Welcome back! For the past six weeks (I’m a little late with this post), I have been reading and participating in a collaborative book study focused on the book Mathematical Mindsets by Jo Boaler. Chapter 4 discussed ways to promote a mathematical mindset by helping students develop flexibility with numbers. (Read Chapter 4’s post here.) Chapter 5 describes tasks that encourage mathematical engagement and create excitement for students.

**Chapter 5 Summary**

In this chapter, Jo Boaler describes six mathematical cases that illustrate what she termed as “mathematical excitement” (p. 57). She describes mathematically exciting tasks as possessing five characteristics– they combine curiosity, connection making, challenge, creativity, and collaboration. After discussing the six cases, she offers six questions for teachers to consider when planning that would increase the learning power of the tasks they assign. The questions are centered around the openness of a task, whether it is inquiry-based, if the task could be completed before formally teaching the procedure, the presence of a visual, possession of a low floor and high ceiling, and the ability for students to convince others that their reasoning is correct.

**My Big Takeaway**

I enjoyed reading the cases that Jo Boaler used to describe engagement and excitement in mathematics. Oddly enough, there was nothing extraordinary about the tasks except for the students’ interest in completing them and excitement for learning. What a powerful thing! Jo Boaler offers six ways to “open” a task and encourage a growth mindset in order to provide the greatest opportunities for learning. I have summarized her suggestions below.

- Use tasks that have multiple solution paths.
- Add an element of inquiry.
- Introduce the problem before teaching the method.
- Add a visual.
- Modify the task to lower the floor and raise the ceiling.
- Encourage students to convince and reason.

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

The author emphasizes that teachers do not need to find new curricular materials. Instead, they can adapt the resources that are currently available using the ideas below.

- When completing math tasks, ask students to explain why their solution makes sense. This will allow students to see that there are multiple ways to arrive at the same solution.
- Create tasks where students have to do the thinking not duplicate a process while rehearsing a skill.
- Allow students to create their own strategies while wrestling with a task before providing the method or procedure to solve it efficiently.
- Ask students to draw a picture to represent a problem or solution.
- Create opportunities for all students to have access to a problem, including low entry points and extensions.
- Encourage students to think of ways they might be able to convince others that their reasoning is correct. Have them practice convincing themselves, a friend, and a skeptic. (p. 87).

Developing rich mathematical tasks encourages a growth mindset and allows students the opportunity to be engaged and get excited about mathematics while increasing their learning potential.

**Sound Off!**How do you engage and excite your students?

**References:**

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

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