5. Rich Mathematical Tasks

• Good math curricular materials are a teachers best friend when it comes to bringing curiosity, connection making, challenge, creativity, and collaboration into your math classes. In this chapter Jo starts with five cases that are examples for what she is talking about. In some cases students play with the activity before the teacher introduces the necessary methods required. These are rich open tasks that the reader can probably engage in as well. Many teachers will have to alter their mindsets in order to become designers who create and adapt tasks. As they do so, Jo offers six questions to guide this activity. 1) Does the task encourage multiple methods, pathways, and representations? 2) Can you make it an inquiry task? 3) Can you ask the problem before you teach the method? 4) Can you add a visual component. 5) Can you make it a low floor and a high ceiling to engage students of a wide range of abilities? 6) Can you add the requirement to convince and reason? At the end of the chapter are fourteen websites with tasks that fit with one or more of these questions.

6. Mathematics and the Path to Equity

• Due to it’s nature, many educators use math as an elitist performance subject to sort and segregate students based on how fast they can do computations. It is often taught as a performance subject rather than one that strives for understanding. Teachers believe that there is raw math talent and only some kids can succeed. Kids that don’t initially compute fast are discouraged and turned off. Jo sites situations where minorities and girls who pass in algebra in eighth grade have to take it again in ninth grade. Teachers who teach the advanced track don’t want to take kids who might not pass. One district didn’t allow kids with a single discipline referral to take advanced math. (Doug: My daughter’s eight-grade algebra teacher tried to weed her out and she got 100% on the state final.)
• Jo argues against having students repeat classes as they often do no better. She also argues against advancing kids at an early age as the are likely to end up doing computations without understanding what they are doing. The chapter ends with the following equitable strategies: 1. Offer all students high-level content. 2. Work to change ideas about who can achieve in math. 3. Encourage students to think deeply about math. 4. Teach students to work together. 5. Give girls and minorities encouragement to learn math and science. 6. Eliminate (or at least change the nature of) homework.

7. From Tracking to Growth Mindset Grouping

• Jo starts here by making a case against tracking. Research shows that countries with little or no tracking outperform countries like the US where tracking is common. Putting a student in a track is a great way to promote a fixed mindset. Exposing all students to high-level content is the best way to promote achievement. In the US, the door slams to taking calculus in high school when students are tracked in 7th grade. (Doug: This happened to me.) Teachers who teach tracked groups often tend to think that all students in each group are the same, which is not the case. Lots of research shows how harmful tracking can be. Kids in lower tracks get the message that they are not “the smart kids” and bad behavior is likely to follow.
• The second half of this chapter explains how to effectively teach heterogeneous classes. Tips include 1. Providing Open-Ended Tasks 2. Offering a choice of tasks 3. Individualizing pathways. Essentially, you have to avoid the standard practice of show students how to do a type of problem and then giving them a large number of similar problems to practice. Jo recommends having students work in groups and offers some advice for how to do it. The chapter concludes with a number of sample tasks.

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