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Theory

  • Widespread availability of desk-top computing allows psychologists to manipulate complex multivariate datasets. While researchers in the physical and engineering sciences have dealt with increasing data complexity by using scientific visualization, reseearchers in the behavioral sciences have been slower to adopt these tools (Butler, 1993). To address this descrepancy, this paper defines scientific visualization, presents a theoretical framework for understanding visulaization, and reviews a number of multivariable visualization techniques in light of this framework.

  • When solvers have more than one strategy available for a given problem, they must make a selection. As they select and use different strategies, solvers can learn the strengths and weaknesses of each. We study how solvers learn about the relative success rates of two strategies in the Building Sticks Task and what influence this learning has on later strategy selections. A theory of how people learn from and make such selections in an adaptive way is part of the ACT-R architecture (Anderson, 1993). We develop a computational model within ACT-R that predicts individual subjects' selections based on their histories of success and failure. The model fits the selection behavior of two subgroups of subjects: those who select each strategy according to its probability of success and those who select the more successful strategy exclusively. We relate these results to probability matching, a robust finding in the probability-learning literature that occurs when people select a response (e.g., guess heads vs. tails) a proportion of the time equal to the probability that the corresponding event occurs (e.g., the coin comes up heads vs. tails).

  • Perspectives on the improvement of college instruction are offered. External forces that focus attention on the quality of college instruction are identified, including: the demand for good teaching by two groups of nontraditional students (low-performing students and adult students); technology, and especially new interactive technologies; the growing interest in assessment and program evaluation; the new emphasis on alterable variables in educational research; the lack of mobility for faculty members; and low morale among the teaching faculty. While the classroom lecture method is the method of choice for college teachers, one promising method for better learning of subject-matter content has been the Personalized System of Instruction, which emphasizes student involvement, high expectations, and assessment and feedback. Problems arise when colleges that are primarily teaching institutions turn to faculty publication as their route to distinction. For undergraduate education to improve, teachers will need support of their colleges, including the commitment to evaluate teaching performance in decisions to hire, promote, and tenure faculty members. It is recommended that research on teaching and learning should be done in classrooms across the nation by classroom teachers ("classroom researchers.")

  • The current mathematics reform movement has recognized that new forms of mathematics teaching will be needed to support the proposed curricular changes. These new forms extend beyond the acquisition of new teaching techniques and trategies to the reconstitution of fundamental notions of teaching, learning, and the nature of mathematics as a discipline, and also to the creation of different classroom opportunities for learning. The means by which teachers effect this kind of transformation are, as yet, little understood. This paper describes a set of component models of the process of teachers' development in mathematics practive. Drawing from theories of cognitive development, the paper focuses on three compoments of the change process: (1) qualitative reorganizations of understanding; (2) orderly progression of changes; and (3) the context and mechanisms by which transitions are effected; and suggests a fourth component--individual motivational and dispositional factors.

  • Six years after the publication of the National Council of Teachers of Mathematics; (NCTM's) Curriculum and Evaluation Standards for School Mathematics, which set the course for a new era of mathematics education reform, professional development for mathematics teachers has moved tothe center of the reform agenda. The argument adequately power the reforms (Cohen, 1990; Little, 1993; Lord, 1994). Rather, they depend on the transformation of teaching in the nation's many classrooms. Many teachers have embarked on the project of changing their teaching toward that envisioned in the Standards. Their work leads us to the follwoing questions: Where are we in our understanding of the nature of this process? How can we help teachers in their efforts to invent a new form of teaching? and How can we continue to learn about what such invention entails?

  • The publication of research findings that are not statistically significant presents a novel probelm in interpretation of research results. The contribution of nonsignificant results depends in part on whether the statistical test was powerful enough to detect an effect of "meaningful" size. The primary responsibility rests with the authors of articles reporting nonsignificant results to demonstrate the worth of the results by discussion the power of the tests. If they do not assume this responsibility, then consumers of research should be prepared to conduct their own power analyses to aid interpretation of the research results. This ariicle demonstrates the use of power analysis for the interpretation of nonsignificant findings. The power of many common statistical tests can be determined without difficult computation using Cohen's (1977) or Stevens's (1980) tables.

  • This paper argues that the two models of curriculum development currently used to interpret Australian mathematics education history--the Colonial Echo model and the Muddling Through model--are both deficient, and proposes a more complex model--the Broad Spectrum Ecological model. This considers the physical, social and intellectual forces operating within a specific environment. One small aspect of mathematics education history, the introduction of probability teaching into Australian schools, is used to illustrate the superiority of this model.

  • We depend on data to make intelligent decisions, yet the data we see is often "tainted." An old saying on the use and misuse of computers was "garbage in - garbage out" but this has become "garbagge in - gospel out" as more and more people get in to the numbers game. So, what can we do? Part of the answer lies in education. Comsumer and producers of data with sreious unbiased objectives to get at the "truth" must be educated in how surbeys an experiments work, how good surveys and experiments can be designed, and how data can be properly analyzed. Every high school graduate must be educated to be an intelligent consumer of data and to know enough about hte production of data to at least judge the value of data produced by others. This education must be built into the K-12 curriculum, primarily in mathematics and science but with consistent support and application from the social sciences, health and other academic subjects.

  • School are flocking to software publishers to equip their newly acquied compuers with the latest in software. Electronic graphing tools are an important component of any computer tool kit. Graphers..Data Explorere...Math Lab Toolkit...Green Globs and Graphing Equations...Symbols and Graphs...First Workshop...The Graph Club.. The 199701998 SUMBURST educational software catalogue alone lists these 7 electronic graphing tools. In many schools today, it is not unusual to see students projects with computer-generated graphs lining school hallways. Parents are delighted that their children are sorking with data and using computers to peoduce neat , professional -looking products that incorporate graphs along with the textk, graphics, and tables they have come to look for.<br><br>Yet the fact that students are graphing with computers doesn't, in and of itself, mean that they are developing rich understandings of data and of the subtleties of data representation. Rather, too often they use the tool to produce "quick but meaningless graphs" without having a real grasp of the nature of the data with which they are working (Ainley and Pratt, 1995, p. 438). Graphs, generated by hand or electronically, must not be relegated to the passive role of presentation tools. Rather, they need to become central components of a wider analytical activity, used to interpret the data, identify trends and make predictions (Parker, 1992; Aily and Pratt, 1995).

  • In this article, Frederick Mosteller, Richard Light, and Jason Sachs explore the nature of the empirical evidence that can inform school leaders' key decisions about how to organize students within schools: Should students be placed in heterogeneous classes or tracked classes? What is the impact of cclass size on students learning? How does it vary? Since tracking (or skill grouping, as the authors prefer to call it) is widely used in U.S. Schools, the authors expected to find a wealth of evidence to support the efficacy of the practice. Surprisingly, they found only a handful of well-designed studies exploring the academic benefits of tracking, and of these, the results were equivocal. With regard to class size, the authors describe the Tennessee class size study, using it to illustrate that large, long-term, randomized controlled field trials can be carried out successfully in education. The Tennessee study demonstrates convincingly that student achievement is better supported in smaller classes in grades K-3, and that this enhanced achievement continues when the srudents move to regular-size classes in the fourth grade and beyond. The authors suggest in conclusion that education would benefit from a commitment to sustained inquiry through well-designed, randomized controlled field trials of education innovations. Such sustained inquiry could provide a source of solid evidence of which educators could base their decisions about how to organize and support student learning in classes and schools.

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