How Children Learn Math

 I believe that children learn math best by:

• being offered a wide range of increasingly challenging hands-on math games and puzzles (starting in toddlerhood and continuing indefinitely)

• being offered clear and direct instruction, starting at age 5 or 6

• being offered a multi-sensory approach made up of clear visual presentations, discussion, hands-on 3-dimensional challenges, and Cuisenaire rods and other high-quality manipulatives to build models of problems in the early years

• mastering math facts and algorithms in the early grades, using math symbols, models, and manipulatives, with minimal use of written words

• developing a sturdy foundation in arithmetic before being asked to solve word problems

• memorizing basic arithmetic facts and mastering procedures so more interesting math can be learned efficiently and enjoyably

• being skillfully guided in carefully structured mathematical exploration and discovery by mathematicians who love and deeply understand math and are able to convey this passion to children

• actively and independently solving thousands of problems

• exploring carefully selected, accessible topics from algebra, geometry, logic, number theory, and topology 

• being directly taught efficient problem-solving methods in the context of engaging mathematics

• being allowed to progress at a pace that matches the child’s enthusiasm, interest, and level of mastery 

A crucial element of good math instruction is identifying a child’s cognitive strengths and weaknesses. Weaknesses should be directly addressed with carefully structured exercises. Strengths should be actively developed as well.