When I wanted to homeschool my daughter I investigated different math curricula. I discovered there are basically two methods of teaching: mastery and spiral. This is a debate that has been going on for a while now. These days, most math curricula lean toward mastery. However, in the 1960’s the trend was to use the spiral method. What changed?
The idea behind math mastery is that students learn math best when it is taught incrementally with one skill building on the next. For example, in a mastery math program, the student develops an in-depth comprehension of one topic before moving on. A student may learn multiplication including muti-digit regrouping before moving on to division.
In the spiral approach, topics repeat from level to level. Each time the student revisits the material, it includes more depth. Thus linking new concepts to the learning that has already taken place. A spiral curriculum might have the student learn multiplication facts on one level, two-digit multiplication on the next level, and so on.
Both teach styles cover the same material, but not in the same order. So, which one is better? In the 1990, a shift began when the US started participating in international tests. The US students scored significantly lower than students from other countries. US Educators started looking at how math is taught in the top performing countries (Finland, Singapore, Japan, etc.). They discovered that these countries’ curricula leaned toward mastery instead of the spiral teaching style. Today, in the US text books support more of a mastery approach.
There are some criticisms of the mastery approach. First, is that students cannot review past math concepts. This is easily corrected by adding some spiral teaching to the mastery program. Second, the mastery teaching method tends to focus on individual concepts and not show how they are related to other aspects of math. This is also easily addressed with math stories and manipulatives.
Some math curricula that use mastery are Singapore Math and Math Mammoth. I use Math Mammoth to teach my daughter. Math Mammoth includes mostly mastery content with a bit of the spiral approach. I have discovered that the math word problems are really good. There have been a few occasions where I thought my daughter understood a concept. But, sometimes there’s just one tiny thing she has missed, and I’m just not aware of it until we do a word problem. Then, it all comes out and I’m able to fix things. I also use a lot of manipulatives, mostly because my daughter does really well with them. Math manipulatibes are not part of the Math Mammoth program so I create new games as we go.