The Reasonable Ineffectiveness of Research in Mathematics Education JEREMY KILPATRICK You may recognize the title above as a play on the title of an pact) or benefit5 Scriven is pushing a much more demand­ article by Richard W Hamming, ''The Unreasonable Effec­ ing criterion than is Suppes. But even if one limits the tiveness of Mathematics,'' which appeared in the American question to effectiveness, one has only to glance at the Mathematical Monthly in February 1980 In his article, pages of journals such as the Educational Researcher over Hamming asks the question, "Why is mathematics so un­ the past couple of years or attend some of the sessions at the reasonably effective?" He offers some partial explanations annual meetings of the American Educational Research As­ but ends by saying that these explanations are so insufficient sociation to sense that there is a crisis of faith in educational "as to leave the question essentially unanswered" [p 82] research Have we been doing the wrong things? Have we I am going to follow the same strategy but with a different failed to make contact with school practice? Who, if any­ question. My question is, 'Why is research in mathematics one, is listening to what we have to say? Is it all an empty education so ineffective?" 1 shall offer some tentative exercise? These are the kinds of questions one senses are thoughts on this question, but you will soon discern that I, below the surface of the articles and talks Many of these too, must leave my question "essentially unanswered." In same questions undoubtedly occur to researchers in addressing my question, I shall make two claims: (I) much mathematics education. but we do not seem to be addres­ of the ineffectiveness of research in mathematics education sing them in even the oblique fashion of our colleagues in is more perceived than real, and (2) most of the perceived educational psychology ineffectiveness is reasonable The issue of whether or not educational research is effec­ tive seems to get tangled up, in some people's minds, with The effectiveness of r·esearch in education the distinction between pure and applied resear·ch What is Before asking whether research in mathematics education is the difference between pme research and applied research in really ineffective, I should like to broaden the context and education'~ Which is more likely to have a greater impact on ask whether research in education is, or has been, effective educational practice) Two models seem to be implicit when In 1978, the National Academy of Education published a people make the distinction between pme and applied re­ thick book - 672 pages- edited by Suppes [ 1978], whose search title suggests the positive claims that are made in its pages: The first model is hierarchi[a/ Basic research is at the Impact of research on education some case 5tudies The top - so high in status that it is often seen as '·up in the book contains nine studies that purport to show how educa­ clouds., Below it is applied research, and below that tional research has contributed to school practice. Scriven somewhere is the mundane world of practical affUiis The [ 1980] has argued that the book does not address the ' pay­ simplest version of this model is what Greeno (1978) calls offs" from educational research; it the pipe-line model' turns out to be . concerned with such questions as According to this model, fundamental knowledge and whether the results of basic research in psychology and theories are like crude oil, which gets pumped out of the social sciences trickle down to the educational re­ the gwund in basic research Basic knowledge is ship­ search journals (which, you will not be surprised to ped to applied research settings where it is transformed hear, they do). That does not show that educational into something more useful; this is like shipping crude research benefitted from that othe1 research and, more oil to refineries, and transforming the pwduct into use­ importantly, it does not show that educational research able forms Finally, results of applied research are benefitted anything el~e [p. 10, italics in original] shipped to developers and disseminators who use the Whether or not you agree with Scriven's analysis, the knowledge in making products for use in school and somewhat defensive tone Suppes adopts in the book's pre­ send the stuff around to school users. This is analogous face makes it clear that even in his view the effects of to sending refined gasoline to filling stations, where educational research have not been overwhelming: customers can drive up and fill their tanks [pp 7-8] I like to think of the case studies presented here as Greeno argues that this model is at best a weak reflection of representing only a sampling on the beginning of edu­ the relation between science and technology in any field, cational research in its early years of development and that it is grossly misleading in education. He argues that What the future holds should be brighter and better, basic and applied research are not hierarchical; they overlap because it will'be able to build on the kind of work substantially, each contributing to the other, and the sig­ reported in this volume and, as that building takes nificant research questions are both basic and applied place, the impact on practice should become more I shall return to this argument after further consideration marked. [p xvi] of the hierarchical model. Some of the difference of opinion between Scriven and People who do not adhere to the oversimplified pipeline Suppes concerns whether one should talk about effect5 (im- model may still view basic resear·ch as higher in status be- For the Learning of Mathematics 2, 2 (November 1981) 22 FLM Publi~hing A~~ociation Montreal Quebec Canada cause it is theory-oriented and because it aims at generaliza­ bitious, but more achievable, "local" theories; for exam­ tion, whereas applied research, with its lack of theory and ple. "theories that apply to the teaching of arithmetic in specificity, is necessarily lower in status Suppes [1967], in grades 1·2-3 in Washington and Lincoln schools in Little an article written for a booklet that was the forerunner of the City, but perhaps not to the two other elementary schools in Journal fm Re~earch in Mathematics Education, seemed to that town" [Snow, quoted by Gelbach, 1979, p. 9] Gel­ adopt this hierarchical view He argued that basic research bach criticizes this view, saying that ''local theory de­ could have a direct impact on practice, that we needed more velopment should be our last resort rather than our next basic research in mathematics education, and that we move" [p 9, italics in original] Certainly, Snow's position ld­ needed both theoretical and empirical basic research He implies a convergence between basic and applied research :he seemed to be suggesting that basic research in our field I propose a third model for the difference between basic he should be largely concerned with how students learn and applied research that can be used to address the question 1er mathematics, that applied problems in our field include of the effectiveness of research. Although it may appear to he more effective ways of organizing the curriculum, and that conflict with the other two models, I think it is equally IS­ basic research will necessarily be more helpful than applied valid Recall the story of the married couple who went to la! -research in addressing such curriculum questions I should the rabbi to help resolve their quanel The wife went in to Ne not have to point out that this is a somewhat restricted view the rabbi and told her story, whereupon the rabbi nodded IY­ T'yler [ 1981] seemed to assume the same sort of hierarchy and said, You are right ·' Then the husband told his side of >ty between basic and applied research recently when he spoke the story to the rabbi, who nodded and said, ""You are rre to some directms of projects sponsored by the National right., After the couple had gone on their way, the rabbi's se Science Foundation Where he uses 'science education,'' wife. who had herud both exchanges, said to her husband, in one can read ·'mathematics education'': They cannot both be right ·' And the rabbi nodded and said, 'You are right It is in this sense that I claim my ~s­ Research needed in science education is not only basic model is right in research which results in widely generalizable con­ When people talk about research as being basic· ' or cepts and principles but also applied research, that is, applied," '· conclusion-oriented" or · "decision-oriented,'· c­ inquiries focused on particular situations and particular descriptive·· or ··prescriptive.·· and so forth. they are re- th kinds of students, teachers, and institutions, which fening not to anything that can be considered an intrinsic is furnishes information of importance in improving sci­ quality of the resemch study itself, but rather to either the in ence education in the particular circumstances where researcher· s purpose in conducting the study or the uses to m efforts to improve science education are being made which the study is put In other wmds. the same study can 'n [p 6] e- be either basic or applied. depending on who is doing the Again, one has the connection between basic/general and labeling and for what purpose Basic research is not defined 1e applied/specific and, it seems to me, an implied status diffe­ by whether it is conducted in a laboratory rather than a 1e rential school nor is it defined by whether analysis of variance is at The other dominant model for thinking about basic and used rathe1 than chi-square One cannot unambiguously 1e applied research might be called the ( omplementarit} label a piece of research as either basic or applied; one can Is model: the two types of research are seen as comple­ only ask what connection the research study appears to have mentary.