Thursday, July 21, 2016

Mathematical Mindsets: Chapter 3

Welcome back! For the past two weeks, I have been reading and participating in a collaborative book study focused on the book Mathematical Mindsets by Jo Boaler. Chapter 2 described the importance of mistakes in the learning of mathematics. (Read Chapter 2's post here.) Chapter 3 takes an in-depth look at how people view the world of mathematics and how school mathematics differs from real-mathematics. 

Chapter 3 Summary

In this chapter, Jo Boaler discusses how our view of mathematics affects how effectively we are able to learn and understand the subject. She states that people see mathematics as different from other subjects, a series of rules and procedures, because they do not understand the complex nature and beauty of mathematics. Because it is often viewed as a series of right or wrong calculations, Boaler describes school mathematics as a disconnect between "the mathematics that mathematicians use and the mathematics of life"-- "a creative, visual, connected, and living subject" (p. 27). 

My Big Takeaway

Mathematics is mathematics. There is no difference between school mathematics and the mathematics that mathematicians study every day. Jo Boaler states, "when we teach mathematics-- real mathematics, a subject of depth and connections-- the opportunities for a growth mindset increase, the opportunities for learning increase, and classrooms become filled with happy, excited, and engaged students" (p. 32). In addition, being good at math is not about being fast or first, it's about being a powerful thinker.

Ways to Use this New Knowledge to Support Our Students in the Classroom

1. Investigate the role of mathematicians. Post a chart entitled, "How to Think Like a Mathematician" with verbs that describe what mathematicians do, such as wonder, guess and check, ask questions, make conjectures, make connections, solve problems, etc. Continue adding to the chart throughout the year as students find other verbs to describe the work of mathematicians. When solving problems, refer to the chart and ask students to reflect on something that they did that made them "Think Like a Mathematician."  

2. Ask students to wonder! I love to use Dan Meyer's 3-Act Mathematical Stories for this. For example, show the students the video portion of the Girl Scout Cookies 3-Act with no leading information. Just show the video. After the video is over, go back to the 17-second mark and pose the question, "What are you wondering now?" Allow students to contribute their ideas during a class discussion before focusing on what question to tackle. This 3-Act is set-up to answer the question how many boxes fit in the trunk; however, there are many other questions to explore. Once a question is determined, discuss how students will investigate the question and find a solution. The beauty of this task-- it's tough to find an exact answer, so the focus is on the process, not the final answer. Give it a try!  

3. Look for math in nature and have students describe how what they see relates to mathematics. Collecting and posting pictures of math in nature is a good reminder to students that math stretches beyond the walls of the classroom.

Changing how we view the role of and purpose for mathematics in the classroom will help our students see it as more than a series of rules, procedures, and calculations. By showing them what real mathematics is and what mathematicians do, we may encourage more positive feelings about and increased success in the subject.   

       Sound Off! How do you describe mathematics?

  • Boaler, J. (2016). Mathematical Mindsets. San Francisco, CA: Jossey-Bass

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  1. What fabulous ideas! We started school last week and I'm looking for creative ideas for my math group while I get to the next chapters. Thanks!!

  2. What a great idea to use Dan Meyer's 3-Act Mathematical Stories! As a Girl Scout leader, the cookie problem will be fun! :) And I'm definitely going to create a "Think like a Mathematician" chart with my class! Thanks for all the wonderful ideas!

  3. Oh, my, love the idea to create verbs to describe what mathematicians do. I have used "Think Like a Mathematician" with the Standards of Mathematical Practice. This will be a great new twist. Ooo, thanks for the reminder for 3-Acts by Dan Meyer and 101 questions. Both great resources to pull in rich tasks and get my mathematicians engaged.