Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade K

Jo Boaler, Jen Munson, Cathy Williams

• Publisher: Jossey-Bass
• Year: 2020
• Print ISBN: 9781119357605
• eBook ISBN: 9781119358602
• Edition: 1
• Topic: Bildung
• Subtopic: Mathematik unterrichten

Engage students in mathematics using growth mindset techniques

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the kindergarten-grade level through visualization, play, and investigation.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. 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.

BIG IDEA 1
Understanding the Physical Quantity of Number

The most important goal for any teacher of mathematics, in my view, should be the development of curiosity and wonder in students. When students are curious, they become motivated and inspired to learn anything they set out to learn. There is probably no more important time to spark this journey of curiosity than when students are beginning kindergarten. This becomes particularly important if students are in homes where parents think they should get their children ahead in school by teaching mathematical methods to memorize. If students think their role is to remember inflexible sets of rules, they will be hampered in their mathematical journeys. There is a very strong danger that this approach leads them to believe that this is what math is—a set of rules—that they do not need to make sense of, only memorize. In an international survey given to over 13 million students as part of the international PISA testing, from the OECD, it was found that students who took a memorization approach to mathematics were the lowest-achieving students in every country (Boaler & Zoido, 2016). Unfortunately, the elementary school years are often when students develop the idea, from damaging practices such as timed tests (Boaler, 2014), that mathematics is all about memorization. The opposite of a dry, unappealing, memorization approach to mathematics is one that encourages curiosity and wonder.

We invite students to wonder in all of the activities in this book, starting with Big Idea 1. In the Visualize activity, we ask students to discuss times when they have wondered “How many?” and then give students different groups of objects and invite them to work out how many there are.

In our Play activity, we have chosen photographs for students that include several different things to count, and different ways to count them. We have chosen photographs that offer different ways to count in order to help students know that in mathematics there are usually many different ways to see things and varied ways to approach them, and that different approaches can all be correct if students justify their thinking and give reasons for their approach.

In our Investigate activity, we invite students to make their own books. We recommend that students work in pairs. Each pair is given a number for which to make a page for the class counting book and, if possible, a digital camera. Students can then be taken to spaces where they look for numbers in the world. Together the class makes a whole book that they can refer back to during the rest of the year.

Jo Boaler

References

1. Boaler, J., & Zoido, P. (2016, November 1). Why math education in the US doesn't add up. Scientific American. Retrieved from https://www.scientificamerican.com/article/why-math-education-in-the-u-s-doesn-t-add-up/
2. Boaler, J. (2014). Fluency without fear: Research evidence on the best ways to learn math facts. Retrieved from http://youcubed.org/teachers/2014/fluency-without-fear/

Count a Collection

Snapshot

Students stretch their counting capacity by counting collections of classroom objects and coming to agreement with a partner about how many objects there are.

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Connection to CCSS

K.CC.4, K.CC.5, K.CC.1

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Agenda

Activity	Time	Description/Prompt	Materials
Launch	5–10 min	Ask students what kinds of “How many?” questions they have asked themselves. Tell students that they are going to work with a partner to come to agreement about how many objects are in a given group. Model with a partner how to compare counts and resolve any disagreement.	Collection of objects (fewer than 10) in a container
Explore	15–30 min	Partners work together to count a collection of objects and come to agreement about how many there are.	Collections of various classroom or everyday objects in containers Optional: sticky notes or index cards
Discuss	10 min	Gather the class in a circle and invite partners to share how they counted their collections. Partners can demonstrate the ways they counted. Highlight features of counting that you'd like to see others try, such as moving objects to count.	Optional: chart and markers
Extend	Ongoing	Create a counting station with a collection of objects for the class to count in small groups or independently over the course of several days. Provide tools for recording the various counts. Discuss how many are in the collection and come to agreement.	Collection to count Tools for recording, such as sticky notes or index cards

To the Teacher

Counting concepts are at the heart of kindergarten mathematics, and educators who both research mathematics learning and write for teachers have made counting central to considering early mathematics. The notion of repeated, ongoing counting of collections of objects is the subject of two books that we recommend: Franke, Kazemi, and Turrou's (2018) Choral Counting & Counting Collections and Liu, Dolk, and Fosnot's (2007) unit of study Organizing and Collecting, which is part of the Contexts for Learning curriculum series. Both of these resources provide clear ideas for how to incorporate counting collections of classroom and everyday objects into the long-term trajectory of the ear...

Table of contents

• Cover
• Table of Contents
• Introduction
• Note on Materials
• BIG IDEA 1: Understanding the Physical Quantity of Number
• BIG IDEA 2: Using Fingers as Numbers
• BIG IDEA 3: Talking about and Making Shapes
• BIG IDEA 4: Seeing Numbers inside of Numbers
• BIG IDEA 5: Putting Numbers Together
• BIG IDEA 6: Describing and Sorting Objects
• BIG IDEA 7: Seeing and Making Patterns Everywhere
• BIG IDEA 8: Stretching Counting toward 100
• Appendix
• About the Authors
• Acknowledgments
• Index
• End User License Agreement