The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

Scholars often define historical reasoning as constructing defensible interpretations of past events. Drawing on critical theory, this article suggests that it also entails consciously framing one's topic of inquiry. The article examines an instructional unit that aimed to foster this expanded view of historiography. Forty students, ages 14-15,…

Solving simple arithmetic word problems is a major ability that children must acquire throughout the primary-grade mathematics curriculum. However, this skill is often challenging for them. For instance, "unknown referent problems" are more difficult to solve than "unknown compare problems." In unknown compare problems, the…

This study sought to evaluate the adequacy of integration of problematic situations and general problem-solving strategies (heuristics) in grades 9 and 10 mathematics textbooks. Grade 9 and grade 10 mathematics textbooks were used for analysis. Document analysis and interview were used as data gathering instruments. Document analysis was carried…

This study investigated the effect of the Science Writing Heuristic (SWH) approach on grade 9 students' understanding of chemical change and mixture concepts. Four intact classes taught by two chemistry teachers from a Turkish public high school were selected for the study; one class was assigned as the treatment group, and the other class was…

This study investigates the effects of the Science Writing Heuristic (SWH), known as an argumentation-based science inquiry approach, on Grade 9 students' performance on a post-test in relation to their academic achievement levels. Four intact classes taught by 2 chemistry teachers from a Turkish public high school were selected for the study; one…

Simulation games can play a critical role in enabling students to navigate the problem spaces of the past while simultaneously critiquing the models designers offer to represent those problem spaces. There is much to be gained through their use. This includes rich opportunities for students to engage the past as independent historians; to consider…

Student difficulty in the study of probability arises in intuitively-based misconceptions derived from heuristics. One such heuristic, the one of note for this research study, is that of representativeness, in which an individual informally assesses the probability of an event based on the degree to which the event is similar to the sample from…

Teacher-educator and researcher Daniel L. Kohut suggests in "Musical Performance: Learning Theory and Pedagogy" that there are many problems that result from the way music teachers often teach. Most teachers focus on the process, not the goal. The Natural Learning Process that Kohut advocates is the same process that young children use when they…

This article reports on a subset of results from a larger study which examined middle and high school students' probabilistic reasoning. Students in grades 5, 7, 9, and 11 at a boys' school (n = 173) completed a Probability Inventory, which required students to answer and justify their responses to ten items. Supplemental clinical interviews…

This study investigates the relationship between the students' understanding of the aims of an investigative activity and their performance when conducting it. One hundred and eighty-one year nine students from a public middle school in Brazil took part in the study. Students working in pairs were asked to investigate two problems using a…