powerful problem solving activities for sense making with the mathematical practices

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Powerful Problem Solving (eBook)

Activities for sense making with the mathematical practices.

By Max Ray-Riek Foreword by Susan O'Connell

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How can we break the cycle of frustrated students who “drop out of math” because the procedures just don’t make sense to them?  Or who memorize the procedures for the test but don’t really understand the mathematics?  Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say “problem solved,” by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices.  They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core:

• communicating ideas and listening to the reflections of others
• estimating and reasoning to see the “big picture” of a problem
• organizing information to promote problem solving
• using modeling and representations to visualize abstract concepts
• reflecting on, revising, justifying, and extending the work.

Powerful Problem Solving shows what’s possible when students become active doers rather than passive consumers of mathematics.  Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students’ own thoughts and ideas.  By asking “What do you notice?  What do you wonder?”  we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem.  Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be “over and done,” but to realize the many different ways to approach problems.

Read a sample chapter .

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Max has distilled the Math Forum's years of experience, thousands of hours of classroom observation, and abundant creativity into a brisk book full of practice and theory. Dan Meyer , international speaker on mathematics education and one of Tech & Learning’s “30 Leaders of the Future”

Max Ray and his Math Forum colleagues have crafted a powerful guide to bringing the Standards for Mathematics Practice to life in our classrooms. Packed with real classroom experiences and easy-to-adopt activities, this book will help every teacher of mathematics overcome the instructional obstacles we face when trying to engage students in problem solving, reasoning and communication. Steve Leinwand , American Institutes for Research and author of Accessible Mathematics

Powerful Problem Solving draws attention to a greater understanding of how to integrate the Standards for Mathematical Practice into daily teaching to ensure that students develop critical thinking and problem solving skills.  Helpful features in this book include learning through listening, noticing and wondering, seeing the big picture, engaging student’s number sense through guessing, looking for structure,  abstracting and modeling.  This book is every teacher’s roadmap for the development of mathematically proficient problem solvers. Suzanne Mitchell , past president, NCTM

Whether you read this book from front to back or simply dive into chapters that address the needs of your students, you will find it practical, understandable, and enlightening.  Don't wait another minute—dive into it! Sue O'Connell , author of Putting the Practices Into Action

This is an extremely useful book full of ideas and strategies to promote "powerful problem solving" for all students. I have begun to use the "I Notice, I Wonder" strategy, as presented in chapter 4, in my own classroom (grades 5–8) and have received positive feedback from my mathematics students. I recommend that this book be a part of every teacher’s "tool chest." Shelli Casler-Failing , Mathematics Teaching in the Middle School

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Powerful problem solving : activities for sense making with the mathematical practices

• Communication and community
• Learning through listening
• Noticing and wondering
• Change the representation: seeing the big picture
• Engaging students' number sense through guessing
• Getting organized
• Generalizing, abstracting, and modeling
• Looking for structure
• The problem solving process
• Reflecting, revising, justifying, and extending.

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• Problem solving in the mathematics classroom QA63 .P763
• Problem solving : tips for teachers : selections from the Arithmetic teacher QA63 .P763 1988
• Powerful problem solving : activities for sense making with the mathematical practices Ray, Max QA63 .R29 2013
• Word problems : research and curriculum reform Reed, Stephen K. QA63 .R4 1999
• Roddles QA63 .R63 2004

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Powerful problem solving (print ebook bundle): activities for sense making with the mathematical practices - softcover, of the math forum@drexel univ, max ray.

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How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core:

communicating ideas and listening to the reflections of others estimating and reasoning to see the "big picture" of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work.

Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems. Read a sample chapter. Save 15% when you purchase 15 copies with a Book Study Bundle!

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

• Publisher Heinemann
• Publication date 2013
• ISBN 10  032505892X
• ISBN 13  9780325058924
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Powerful Problem Solving: Activities for Sense Making with the Mathematical Practices Paperback – Illustrated, 24 Sept. 2013

How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core:

• communicating ideas and listening to the reflections of others
• estimating and reasoning to see the "big picture" of a problem
• organizing information to promote problem solving
• using modeling and representations to visualize abstract concepts
• reflecting on, revising, justifying, and extending the work.

Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems.

Read a sample chapter.

• ISBN-10 0325050902
• ISBN-13 978-0325050904
• Edition Illustrated
• Publisher Heinemann Educational Books
• Publication date 24 Sept. 2013
• Language English
• Dimensions 21.59 x 1.02 x 27.94 cm
• Print length 208 pages
• See all details

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About the author.

Max Ray-Riek is a curriculum writer at Illustrative Mathematics and is the lead author of Powerful Problem Solving: Activities for Sense Making with the Math Practices . He previously worked for The Math Forum, focusing on fostering problem solving, communication, and valuing student thinking. Max is a former secondary mathematics teacher who regularly presents at regional and national conferences.

Watch Max and Suzanne Alejandre talk about giving students effective feedback.

Follow him on Twitter @maxmathforum.

Product details

• Publisher ‏ : ‎ Heinemann Educational Books; Illustrated edition (24 Sept. 2013)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 208 pages
• ISBN-10 ‏ : ‎ 0325050902
• ISBN-13 ‏ : ‎ 978-0325050904
• Reading age ‏ : ‎ 8 - 13 years
• Dimensions ‏ : ‎ 21.59 x 1.02 x 27.94 cm
• 12,067 in Child & Developmental Psychology in Education
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• Publisher Heinemann
• ISBN-10 0325050902
• ISBN-13 9780325050904
• eBay Product ID (ePID) 166442746

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• Author Max Ray-Riek
• Publication Name Powerful Problem Solving : Activities for Sense Making with the Mathematical Practices
• Format Trade Paperback
• Language English
• Publication Year 2013
• Type Textbook
• Number of Pages 208 Pages
• Item Length 11in
• Item Height 0.4in
• Item Width 8.5in
• Item Weight 17.8 Oz

Additional Product Features

• Grade from Third Grade
• Grade to Eighth Grade
• Table of Content Communication and Community Learning Through Listening Noticing and Wondering Change the Representation: Seeing the Big Picture Engaging Students' Number Sense Through Guessing Getting Organized Generalizing, Abstracting, and Modeling Looking for Structure The Problem-Solving Process and Metacognition Reflecting, Revising, Justifying, and Extending
• Copyright Date 2013
• Topic Decision-Making & Problem Solving, Teaching Methods & Materials / Mathematics
• Genre Education

Mathematics Paperback Textbook

Mathematics paperback textbooks, mathematics paperback textbooks in english, mathematics nonfiction paperbacks books in english, revision/practice study paperbacks prep, vintage paperback mathematics antiquarian & collectible books.

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Powerful Problem Solving: Activities for Sense Making with the Mathematical Practices Capa comum – Ilustrado, 24 setembro 2013

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How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray-Riek and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core:

• communicating ideas and listening to the reflections of others
• estimating and reasoning to see the "big picture" of a problem
• organizing information to promote problem solving
• using modeling and representations to visualize abstract concepts
• reflecting on, revising, justifying, and extending the work.

Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems.

Read a sample chapter.

• ISBN-10 0325050902
• ISBN-13 978-0325050904
• Edição Illustrated
• Editora Heinemann Educational Books
• Data da publicação 24 setembro 2013
• Idioma Inglês
• Dimensões 21.59 x 1.02 x 27.94 cm
• Número de páginas 192 páginas
• Ver todos os detalhes

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Sobre o autor.

Max Ray-Riek is a curriculum writer at Illustrative Mathematics and is the lead author of Powerful Problem Solving: Activities for Sense Making with the Math Practices . He previously worked for The Math Forum, focusing on fostering problem solving, communication, and valuing student thinking. Max is a former secondary mathematics teacher who regularly presents at regional and national conferences.

Watch Max and Suzanne Alejandre talk about giving students effective feedback.

Follow him on Twitter @maxmathforum.

Detalhes do produto

• Editora ‏ : ‎ Heinemann Educational Books; Illustrated edição (24 setembro 2013)
• Idioma ‏ : ‎ Inglês
• Capa comum ‏ : ‎ 192 páginas
• ISBN-10 ‏ : ‎ 0325050902
• ISBN-13 ‏ : ‎ 978-0325050904
• Idade de leitura ‏ : ‎ 8 - 13 anos
• Dimensões ‏ : ‎ 21.59 x 1.02 x 27.94 cm

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Intervention based on science of reading, math boosts comprehension, word problem-solving skills

English learners with math difficulty showed improvement following culturally-responsive training.

New research from the University of Kansas has found an intervention based on the science of reading and math effectively helped English learners boost their comprehension, visualize and synthesize information, and make connections that significantly improved their math performance.

The intervention, performed for 30 minutes twice a week for 10 weeks with 66 third-grade English language learners who displayed math learning difficulties, improved students' performance when compared to students who received general instruction. That indicates emphasizing cognitive concepts involved in the science of reading and math are key to helping students improve, according to researchers.

"Word problem-solving is influenced by both the science of reading and the science of math. Key components include number sense, decoding, language comprehension and working memory. Utilizing direct and explicit teaching methods enhances understanding and enables students to effectively connect these skills to solve math problems. This integrated approach ensures that students are equipped with necessary tools to navigate both the linguistic and numerical demands of word problems," said Michael Orosco, professor of educational psychology at KU and lead author of the study.

The intervention incorporates comprehension strategy instruction in both reading and math, focusing and decoding, phonological awareness, vocabulary development, inferential thinking, contextualized learning and numeracy.

"It is proving to be one of the most effective evidence-based practices available for this growing population," Orosco said.

The study, co-written with Deborah Reed of the University of Tennessee, was published in the journal Learning Disabilities Research and Practice .

For the research, trained tutors developed the intervention, developed by Orosco and colleagues based on cognitive and culturally responsive research conducted over a span of 20 years. One example of an intervention session tested in the study included a script in which a tutor examined a word problem that explained a person made a quesadilla for his friend Mario, giving him one-fourth of it, then needed to students to determine how much remained.

The tutor first asked students if they remembered a class session in which they made quesadillas, what shape they were and demonstrated concepts by drawing a circle on the board, dividing it into four equal pieces, having students repeat terms like numerator and denominator, and explaining that when a question asks how much is left, subtraction is required. The students also collaborated with peers to practice using important vocabulary in sentences. The approach both helps students learn and understand mathematical concepts while being culturally responsive.

"Word problems are complex because they require translating words into mathematical equations, and this involves integrating the science of reading and math through language concepts and differentiated instruction," Orosco said. "We have not extensively tested these approaches with this group of children. However, we are establishing an evidence-based framework that aids them in developing background knowledge and connecting it to their cultural contexts."

Orosco, director of KU's Center for Culturally Responsive Educational Neuroscience, emphasized the critical role of language in word problems, highlighting the importance of using culturally familiar terms. For instance, substituting "pastry" for "quesadilla" could significantly affect comprehension for students from diverse backgrounds. Failure to grasp the initial scenario can impede subsequent problem-solving efforts.

The study proved effective in improving students' problem-solving abilities, despite covariates including an individual's basic calculation skills, fluid intelligence and reading comprehension scores. That finding is key as, while ideally all students would begin on equal footing and there were little variations in a classroom, in reality, covariates exist and are commonplace.

The study had trained tutors deliver the intervention, and its effectiveness should be further tested with working teachers, the authors wrote. Orosco said professional development to help teachers gain the skills is necessary, and it is vital for teacher preparation programs to train future teachers with such skills as well. And helping students at the elementary level is necessary to help ensure success in future higher-level math classes such as algebra.

The research builds on Orosco and colleagues' work in understanding and improving math instruction for English learners. Future work will continue to examine the role of cognitive functions such as working memory and brain science, as well as potential integration of artificial intelligence in teaching math.

"Comprehension strategy instruction helps students make connections, ask questions, visualize, synthesize and monitor their thinking about word problems," Orosco and Reed wrote. "Finally, applying comprehension strategy instruction supports ELs in integrating their reading, language and math cognition… Focusing on relevant language in word problems and providing collaborative support significantly improved students' solution accuracy."

• Learning Disorders
• K-12 Education
• Educational Psychology
• Intelligence
• Special education
• Problem solving
• Developmental psychology
• Child prodigy
• Intellectual giftedness
• Lateral thinking

Story Source:

Materials provided by University of Kansas . Original written by Mike Krings. Note: Content may be edited for style and length.

Journal Reference :

• Michael J. Orosco, Deborah K. Reed. Supplemental intervention for third-grade English learners with significant problem-solving challenges . Learning Disabilities Research & Practice , 2024; 39 (2): 60 DOI: 10.1177/09388982241229407

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Intervention based on science of reading and math boosts comprehension and word problem-solving skills

by University of Kansas

New research from the University of Kansas has found that an intervention based on the science of reading and math effectively helped English learners boost their comprehension, visualize and synthesize information, and make connections that significantly improved their math performance.

The intervention , performed for 30 minutes twice a week for 10 weeks with 66 third-grade English language learners who displayed math learning difficulties, improved students' performance when compared to students who received general instruction. This indicates that emphasizing cognitive concepts involved in the science of reading and math are key to helping students improve, according to researchers.

"Word problem-solving is influenced by both the science of reading and the science of math. Key components include number sense, decoding, language comprehension and working memory. Utilizing direct and explicit teaching methods enhances understanding and enables students to effectively connect these skills to solve math problems . This integrated approach ensures that students are equipped with necessary tools to navigate both the linguistic and numerical demands of word problems," said Michael Orosco, professor of educational psychology at KU and lead author of the study.

The intervention incorporates comprehension strategy instruction in both reading and math, focusing and decoding, phonological awareness, vocabulary development, inferential thinking, contextualized learning and numeracy.

"It is proving to be one of the most effective evidence-based practices available for this growing population," Orosco said.

The study, co-written with Deborah Reed of the University of Tennessee, was published in the journal Learning Disabilities Research and Practice .

For the research, trained tutors implemented the intervention, developed by Orosco and colleagues based on cognitive and culturally responsive research conducted over a span of 20 years. One example of an intervention session tested in the study included a script in which a tutor examined a word problem explaining that a person made a quesadilla for his friend Mario and gave him one-fourth of it, then asked students to determine how much remained.

The tutor first asked students if they remembered a class session in which they made quesadillas and what shape they were, and demonstrated concepts by drawing a circle on the board, dividing it into four equal pieces, having students repeat terms like numerator and denominator. The tutor explains that when a question asks how much is left, subtraction is required. The students also collaborated with peers to practice using important vocabulary in sentences. The approach both helps students learn and understand mathematical concepts while being culturally responsive.

"Word problems are complex because they require translating words into mathematical equations, and this involves integrating the science of reading and math through language concepts and differentiated instruction," Orosco said. "We have not extensively tested these approaches with this group of children. However, we are establishing an evidence-based framework that aids them in developing background knowledge and connecting it to their cultural contexts."

Orosco, director of KU's Center for Culturally Responsive Educational Neuroscience, emphasized the critical role of language in word problems, highlighting the importance of using culturally familiar terms. For instance, substituting "pastry" for "quesadilla" could significantly affect comprehension for students from diverse backgrounds. Failure to grasp the initial scenario could impede subsequent problem-solving efforts.

The study proved effective in improving students' problem-solving abilities, despite covariates including an individual's basic calculation skills, fluid intelligence and reading comprehension scores. That finding is key, as while ideally all students would begin on equal footing and there would be few variations in a classroom, in reality, covariates exist and are commonplace.

The study had trained tutors deliver the intervention, and its effectiveness should be further tested with working teachers, the authors wrote. Orosco said professional development to help teachers gain the skills is necessary, and it is vital for teacher preparation programs to train future teachers with such skills as well. And helping students at the elementary level is necessary to help ensure success in future higher-level math classes such as algebra.

The research builds on Orosco and colleagues' work in understanding and improving math instruction for English learners. Future work will continue to examine the role of cognitive functions such as working memory and brain science, as well as potential integration of artificial intelligence in teaching math.

"Comprehension strategy instruction helps students make connections, ask questions, visualize, synthesize and monitor their thinking about word problems," Orosco and Reed wrote. "Finally, applying comprehension strategy instruction supports ELs in integrating their reading, language and math cognition…. Focusing on relevant language in word problems and providing collaborative support significantly improved students' solution accuracy."

Provided by University of Kansas

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