1. How are manipulatives used in your mathematics instruction?

2. Mathematical practice 5 calls for students to use appropriate tools strategically. How do you allow students to make decisions about the tools they use in their work?

3. How are these tools used to move learning from surface learning to deep learning?

Consider the strategies you use, and the strategies you've read about and tried from this chapter to solidify surface learning. What are some effective ways to build surface learning, and why is that necessary?

1. How are manipulatives used in your mathematics instruction?

2. In what ways are they used for multiple representations as students work on mathematics collaboratively?

3. What strategies can you use to make these tools more available to your students?

Identify two or three mathematics tasks you've asked your students to work on recently. Think about each task in light of its difficulty and complexity (see Figure 3.1 on page 77). In which quadrant does each task fit? 

Is each the right kind of task given your learning intentions? 

Make notes of the questions you typically ask in your math lessons. Think about them in terms of the focusing and funneling questions framework discussed in this chapter.

1. Which way does your questioning sequence lean?

2. How can you make focusing questions a stronger presence in your mathematics classroom?

Learning intentions can help students make connections between current learning and previously learned content. Identify the learning intention for a lesson you have recently taught. What previously learned content is connected to this learning intention? Did your students see the connection? If so, how did this impact thier engagement in the learning? If not, how might you modify the learning intention and experience to bring more attention to this connection?

Learning intentions should be intentionally inviting to students. Look back over your learning intentions from recent lessons and rewrite them to be more inviting to students. Use the examples in Figure 2.1 for guidance.

Think about the instructional strategies you use most often.

1. Which do you believe are the most effective?

2. What evidence do you have for their impact?

Save these notes so you can see how the evidence in this book supports or challenges your thinking about effective practices.