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jeremy Kilpatrick

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Jeremy Kilpatrick

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Jeremy Kilpatrick

Word has come of the death of George Polya in September at the age of 97-a long time on the planet perhaps but not nearly long enough for those who knew him. In recent years, as his eyesight and memory began to fail, he drew on seemingly inexhaustible reserves of joie de vivre and spirit. One got the feeling that if his body had been able, he might simply have gone on forever.

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Jeremy Kilpatrick

At the joint AMS-MAA Mathematics Meetings in Laramie last summer, Saunders Mac Lane gave a splendid address on developments in geometry and topology during the 20th century. He stressed the value of an axiomatic approach in improving our understanding of mathematical phenomena, arguing that we understand such phenomena better when we approach them geometrically and set up the right axioms. He also invited his audience to consider whether the developments he cited constituted a revolution or were no more than a natural outgrowth of developments in the 19th century and earlier.

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Jeremy Kilpatrick

In January at a conference in Berkeley, California, on shaping the research base for science and mathematics education, Lauren Resnick noted that cognitive psychology has begun to amass substantial evidence to support the proposition that humans are builders, not recorders, of knowledge. She used the term constructivism to characterize that thesis, acknowledging at the same time that cognitive psychology has few strong statements to make about how learning occurs. In her opinion, cognitive psychology offers not so much theories as metaphors.

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Jeremy Kilpatrick

As anyone who has ever done copy editing will tell you, it is possible to edit anywhere on a continuum from light to heavy. Light editing simply provides the minimum needed for the printer to use in setting type—correcting typos, marking out hyphens at the end of lines, and the like. Heavy editing involves all of that plus reconstructing faulty sentences—and sometimes whole paragraphs—so that the thoughts trapped therein are freed from the murk of jargon, cliché, and stilted language. Heavy editing ventures away from the rule-bound precincts of punctuation and spelling into the wilds of grammar, syntax, and idiom.

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Jeremy Kilpatrick

Testing is on people's minds these days. In Georgia, students face standardized tests or other state-mandated tests every year but one (fifth grade) between kindergarten and 12th grade. Reports have surfaced of large numbers of Georgia kindergarteners who cried because they could nor do the California Achievement Test, which, as of 1988, they must “pass” to be promoted to first grade. Other reports claim that many high school students have become complacent about taking standardized tests because they cannot see what relevance the tests have. Meanwhile, chambers of commerce offer monetary rewards to those teachers whose students' year-end test scores reach arbitrary targets, and real estate agents add thousands of dollar to rhe prices of houses in suburban school districts where Scholastic Aptitude Test score averages exceed those of neighboring districts. School personnel respond to these developments in various ways—instituting test-preparation units or courses, setting aside class periods for intensive review, discouraging ill-prepared students from taking the tests, and “realigning” curricula to fit test content.

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Jeremy Kilpatrick

Many—probably most—researchers in mathematics education have spent considerable time as teacher educators, working with people who soon will be or currently are reaching mathematics. Perhaps surprisingly, then, these researchers have not viewed teacher education as a potential research site. Immersed in the activities of teacher education, they have not stepped outside the arena of their daily work to view it with the researcher's eye. They resemble the fish in the saying, who, if they were scientists, would be a long time discovering water.

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Jeremy Kilpatrick

The mail brings a stack of envelopes. On the top is a letter from Judy Sowder with information about the NCTM's Research Agenda Project. Four conferences, each on a different topic, are scheduled for this spring to consider research issues and identify directions for further work. Each will result in a monograph, with a fifth monograph providing an overview. The project looks promising, but is it reasonable to set research agendas for mathematics education? An agenda suggests there will be someone to carry it out; do researchers follow agendas in deciding what research to conduct next? Sometimes one has the image of each researcher located on a separate island, sending messages to one another in bottles (journals) that may or may not be read. On most islands, people seem to be busier filling bottles with new messages than reading the messages they have received. What would an agenda mean to such an island community?

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Jeremy Kilpatrick

Because most researchers in mathematics education have spent time in schools reaching mathematics, they rend to undertake studies that entail the improvement of instruction. They are naturally and with good reason attracted to studying not the world as it is but the world as it might be. They identify an instructional problem, find what they consider to be an effective method for dealing with that problem, and undertake research to demonstrate the effectiveness of their method.