Elementary student multiplication problems

Steve Leinwand and Steve Fleischmann said:

In mathematics instruction, a chasm exists between research and practice. For evidence of this gap, look no further than the mismatch between what research says about developing students’ conceptual mathematics understanding and what we actually do. An example is the way we teach math content in elementary and middle schools. A growing body of promising research shows that if initial instruction focuses exclusively on procedural skills, then students may have difficulty developing an understanding of math concepts.


On post-tests, the students who received only meaningful, or relational, instruction performed better in applying the procedure and solving the equations. In contrast, the students who first received procedural instruction on how to solve an equation tended to resist new ideas and appeared to apply procedures without understanding. [emphasis added]


the form of instruction humorously but accurately characterized as yours is not to reason why, just invert and multiply may not enhance the performance of many students. Alternatively, instruction that places a premium from the start on meaning and conceptual understanding may improve classroom productivity.

And yet, despite Common Core and other efforts, our procedural emphases still persist in many, many math classrooms. And parents clamor for them.

FYI, this is from twelve (12!) years ago…

via http://www.ascd.org/publications/educational-leadership/sept04/vol62/num01/-Teach-Mathematics-Right-the-First-Time.aspx

Image credit: maths, Shaun Wood