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Jeremy Kilpatrick

The Department of Education's Office of Educational Research and Improvement is in the process of funding, for the next 3 years, a research and development center for mathematics learning and teaching. In the invitation to applicants, OERI contended that our understanding of how students learn and what they need to learn has advanced so far that now we should concentrate on identifying effective teaching strategies. For example, the first of a long list of questions the proposed center is expected to address is “What are effective instructional strategies and processes that promote the learning of mathematics subject matter and critical thinking and reasoning?” It is incredible, or more precisely unimaginable, to think that we might have the makings of an answer to such a question by 1990, but the center may at least be able to help us understand the question better.

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Jeremy Kilpatrick

In the final panel discussion at the Psychology of Mathematics Education meeting in Montreal last July, Hermine Sinclair (in remarks delivered in her absence by Carolyn Kieran) posed a paradox that she saw underlying much of the wrangling about constructivism that had occurred at the meeting. Everyone accepts the view that there can be no end to human knowledge, that there will always be something new to be added to what we know. The more difficult view is that our present-day knowledge will change. Learning entails both the conservation and the transformation of our knowledge. The paradox is that although change occurs when we push our ideas until we encounter a conceptual gap or obstacle, which signals that our ideas are in some way false, we can change those ideas only by remaining completely convinced of their truth. Only on looking back can we see how our knowledge changed and how it remained the same.

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Jeremy Kilpatrick

Since the founding of the JRME, the editors have, from time to time, sent the reviewers of a manuscript a copy of the editor's letter to the author concerning whether the manuscript was accepted, together with a copy of the comments that each reviewer provided for the author. This practice lets reviewers see how their judgments and comments compare with those of others. It serves both to educate and to calibrate. The novice reviewer lea rns something of the care and thoroughness needed to produce comments that are helpful. The maverick reviewer gets a better sense of the criteria that other reviewers are using in making their judgments.

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Jeremy Kilpatrick

The theme of the first joint conference of the Australian Educational Research Association and the New Zealand Educational Research Association, held in Christchurch in December, was “ Educational Research: Scientific or Political?” The final two adjectives in the question are often taken as antithetical when they are better seen as describing complementary facets of our research.

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Jeremy Kilpatrick

One of the most venerable and vexing issues in mathematics education concerns the trade-off between proficiency and comprehension, between promoting the smooth performance of a mathematical procedure and developing an understanding of how and why that procedure works and what it means. The trade-off is obviously not either-or; rather, as William Brownell pointed out over 30 years ago, some balance needs to be found between meaning and skill. Amid today's arguments that technology has modified, and sometimes supplanted, the skills students need, the issue has grown into not just achieving a balance but finding a balance point.

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Jeremy Kilpatrick

The scientific ideal is that knowledge claims ought to be tested, both by gathering more data and by exposing one's work to the analyses and criticisms of others. That is not to say that science need be strictly objective (indeed we are constantly reminded that intellectual fads and personal vendettas permeate science just as they do other human affairs) but only that it should strive to be falsifiable and public.

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Jeremy Kilpatrick

In May 1970, in the third issue of the Journal for Research in Mathematics Education, the JRME Editorial Board published information for prospective authors, calling for manuscripts of various types. The Board announced a new section tentatively titled “A Forum for Researchers,” manuscripts for which would be short (no more than three typed pages) and offer “analyses, critiques, or proposals about the nature of research in mathematics education.”

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Jeremy Kilpatrick

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Jeremy Kilpatrick

In 1964, samples of students from some 5000 secondary schools in 12 countries took mathematics tests and filled out opinion and informational questionnaires in the first effort by a group now known as the International Association for Educational Achievement (IEA) to compare students' subject maner knowledge crossnationally and relate that knowledge to characteristics of schools, teachers, and educational systems. The release of the report of that study (Husén, 1967), which later became known as the First International Mathematics Study (FIMS), touched off a furor in the United States as American mathematics educators rushed to explain (or explain away) the relatively poor performance of the American students. The study itself was more a study in comparative education that used mathematics as an indicator of what had been learned in school than a study in mathematics education with clear implications for curricula and instruction. The press release and subsequent accounts in the media, however, portrayed the study as an international competition with winners and losers (Japan won, the United States lost). The bulk of a special issue of this journal on the FIMS (Wilson & Peaker, 1971) was given over to critiques by Americans of the IEA's assumptions, instruments, analyses, reporting, and interpretations.

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Jeremy Kilpatrick

The report of the International Study of Achievement in Mathematics has been around for almost four years. During that time it has been damned and defended, distorted and dismissed. Now that the rest of the parade has moved on—the lEA to other curriculum subjects, the book reviewers to other books, the editorial writers and their readers to other diversionsit seems appropriate for mathematics educators to take stock of the study and its findings. In this article, I discuss some of the implications of the study in the hope that the reader will be moved to look at the report more closely, with a greater appreciation of what it does and docs not say.