A major question for the study of learning and memory is how to tailor learning experiences to promote knowledge that generalizes to new situations. In two experiments, we used category learning as a representative domain to test two factors thought to influence the acquisition of conceptual knowledge: the number of training examples (set size)…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

In this study, hypothetical samples of students' work on a task involving pattern generalizations were used to examine the characteristics of the ways in which 154 elementary prospective teachers (PSTs) paid attention to students' work in mathematics. The analysis included what the PSTs attended to, their interpretations, and their suggestions for…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…

The transition from preformal and propaedeutic generalization-actions to a symbolically explicit use of the concept of variable has been a matter of significant attention in mathematics education, for example in the context of generalization processes on a preformal level and regarding the specific nature of algebraic concepts. This contribution…

Learning concepts implies certain attitudes and skills on the part of both teachers and student; means recalling specific perceptions, discovering relationships, and applying these structures to situations. Students who have learned to conceptualize have the ability and training to view their own lives in relations to their physical and cultural…

The authors suggest that simply by changing the method of questioning, a teacher can change not only the intellectual demands in the classroom, but also the range of thinking strategies that provide for understanding and competence. (KC)

The operation of means-ends analysis (MEA) involves attempts at reducing differences between problem states and the goal state. It was paradoxically found that the more problem solvers knew of the goal state, the less they learned of the problem structure during the solution process. (PN)

Among the 12 documents selected for this annotated bibliography of documents and journal articles in the ERIC database is an expert's argument that the brain's multipath and multimodal capacities are ignored by educators. Another writer fears that the "back-to-basics" movement may have eclipsed the prominence earlier accorded to thinking…

This paper describes the rule-assessment approach to cognitive development. The basic question that motivated the rule-assessment approach is how people's existing knowledge influences their ability to learn. Research using the rule-assessment approach is summarized in terms of eight conclusions, each illustrated with empirical examples.…

Investigated in two experiments involving 15- and 16-year-old mentally retarded students was knowledge of conceptual categories as reflected by semantic priming effects. (Author/IM)

Results show that children with flexible styles obtained higher performances on school learning measures than children who used consistent styles. Study results suggest feasibility of identifying children who tend to use a consistent conceptual style for the purposes of prescribing instructional methods and materials. (Author/PC)

This paper describes the methods and techniques called Conceptual Analysis (CA), a rigorous procedure to generate (without involuntary omissions and repetitions) knowledge bases for the development of knowledge-based systems. An introduction is given of CA and how it can be used to produce knowledge bases. A discussion is presented on what is…

In this essay, research done on concept learning is discussed. The study analyzes concept learning as one form of learning, formulating guidelines for teaching concepts, and describes the abilities underlying the attainment of concepts. An analytical model is presented; various operations such as concrete concepts and identity concepts are…