I'll briefly mention the theory behind Excel Math, as it can be summarized in a few main points:
- Direct Instruction - we believe the teacher plays a key role in passing along essential math concepts to students, using a variety of presentation methods, formats, manipulatives and activities.
- Spiraling - concepts are introduced and variations are repeatedly presented throughout the school year. The concepts increase in difficulty, building upon one another. There is no one perfect order - we interleave them as well as we can. Here's a visual depiction of the strategy that has taken me many hours to conceive and refine. [click on the image to enlarge]
- Repeated contact - students first encounter a new concept in the Lesson presented to them by the teacher. Then they explore it during Guided Practice with their classmates, a few times over several weeks. After this exposure, they tackle that concept on their own, in Homework. Finally, the concept appears on a Test about a month after it was first introduced. This phased approach (teacher-down; together with peers; on their own at home; on their own in a test) helps build confidence and improve mastery.
- Self-checking - using our Checkanswer system (shown in my previous post), students can confirm that they have a good grasp of a subject. If their Checkanswer sums don't match, one of their answers in that set of problems is wrong. They go back and trouble-shoot their own work. This builds thinking patterns and work habits which support a lifetime of problem solving.
- Practice - students benefit from mastering a few math concepts so they can be done automatically - such as the times tables or simple addition and subtraction. Practice helps improve our skills in math just like it helps improve a golf swing or a tennis serve. Basic Fact Practice (about a dozen problems) appears 3-4 times a week in the middle grades - it's not the much-criticized drill and kill tedium of yesteryear.
The individual components are supported by research, and the entire curriculum has been used with success by thousands of schools across North America for more than 30 years. I can assure you that I personally understand math a lot better than I did a decade ago when I joined the Excel Math editorial team - thanks to working with this curriculum, and writing this blog.