This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative…

Chemical processes can be fully explained only by employing quantum mechanical models. These models are abstract and require navigation of a variety of cognitively taxing representations. Published research about how students use quantum mechanical models at the upper-division level is sparse. Through a mixed-methods study involving think-aloud…

The article reports the results of a longitudinal research study conducted in three mathematics classes in Czech schools with 62 pupils aged 12-18 years. The pupils were exposed to the use of selected heuristic strategies in mathematical problem solving for a period of 16 months. This was done through solving problems where the solution was the…

Metacognition can be described as an internal conversation that seeks to answer the questions, "how much do I really know about what I am learning" and, "how am I monitoring what I am learning?" Metacognitive regulation skills are critical to meaningful learning because they facilitate the abilities to recognize the times when…

In teaching proportion, the teachers usually give the students a formal formula, such as cross-multiplication, without providing them the meaning of proportionality. Thus, the students just apply it in order to solve proportional problems. However, it does not connote that they understand what proportionality means. In this paper, the authors…

This paper presents the outcomes of teaching an inventive problem-solving course in junior high schools in an attempt to deal with the current relative neglect of fostering students' creativity and problem-solving capabilities in traditional schooling. The method involves carrying out systematic manipulation with attributes, functions and…

Catch 'em young for imparting hands-on rigorous academic training. This is what has been relentlessly pursued while dealing with the undergraduate students of business management who are to be thoroughly exposed to the whole gamut of quality work life. Whether they opt for corporate career or pursue masters or choose be an entrepreneur, their…

Successful teacher preparation programs provide learning experiences that help teacher candidates make the shift from "student" to "teacher." In this paper we present research on the implementation of a process for providing candidates such experiences. Utilizing the Mathematics as Teacher Heuristic (MATH) process, prospective…

This paper presents the outcomes of teaching an inventive problem-solving course to middle school students. Contrary to the common view of creativity as a 'free flow of thought' or 'thinking out of the box,' the method under discussion stresses the use of diverse heuristic approaches for problem-solving and the invention of new products: for…

Common examples of graphic organizers include flow diagrams, concept maps, and decision trees. The author has created a novel type of graphic organizer called a decision map. A decision map is a directional heuristic that helps learners solve problems within a generic framework. It incorporates questions that the user must answer and contains…

Student problem-solving behaviors are analyzed using a four-dimensional framework with related detrimental factors identified for each dimension. General approaches and specific techniques developed to address negative factors are reviewed. Examined are means of developing the components of problem-solving teaching. (KR)

The strategic learning of college and university students begins with their acquisition of knowledge about their academic context and its learning opportunities and demands. However, traditional assessment measures isolate the student outside of the authentic learning context, which limits the information available from these tests. In contrast,…

Presents three problems that help students develop a repertoire of heuristics and persistence in problem solving: the water-jug problem; the missionaries-and-cannibals problem; and the census-taker problem. Discusses methods to encourage students to persist. (MDH)

Describes common beliefs of students about the nature of mathematics and discusses the implications of the student beliefs for problem solving and for teaching. (PK)

Five women university students' representations of their learning were analyzed and related to their on-going adaptations to course demands. Representations involved their goals, working plans and perceptions of difficulties. Qualitative data from students' accounts were tabulated schematically in relation to Duncker's concepts of productive…