In article <email@example.com>, Sarah Seastone (firstname.lastname@example.org) wrote: > >o "One of the problems on the National Assessment of Education Progress >secondary mathematics exam, administered to a stratified sample of 45,000 >students nationwide, was the following: An army bus holds 36 soldiers. If >1128 soldiers are being bused to their training site, how many buses are >needed? Seventy percent of the students who took the exam set up the >correct long division and performed it correctly. However, the following >are the answers those students gave to the question how many buses are >needed: 29% (1 in 3) said the number of buses is '31 remainder 12'; 18% >said the number of buses needed is "31"; 23% said the number of buses >needed is '32,' which is correct; (30% did not do the computation >correctly)... One out of three students said '31 remainder 12'- without >checking to see if the result made sense! In essence, they treated the >problem as calling for a formal computation. Despite the 'cover story' >about the buses, the computation had little or nothing to do with the real >world" (p. 196). >
So often, the focus of doing math, is the "doing" part, the getting it done. In order to get a problem done, a student (and most of us have been this student) will plug in the formula given by the teacher, or will execute the long division, without understanding what the formula means, or why it should be used. I have seen this repeatedly in tutoring. My tutee will quickly do the problem, just as the teacher has shown him. Yet, when asked a simple "why" question, he has no idea how to answer, for the "why" has never been discussed. To him, math is arbitrary steps that he has to do to numbers to get a correct mark on his paper. The use of metacognition in a class seems to move the focus to a real understanding of mathematics, instead of just where to apply formulas.
Students need to be aware of what they are doing and why they are doing it. Mathematics can easily disolve into a jumble of abstract numbers and signs. It's so important to give meaning to mathematics. It's not good enough to just get it done.