Precollege Mathematics Education Research Articles

A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today

T he physical sciences all went through “revolutions”: wrenching transitions in which methods changed radically and became much more powerful. It is not widely realized, but there was a similar transition in mathematics between about 1890 and 1930. The first section briefly describes the changes that took place and why they qualify as a “revolution”, and the second describes turmoil and resistance to the changes at the time. The mathematical event was different from those in science, however. In science, most of the older material was wrong and discarded, while old mathematics needed precision upgrades but was mostly correct. The sciences were completely transformed while mathematics split, with the core changing profoundly but many applied areas, and mathematical science outside the core, relatively unchanged. The strangest difference is that the scientific revolutions were highly visible, while the significance of the mathematical event is essentially unrecognized. The section “Obscurity” explores factors contributing to this situation and suggests historical turning points that might have changed it. The main point of this article is not that a revolution occurred, but that there are penalties for not being aware of it. First, precollege mathematics education is still based on nineteenth-century methodology, and it seems to me that we will not get satisfactory outcomes until this changes [9]. Second, the mathematical community is adapted to the social and intellectual environment of the midand late twentieth century, and this environment is changing in ways likely to marginalize core mathematics. But core mathematics provides the skeleton that supports the muscles and sinews of science and technology; marginalization will lead to a scientific analogue of osteoporosis. Deliberate management [2] might avoid this, but only if the disease is recognized.

Editorial

In the November 1971 issue of this journal, then-editor David Johnson drew the readers' attention to a new feature of the journal, “a selected annotated bibliography of research” prepared by Marilyn Suydam and Fred Weaver. Johnson went on to state that “present plans for JRME include provisions for the bibliography to appear as an annual fearure, published in each November issue.” The bibliography: which focused on research pertaining to precollege mathematics education, appeared annually in the November issue until 1976, when the addition of a July issue devoted to the bibliography expanded the journal from four to five issues per volume to accommodate the growing demand for more space to publish research reports: In that same issue the scope of the listing was extended to include postsecondary-level research.

Just teach them the basics and leave the applications to us

The author suggests that as readily available technology is forcing changes in precollege mathematics education that have been long overdue, it is no longer obvious just what the 'basics' are. Furthermore, a shift in focus, from preparation exclusively for the hard sciences and engineering to preparation that includes combinatorics and the other discrete topics recommended and outlined in the NCTM's 'Curriculum and Evaluation Standards for School Mathematics' published in March 1989, has contributed to the confusion. She considers who the students are that high school teachers have tended to identify as the best math students and who the students are who have tended to go on into engineering, noting that they are not always the same people. She then considers changes in mathematics education in terms of student needs. >

Questions about precollege mathematics education

Questions about precollege mathematics education

Effects of Hand-Held Calculators in Precollege Mathematics Education: A Meta-Analysis

The findings of 79 research reports were integrated by meta-analysis to assess the effects of calculators on student achievement and attitude. Effect sizes were derived by the method invented by Glass and tested for consistency and significance with inferential statistics provided by Hedges. At all grades but Grade 4, a use of calculators in concert with traditional mathematics instruction apparently improves the average student's basic skills with paper and pencil, both in working exercises and in problem solving. Sustained calculator use in Grade 4 appears to hinder the development of basic skills in average students. Across all grade and ability levels, students using calculators possess a better attitude toward mathematics and an especially better self-concept in mathematics than students not using calculators.

Effects of Hand-Held Calculators in Precollege Mathematics Education: A Meta-Analysis

The findings of 79 research reports were integrated by meta-analysis to assess the effects of calculators on student achievement and attitude. Effect sizes were derived by the method invented by Glass and tested for consistency and significance with inferential statistics provided by Hedges. At all grades but Grade 4, a use of calculators in concert with traditional mathematics instruction apparently improves the average student's basic skills with paper and pencil, both in working exercises and in problem solving. Sustained calculator use in Grade 4 appears to hinder the development of basic skills in average students. Across all grade and ability levels, students using calculators possess a better attitude toward mathematics and an especially better self-concept in mathematics than students not using calculators.