When I first began teaching, I used Saxon Math, published by Houghton Mifflin Harcourt, to teach my second graders.
Saxon largely uses traditional teaching methods for teaching arithmetic and problem solving skills, with homework problems for each lesson. The homework has five or so problems focusing on that day’s lesson, while the majority of the homework is spiral review.
I found Saxon to be rather trying. For me, not necessarily the students. Each lesson was on a different topic. For example, one day we might be working on fractions, and the next day we’d be doing word problems, then decimals, then something else, then finally back to fractions. Every day I had to begin my lesson with significant review, since we hadn’t discussed that day’s concepts for awhile. I thought this was a huge pain.
Little did I know.
The next school I taught at adopted Go Math!, also published by Houghton Mifflin Harcourt.
Go Math! does not use traditional methods of teaching math. By this, I don’t just mean using modern technology, though Go Math! does provide for that. Go Math! attempts to teach a fundamentally different way of thinking about arithmetic and problem solving.
For each concept in arithmetic, Go Math! presents a variety of ways to solve them. For example, in the first grade curriculum, students learn to solve addition problems using counters, ten frames, and number lines. There is little emphasis, however, on memorizing math facts. In third grade, students are using number lines to solve three-digit addition problems. Why on earth are third graders still using number lines to do addition? Why can’t they do it themselves? These “alternate methods” are being used as a crutch, not a tool.
Furthermore, on assessments, students are told which method to use to solve any given problem. I though the point of teaching students alternate ways of solving problems was to allow them to use the method that works best for them, since not all methods will make sense to all students. What is the point of teaching multiple methods if you’re going to dictate which method they use?
The majority of word problems (at least in the first grade curriculum) were multiple choice. So much for teaching them to solve problems independently.
There is also precious little spiral review. Typical homework assignments only contained two to three review questions.
When we got close to the end of the year, I realized my students didn’t remember half the concepts I’d taught. There was no time built into the curriculum for review, and the “critical thinking” segments didn’t actually build critical thinking.
This caused me to look at Saxon Math rather differently. The lesson order that drove me crazy helped students retain each concept. The straightforward approach to arithmetic and problem solving allowed students to solve problems in whatever way made sense to them. These two things built true critical thinking in my students.
This upcoming year, I will again be using Saxon Math in my teaching. I return to it with tears of repentance in my eyes.