### 5. Identity in Mathematics Education

- It seems that math textbooks are written with middle and upper class white kids in mind. Teachers need to know their students and the worlds they inhabit well. We know that positive identities are predictors of success. Schools with more access to enriched courses serve minority children better than schools that focus on remediation. A positive math identity can be fostered and Lidia offers suggested reading.

### 6. School Mathematics

- Traditional math teaching involves the teacher presenting a procedure involving the steps (an algorithm) for solving a problem featuring little or no context to students who are largely passive. Other similar problems are solved prior to students working on their own to solve more similar problems. The focus is on understanding procedures not on conceptual understanding. This is a recipe for disaster.
- To move beyond traditional teaching add context from the students’ world, include math history from diverse cultures, allow for creativity, and make sure that students are active. Let them do research so they can go find quantities that they grapple with. If you use a text ask yourself if the problems are removed from the students’ experiences. There are many references here including Jo Boaler’s
*Mathematical Mindsets*summarized here.

### 7. Mathematics as Gatekeeper

- The more math students take in high school, the more likely they are to complete and have success in college. Students who don’t finish college in six years are likely to quit due to the fact that they can’t pass the required math course. Students who have to take no-credit remedial course are even less likely to graduate. The math that acts as the gate keeper is usually algebra. Math reasoning appears to translate to the real world.
- Standardized testing, math and ELA, tends to narrow the curriculum with a focus on memorization and drill. This is more likely to happen in schools serving poor children. Lidia would rather see more imaginative assessments created by teachers who know students best rather than assessments created by companies who don’t. The savings could be used to improve instruction in many ways.

### 8. Achievement Gaps or Opportunity Gaps?

- Lidia makes a compelling case that what are commonly called achievement gaps are really
*opportunity gaps*. Poor performing students are likely to attend schools that simply have fewer resources, and students of color are more likely to fall into this category. The resources include experienced teachers, smaller class sizes, well lit facilities with lots of space and amenities such as swimming pools and labs, access to AP classes, enrichment classes and technology; and smaller case loads for counsellors and special education teachers. - Private schools and public schools in wealthy communities have way more resources. Simply put, better funded schools have better outcomes. While each of us may not be able to do much, we all need to raise our voices so that politicians and policy makers know that achievement gaps are really opportunity gaps.

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