I designed and taught a course titled "Engaging Students in Active Mathematics Learning". The course enrolled graduate students and undergraduates, mathematics majors and education majors, with about a 50-50 split along both dimensions.
The first activity we undertook in this class was reading selected chapters in the book How Students Learn: History, Mathematics, and Science in the Classroom. I picked this book to start with because (1) it was a recent publication; (2) I had read How People Learn: Brain, Mind, Experience, and School, which How Students Learn built on; (3) it was targeted at practitioners, meaning that it would minimize the amount of jargon it used (compared to How People Learn, which is filled with jargon); and, of course, (4) it contained mathematics-specific chapters.
Before turning to the mathematics chapters, the class read Chapter 1: Introduction. This chapter discussed the framework developed in the foundation book, How People Learn. In particular, the chapter introduced three principles from How People Learn:
Principle #1: Engaging Prior Understandings,
Principle #2: The Essential Role of Factual Knowledge and Conceptual Frameworks in Understanding,
Principle #3: The Importance of Self-Monitoring
These principles provided threads that were woven throughout the mathematics chapters (presumably also the history and science chapters), revisited with specific mathematics curricula. This chapter did a nice job of translating the abstract research theory from How People Learn into concrete ideas that practitioners can consider, illustrating with a number of well-chosen examples.
The mathematics-specific chapters are chapters 5 to 8, which cover:
- Mathematical Understanding: An Introduction
- Fostering the Development of Whole-Number Sense: Teaching Mathematics in the Primary Grades
- Pipes, Tubes, and Beakers: New Approaches to Teaching the Rational Number System
- Teaching and Learning Functions
As is evident, the chapters followed the hierarchy of mathematics content and grade level. Each chapter illustrated the three principles of How People Learn with a specific curricula. The preface to How Students Learn had indicated that the chapters would offer examples and that these examples were not meant to be exhaustive, but rather were meant to lead the reader to come up with ideas of their own. I had expected that each chapter would have multiple examples in it. Instead, each chapter focused on one set of curriculum materials (for example, Chapter 7 described a curriculum that introduces percents first instead of fractions).
Each chapter explored how that particular curriculum fit the three principles. It was an interesting exercise, but it was not clear to me how the example curricula were chosen. I also understood that the book meant to translate research results into practical ideas, thus offering a bridge over the historically wide gap between education research and classroom practice. I thought that some chapters were better than others about synthesizing and presenting the results of education research that led to the design of the particular curriculum. Chapter 7, for example, did the best job of drawing on a large and varied body of research, rather than making claims without citing references.
As I explored the details for this book before classes began, I saw that not only was it available in the hardback version that I have, and paperback, but also as a PDF at the National Academy Press website. To download the PDF, one has to pay a fee. However, the book can be read online for free. I appreciate that all of these options are available because it gives people the opportunity to decide for themselves which format(s) fits their preferences and needs. It's also very cool that the book can be purchased in pieces, so a person can buy just the history piece, just the mathematics piece, just the science piece. These pieces come with the introductory chapter that establishes the framework (Chapter 1: Introduction) and the summary chapter (Chapter 13: Pulling Threads).
I highly recommend the book for anyone interested in K–12 teaching and learning. As college teachers, we should know what our students may be experiencing and learning before they become college students. In addition, many of us have contact with pre-service and/or in-service teachers, another reason to have an understanding of the latest thoughts on K–12 teaching and learning. In the context of the class I was teaching, I found chapters to be very useful for bridging distances among the students in the class (graduate students and undergraduates, mathematics majors and mathematics education majors). The students understood the importance of learning about education at levels different than the ones they intended to teach and the chapters gave us a common vocabulary. Finally, I would hope that all of us could appreciate ideas about education and think carefully about what aspects of those ideas we can take into our our teaching.
Teri J. Murphy is an associate professor of mathematics at the University of Oklahoma with specialty in research in undergraduate mathematics education.