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The Reasonable Ineffectiveness of Research in Mathematics EducationAuthor(s): Jeremy Kilpatrick
Source: For the Learning of Mathematics, Vol. 2, No. 2 (Nov., 1981), pp. 22-29
Published by: FLM Publishing Association
Stable URL: http://www.jstor.org/stable/40247734
Accessed: 07/01/2015 04:14
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By glancing over the title and the first paragraph of the article, I think that the author would be discussing about the existing state of research in mathematics education. In addition, the author will be using two assumptions, a) ineffectiveness of research in mathematics education is well understood and real and b) the understanding of the ineffectiveness is real, to justify why research in mathematics education is ineffective. My expectation is that the author would provide reasonable insights, which may be of interest when conducting research in mathematics education.The article begins by questioning whether research in education is effective or has any value. The author uses Suppes' cautious optimism and Scriven's rigorous analysis to question the effectiveness or pay-off of research in education on classroom practice through Suppe's book, Impact of research on education: some case studies. The author extends this "crisis of faith" to probe whether researchers in mathematics education are trying to address questions such as:
1. Have we been doing the wrong things?
2. Have we failed to make contact with school practices?
3. Who, if anyone, is listening to what we have to say?
In trying to address these questions, there appears to be confusion between the impacts of pure (basic) and applied research. Basic research was assumed to be "up in the clouds" seeking generalization theories and seen to be higher in status, whereas applied research was thought to lack "specificity." The author goes on to suggest another model of research where "one cannot label a piece of research as either basic or applied." This is the lens model, in which the reader decides whether the purpose or usefulness of the research is basic or applied.
It was surprising for me to learn that the majority of dissertations in mathematics education do not come from the department of mathematics education or under the supervision of researchers in mathematics education. Even if this unsubstantiated claim is valid, the author seems to suggest that it is not surprising why the research outcomes are ineffective. Should research in mathematics education always come from the community of researchers in mathematics education for the research to have any value? I am suspicious of this line of thought, because Piaget was not a researcher in mathematics education. However, many researchers in mathematics education and mathematics teachers subscribe to Piaget's concepts of accommodation and assimilation, which ties to the Mathematics-Psychology-Philosophy (MAP) vertex on the MAPS perspectives of mathematical education.
Finally, it is startling to note that the author suggests that "lack of attention to theory" as a reason for the ineffectiveness of research in mathematics education. This suggestion implies that researchers in mathematics education hold knowledge-as-elements perspective. According to Ozdemir, novices hold this perspective of knowledge, whereas experts hold knowledge-as-theory perspective. I wonder if the author is vaguely suggesting that the majority of the research articles and dissertations in mathematics education are for or by novices. From the author's point of view, this may imply that the research findings may collectively "not add up to very much."
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An Overview of Conceptual Change Theories
Gökhan Özdemir
Niğde
Üniversitesi, Niğde,
TURKEY
Douglas B. Clark
Arizona State University, AZ, USA
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I remember being surprised earlier this summer at the PME-NA conference that many of the scholars presenting research on mathematics education came from a diverse number of backgrounds; one fellow with whom I spoke on his comparison of fractions in elementary school children was a civil engineer in Chile prior to embarking on his research! While I think the answers to "who can do math?" and "who can do math research?" differ, I wonder if the schism between "formal mathematics" and "school mathematics" is caused merely by epistemological differences in what constitutes mathematics and its use, as seems to be outlined by "knowledge-as-elements" vs "knowledge-as-theory" views.
ReplyDeletePersonally, I support the second model of basic and applied research being complementary. Both domains are equally significant and valuable to math education. Theory teaches you reasoning and guides you to a better understanding of a concept in a general context. Similarly, practical knowledge allows you to see the conceptual logic behind a theory and tests the usefulness of the theory from an applied viewpoint.
ReplyDeleteIn math research, it is a common practice to examine a subject's mathematical thinking through task-based interviews. In particular, in a geometry task at an interview, the investigator can relate the subject's thought processes to a certain theory, such as the Van Hiele model. Using this model can guide the investigator to understand better why the subject is struggling at a particular stage in the task and how he/she comes up with a special strategy for solving the problem. That's from basic to applied. If this research is repeated with different subjects over time, researchers can use their practical knowledge to come up with a new theory of mathematical thinking based on the large amounts of qualitative data collected. That's from applied to basic.