In my previous post I wrote about the overemphasis on memorization and drills and brought some arguments for balancing all three aspects of knowledge in mathematics: factual, procedural, and conceptual. Let’s review:

**Memorization of math facts is important. It allows for complex tasks to be carried out.****Procedures should be taught***after or in tandem*with concepts. One supports the comprehension of the other.**Block practice (in textbooks and in teaching) is detrimental to learning. The overlearning as well as familiarity effects occur.****Excessive modeling and examples in math can actually interfere with learning. They increase performance in the short term but hinder learning in the long run.****Space out practice and interleave mathematical concepts.****If you focus on a topic (i.e. fractions) make sure your students not only apply it in different contexts, but are also engaged in solving problems you previously taught (i.e. geometry or measurement topics).**Even better, use fractions, measurement, and geometry together (Example:*1/3 of the area of a rectangle is red. Knowing that the perimeter is 64m and one of the sides is 1,000cm, find out what part of the rectangle is red.*– Knowledge of area and perimeter, knowledge of fractions, and knowledge of measurement conversion).