ALPHABETICAL BRAIN™ VOCABULARY
HUMANIST GALAXY
OF SECULAR SCIENCE STARS
JO BOALER
June 26, 2020


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MATHEMATICAL MINDSETS:
Unleashing Students' Potential Through
Creative Math, Inspiring Messages,
and Innovative Teaching.

by Jo Boaler.
Jossey-Bass/A Wiley Brand, 2016
(i-xiii, 292 pages)

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BOOK OUTLINE
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note = www.youcubed.org

[Numbers in parentheses = page numbers]

FOREWORD by Carol Dweck, Stanford Professor and author of the book, Mindset: The new Psychology of Success (vii-viii)

note = "All students can learn math." (vii)

note = "Imagine your students joyfully immersed in really hard math problems. Imagine them begging to have their mistakes discussed in front of the class. Imagine them saying, 'I am a math person!' This utopian vision is happening in classrooms around the world, and as you follow the advice in this book, you may well see it happening in your classroom too." (viii)

INTRODUCTION (ix-xiii)

1) THE BRAIN AND MATHEMATICS LEARNING (1-9)

2) THE POWER OF MISTAKES AND STRUGGLE (11-20)

3) THE CREATIVITY AND BEAUTY IN MATHEMATICS (21-32)

4) CREATING MATHEMATICAL MINDSETS — The Importance of Flexibility with Numbers (33-55)

5) RICH MATHEMATICAL TASKS (57-91)

6) MATHEMATICS AND THE PATH TO EQUITY (93-110)

7) FROM TRACKING TO GROWTH MINDSET GROUPING (111-140)

8) ASSESSMENT FOR A GROWTH MINDSET (141-169)

note = Assessment for learning (148-150)

note = Developing student self-awareness and responsibility (150-167)

note = (1) Self-Assessment (151); (2) Peer Assessment (156); (3) Reflection Time (158); (4) Traffic Lighting (159); (5) Jigsaw Groups (159); (6) Exit Ticket (161); (7) Online Forms (162); (8) Doodling (162); and (9) Students Write Questions and Tests (164)

note = Diagnostic comments (164-167)

note = Conclusion (168-169)

9) TEACHING MATHEMATICS FOR A GROWTH MINDSET (171-208)

CONCLUSION (208)

REFERENCES (209-216)

APPENDIX A — (217-268)

note = Ten Math Homework Reflection Questions (218-219)

APPENDIX B — (page 269-277)

note = Setting Up 7 Positive Norms in Math Class by Jo Boaler (269-277)

[1] Everyone can learn math to the highest levels (270)

[2] Mistakes are valuable (271)

[3] Questions are really important (272)

[4] Math is about creativity and making sense (273)

[5] Math is about connections and communicating (274)

[6] Math class is about learning and performing (275)

[7] Depth is more important than speed (276)

note = Summary (page 277)

ABOUT THE AUTHOR (279)

ACKNOWLEDGMENTS (280)

INDEX (281-292)

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AUTHOR NOTES, SUMMARY,
AND BOOK DESCRIPTION

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AUTHOR NOTES = Dr. Jo Boaler is a professor of mathematics education at Stanford University. The author of seven books and numerous research articles, she serves as an advisor to several Silicon Valley companies and is a White House presenter on girls and STEM (Science, Technology, Engineering, and Math). She is a regular contributor to news and radio in the United States and England and recently formed youcubed.org to give teachers and parents the resources and ideas they need to inspire and excite students about mathematics.

SUMMARY = The Mindset Mathematics series offers a unique, research-based visual approach to exploring the big ideas in mathematics, which is essential to future mathematics success. Teachers and parents can banish math anxiety and give students of all ages a clear roadmap to success. The book explains how the brain processes mathematics learning; reveals how to turn mistakes and struggles into valuable learning experiences; provides examples of rich mathematical activities to replace rote learning; explains ways to give students a positive math mindset; gives examples of how assessment and grading policies need to change to support real understanding; and engages students in visual, creative explorations of the big ideas in mathematics.

Millions of students hate and fear math, so they end up leaving school without an understanding of basic mathematical concepts. Their evasion and departure hinders math-related pathways and STEM career opportunities. Research has shown very clear methods to change this phenomena, but the information has been confined to research journals --- until now. The series of books, Mathematical Mindsets for different grade levels, provide a proven, practical roadmap to mathematics success for any student at any age by engage students in mathematics using growth mindset techniques.

BOOK DESCRIPTION = This hands-on resource is for any teacher or parent who wants to engage their grade school students in reasoning and persisting through problems. It provides activities that will engage students' interest and show them the many ways that mathematics is important in their lives. The book is filled with engaging questions, open-ended tasks, and four-color visuals, Mindset Mathematics is designed to be flexible so that it can be used with any current curriculum. All of the activities and tasks include instructions for launching in the classroom, suggestions for facilitating dynamic discussions, and guidance for what to look for in student thinking as it develops.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message: Teachers want to incorporate more brain science into their mathematics instruction, but they need guidance in the techniques that work best to promote learning of mathematics concepts. In this much-needed volume, the authors clearly show what the big ideas are at various grade levels, why they are important to know, and how students can best learn those big ideas. Mathematical Mindsets provides practical strategies and activities to help teachers and parents show all children, even those who are convinced that they are bad at math, that they can enjoy and succeed in math. Jo Boaler — Stanford researcher, professor of math education, and expert on math learning — has studied why students do not like math and often fail in math classes. She has followed thousands of students through middle and high schools to study how they learn and to find the most effective ways to unleash the math potential in all students.

There is a clear gap between what research has shown to work in teaching math and what happens in schools and at home. This book bridges that gap by turning research findings into practical activities and advice. Boaler translates Carol Dweck's concept of 'mindset' into math teaching and parenting strategies, showing how students can go from self-doubt to strong self-confidence, which is so important to math learning. Boaler reveals the steps that must be taken by schools and parents to improve math education for all. The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you will find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the sixth-grade level through visualization, play, and investigation. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:

There is no such thing as a math person --- anyone can learn mathematics to high levels; mistakes, struggle and challenge are the most important times for brain growth; speed is unimportant in mathematics, mathematics is a visual and beautiful subject; and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

For each big idea, the Mindset Mathematics series has three activities, one that engages the students visually, one that engages them through investigation, and one play activity:

[1] VISUALIZE = Brain scientists now know that when we work on mathematics, even when we perform a bare number calculation, five areas of the brain are involved. Two of the five brain pathways—the dorsal and ventral pathways—are visual. Now brain scientists know that our brains "see" fingers when we calculate, and knowing fingers well --- what they call "finger perception" --- is critical for the development of an understanding of numbers.

Our brain wants to think visually about mathematics, yet few curriculum materials engage students in visual thinking. Some mathematics books show pictures, but they rarely ever invite students to do their own visualizing and drawing.

In addition to the brain development that occurs when students think visually, we have found that visual activities are really engaging for students. Connecting visual and numerical representations encourages important brain connections as well as deep student engagement.

[2] INVESTIGATE = A crucial finding from neuroscience is the importance of students struggling and making mistakes—these are the times when brains grow the most. In one of my meetings with a leading neuroscientist, he stated it very clearly: if students are not struggling, they are not learning. We want to put students into situations where they feel that work is hard, but within their reach.

Do not worry if students ask questions that you don't know the answer to; that is a good thing. It is good to say to your students, "That is a great question that we can all think about" or "I have never thought about that idea; let's investigate it together." It is even good to make mistakes in front of students, as it shows them that mistakes are an important part of mathematical work.

[3] PLAY = Opening mathematics involves inviting students to see ideas differently, explore with ideas, and ask their own questions. Students can gain access to the same mathematical ideas and methods through creativity and exploration that they can by being taught methods that they practice. Albert Einstein famously once said that "play is the highest form of research." This is because play is an opportunity for ideas to be used and developed in the service of something enjoyable. Play activities can invite students to work with each other, building understanding together.

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AMAZON BOOK REVIEWERS
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[1] JL- Best approach to math I've ever found! = I could not love Jo Boaler and youcube more! The visual math approach and creative side of math have helped my kids to live math. This book helps bring more fun with math to our family. My kids often tell me: I don't like the boring math they teach in school. Let us do the fun math that I really can understand and we find in life all around us. This approach really helps them understand the why behind how math works.

[2] David G. Bories - Will low performing students respond to activities?

[3] Amazon Customer - This book has some very clever activities = We are testing some of the ideas for Algebra now. Ms. Boaler says that almost all students will respond to the activities and that is what we are hoping.

[4] Jennifer Rivera - Great Geometry Activity Ideas! = I purchased this book for a masters class for geometry. Math is not my strongest subject but this book was really good. I actually enjoyed the introduction and the chapter I was assigned. I highly recommend it for Geometry teachers grades 8th or 9th.

[5] Amazon Customer - Jo Boaler knows math = It is Jo Boaler! What else do you need to know?

[6] AD - Love it = Love her books. Have all the grade levels. Great things you can take immediately into the classroom.

[7] Teresa Vaughn - Low floor, high ceiling. All the way through.

[8] Robin A - Great Author = Some of the pages were cut wrong but the pages are readable. Love this author. [9] Anthony - Love my math = I enjoy Jo's theory and reasoning provided for lessons. Book is split up into different "big ideas", similar to Marian Small, however carries a different tone. Activities and lesson sequences are all decent (have not used them all yet). All are multi-strand and hit on the different learning styles experienced in a classroom.

Only thing that has been brought up between myself and some other teachers is that the different grades are very similar. It would not be beneficial for me to purchase the 4th or the 5th grade books since many of the tasks are the same as in this 6th grade book.

[10] Jayjay - Get this! = Great ideas and forward pedogody as always from the authors.

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Jo Boaler

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