The MAA (Mathematical Association of America) sent me a review copy of their new book "Learning Modern Algebra: From Early Attempts to Prove Fermat's Last Theorem." I don't typically review textbooks but the title and then the contents of the book convinced me that I needed to interview the authors. Joe Rotman wasn't available but I was able to chat with the other co-author, Al Cuoco. I was really struck with Al's passion about teaching the teachers as well as the students. Al shared some great insights about the ingredients that I think should go into every math textbook to help teachers and students to develop the right habits of mind to succeed.
Here are some of the questions we discussed.
1. What is your background and your experience teaching high school math to students and to teachers?
2. I attended the Ross program and you have a key role in a program that has its roots in the Ross program. Tell me about this program and your involvement with it.
3. There's something special about number theory and algebra that makes it accessible to bright students without a deep background in math. What do you think of that thought?
4. What is "Learning Modern Algebra" about and who is the audience?
5. How does Fermat's Last Theorem unite the book's chapters?
6. What are the challenges with how Modern Algebra is taught?
7. Why is exploration so important and how do you promote it?
8. Rigorous thinking about open-ended problems runs through the book. PODASIP (prove or disprove and salvage if possible) problems contribute to this. Can you speak to that?
9. Why is historical setting important in learning math and how do you weave history into the book?
10. Tell us about the importance of the "Connections" sections in the book.
11. Is there a next book or project?
12. The question I ask everyone: "What advice would you give to a parent whose child was struggling with math?"
About Al Cuoco
From the EDC web-site:
Al Cuoco is the lead author of CME Project, a National Science Foundation (NSF)-funded high school curriculum published by Pearson. Recently, he served as part of a team that revised the Conference Board of the Mathematical Sciences (CBMS) recommendations for teacher preparation and professional development.
Cuoco is carrying out several professional development streams of work devoted to the implementation of the Common Core State Standards for Mathematics (CCSSM) Standards for Mathematical Practice, including EDC’s Mathematical Practice Institute (MPI). Through the MPI, he and his colleagues have launched a new course for teachers and facilitators, Developing Mathematical Practice in High School.
He co-directs Focus on Mathematics, a partnership among universities, school districts, and EDC that has established a community of mathematical practice involving mathematicians, teachers, and mathematics educators. The partnership evolved from his 25-year collaboration with Glenn Stevens on Boston University’s PROMYS for Teachers, a professional development program for teachers based on an immersion experience in mathematics. He also co-directs the development of the course for secondary teachers in the Institute for Advanced Study program at the Park City Mathematics Institute. More
About "Learning Modern Algebra"
Learning Modern Algebra aligns with the CBMS Mathematical Education of Teachers–II recommendations, in both content and practice. It emphasizes rings and fields over groups, and it makes explicit connections between the ideas of abstract algebra and the mathematics used by high school teachers. It provides opportunities for prospective and practicing teachers to experience mathematics for themselves, before the formalities are developed, and it is explicit about the mathematical habits of mind that lie beneath the definitions and theorems.
This book is designed for prospective and practicing high school mathematics teachers, but it can serve as a text for standard abstract algebra courses as well. The presentation is organized historically: the Babylonians introduced Pythagorean triples to teach the Pythagorean theorem; these were classified by Diophantus, and eventually this led Fermat to conjecture his Last Theorem. The text shows how much of modern algebra arose in attempts to prove this; it also shows how other important themes in algebra arose from questions related to teaching. Indeed, modern algebra is a very useful tool for teachers, with deep connections to the actual content of high school mathematics, as well as to the mathematics teachers use in their profession that doesn't necessarily "end up on the blackboard." More