This study compares two methods of using computer graphing technology to teach the concept of derivative to undergraduate students enrolled in introductory calculus. One method uses microcomputer-based laboratories, where students walk in front of a motion sensor and see a graph of their motion produced on the computer screen. Previous studies have shown this method to be quite effective in teaching graph interpretation, but it is expensive and often inconvenient. The other method uses a Java applet, written by the researcher, in which students use a mouse to move a stick figure across the top of the computer screen while a graph of the figure's motion is produced below. This method is less expensive and more convenient. Earlier researchers had speculated that the motion sensor approach relies on whole-body motion and the kinesthetic sense, which suggests that the Java approach, in which motion of the whole body over several feet is replaced by moving one hand a few inches, might not be as successful. This study refutes that assertion, showing that the Java applet is as effective as the motion sensors in this application. Sixty first-semester calculus students participated in a few hours of instructional activities outside of class. Thirty-two used motion sensors, and 28 used the Java applet. In all other regards, the instruction was as identical as possible. Before and after instruction, subjects completed a multiple-choice achievement test and an attitude survey. Half of the subjects also drew graphs to depict given situations involving motion, and eight participated in individual interviews. Several measures of prior achievement indicated that the two treatment groups were similar prior to instruction. The achievement test established that the subjects had made significant progress in their ability to interpret line graphs of motion events. The graph production showed substantial improvement in ability to draw velocity graphs. Interview subjects identified many pre-test answers as guesses, or explained them as coming from incorrect reasoning, whereas the reasoning used during the post-test and interviews was more often correct. The attitude instrument revealed little change. None of the dependent measures revealed significant differences between treatment groups.

This chapter examines the longitudinal version of the second international mathematics study. The purpose of the Second International Mathematics Study is to compare, and contrast, in an international context, the varieties of curricula, instructional practices, and student outcomes, both attitudinal, and cognitive. By portraying the mathematics program and outcomes of each participating system against a cross-national backdrop, each system is afforded an opportunity to better understand the relative strengths, and shortcomings of its own endeavors in mathematics education. The study was therefore conceptualized as an examination of mathematics curricula at three levels which includes the intended curriculum as transmitted by national, or system level authorities, the implemented curriculum as interpreted, and translated by teachers according to their experience, and beliefs for particular classes, and the attained curriculumlearnt by students as manifested in their achievements, and attitudes. The curriculum at each of these levels is influenced by the context in which it occurs, and the contexts themselves are determined by a number of antecedent conditions and factors.

A U.S.–Japan Seminar on Mathematical Problem Solving was held at the East-West Center in Honolulu 14– 18 July 1986 (Becker and Miwa 1987). Among the seminar's proposals was that cross-cultural research on American and Japanese students' problem-solving behaviors be organized and carried out. The author were in Japan in the fall of 1988 to meet with their Japanese counterparts, plan research, and make visits to mathematics classrooms preliminary to conducting a two-year program of research. In addition to planning the research, we were on a fact-finding visit to classrooms to better acquaint ourselves with mathematics teaching and learning in Japan.

A large team of educational researchers, taking the world as its laboratory, undertook in 1976 a comparative study of mathematical education in a representative sample of twenty results. Dense with elaborately produced graphs, charts and tables (one suspects that were one to ask in the offices of

What mathematics is taught to twelfth grade students in high schools in the U.S. who are enrolled in at least their fourth year of college preparatory mathematics? What are the teachers like who provide this instruction? How do they spend their time? How do the students spend their time? How well do the students do? What are their attitudes toward mathematics? Do they gain much in mathematics achievement during the year? How does their achievement compare with that of students at the end of secondary schooling in other countries? How do they compare with twelfth-grade college preparatory mathematics students of twenty years ago?

Performance of U.S. students on international tests of math ematics achievement continues to lag, say these authors, who review the results of a study conducted by the International Association for the Evaluation of Educational Achievement.

F or over two decades a network of educational researchers has coop erated on a number of international studies of school achievement. Under the leadership of Benjamin Bloom, Robert Thomdike, Torsten Husdn, and Neville Postlethwait, the International Association for the Evaluation of Edu cational Achievement (IEA) has con ducted research in mathematics, read ing, science, literature, English and French as foreign languages, and civics. Currently it is undertaking second stud ies in mathematics and science and new studies in early childhood education, writing, classroom environment, and vocational education. IEA has a number of purposes: to look at educational systems from an in ternational perspective, to explore major issues of educational policy, to tram educational researchers, and to raise the standards of educational re search and evaluation. In the course of its brief history IEA has sponsored numerous international and national technical reports and monographs; it has developed and validated new kinds of tests and attitude scales; and it has initi ated a rethinking of many educational issues. In this article, we will describe what IEA has done in mathematics and language arts (reading, literature, and written composition).

Now you can find out how long it would have taken you to get that complete set of prizes f rom your candy boxes or cards from your pack ages of gum

Help in producing examples of patterned data for illustrations.

Julian C. Stanley, Daniel P. Keating, and Lynn H. Fox (Eds.). Mathematical Talent: Discovery, Description and Development. Baltimore, Maryland: The Johns Hopkins University Press, 1974. xvii + 215 pp. $ 10.00 and $2.95 (paperback).

In 1964, the International Association for the Evaluation of Educational Achievement (IEA) surveyed mathematics achievement in the schools of 12 countries, including the United States (Hus6n, 1967). Subsequently, surveys were conducted in six other school subjects involving some 23 nations (e.g., Comber & Keeves, 1973; Walker, 1976). In the United States, a special issue of JRME was devoted to the IEA mathematics survey (Volume 2, November 1971), and articles on the survey were written for NCTM publications (Willoughby, 1968) as well as for the press. Some countries, Australia for example, prepared national reports on the findings of the survey (Keeves & Radford, 1969). Recently, critiques of the IEA studies (Coleman, 1975) and (Freudenthal, 1975) have generated considerable discussion in some quarters. Interest in taking part in a second international survey of achievement in school mathematics had been expressed by several countries, and in 1974 the IEA Council decided to proceed with such a study. Since that time, about 10 countries have taken the first step toward full commitment to participation, which includes identifying a national committee to oversee the survey and conducting a curriculum analysis for that particular country.

Eastman's (1975) recent expression in the JRME of concern over so few replication studies is a concern that should be shared by all who have an interest in research. Replication is critical in assessing the “significance” of research results. A correlation coefficient of .20, which is statistically significant at the .01 level, will be much more “significant” if we can demonstrate by replication that the same result occurs again and again. By replicating, we help rule out the possibility that a Type I error (we rejected the null hypothesis when it was true) occurred in the original experiment. Furthermore, by independently replicating with different subjects, at different times and places, we also are helping to increase the generalizability of any “significant” results we do obtain.

Teachers are decision makers. Every day requires decisions about what students should learn and what should be done to teach them. In their planning for daily lessons or for units, teachers develop objectives and activities, and, in so doing, they make decisions. Teachers also judge when their students have attained the desired goals for the lesson or unit. Perhaps more importantly, teachers decide what to do differently to facilitate learning in future lessons. Maybe the lesson does not go well; and, unexpectedly, the children have difficulty in grasping a concept. Sometimes a new and valuable bit of learning is discovered almost by accident. Or again, the criteria for judging the attainment of concepts may have to be changed because of an unanticipated development during the lesson. These and other kinds of decisions are made so frequently that the teacher may not be aware of making many of them. Yet, students are continually affected by such decisions.