My Favorite Resource
Today one of my math teaching buddies asked me to recommend a math pedagogy book she could read on an upcoming road trip. I recommended Elementary and Middle School Mathematics: Teaching Developmentally even though it is not a book you read cover to cover. Instead, it is organized by topic and you can skip around as needed.
I like a lot of other books, but this book is my compass because it addresses both content and pedagogy. It is the ONLY resource that I go back to on a regular basis, and here’s why:
1. It tells you where the “ah-ha moments” should be.
I know how to read a graph but when it came to teaching students how to do it I thought to myself, “What can I say besides ‘read the question and use the graph to answer it’ ?”
This book breaks graphs into two categories – those without numeric ordering (bar graph and pictographs) and those with numeric ordering (graphs with number lines). This is a simple idea, but one that is very useful in planning because it provides a structure around which teachers can organize their teaching and students can organize their observations.
2. It tells you where the “uh-oh moments” might be.
I taught students that a fraction was the part out the total, but it was still very difficult for them to remember. When I turned to this book I understood why.
It said, “The way that we write fractions with a top and a bottom number and a bar between is a convention – an arbitrary agreement for how to represent fractions. (By the way, always write fractions with a horizontal bar, not a slanted one. Write not 3/4.) As a convention, it falls in the category of things that you simply tell students. However, a good idea is to make the convention so clear by way of demonstration that students will tell you what the top and bottom numbers stand for.”
3. It tells you how to sequence ideas so that they build on each other.
Now you would have to read all of Chapter 20 to understand what I mean. But seriously, it is mind-blowing. Basically, it breaks the development of geometric thinking into three levels and tell you what kind of thinking characterizes each level. It provides specific examples and lots of pictures. It is the way to teach geometry.
4. It tells you which activities you might use.
Models for fractions? There are ten different kinds on page 245. Teaching measurement? Start with informal units on page 319. Multi-digit multiplication? Model it the way they do on page 219.
The book is expensive, but completely worth it especially because one copy can be shared by a school. You can buy it at the link below or maybe find it at a library: