The Reasonable Ineffectiveness of Research in Mathematics Education
by JEREMY KILPATRICK (1980)
Kilpatrick, (1981) have written this article trying to follow Hamming’s (1980) strategy in "The Unreasonable Effectiveness of Mathematics”. He starts his article with this question: "Why is research in mathematics education so ineffective?" then claims most of this ineffectiveness of researches in mathematics are perceived rather than real but these are reasonable. To prove his claims, author, brings up the idea of the effectiveness of research in education, explores why research in mathematics education is ineffective, puts emphasis on the differences between mathematics and research in mathematics education, finds reasons for why it is not easy to implement research in mathematics and finally proposes some suggestions to make research in mathematics more effectively.
To find to what extent research in education is effective, Author investigates the content of a thick book; “Impact of research on education: some case studies” edited by Suppes (1978); and the argument of Scriven’s (1980) about this book. Based on Scriven’s (1980) explanations, although Suppes’s (1978) book mentions several case studies to prove the benefits of research in education, at the end, it is not clear how these researches are beneficial. Kilpatrick believes that the major difference between Scriven’s (1980) and Suppes (1978) opinion is their usage of “effect” or “benefit” of research in education. These researches have effects on education but studies do not show these are beneficial.
The author points out that people; who think about the effectiveness of research in education; can distinguish between pure and applied research. There are two models to explain the differences between pure and applied research. Hierarchical and complementarity models. To illustrate the Hierarchical model, Greeno (1978) proposes “the pipeline model". This model explains similar to crude oil that gets pumped out of the ground, the fundamental knowledge and theories have been gotten from the basic research. Then like crude oil that is shipped to be transformed to the useable forms, fundamental knowledge and theories have been sent to apply research settings where it is transformed into something more useful. Finally as the product of transformed crude oil such as gasoline has been sent to filling stations where customers can actually use it, the results of applied research have been sent to the developers who use knowledge in making products for schools and students. In complementarity model “the two types of research are seen as complementary, each with its own domain and its own agenda, and equal (supposedly) in status. When one sees basic research characterized as "conclusion- oriented" and applied research as "decision-oriented," one can be fairly sure these types of research are being viewed as separate but equally valid - for their own domain of relevance.” The Adherents of the complementarity model believe that the differences between two types of research are decreased dramatically in recent years because 1) theory-building has been prescriptive, not descriptive and 2) research methodologies have new capabilities and improvement. The author proposes a third model (lens model) and explains “a study may be basic or applied depending upon the lens you use in reading a report of it. The same study can be either basic or applied, depending on who is doing the labeling and for what purpose. In fact, one can only ask what connection the research study appears to have to theory and what connection to practice. Both of these, to a large extent, are in the eye of the beholder.”
Kilpatrick believes that “One reason [behind lack of effectiveness in mathematics education] may be that, “despite what appears to be a flood of research in our field, we actually have very little in the way of research to go on in drawing implications for practice”. Besides, he investigates several studies to show; do we have enough data to answer the important questions in mathematics education? The results of his investigation reveal that there is very little trustworthy data representing the facts of the educating process. Also, he discovers that lack of true community for mathematics education research is another reason behind ineffectiveness of research in mathematics education. Moreover, he also finds out that most of the researches in mathematics education have been done by researchers who are not recognized as researchers in mathematics education. So it is not surprisingly if these researchs are not “arise from common concerns, shared knowledge, and mutual interaction”. Kilpatrick also highlights that there are two additional reasons, however, that appear most compelling of all: (1) our lack of attention to theory, and (2) our failure to involve teachers as participants in our research.
Kilpatrick explains why the lack of attention to the theory such a serious problem? “I contend that it is only through a theoretical context that empirical research procedures and findings can be applied. Each empirical research study in mathematics education deals with a unique, limited, multi-dimensional situation, and any attempt to link the situation considered in the study with one's own "practical" situation requires an act of extrapolation.” Kilpatrick reviews several related studies in mathematics education and understands that these researches do not affect practice in mathematics education. Too many mathematics educators think teachers need to know the results of research. Kilpatrick, 1981 highlighted that what mathematics teachers do every day comes close to being research; it is just not quite so deliberate, systematic, or reflective. So teachers can borrow three things from researchers: their procedures, their data, and their constructs (Alan Bishop [1977]).
The author put emphasis on the differences between mathematics and research in mathematics education. In this regard, he uses Hamming’s [1980] explanations (four reasons) of the effectiveness of mathematics. Based on Hamming, first, mathematics has been highly creative in inventing tools and the phenomena we see arise from the tools we use, however, research in mathematics education does not have these tools. Second, we select the kind of mathematics to use and when the mathematics we have, does not work, we invent something new. In research in mathematics education, we have not shown the same ingenuity in adapting our tools to our problems. Third, science, in fact, answers comparatively few questions. Perhaps one reason for the perceived ineffectiveness of research in mathematics education is that too much has been expected of it. Fourth, Hamming contends that “the evolution of man has provided the model for mathematics by selecting for "the ability to create and follow long chains of close reasoning" [p. 89]. However, the history of research in mathematics education is much shorter, and evolution has not had time to select for a research attitude”. Kilpatrick adds that “applying educational research to mathematics teaching practice is not an engineering problem like applying mathematics to a practical situation. “Doing something about education means doing something about people such as teachers, students, parents, politicians and people are just not that manipulable. They are what they are and do not become new people to suit any new ideas we might have” (Kristol [1973]).
Kilpatrick proposes some suggestions to make research in mathematics more effective. He believes researchers should: (1) “develop a stronger sense of community, which would include practicing teachers as collaborators in research; (2) create their own theoretical constructs for viewing their work; and (3) recognize the limits of their domain as well as its complexity”.
My stops and question
The first stop was the title of the paper. I suppose every research has some merits so how it is possible that research in mathematics might be ineffective??
Facing this word was another stop for me, extrapolation…what does author mean with extrapolation? How it might help us in this paper?
This is another stop for me when the author stated that “however, the results are the least important (for teacher) aspect of a research study”. As I always though the results is an important part of a study that helps teachers.
My Questions
Since author talked about 1979 and 1980’s researches, I am wondering to what extent the situation has been changed after almost 36 years?
My first thought about this question concerns Kilpatrick’s concern about teachers not being more involved in research. I have certainly read some examples of teachers themselves not being aware of math theories, or not understanding them in a way that informs their practice. In Liping Ma’s book, Knowing and Teaching Elementary Mathematics (1999), she interviews many U.S. teachers who are unable to explain the theories behind the formulas and the mathematics they use on a daily basis. As Kilpatrick discusses, I’m not sure much has changed from the teacher standpoint in 36 years. Most teachers I have met and interacted with are reluctant and do not participate in mathematics research. Perhaps my sample set is small, but that has been my experience.
ReplyDeleteThinking about the mathematics community being fragmented, it certainly seems to me that there are still many different organizations within the mathematics community in North America, leading to a lack of a community. There continue to be many different journals, both in the U.S. and internationally, focusing on mathematics research.
In terms of research being grounded in theory, I have read some articles recently that do achieve this goal. I am at the beginning of my masters, and therefore the number of articles I have read is likely comparatively small, but I have noted researchers linking theories to their studies. In particular, Ed Dubinsky and Michael A. Mcdonald wrote a paper entitled, A Constructivist Theory of Learning in Undergraduate Mathematics Education Research (2002), where they explain, “research in mathematics education is strengthened in several ways when based on a theoretical perspective.”
Some general questions such as “What works?” or “Which teaching method works best in math?” which rely on successful isolation of variables cannot be best answered by mathematics education researchers who are using qualitative approach. The way I understand the discrepancy between mathematics practice and mathematics research links to the differences of foundations of qualitative and quantitative inquiries. So, I am afraid that the situation hasn’t changed much since the two methodologies have not widely complimented each other yet.
ReplyDeleteThe development of educational theory in general to address and include social and cultural dimensions hopefully has an impact on mathematical education research. Any research that is purely theoretical will not be useful if the subjects to which it is applied do not exactly match the subjects from which it was derived. This seems obvious to me, especially after years of working with vastly differing and diverse groups of students. Perhaps there is a need for further subjectivity, educator and learner, research in mathematics education.
ReplyDelete(Malihe, I want to suggest that for future readings you offer a briefer summary of the article, and devote more space to your own 'stops', interpretations and questions about the piece.)
ReplyDelete