The Mathematics students who perform truth-seeking process upon solving mathematical problems were unique. Therefore, the study deems it necessary to know students' mental structure and mechanism so that they can make the right decision by performing truth-seeking. However, no research has delved into the mental structures and mechanisms of…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

Illustrates distinctions among kinds of knowing. Distinguishes knowing-to from other forms of knowing, and explores implications of that distinction for teaching and learning mathematics. Proposes that knowing-to act in the moment depends on the structure of attention at the moment, and on what one is aware of. (Contains 75 references.)…

Studies the amount of attention to various kinds of activities and how students are called upon to process information in typical mathematics lessons, and whether this focus indicates a balanced program with respect to procedural knowledge, conceptual knowledge, and mathematical activity. (Contains 15 references.) (ASK)

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

How the computer as a metaphor affects our understanding of the processes of learning and teaching is explored. After describing reflection and recursion in mathematics and their roles in thinking and learning, models of the mind and teaching effects are discussed, with self-awareness as a theme. (MNS)

Didactic transposition theory asserts that bodies of knowledge are designed not to be taught but to be used. Discusses didactic transposition, the transposition of knowledge regarded as a tool to be used to knowledge as something to be learned in mathematics textbooks. (14 references) (MDH)

Addresses issues related to the ways teachers learn mathematics and the teaching of mathematics, and the relevance of those ways to their professional development. Mathematical experiences need to be congruous with the kind of teaching expected of the reflexive, adaptive teacher. Presents both practical and theoretical considerations of how these…

Discusses what important ideas about forms of knowing mathematics should be included in mathematics methods courses for preservice teachers. Proposes ideas related to Shulman's framework of teacher knowledge. Provides a brief discussion of the implications each idea holds for teaching mathematics, and makes some suggestions about experiences that…

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

This article discusses ways to improve mathematics performance of students with learning disabilities through cognitive strategies instruction. Principles of a strategic classroom environment are explained, such as involving students in goalsetting and providing advance organizers. Three specific strategies for math instruction are described:…

Presents two cognitive models that illustrate the commonalities between reading for meaning and solving mathematical problems with meaning. Discusses the importance of number sense in the prior knowledge component of the solving with meaning model and the implications of the models in teaching mathematics. (MDH)

The concept of probability is not an easy concept for high school and college students to understand. This paper identifies and analyzes the students' alternative frameworks from the viewpoint of constructivism. There are various interpretations of probability through mathematical history: classical, frequentist, and subjectivist interpretation.…

Participants at a conference on mathematics teaching discussed what it means to know and understand a subject and what teachers need to know, understand, and believe in order to teach a subject to elementary learners. The first section of the report covers the first day of the conference that was spent in a series of whole-group sessions.…