Exploring Limitless Growth: On Math, Mindset and Metacognition

[Jo Boaler]

Run Time: 52:32 - May, 2023
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This is episode two from Toddle's "School Leadership Project"

Listen to this incredible conversation about Jo Boaler's groundbreaking research on what truly makes a difference in math education. Learn about how we can all become leaders in transforming math classrooms into places where all students can thrive. Jo also gives you an exclusive sneak peek into the research she's conducting for her exciting new book.

Discover how to unleash the potential in every student, because math is for everyone.

** Related resources connected to the podcast

Jo's book she mentioned in the podcast

What’s in Store:

Mathematical Mindset Practices Rubric

Many teachers ask what a growth mindset looks like in the classroom, and how it may be measured. Youcubed have developed a rubric that you can use to help students understand the importance of developing a growth mindset toward mathematics. 

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Source: Youcubed Website

Figure Me Out?

Here's a cool activity to do with your students at the beginning of the year. It's a good way to determine prior knowledge. It's differentiated because each student can choose the operations and complexity to answer the questions. You could use it again mid-year and end year by asking students to demonstrate what they learned throughout the year by using more sophisticated math.

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How Old Is the Sheppard?

How do you think 32 eighth grade students would respond to this nonsensical question: “There are 125 sheep and 5 dogs in a flock.  How old is the shepherd?”  Take a guess as to what percentage of them would give a numerical answer and then watch the video. 

The video would be a wonderful provocation for parents who are frustrated by how differently math is taught now as compared to when they were in school.  They speak like everything was so much better back then.  It can be challenging to get parents to realize that maybe things weren't so great before. Whaty would your student's think of it? Read Robert Kaplinsky's blog explaining the video and it's outcomes.

Run Time: 3:07 - Dec 1, 2013

NRICH Outdoor Maths

NRICH offers several outdoor math tasks for 5-11 year olds to experience at school. Offering outdoor mathematics can be motivating and intriguing for many learners. The tasks suggest several different ways in which we can engage children in mathematics outside...

You can watch a recording of the webinar in which the mathematical thinking which can be prompted by these activities is discussed. 

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Math Progressions/Standards

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In this article - New Data Science Standards Are Needed for a Data-Filled World. Here’s What is Proposed - Jo Boaler explains the reason behind creating the Big Ideas website and the importance of teaching children K-12 data literacy.

The Importance of Data Literacy

Jo Boaler and the YouCubed team have created a website - Big Ideas - that focuses on the development of Data Literacy. The need for data literacy has increased in recent years, not only to prepare students for 21st century jobs and support an informed citizenry. This has implications throughout the school years: teachers of younger students have the important task of helping them develop data literacy, and as students move through the grades they can start to learn the exciting and new discipline of data science.

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The Big Ideas website offers ideas for the development of data literacy and data science through the grades! For each grade range, the website links to tasks and data talks that Youcubed has curated which are appropriate for addressing the content at that level.  Data talks support student development in reading and understanding data visuals – an important form of data literacy. The ones found on the Big Ideas website are among the most popular data science resources and a full collection can be found HERE

Early Number & Counting

Source: Graham Fletcher | Run Time: 7:34

Addition & Subtraction

Source: Graham Fletcher | Run Time: 7:20

Progression of Division

Source: Graham Fletcher | Run Time: 7:48

Progression of Multiplication

Source: Graham Fletcher | Run Time: 5:56

Fractions: The Meaning, Equivalence, & Comparison

Source: Graham Fletcher | Run Time: 7:24

New Mathematics Framework

A new Mathematics Framework for the State of California has just released for public comments. Jo Boaler was one of 5 writers of this new framework. The framework is worth some consideration by educators beyond California. Some highlights of the recommendations in the new proposed framework are these:

Math Websites

The NRICH Project

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The NRICH Project aims to enrich the mathematical experiences of all learners. The NRICH website hosts a large collection of math problems and solutions for teachers and students. An interesting section of the website is the Features section where students are presented with a problem which they are encouraged to solve using a variety of strategies and words.  Live web-based sessions are scheduled where problem solutions for each feature are discussed. This is wonderful PD and could be used for feedback to students.

Primary Math Strategies & Resources 

Early Years Math Strategies & Resources 

Professional Development 

Student Games and Activities

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Open Middle (Robert Kaplinski)

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What’s Open Middle?

The name Open Middle created by Robert Kaplinski might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:

Open middle problems generally require a higher Depth of Knowledge (Open Middle Math Depth of Knowledge Matrix) (Download Matrix Here) than most problems that assess procedural and conceptual understanding.   They provide students with opportunities for discussing their thinking. 

Here are Two Blogs to get you started: Why Are You Using That Problem?  & Is Depth of Knowledge Complex or Complicated?

**Download a Student Work Sheet

Some additional characteristics of open middle problems include:

You can even have your students create new problems and send them in to have them added to the website

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What’s Zearn Math?

Zearn is the top-rated math learning platform that helps kids explore concepts, discover meaning, and make sense of math. It is free for classroom teachers and there is a pay option for schools. Zearn is striving for is large cultural change in student attitude, hoping to move toward a new normal where math isn’t perceived as uniquely scary. . To use you will need to create a free account.

Zearn can be used for differentiating instruction, discovering prior knowledge, review, personal inquiry and learning math content.

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Byrdseed math archives host a variety of  articles about developing high level math problems.

Here are a few examples:

Differentiate Math: Getting Started

Working with a student who is bored in math? Quickly finishing lessons? Needs something more? Here are three ways you can get started differentiating in math.

Differentiating in Math: Running Multiple Groups in One Class

100%, 100%, 100%. If you've ever taught gifted students math, you're probably familiar with those kids who can knock perfect scores out week after week. You've probably also questioned what good you're doing for those students. A differentiated math program may be just what you need.

Constructing Meaningful Math Projects

Here are four key attributes I look for when developing math projects: juicy data, interesting conflict, an expert's lens, and a final product.

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Graham Fletcher Website

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Graham Fletcher has served in education as a classroom teacher, math instructional lead, and currently as a math specialist.  His work with the math progressions and problem-based lessons has led him to present throughout North America and beyond.

Graham is continually advocating for best practices in elementary mathematics by seeking new and innovative ways to support students and teachers in their development of conceptual understanding. He is the author of Building Fact Fluency: A Toolkit for Addition and Subtraction.

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Robert Kaplinski has been an educator since 2003 as a classroom teacher, teacher specialist for Downey Unified School District, instructor for the University of California, Los Angeles (UCLA), and presenter at conferences around the world.

He is also the author of Open Middle Math: Problems That Unlock Student Thinking, Grade 6-12, creator of the #ObserveMe movement, president of Grassroots Workshops, and runs the website Open Middle.

Blog Sections

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Math is Visual

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This website was created to assist in building a better conceptual understanding of mathematics through the use of visuals. The images, videos and resources shared here are intended to help all teachers, parents and students understand that Math Is Visual and we should take every opportunity to teach it that way.

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Estimation 180

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ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together. Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning. 

Estimation 180 is the love of Andrew Stadel, a math educator who has also created many problem-based lessons including 3-Act problems.

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Youcubed provided a variety Math Problems/Tasks for all grades. Curated by Jo Boaler and Stanford Graduate School of Education | 100% free

Inspiring Math Success for all Students through Growth Mindsets and Innovative Teaching. Headed up by Jo Boaler, Youcube's main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on math learning into accessible and practical forms.



*Week of Inspiration Math (WIM)

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Would You Rather Math

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Would You Rather Math presents students with two scenarios of a problem and asks them to choose one of them and then defend their answer. There is no right or wrong answer. It provides opportunities for students to strengthen their critical thinking skills by taking a stance and defending 

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(Focus: Math & Science - Inquiry, Assessment, Early Years, Critical Thinking)

Math Resources/Articles

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Math Resource Books

Understanding the Math We Teach and How to Teach It, K-8

By: Marian Small

Marian Small has written a landmark book for a wide range of educational settings and audiences, from pre-service math methods courses to ongoing professional learning for experienced teachers. Understanding the Math We Teach and How to Teach It, K-8 focuses on the big mathematical ideas in elementary and middle school grade levels and shows how to teach those concepts using a student-centered, problem-solving approach.

Click/Tap to Continue ISBN-13 ‏: ‎78-1625313355 / Stenhouse Publishers (August 26, 2019)/ 648 pages

Dr. Small, a former dean with more than 40 years in the field, conceived the book as an essential guide for teachers throughout their career: "Many teachers who teach at the K-8 level have not had the luxury of specialist training in mathematics, yet they are expected to teach an increasingly sophisticated curriculum to an increasingly diverse student population in a climate where there are heightened public expectations. They deserve help."

Also, check out these two blogs about the book.

Mathematical Mindsets:

Unleashing Students' Potential through Creative Mathematics, Inspiring Messages and Innovative Teaching (2nd Ed)

By: Jo Boaler 

In the newly revised Second Edition of Mathematical Mindsets, distinguished Stanford math education professor Jo Boaler demonstrates what it takes to help students become high achievers in mathematics. Filled with brand-new material and updated references, the book integrates a social justice perspective and new research regarding the teaching of data science and math gathered over the past five years.

“Jo Boaler calls out the mindsets that can limit a student’s aptitude for math and ways to change them. More than just a replacement set of positive messages, Jo’s book elaborates practical, research-tested strategies for teaching, assessment, practice, and homework—all to help a student learn and love to learn mathematics.” —Dan Meyer

Click/Tap to Continue ISBN-13 ‏: ‎978-1119823063 / Jossey-Bass; 2nd edition (February 23, 2022) / 320 pages

Reverse mathematics trauma and find a universal blueprint for math success.

In Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching mathematics education expert and best-selling author Jo Boaler delivers a blueprint to banishing math anxiety and laying a foundation for mathematics success that anyone can build on.

Perfect for students who have been convinced they are naturally "bad at math," the author offers a demonstration of how to turn self-doubt into self-confidence by relying on the "mindset" framework.

Mathematical Mindsets is based on thousands of hours of in-depth study and research into the most effective—and ineffective—ways to teach math to young people. This new edition also includes:

Mathematical Mindsets is ideal for K-12 math educators. It also belongs on the bookshelves of the parents interested in helping their K-12 children with their math education, as well as school administrators and educators-in-training.  Here is a one-page explainer about how parents can help their child get excited about mathematics.

Teaching Student-Centered Mathematics: 

Developmentally Appropriate Instruction for Pre K-2 (Vol. 1) &  Gr. 3-5 (Vol. 2) with Enhanced Pearson eText - Access Card Package (Vol. 1) & (Vol. 2) - 3rd Ed.

By: John Van de Walle, Karen Karp, LouAnn Lovin, Jennifer Bay-Williams

Note: These packages includes the Enhanced Pearson eText and the bound book version.

These books & eText help students make connections between mathematics and their worlds―and helping them feel empowered to use math in their lives. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM’s teaching practices, and engaging families. 

The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions.

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Improve Mastery and Retention with the Enhanced Pearson eText

The Enhanced Pearson eText provides a rich, interactive learning environment designed to improve student mastery of content. The Enhanced Pearson eText is:

*The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads.

*The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7” or 10” tablet, or iPad iOS 5.0 or later.

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