"Maths Wars" refers to the tension between instruction and construction in teaching/learning
The following interesting quote came via Artichoke
"Many of those wanting to build relational understanding with students assume that spending time on rote procedural knowledge is an important precursor for developing deeper conceptual understanding. This seems like a common sense approach – a let’s keep a foot in both camps kind of approach. However, research findings in math education suggest otherwise (Pesek and Kirshner 2000). It seems more likely that, in maths education at least, time spent building prior instrumental understanding is an interference to, not an aid to, developing relational understanding."Interesting because Australia schools at least seem to spend a lot of time on rote procedural knowledge in mathematics.
More on Pesek and Kirshner 2000
"Students who received the procedural instruction prior to the conceptual instruction learned less than did students who received only the conceptual instruction. Somehow, exposure to routine application of formulas inhibited or interfered with students' subsequent conceptual learning."It still seems likely to me that the best teaching will incorporate both solid procedural knowledge and problem solving in authentic and relevant contexts. This study does not destroy that belief, but it does sound a warning that you can't just mix a bit of both and always get good results.