Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 1

Jo Boaler, Jen Munson, Cathy Williams

• Publisher: Jossey-Bass
• Year: 2021
• ISBN:
  9781119358732
• Edition: 1
• Topic: Didattica
• Subtopic: Didattica della matematica

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 first-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
Building with and Talking about Shapes

If you are reading this introduction, I am going to assume that you love beautiful, creative mathematics and want to introduce this mathematics to your students. After many years of working in mathematics education, researching and teaching different groups of students, I have come to realize that there are two completely different versions of mathematics. One version is all that many people know; it is a subject of rules and procedures. But there is another mathematics—a subject of beauty and creativity, of openness and exploration—and when people encounter this mathematics, they are forever changed. That is because this mathematics illuminates our world; and when people learn it, they start to see the world in a new light. Paul Lockhart is a mathematician who has worked to communicate the real nature of mathematics to readers. He writes:

What makes a mathematician is not technical skill or encyclopedic knowledge but insatiable curiosity and a desire for simple beauty. Just be yourself and go where you want to go. Instead of being tentative and fearing failure or confusion, try to embrace the awe and mystery of it all and joyfully make a mess. (Lockhart, 2012, p. 10)

I love this advice. Your students are young mathematicians, and you can introduce them to the mathematics that will capture their interest and curiosity if you share with them tasks that invite their thinking and their creativity. This big idea is the first opportunity for that lovely work. As a teacher myself, I am always excited to introduce my students to this version of mathematics.

This big idea is all about composing and decomposing shapes—or, to say it another way, putting shapes together and taking them apart. This is a mathematically worthwhile activity, as it helps students learn the qualities and characteristics of shapes. It also gives students opportunities to build and to move shapes around, helping them get to know their world and the role of mathematics within it.

In our Visualize activity, we give students the opportunity to study two-dimensional images of buildings and notice the shapes that make up the buildings. Students work to decompose the two-dimensional representations of three-dimensional buildings. They then get to design and build their own large city, paying attention to the shapes that make up the buildings. Students will be able to stroll through the streets of their city as if they were giants!

Our Play activity introduces a historical puzzle called the tangram. A tangram is made up of seven two-dimensional pieces that can be cut from a square. Students will be working out how they can fit their seven shapes into a frame, which will engage their minds in important mathematical thinking. Students will turn and flip their shapes as they try to solve the puzzles. We then ask students to make some of their own puzzles. Students get to create a design, name it, and the trace the outline of the shape for another student to try to build. Tangrams, comprising these seven simple pieces, have brought lots of enjoyment to people all over the world.

Our Investigate activity asks students to use tangram pieces to make different squares. We ask students to make as many squares as possible using their pieces, which will be an exciting challenge. Students have the opportunity to discuss shapes by name as they create squares of different sizes using the tangram pieces. When their collection of squares is complete, they talk about the different sizes of the shapes they have made.

Jo Boaler

Reference

1. Lockhart, P. (2012). Measurement. Cambridge, MA: Harvard University Press.

Build(ings)

Snapshot

Students explore how three-dimensional shapes can be composed into more complex figures by first constructing buildings out of recycled materials and then designing a community as a class.

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Connection to CCSS

• 1.G.2, 1.G.1

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Agenda

Activity	Time	Description/Prompt	Materials
Launch	10–15 min	Show students the Noticing Buildings sheet and ask what students think makes these buildings different or the same, then discuss what shapes are used to make the buildings. Support students in noticing different shapes. Connect these two-dimensional shapes to a simple building you have created with blocks, and discuss what shapes are used to make your building. Tell students about the activity and introduce them to the materials available for constructing buildings.	Noticing Buildings sheet, to display Simple building made from two blocks Materials for building construction, to show
Explore	30–45 min	Partners make a plan for the type of building they want to create and the shapes they will need to construct it. Th...