Maths Wars
http://commons.wikimedia.org/wiki/File:Euler%27s_formula.png
"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.
Labels: constructivism, instruction, maths
posted by Unknown at 6:34 PM
4 Comments:
that's a bit strange because Kirschner said that minimal guidance during instruction did not work
Yes, I presume its the same Kirschner as the Kirschner and Sweller paper. It shows its all a bit complex and there isn't just one instruction/construction dimension.
For a start, Kirschner is discussing the rote procedure vs conceptual dimension, all of which could still be didactic rather than exploratory.
Secondly, even if procedural competence is no aid to conceptual understanding, it is still a valid end in itself. For example (a pre-computer example) learning the times tables might not help with the conceptual understanding of multiplication, but it is(was) a necessary foundation skill for maths.
Take away messages,
1 its complicated
2 mixing a bit of this and that might not get the expected result
Liping Ma's book would seem to say teach the algorithm and conceptual understanding together ... and criticise US teachers for being to algorithmic
we tend to think one or other (we're too algorithmic so lets do more student exploration*) - but as Bill commented when he read her book, so resolves it by bringing the poles in
* a lot of research seems to do that as well / re-inforce that divsion / polarity
Thanks Rob
"a lot of research seems to do that as well / re-inforce that divsion / polarity"
Pearson explains this well in the Quarterly Essay
http://billkerr2.blogspot.com/2009/10/radical-hope-education-and-equality-in.html
Theres no political power in the centre.
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