In this study, we examined 10 expert and 10 novice teachers' noticing of classroom events in China. It was found that both expert and novice teachers, who were selected from two cities in China, highly attended to developing students' mathematics knowledge coherently and developing students' mathematical thinking and ability; they also paid…

Analogies are known to foster concept learning, whereas discovery learning is effective for transfer. By combining discovery learning and analogies or similarities of concepts, attractive new arrangements emerge, but do they maintain both concept and transfer effects? Unfortunately, there is a lack of data confirming such combined effectiveness.…

This activity involved constructing parallelograms on the sides of an arbitrary triangle and discovering a relationship between the areas of the parallelograms. (MP)

The purpose of this paper is to open lines of thinking about discovery learning not tried before. This effort is a strident attempt to establish new insights and outlooks that will improve the language, theory, and practices connected with this teaching method. (Author/MK)

Describes physiological, affective, and cognitive mechanisms by which didactic and discovery methods appear to work, as revealed by research literature. The optimal instructional method depends on the instructional objective, the educator's skills, and the nature of the students. Suggests more use of discovery methods. (69 references) (Author/MKR)

Describes three major difficulties plaguing most discovery-learning teaching systems and presents a theoretical operational approach for offsetting these difficulties. (SL)

A way that allows students to discover a strategy for determining the area of rectangles, squares, parallelograms, triangles, and trapezoids is described. Students use grid paper and scissors to determine the number of square units that cover a specified space. (KR)

The objective were to explore some of the ways in which the calculator can be used and to determine the effects. Areas covered are: computation, mathematics readiness, problem solving, and discovery learning. (MP)

Forty seventh-grade students, grouped by ability and instructed by intermediate or maximal guidance with or without concrete aids, were given post and retention tests. Low-ability students using aids achieved higher than those taught without aids. Intermediate-guidance groups had higher mean transfer scores when using aids, with no differences…

Examples of activities involving geometric construction are suggested for discovery-oriented instruction. (SD)

Presents an extension of Pick's theorem for simple closed polygonal regions to unions of simple closed polygonal regions. Students are guided to discover Pick's theorem from sets of data including numbers of boundary points and numbers of interior points. (Author/MKR)

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)