Ten Myths of Science: Reexamining What We Think We Know About the Nature of Science

This article addresses and attempts to refute several of the most widespread and enduring misconceptions held by students regarding the enterprise of science. The ten myths discussed include the common notions that theories become laws, that hypotheses are best characterized as educated guesses, and that there is a commonly-applied scientific method. In addition, the article includes discussion of other incorrect ideas such as the view that evidence leads to sure knowledge, that science and its methods provide absolute proof, and that science is not a creative endeavor. Finally, the myths that scientists are objective, that experiments are the sole route to scientific knowledge and that scientific conclusions are continually reviewed conclude this presentation. The paper ends with a plea that instruction in and opportunities to experience the nature of science are vital in preservice and inservice teacher education programs to help unseat the myths of science.     

What Do Composition Operators Know About Inner Functions?

 This paper gives several different ways in which operator norms characterize those composition operators that arise from holomorphic self-maps ϕ of the unit disc that are inner functions. The setting is the Hardy space H ² of the disc, and the key result is a characterization of inner functions in terms of the asymptotic behavior of the Nevanlinna counting function. The case offers an interesting surprise.     

Who You Know vs. What You Know: The Impact of Social Position and Knowledge on Team Performance

Organizational behavior theories generally agree that human capital is critical to teams and organizations, but little guidance exists on the extent to which such theories accurately explain the relative contributions of individual actors to overall performance. Using newly created network measures and simulations based on data obtained from a software development firm, we investigate the relative effectiveness of social network theory and resource dependency theory as predictors of individuals' contributions to team performance. Our results indicate that individual impacts on team performance are more closely associated with knowledge and task dimensions than with social network structure. Furthermore, given that knowledge may be assessed a priori, these factors provide useful guidance for structuring teams and predicting team performance.     

Students Talk About Prime: What We Heard About Definitions

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the ways students used the evidence they cited. Findings suggest that students attend to important features of mathematical definitions, with some students giving preference to usability and others giving preference to definitions that are unambiguous.     

How Do Students Know What They Learn in Middle School Mathematics Is True?

This article presents ways in which students ascertain that what they have learned in mathematics is true. Students in the middle school (and a few from other grades) were interviewed by prospective and in‐service teachers. Students were asked what they had learned recently in mathematics and how they knew it was true. The answers were grouped by the author according to the justification schemes used by the students in their explanations. Students interviewed used three kinds of justification schemes: externally based, empirical, and analytic. For each kind, examples are provided of students' justifications. Additional insights are included from the reflections of the interviewers. Some suggestions are offered regarding how teachers can help increase their students' ability to give convincing arguments in mathematics.