### 9. Dear Math, You Are Useful

- Sarah states that mathematical modeling can explain any question. It is one of the most useful things a mathematician can do. It can also be a foundational aspect of project-based learning. There is a five-step process involved in modeling. The steps are 1. Define the problem, 2. Define the variables, 3. Make assumptions, 4. Get a solution, and 5. Analyze and model assessment. Steps three, four, and five might iterate until your solution is satisfactory. Students might come up with graphical or spreadsheet representations of data and elaborate posters as part of the process.
- Mathematical modeling can take on just about any topic. Sara suggests you consider topics from the realm of social justice on occasion. Possible topics are racial profiling, climate change, border issues, tax laws, and abortion. I would also look to topics of student interest as content for a math modeling project.

### 10. Dear Math, You Are Powerful

- Projects should start with
*essential questions*. They will guide the project and should be open-ended. They provide a framework that students often revisit as the project progresses.*Benchmarks*are stopping points where students reflect on their progress. They can also allow for learning consolidation. - The idea of the
*audience*is something that should show up here. It is important that the audience goes beyond the teacher. Students will be learning various skills as they create their projects. You should have project exhibitions at the end of each semester. Starter projects can be as simple as math portfolios. The ideal project should also be interdisciplinary. Teachers must keep their ears open for creative mathematical thinking.

### 11. Dear Meth, You Are Raeadoxical

- A key thing is for teachers to be comfortable as
*teachers and learners*. This means that teachers have to face situations where they struggle at times as their students do. You also want to expose students to paradoxes where they can recognize and embrace contradictions. Sarah gives Zeno’s and Simpson’s paradoxes as examples. Your students should Google these. - You can have students graph their feelings during the school day or about anything else. Look for opportunities to make activities all about data collection and visualization. It’s natural to be torn between providing opportunities for open-ended creative work and test prep. It will be difficult for most teachers to break away from a system they think works.

### Conclusion

- We can design a community where math is a liberator rather than a gatekeeper. Rather than give one-size-fits-all lessons, we can have students learn from discourse with people who are different from them.
- At the end, twenty pages of appendices are associated with six of the eleven chapters.

### Sarah Strong and Gigi Butterfield

- Sarah works for High Tech High Graduate School of Education, teaching math methods and advanced math pedagogy. She supports new math teachers and leads workshops on project-based learning in math, student-centered assessment, and alternative grading systems. She has a strong interest in hearing math stories that children tell. Follow her on Twitter @sstrong57
- Gigi is a screenwriting major at Loyola Marymount University. She has attended project-based learning schools since she was five and even in college. She hopes to see PBL help revitalize some of today’s heavily antiquated math pedagogies.

DrDougGreen.com If you like the summary, buy the book