A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…

Explicit information-seeking actions are needed to evaluate alternative actions in problem-solving tasks. Information-seeking costs are often traded off against the utility of information. We present three experiments that show how subjects adapt to the cost and information structures of environments in a map-navigation task. We found that…

Learner-generated drawing is a strategy that can improve learning from expository text. In this paper, a model of drawing construction is proposed and the experimental design tests hypotheses derived from this model. Fourth and sixth grade participants used drawing under three experimental conditions with two conditions including varying degrees…

This paper explores the development of students' knowledge of mathematical procedures. Students' tendency to develop rote knowledge of procedures has been widely commented on. An alternative, more flexible endpoint for the development of procedural knowledge is explored here, where students choose to deviate from established solving patterns on…

This study investigated the extent to which interspersing effects are consistent with the effects of reinforcement on predicting students' preferences for mathematics assignments. Students were exposed to 4 pairs of assignments. Each assignment pair contained a control assignment with 15 problems requiring multiplication of a three digit number by…

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…

Because problem-solving appraisal has been demonstrated to be a critical variable in psychological adjustment, this study examined its potential role as both a static and dynamic client attribute influencing the process and outcome of career counseling. Participants were 151 adults who received an average of five sessions of naturally occurring…

This study examined changes in 26 fourth-grade students' early conceptions of rational number representations as a function of receiving one of two curricular interventions. The first group of 12 students received a curriculum that emphasized constructing knowledge through extended problem solving with a single perspective of the rational number…

Sixty-five undergraduates were classified into field-dependent, field-mixed, and field-independent learners, and were randomly assigned to two groups: text-only and text-and-visual. Participants in the text-only group received a description of a model in textual format, whereas participants in the other group received the same description in…

Ethnic identity, in combination with approach-type coping strategies (i.e., social support seeking, cognitive restructuring, and problem solving), was hypothesized to moderate the effects of perceived racial discrimination on the well-being of Asian American college students. Results found that individuals with a strong ethnic identity were more…

Gaining expertise in leadership requires time, commitment, an adequate knowledge base, and a working plan for learning and growth. Without a plan for learning, only tacit or "how-to" expertise is developed. Leaders often know how to solve the problems facing them, but they fail to analyze and act on the underlying causes. This results in…

Purpose--In an empirical study learning opportunities were identified. Learning opportunities are enablers or disablers for the achievement of shared understanding. Design/methodology/approach--Actors were interviewed about their communication process. The learning history method was used to analyze and structure the data. From the learning…

This paper illustrates the role of a "Thinking-about-Derivatives" task in identifying learners' derivative conceptions and for promoting their critical thinking about derivatives of absolute value functions. The task included three parts: "Define" the derivative of a function f(x) at x = x[subscript 0], "Solve-if-Possible" the derivative of f(x) =…

This article takes a critical look at administrative decision making in schools and the extent to which complex decisions conform to normative models and common expectations of rationality. An alternative framework for administrative decision making is presented that is informed, but not driven, by theories of rationality. The framework assumes…