Edward A. Silver
Judith Roitman and Edward A. Silver
Edward A. Silver and Kwame Yankson
The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science. (Einstein & Infeld, 1938, p. 95)
Edward A. Silver and Jeremy Kilpatrick
Our task in preparing this article on the occasion of the 25th anniversary of the Journal for Research in Marhematics Education (JRME) was to look ahead to the future of research in the field and to identify and discuss issues that might be important for the next decade or two in the life of the journal. Rather than merely offering our own opinions and speculations. we decided to interview a number of other researchers, some from the United States and some from other countries, to sample their views regarding the current state of research in mathematics education, the issues that may affect the future of the field, and the role of the JRME in the current and future scene. In particular, we asked these researchers to identify examples of work they considered significant and to comment on its imponant characteristics. We probed their definitions of the field by asking them to identify the types of work (e.g., empirical studies, historical or theoretical analyses) they judged could legitimately be called research in mathematics education. We explored their visions of the future of research over the next few decades. And we questioned them about the role and place of the JRME in the research community and about its impact on the field. In addition, we participated in a conference on Research in Mathematics Education and Its Results in May 1994 that was part of a study conducted by the International Commission on Mathematical Instruction (ICMI). The discussion document framing the study (Sierpinska et al., 1993) and many of the presentations and conversations at the ICMI Research Conference should be acknowledged as sources of ideas for the article. Naturally, we have included our own opinions, analyses, and perspectives.
Jinfa Cai and Edward A. Silver
During the past several decades, there has been considerable attention to crossnational comparisons of mathematics achievement. A number of studies have examined the performance in various mathematical topic areas by students from different countries (e.g., Lapointe, Mead, & Askew, 1992; Robitaille & Garden, 1989; Stevenson et al., 1990; Stigler, Lee, & Stevenson, 1987). In general, when crossnational studies in mathematics have included samples of Chinese and U.S. students, the findings have been that Chinese students perform mathematical tasks at much higher levels of proficiency than U.S. students (e.g., Lapointe et al., 1992; Stevenson et al., 1990).
Edward A. Silver and Jinfa Cai
The mathematical problems generated by 509 middle school students, who were given a brief written “story-problem” description and asked to pose questions that could be answered using the information, were examined for solvability, linguistic and mathematical complexity, and relationships within the sets of posed problems. It was found that students generated a large number of solvable mathematical problems, many of which were syntactically and semantically complex, and that nearly half the students generated sets of related problems. Subjects also solved eight fairly complex problems, and the relationship between their problem-solving performance and their problem posing was examined to reveal that “good” problem solvers generated more mathematical problems and more complex problems than “poor” problem solvers did. The multiple-step data analysis scheme developed and used herein should be useful to teachers and other researchers interested in evaluating students' posing of arithmetic story problems.
Edward A. Silver and Jinfa Cai
Posing problems is an intellectual activity that is crucially important in mathematics research and scientific investigation. Indeed, some have argued that problem posing, as a part of scientific or mathematical inquiry, is usually at least as important as problem solving (Einstein and Infeld 1938; Hadamard 1945).
Margaret Schwan Smith and Edward A. Silver
Current reform efforts have emphasized the need to change the way that mathematics is taught and learned so that all students have access to a mathematics education rich in opportunities for thinking, reasoning, and problem solving. Reaching all students may not be easy, however, since students in a mathematics classroom may be considerably diverse, not only with respect to prior mathematics achievement but also with respect to ethnicity, language, and life expelience. The challenge is even greater because teachers often do not share the ethnicity, primary language, or life experiences of the children they teach. The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and the Professional Standards for Teaching Mathematics (NCTM 1991) urge teachers to consider classroom diversity by-
Edward A. Silver and Patricia Ann Kenney
For about 20 years, the National Assessment of Educational Progress (NAEP) has reported on the status and progress of U.S. educational achievement in a variety of subject areas, including mathematics (Mullis, 1990). The 1990 NAEP mathematics assessment, which was the fifth in this subject area, was different from the previous four assessments in some important ways. For example, the 1990 NAEP assessment was the first NAEP for which it was possible to report state-level results for those states willing to participate. In fact. the 1990 NAEP consisted of two tests: one given to a national sample at grades 4, 8, and 12 as in prior assessments, and the other given only at grade 8 to a different sample drawn specifically for the stateby-state reporting of results.