

Articles / Reading

A Way to Increase Free Reading Outside of Class

Book Reviews / Writing

100-Word Stories to Support SLIFE Literacy

20 Things I’ve Learned to Start the Year Strong

Articles / Critical Reading

Critical Readers Search Beyond ‘Right’ Answers

Engaging All Students with Imaginative Writing

Engage All Students with Offbeat Math Problems

Artificial Intelligence / New Teacher Tips

What Will You Teach Your Students About AI?

Articles / Coteaching

How to Create a Co-Teaching Power Zone

Book Reviews / Teaching Insights

Reflections on Teachers’ Life-Shaping Power

Articles / Mathematics

Do Less This Year to Let Kids Do More in Math

Articles / Literacy

2 Questions Help Move Kids Deeper into Texts

• Debbie Silver says: Excellent compilation of great ideas and resources. Thanks for all you...
• P House says: Great, Laurie. Such a happy approach!!
• Anne Jolly says: Thanks, Daniel, for your insight. I agree with you wholeheartedly. Business...
• Daniel Bassett says: Thanks for providing a wealth of knowledge for new STEM teachers.
• Matthew Kinney says: As a middle school reading intervention teacher, I find MiddleWeb’s resources...

Sign Up & Receive the Latest News about Our Content…

Email address:

First Name:

Read our Privacy Policy

Modeling with Mathematics (eBook)

Authentic problem solving in middle school.

By Nancy Butler Wolf Foreword by Max Ray-Riek

.internal').css('display','block');$('#content_sectionFullDesc > .slider').find('span.rspv-up-arrow').toggleClass('rspv-down-arrow');" href="#fulldesc" >Read Full Description below »

List Price: $30.93

Web/School Price: $21.65

Please note that all discounts and final pricing will be displayed on the Review Order page before you submit your order.

Share This Resource

“Nancy’s in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms.” — Cathy Seeley , Past President of NCTM, author of Faster Isn’t Smarter and Smarter Than We Think

“This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level.” —David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America

We all use math to analyze everyday situations we encounter. Whether we realize it or not, we’re modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics , Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including:

• collecting data and formulating a mathematical model
• interpreting results and comparing them to reality
• learning to communicate their solutions in meaningful ways.

This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark.

(click any section below to continue reading)

Chapter 1 Introduction: Modeling with Mathematics

• What is Mathematical Modeling?
• The Process of Modeling?
• Why Modeling?
• Mathematical Autonomy

Chapter 2 Rich Mathematical Modeling Tasks

• Characteristics of Rich Modeling Tasks
• Word Problems versus Modeling Tasks
• Finding Rich Mathematical Modeling Tasks

Chapter 3  Investigation and Problem Identification

• Getting Started: Student Autonomy
• The Teacher's Role
• More Problem Identification: Old MacDonald's Farm
• 1000 Paper Cranes: Getting Started

Chapter 4 Mathematical Formulation of the Model, Data Collection, and Finding a Solution

• Formulating a Model
• Multiple Representations
• The 1000 Cranes Problem: Formulating the Model and Collecting Data

Chapter 5 Interpreting the Solution and Comparing with Reality

• The Importance of Interpretation
• Interpreting the Solution
• Examples of Students Interpreting Solutions

Chapter 6 Communicating and Implementing the Solution

• Communicating the Solution
• Implementing the Solution
• 1000 Cranes Work

Chapter 7 Assessment of Mathematical Modeling

• Goals of Assessment
• Informal Assessment
• Formal Assessments

Chapter 8 Conclusion

• View Sample Chapter
• Download a Flyer

Companion Resources

• The Road Trip: A Mathematical Modeling Task
• The Vegetable Garden: A Fixed Perimeter Investigation
• Setting Up a Budget: A Modeling Application Problem
• Kicker Ramps
• 1,000 Paper Cranes
• The Block Tower Problem: An Introduction to Mathematical Modeling
• Old MacDonald's Farm
• The Tortoise and the Hare: A Rate, Time, Distance Investigation
• Barbie Bungee
• Mixing Paint: Finding the Goof
• The BMX Bike Race
• School District Pay Raises
• The Giant's Footprint
• The Thanksgiving Dinner Party: An Algebraic Thinking Investigation
• The Pasta Box Task: A Geometric Modeling Investigation

“Mathematical modeling is one of the hottest topics in the school curriculum. And one of the least understood. Nancy’s in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms.”

— Cathy Seeley , Past President of NCTM, author of Faster Isn’t Smarter and Smarter Than We Think

“This is the book that math teachers and parents have been waiting for. Writing in clear and entertaining prose, Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level. She shows that the new math standards need not be intimidating or confusing. Instead, students will learn how modeling relates directly to real life problems and decisions through a series of terrific examples. Unlike most books about mathematical modeling, this book is both thorough and accessible, focused and fun. A tour de force!”

—David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America

“Nancy’s book is an excellent guide for middle school teachers who want to incorporate mathematical modeling in their classrooms. It provides both theoretical and practical discussions on how teachers can change their teaching so that their students become more independent and thoughtful problem solvers.”

— Judith E. Jacobs , Past President of the Association of Mathematics Teacher Educators

“Between the stories, the examples, the extensive citing of research, and the way Nancy describes her own transformation as a teacher, I’m confident that you’ll be excited and ready to try modeling tasks with your students as soon as you finish this book.”

—Max Ray-Riek, author of Powerful Problem Solving

Related PD Services

• Invite Nancy Butler Wolf, Consulting Author to speak at your school, district, or conference through Heinemann Speakers.

Sorry, there was a problem.

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required .

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

Image Unavailable

• To view this video download Flash Player

Follow the author

Modeling with Mathematics: Authentic Problem Solving in Middle School by Wolf, Nancy Butler (September 17, 2015) Paperback Unknown Binding

• Publisher Heinemann
• See all details

Product details

• ASIN ‏ : ‎ B014I64TXA

About the author

Nancy butler wolf.

Discover more of the author’s books, see similar authors, read author blogs and more

Customer reviews

• 5 star 4 star 3 star 2 star 1 star 5 star 79% 21% 0% 0% 0% 79%
• 5 star 4 star 3 star 2 star 1 star 4 star 79% 21% 0% 0% 0% 21%
• 5 star 4 star 3 star 2 star 1 star 3 star 79% 21% 0% 0% 0% 0%
• 5 star 4 star 3 star 2 star 1 star 2 star 79% 21% 0% 0% 0% 0%
• 5 star 4 star 3 star 2 star 1 star 1 star 79% 21% 0% 0% 0% 0%

Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them.

To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzed reviews to verify trustworthiness.

• Sort reviews by Top reviews Most recent Top reviews

Top reviews from the United States

There was a problem filtering reviews right now. please try again later..

• About Amazon
• Investor Relations
• Amazon Devices
• Amazon Science
• Sell products on Amazon
• Sell on Amazon Business
• Sell apps on Amazon
• Become an Affiliate
• Advertise Your Products
• Self-Publish with Us
• Host an Amazon Hub
• › See More Make Money with Us
• Amazon Business Card
• Shop with Points
• Reload Your Balance
• Amazon Currency Converter
• Amazon and COVID-19
• Your Account
• Your Orders
• Shipping Rates & Policies
• Returns & Replacements
• Manage Your Content and Devices

• Conditions of Use
• Privacy Notice
• Consumer Health Data Privacy Disclosure
• Your Ads Privacy Choices

• Children's Books
• Growing Up & Facts of Life

We will collect Import Charges at the time of your purchase and use it to cover applicable taxes and duties on import. Learn more. The total may change depending on the chosen shipping option and items in cart during checkout.

Amazon Global Store

• International products have separate terms, are sold from abroad and may differ from local products, including fit, age ratings, and language of product, labeling or instructions.
• Any warranty descriptions were intended for purchasers in the country of origin. Warranty may not be valid in the UAE.
• Learn more about Amazon Global Store.

Sorry, there was a problem.

Image unavailable.

• To view this video download Flash Player

Modeling with Mathematics: Authentic Problem Solving in Middle School Paperback – Illustrated, 18 September 2015

Purchase options and add-ons

"Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." -Cathy Seeley , Past President of NCTM, author of

• ISBN-10 0325062595
• ISBN-13 978-0325062594
• Edition Illustrated
• Publisher Heinemann Educational Books
• Publication date 18 September 2015
• Language English
• Dimensions 18.54 x 0.86 x 23.37 cm
• Print length 152 pages
• See all details

Product description

About the author, product details.

• Publisher ‏ : ‎ Heinemann Educational Books; Illustrated edition (18 September 2015)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 152 pages
• ISBN-10 ‏ : ‎ 0325062595
• ISBN-13 ‏ : ‎ 978-0325062594
• Reading age ‏ : ‎ 10 - 13 years
• Dimensions ‏ : ‎ 18.54 x 0.86 x 23.37 cm

Customer Reviews

• 5 star 4 star 3 star 2 star 1 star 5 star 78% 22% 0% 0% 0% 78%
• 5 star 4 star 3 star 2 star 1 star 4 star 78% 22% 0% 0% 0% 22%
• 5 star 4 star 3 star 2 star 1 star 3 star 78% 22% 0% 0% 0% 0%
• 5 star 4 star 3 star 2 star 1 star 2 star 78% 22% 0% 0% 0% 0%
• 5 star 4 star 3 star 2 star 1 star 1 star 78% 22% 0% 0% 0% 0%
• Sort reviews by Top reviews Most recent Top reviews

Top reviews from United Arab Emirates

Top reviews from other countries.

• About Amazon
• Amazon Science
• Your Account
• Your Orders
• Your Addresses
• Protect and build your brand
• Sell on Amazon
• Fulfillment by Amazon
• Supply to Amazon
• Become an Affiliate
• Advertise Your Products
• Shipping & Delivery
• Returns & Replacements
• Recalls and Product Safety Alerts
• Amazon App Download

• Conditions of Use & Sale
• Privacy Notice
• Interest-Based Ads

You are using an outdated browser. Please upgrade your browser to improve your experience and security.

ISBN: 0325062595

ISBN13: 9780325062594

Modeling with Mathematics: Authentic Problem Solving in Middle School

Select Format

Select condition, recommended.

Format: Paperback

Condition: Very Good *

*Best Available: ( ex-library )

Book Overview

"Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." --Cathy Seeley , Past President of NCTM, author of Faster Isn't Smarter and Smarter Than We Think

We all use math to analyze everyday situations we encounter... Read Full Overview

Related Subjects

Customer Reviews

Popular categories.

• Teen and Young Adult
• Literature & Fiction
• Mystery & Thriller
• Sci-fi & Fantasy
• Large Print Books
• Rare & Collectible Books
• ShareBookLove
• Educator Benefits
• Librarian Benefits
• e-Gift Cards
• View Mobile Site
• Shopping Cart
• Order History

Partnerships

• Library Program
• Help & Support
• Shipping Costs
• Return Policy
• Website Suggestions
• Our Purpose
• Social Responsibility
• Testimonials

• For educators

Modeling with Mathematics 1st edition

Authentic problem solving in middle school.

Nancy Butler Wolf , Max Ray of the Math Forum@Drexel Univ

• eTextbook Instant Access From $30.00

eTextbook $30.00

Included with your book.

• Access anytime on connected devices
• Search and highlight directly in your eBook

If you're not satisfied with your eTextbook for any reason, you can cancel the book within 10 days & you will receive a full refund. No cheating! - you can only do this once per eTextbook.

Total Price: $30.00

Book Details

Standard Shipping Options

• Standard shipping
• 2-day shipping
• 1-day shipping

Return Policy

• Physical textbooks must be returned within 21 days of ordering
• eTextbooks must be canceled within 10 days of ordering See policy details

Rent 📙Modeling with Mathematics 1st edition (978-0325062594) today, or search our site for other 📚textbooks by Nancy Butler Wolf. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Heinemann.

Publisher Description

"Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." -Cathy Seeley, Past President of NCTM, author of Faster Isn't Smarter and Smarter Than We Think "This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level." -David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America We all use math to analyze everyday situations we encounter. Whether we realize it or not, we're modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics, Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including: collecting data and formulating a mathematical model interpreting results and comparing them to reality learning to communicate their solutions in meaningful ways. This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark. Through detailed examples and hands-on activities, Nancy shows how to guide your students to become active participants in mathematical explorations who are able to answer the question, "What did I just figure out?" Her approach values all students as important contributors and shows how instruction focused on mathematical modeling engages every learner regardless of their prior history of success or failure in math.

Popular Textbooks

Epidemiology 101

Robert H. Friis

ISBN-13: 9781284107852

Essentials of the U.S. Health Care System

Leiyu Shi, Douglas A. Singh

ISBN-13: 9781284100556

On Course Study Skills Plus Edition

Skip Downing

ISBN-13: 9781305397484

ISBN-13: 9781305397477

Strategies That Work, 3rd Edition

Stephanie Harvey, Anne Goudvis

ISBN-13: 9781625310637

Revel for Exceptional Children

William L. Heward, Sheila Alber-Morgan, Sheila R. Alber-Morgan, Moira Konrad

ISBN-13: 9780134027111

• Sign in
• My Account
• Basket  

Items related to Modeling with Mathematics: Authentic Problem Solving...

Modeling with mathematics: authentic problem solving in middle school - softcover, ray-riek, max ; wolf, nancy butler.

• 3.8 3.8 out of 5 stars 5 ratings by Goodreads

• About this title
• About this edition

"Nancy's in-depth look at mathematical modeling offers middle school teachers the kind of practical help they need for incorporating modeling into their classrooms." -Cathy Seeley , Past President of NCTM, author of Faster Isn't Smarter and Smarter Than We Think

"This is the book that math teachers and parents have been waiting for. Nancy provides a comprehensive step-by-step guide to modeling in mathematics at the middle school level." -David E. Drew, author of STEM the Tide: Reforming Science, Technology, Engineering, and Math Education in America

We all use math to analyze everyday situations we encounter. Whether we realize it or not, we're modeling with mathematics: taking a complex situation and figuring out what we need to make sense of it. In Modeling with Mathematics , Nancy Butler Wolf shows that math is most powerful when it means something to students. She provides clear, friendly guidance for teachers to use authentic modeling projects in their classrooms and help their students develop key problem-solving skills, including:

• collecting data and formulating a mathematical model
• interpreting results and comparing them to reality
• learning to communicate their solutions in meaningful ways.

This kind of teaching can be challenging because it is open-ended: it asks students to make decisions about their approach to a scenario, the information they will need, and the tools they will use. But Nancy proves there is ample middle ground between doing all of the work for your students and leaving them to flail in the dark.

"synopsis" may belong to another edition of this title.

About the Author

Nancy Butler Wolf, Ph.D., is a national math consultant and curriculum developer who has served as a member of NCTM's Illuminations Writing Group. She has over 30 years of classroom teaching experience and has presented at various conferences on mathematical modeling and algebraic reasoning.

"About this title" may belong to another edition of this title.

• Publisher HEINEMANN
• Publication date 2015
• ISBN 10  0325062595
• ISBN 13  9780325062594
• Binding Paperback
• Edition number 1
• Number of pages 152

Convert currency

Shipping: FREE Within U.S.A.

Add to basket

Shipping: US$ 4.99 Within U.S.A.

Top Search Results from the AbeBooks Marketplace

Modeling with mathematics: authentic problem solving in middle school.

Seller: SecondSale , Montgomery, IL, U.S.A.

(5-star seller) Seller rating 5 out of 5 stars

Condition: Good. Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc. Seller Inventory # 00071844809

Contact seller

Quantity: 1 available

Seller: Dream Books Co. , Denver, CO, U.S.A.

Condition: good. Minimal signs of wear. Corners and cover may show wear. May contain highlighting and or writing. May be missing dust jacket. May not include supplemental materials. May be a former library book. Seller Inventory # DBV.0325062595.G

Quantity: 2 available

Seller: Books Unplugged , Amherst, NY, U.S.A.

Condition: Fair. Buy with confidence! Book is in acceptable condition with wear to the pages, binding, and some marks within 0.5. Seller Inventory # bk0325062595xvz189zvxacp

Seller: Book Deals , Tucson, AZ, U.S.A.

Condition: Good. Good condition. This is the average used book, that has all pages or leaves present, but may include writing. Book may be ex-library with stamps and stickers. 0.5. Seller Inventory # 353-0325062595-gdd

Seller: ThriftBooks-Atlanta , AUSTELL, GA, U.S.A.

Paperback. Condition: Very Good. No Jacket. Former library book; May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less 0.6. Seller Inventory # G0325062595I4N10

Seller: ThriftBooks-Dallas , Dallas, TX, U.S.A.

Paperback. Condition: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 0.6. Seller Inventory # G0325062595I3N00

Seller: Goodwill San Antonio , San Antonio, TX, U.S.A.

Condition: Good. Good Reading Copy, May have minor shelf wear, Fast Shipping - Safe and Secure in Mailer. Seller Inventory # 4Q2SPP001MVM

Quantity: 3 available

Modeling With Mathematics

Seller: eCampus , Lexington, KY, U.S.A.

Condition: Very Good. Seller Inventory # U:9780325062594:ONHAND

Seller: Half Price Books Inc. , Dallas, TX, U.S.A.

Paperback. Condition: Very Good. Connecting readers with great books since 1972! Used books may not include companion materials, and may have some shelf wear or limited writing. We ship orders daily and Customer Service is our top priority!. Seller Inventory # S_398213178

There are 18 more copies of this book

Modeling With Mathematics: Authentic Problem Solving in Middle School.

• MLA style: "Modeling With Mathematics: Authentic Problem Solving in Middle School.." The Free Library . 2016 Ringgold, Inc. 13 Sep. 2024 https://www.thefreelibrary.com/Modeling+With+Mathematics%3a+Authentic+Problem+Solving+in+Middle+School.-a0451474036
• Chicago style: The Free Library . S.v. Modeling With Mathematics: Authentic Problem Solving in Middle School.." Retrieved Sep 13 2024 from https://www.thefreelibrary.com/Modeling+With+Mathematics%3a+Authentic+Problem+Solving+in+Middle+School.-a0451474036
• APA style: Modeling With Mathematics: Authentic Problem Solving in Middle School.. (n.d.) >The Free Library. (2014). Retrieved Sep 13 2024 from https://www.thefreelibrary.com/Modeling+With+Mathematics%3a+Authentic+Problem+Solving+in+Middle+School.-a0451474036

Terms of use | Privacy policy | Copyright © 2024 Farlex, Inc. | Feedback | For webmasters |

• Скидки дня
• Справка и помощь
• Адрес доставки Идет загрузка... Ошибка: повторите попытку ОК
• Продажи
• Список отслеживания Развернуть список отслеживаемых товаров Идет загрузка... Войдите в систему , чтобы просмотреть свои сведения о пользователе
• Краткий обзор
• Недавно просмотренные
• Ставки/предложения
• Список отслеживания
• История покупок
• Купить опять
• Объявления о товарах
• Сохраненные запросы поиска
• Сохраненные продавцы
• Сообщения
• Развернуть корзину Идет загрузка... Произошла ошибка. Чтобы узнать подробнее, посмотрите корзину.

Oops! Looks like we're having trouble connecting to our server.

Refresh your browser window to try again.

Related Searches

• Mathematics Analysis
• Mathematics For Self Study
• Principles Of Mathematical Analysis
• Basic Mathematics
• Engineering Mathematics
• Real Mathematical Analysis
• Mathematical Proofs
• Mathematical Statistics
• Math 7 Teaching Textbooks
• Textbooks Used
• Principles Of Mathematical Analysis Rudin
• Teaching Textbooks Math 3
• Math Books For Adults
• Math 3 Teaching Textbooks
• Math Lessons For A Living Education

Keeping Modeling with Mathematics as the Focus in Authentic Tasks

• Ryan Griesmer Bowling Green State University

Modeling with mathematics is essential in connecting mathematics to everyday life. In the preparation of teacher candidates, it becomes a mechanism to support the learning of mathematics as well as strengthening pedagogical approaches. This article focuses on a task that engaged teacher candidates in modeling with mathematics. After analyzing how teacher candidates solved problems, we categorized their methods into three categories of approaches. The alignment of the modeling task to the elementary mathe- matics curriculum is highlighted. Benefits of engaging teacher candidates in these types of tasks are also discussed.

Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83–104). Ablex Publishing.

Bezuk, N., Bay-Williams, J., Clements, D. H., Martin, W. G., Aguirre, J., Boerst, T., & Thomas, C. D. (2017). AMTE standards for mathematics teacher preparation.

Bostic, J. D. (2015). A blizzard of a value. Mathematics Teaching in the Middle School, 20(6), 350–357. https://doi.org/10.5951/mathteacmiddscho.20.6.0350

Bostic, J. D., Matney, G. T., & Sondergeld, T. A. (2017). A validation process for observation protocols: Using the revised SMPS look-for protocol as a lens on teachers’ promotion of the standards. Investigations in Mathematics Learning, 11(1), 69–82. https://doi.org/10.1080/19477503.2017.1379894

Chamberlin, S., Payne, A. M., & Kettler, T. (2020). Mathematical modeling: A positive learning approach to facilitate student sense making in mathematics. International Journal of Mathematical Education in Science and Technology, 53(4), 858–871.

de Araujo, Z. (2012). An examination of non-mathematical activities in the mathematics classroom. In Proceedings of the 34th annual meeting for the North American chapter for the Psychology of Mathematics Education (pp. 339–342). Kalamazoo, MI: Western Michigan University.

Greenhaus, K. (2016, May 24). Multiple entry points and rich math tasks. Casio Education. https://casioeducation.wordpress.com/2016/05/24/ multiple-entry-points-and-rich-math-tasks/

National Governors Association Center for Best Practices (NGA Center) and Council of Chief State School Officers (CCSSO). (2010). Common Core State Standards for Mathematics. Washington, DC: NGA Center and CCSSO. http://www.corestandards.org

Roberts, T., Bostic, J. D., & Matney, G. T. (2020). GPS: Modeling with mathematics in the moment. Mathematics Teacher: Learning and Teaching PK-12, 113(10), 864–867. https://doi.org/10.5951/mtlt.2020.0099

Sevinc, S., & Lesh, R. (2018). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM, 50, 301–314.

Swars, S. L., Smith, S. Z., Smith, M. E., & Hart, L. C. (2009). A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. Journal of Mathematics Teacher Education, 12, 47–66.

Wolf, N. B., & Ray-Riek, M. (2015). Modeling with mathematics: Authentic Problem Solving in middle school. Heinemann.

How to Cite

• Endnote/Zotero/Mendeley (RIS)

Copyright (c) 2024 Ryan Griesmer, Stefanie D. Livers, Thomas Roberts

Most read articles by the same author(s)

• Thomas Roberts, Lynne Pachnowski, Advocacy Corner: The Value of Middle Grades Licensure on K-12 Mathematics Achievement (pp. 31--36) , Ohio Journal of School Mathematics: Vol. 85: Summer 2020

Similar Articles

• Anita O'Mellan, Karl W. Kosko, Lynne M. Pachnowski, Gabriel Matney, Shannon O. Driskell, The Potential Impact of the Removal of a Middle Grades Licensure Band on Ohio’s Teacher Education Majors , Ohio Journal of School Mathematics: Vol. 96: Spring 2024
• Gabriel Matney, Corrinne Fischer, Jack Jackson, A Picture is Worth a Thousand Words , Ohio Journal of School Mathematics: Vol. 93: Spring 2023
• Kelsly Chatraw, Melissa Soto, Drawing Taylor Swift, Orcas are Dolphins, & “What if” Questions , Ohio Journal of School Mathematics: Vol. 97: Summer 2024
• Alesia Mickle Moldavan, Asia Franks, Marquette Richardson, Fruitful Fraction Models with Digital Tools , Ohio Journal of School Mathematics: Vol. 90: Spring 2022
• Ahmad Alhammouri, Jami Durkee, Gregory D Foley, Where to Place a Post? Engaging Students in the Mathematical Modeling Process , Ohio Journal of School Mathematics: Vol. 75: Spring 2017
• Wayne Nirode, Brian Boyd, Teacher Tracking in High School Mathematics , Ohio Journal of School Mathematics: Vol. 96: Spring 2024
• Madeline Negrelli, Marilyn Ortiz, Bridget Druken, Bridging Math Content and Teaching through Pre-Service Undergraduate Apprenticeship , Ohio Journal of School Mathematics: Vol. 93: Spring 2023
• Samuel Otten, Andrew Otten, Faustina Baah, Maria Nielsen Stewart, Modeling the Functions of Atmospheric Carbon , Ohio Journal of School Mathematics: Vol. 96: Spring 2024
• Montana Smithey, Alesia Mickle Moldavan, The Food Drive Task: Problem Solving for Social Justice in the Elementary Grades , Ohio Journal of School Mathematics: Vol. 95: Fall 2023
• Meghan Miller, Aidong "Linda" Zhang, Iris DeLoach Johnson, Dr. Jianan ”Gianna” Yang, Novice Teacher Supports the Mathematics Learning of English Language Learners in Any Language , Ohio Journal of School Mathematics: Vol. 93: Spring 2023

1   2   3   4   5   6   7   8   9   10   >   >>  

You may also start an advanced similarity search for this article.

About the Journal

The Ohio Journal of School Mathematics is the journal of the Ohio Council of Teachers of Mathematics. It is intended to be a medium for teachers from elementary to college level to present their ideas and beliefs about the teaching and learning of mathematics. Mathematics educators at all levels are encouraged to submit manuscripts for upcoming issues of the Journal .

Make a Submission

Non-routine mathematics problems for middle and high school students.

Are you a fan of rich mathematics tasks? If so, take a moment to visit the Stella's Stunners website ---home to a library of more than 700 engaging and challenging mathematics problems, arranged for easy access by topic, with numerous suggestions for using them with students.

The Ohio Journal of School Mathematics is published by the Ohio Council of Teachers of Mathematics and hosted by The Ohio State University Libraries.

If you encounter problems with the site or have comments to offer, including any access difficulty due to incompatibility with adaptive technology, please contact [email protected] .

ISSN 2472-5986 (print) ISSN 2472-601X (online)

Chapter 9: The Complex Relationship Between Mathematical Modeling and Attitude Towards Mathematics

• First Online: 04 June 2019

Cite this chapter

• Pietro Di Martino 11  

Part of the book series: Advances in Mathematics Education ((AME))

778 Accesses

7 Citations

This chapter addresses the relationship between the promotion of mathematical modeling in the classroom – in particular linking mathematics and authentic real mathematics problem – and students’ attitude towards mathematics. This relationship has a twofold nature, based on two assumptions: on one hand mathematical modeling can help to construct or reinforce the belief concerning the utility and concreteness of mathematics, and therefore it can foster motivation in studying mathematics; on the other hand a positive attitude towards mathematics can strongly affect the way students approach real mathematics problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime
• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Durable hardcover edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Mathematical Modeling and the Teachers’ Tensions

The Impact of Real-World Mathematical Modelling Problems on Students’ Beliefs About the Nature of Mathematics

“Mathematics Is My Favorite Subject!”

Here and in the next excerpts the first number refers to the grade, the letter refers to the school level (Primary/Middle/High), the last number indicates the progressive numbering of the essay within the category.

Our view is different from the one of Lingerfjard ( 2002 ): according to him it is unreasonable to compare the activity around word problems with that around modeling.

Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1 , 45–58.

Google Scholar  

Bruner, J. (1990). Acts of meaning . Cambridge, MA: Harvard University Press.

Burkhardt, H. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future. ZDM, 38 (2), 178–195.

Article   Google Scholar  

Cirillo, M., Pelesko, J., Felton-Koestler, M., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In Annual perspectives in mathematics education: Mathematical modeling and modeling mathematics (pp. 3–16). Reston: NCTM.

D’Amore, B., & Martini, B. (1999). Didactical contract, mental and intuitive models in solving standard school problems. In A. Gagatsis (Ed.), A multidimensional approach to learning in mathematics and science (pp. 3–24). Nicosia: Intercollege.

De Corte, E., Verschaffel, L., & Greer, B. (2000). Connecting mathematics problem solving to the real world. In A. Rogerson (Ed.), Proceedings of the international conference on mathematics education into the 21st century: Mathematics for living (pp. 66–73). Amman: National Center for Human Resources Development.

Di Martino, P., & Morselli, F. (2006). Maths avoidance and the choice of university. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 425–432). Prague: PME.

Di Martino, P., & Zan, R. (2001). Attitude toward mathematics: Some theoretical issues. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25 th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 351–358). Utrecht: PME.

Di Martino, P., & Zan, R. (2010). ‘Me and maths’: Towards a definition of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13 (1), 27–48.

Di Martino, P., & Zan, R. (2011). Attitude towards mathematics: A bridge between beliefs and emotions. ZDM – The International Journal on Mathematics Education, 43 (4), 471–482.

Di Martino, P., & Zan, R. (2015). The construct of attitude in mathematics education. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 51–72). Heidelberg: Springer.

Donaldson, M. (1978). Children’s minds . London: Fontana Press.

Dossey, J., McCrone, S., Giordano, F., & Weir, M. (2002). Mathematics methods and modeling for today’s classroom: A contemporary approach to teaching grades 7–12 . Pacific Grove: Brooks/Cole.

Erbas, A., Kertil, M., Cetinkaya, B., Cakiroglu, E., Alacaci, C., & Bas, S. (2014). Mathematical modelling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory & Practice, 14 (4), 1621–1627.

Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7 , 293–307.

Hughes, M. (1975). Egocentrism in pre-school children . Unpublished doctoral dissertation, Edinburgh University.

Lappan, G. (1999, September). Fostering a good mathematical disposition. NCTM News Bulletin .

Lesh, R., & Doerr, H. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah: Lawrence Erlbaum.

Chapter   Google Scholar  

Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), The handbook of research on mathematics teaching and learning (pp. 763–804). Reston: National Council of Teachers of Mathematics.

Lingefjärd, T. (2002). Mathematical modeling for preservice teachers: A problem from anesthesiology. International Journal of Computers for Mathematical Learning, 7 , 117–143.

Mellone, M., Verschaffel, L., & Van Dooren, W. (2017). The effect of rewording and dyadic interaction on realistic reasoning in solving word problems. The Journal of Mathematical Behaviour, 46 , 1–12.

Mershet, K. (1993). How old is the shepherd? An essay about mathematics education. Phi Delta Kappan, 74 , 548–554.

MIUR. (2010). Indicazioni Nazionali per i licei [Italian National Standards for Lyceums]. Retrieved February 22, 2018, from http://www.indire.it/lucabas/lkmw_file/licei2010/indicazioni_nuovo_impaginato/_decreto_indicazioni_nazionali.pdf

MIUR. (2012). Indicazioni Nazionali per il curricolo della scuola dell’infanzia e del primo ciclo di istruzione [Italian National Standards for kindergarten and the first cycle of instruction]. Retrieved February 22, 2018, from http://www.indicazioninazionali.it/documenti_Indicazioni_nazionali/indicazioni_nazionali_infanzia_primo_ciclo.pdf

Niss, M. (2003). Mathematical competencies and the learning of mathematics: The Danish KOM project. In A. Gagatsis & S. Papastavridis (Eds.), Proceedings of the 3rd Mediterranean conference on mathematical education (pp. 115–124). Athens: Hellenic Mathematical Society.

Niss, M. (2012, December). Models and modelling in mathematics education. EMS Newsletter, 2012 , 49–52.

OECD. (2016). PISA 2015 assessment and analytical framework: Science, reading, mathematic and financial literacy . Paris: PISA, OECD Publishing.

Book   Google Scholar  

Piaget, J., & Inhelder, B. (1967). The child’s conception of space . New York: Norton.

Pollak, H. (2003). A history of the teaching of modeling. In G. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (pp. 647–669). Reston: NCTM.

Schoenfeld, A. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. Voss, D. Perkins, & J. Segal (Eds.), Informal reasoning and education (pp. 311–343). Hillsdale: Lawrence Erlbaum Associates.

Spence, D. P. (1982). Narrative truth and historical truth: Meaning and interpretation in psychoanalysis . New York: Norton.

Van Dooren, W., Verschaffel, L., Greer, B., & De Bock, D. (2006). Modelling for life: Developing adaptive expertise in mathematical modelling from an early age. In L. Verschaffel, F. Dochy, M. Boekaerts, & S. Vosniadou (Eds.), Instructional psychology: Past, present and future trends (pp. 91–112). Oxford: Elsevier.

Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modelling of school arithmetic word problems. Learning and Instruction, 4 , 273–294.

Verschaffel, L., Greer, B., & De Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In K. Gravemeijer, R. Lehrer, B. Van Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 257–276). Dordrecht: Kluwer Academic Publisher.

Vinner, S. (2007). Mathematics education: Procedures, rituals and man’s search for meaning. The Journal of Mathematical Behavior, 26 (1), 1–10.

VV.AA. (2016). Guidelines for assessment and instruction in mathematical modeling education . Philadelphia. Retrieved February 22, 2018, from http://www.siam.org/reports/gaimme.php

Yerushalmy, M. (1997). Mathematizing verbal descriptions of situations: A language to support modelling. Cognition and Instruction, 15 (2), 207–264.

Zan, R. (2011). The crucial role of narrative thought in understanding story problems. In K. Kislenko (Ed.), Current state of research on mathematical beliefs XVI (pp. 287–305). Tallinn: Estonia.

Zbiek, R., & Conner, A. (2006). Beyond motivation: Exploring mathematical modelling as a context for deepening students’ understandings of curricular mathematics. Education Studies in Mathematics, 63 , 89–112.

Download references

Author information

Authors and affiliations.

Dipartimento di Matematica, Università di Pisa, Pisa, Italy

Pietro Di Martino

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Pietro Di Martino .

Editor information

Editors and affiliations.

School of Teacher Education, University of Wyoming, Laramie, WY, USA

Scott A. Chamberlin

Department of Mathematical Sciences, University of Montana, Missoula, MT, USA

Bharath Sriraman

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Di Martino, P. (2019). Chapter 9: The Complex Relationship Between Mathematical Modeling and Attitude Towards Mathematics. In: Chamberlin, S.A., Sriraman, B. (eds) Affect in Mathematical Modeling. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-04432-9_14

Download citation

DOI : https://doi.org/10.1007/978-3-030-04432-9_14

Published : 04 June 2019

Publisher Name : Springer, Cham

Print ISBN : 978-3-030-04431-2

Online ISBN : 978-3-030-04432-9

eBook Packages : Education Education (R0)

Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research