Research has shown that although teachers' knowledge about the subject or pedagogy is important, a teacher's professional vision (including their perceptions and pedagogical decisions) can also have a significant impact on the efficacy of their practice. Firmly grounded in the long-standing field of teacher professional vision research, this…

This toolkit provides activities and resources to assist practitioners in designing and delivering intensive interventions in reading and mathematics for K-12 students with significant learning difficulties and disabilities. Grounded in research, this toolkit is based on the Center on Instruction's "Intensive Interventions for Students Struggling…

This project was designed to address gender issues in mathematics education. The author's findings led her to conclude that students construct their own understanding and knowledge as a result of activities in the classroom. Constructivism, a theory of knowledge based on the idea that people construct their own realities by interacting with the…

The open-approach teaching method, a problem-solving method, is described, with examples of situations and problems that are suitable for this approach. The teaching-learning process and educational implications are discussed. (MNS)

Challenges teachers to explore teacher talk and distinguish messages that unwittingly encourage dependence on authority from those that support the growth of academic autonomy through discovering relationships, developing speed and accuracy in skills, and developing understandings that serve problem solving in projects and activities. (MKR)

This bulletin concerns the role of memorization in mathematics instruction. Sections of the bulletin are devoted to discussions of: old math vs. new math; the importance of memorization ability on mathematics learning; misconceptions about memory; how to enhance the memory, including short-term vs. long-term memory systems, attention, interest,…

The forum is focused on thinking about and with algorithms as a way of unifying all one's mathematical endeavors. The lead article by Maurer presents examples and discussion of this point. Responses, often disagreeing with his views, are by Douglas, Korte, Hilton, Renz, Smorynski, Hammersley, and Halmos. (MNS)

Provides examples which suggest the importance of giving children opportunities to create their own arguments and of allowing them the opportunity to verbalize these arguments in clinical interviews. Also indicates that if time is spent interviewing children individually, instruction can be matched to the way they think. (JN)

Describes second graders' responses to finding the sum of the numbers from 1 through 10 after reading the book, Ten Black Dots. Includes student work demonstrating their problem solving. (MKR)

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)

This monograph presents research findings from a series of 11 studies conducted in grades 5 through 10 on the role of games in learning mathematics. The first chapter considers "What is learning from a game?" and includes two examples of mathematical instructional games, with a definition of such games, cognitive effects, game-related…

Two transcripts of children exploring and solving problems presented by computer programs are given. The transcripts show the insight that occured. (MNS)

Differences in cognitive structure are approached through consideration of cartesian and non-cartesian knowing. Figuration and configuration are described as two layers of cartesian knowing leading to the third layer, the cognitive structure. Knowing in general is then discussed, with comments on learning in another culture, Botswana. (MNS)

How the author moved from concern about research to development of prescriptive models of heuristic problem solving and the exploration of metacognition and belief systems is discussed. Student beliefs about problem solving, and their corollaries, are included. (MNS)

A noncredit course in a workshop format is described, with sessions focusing on recognizing and defining problems; organizing information and using modeling techniques; analyzing data, recognizing trends, and making decisions; being flexible and thinking creatively; and generalizing and consolidating. (MNS)