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.…

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)

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)

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…

It is viewed understandable that many teachers consider fractions one of the most difficult mathematical topics to teach. School experiences need careful planning to include sequential activities which develop accurate concepts, and concepts are thought best developed by activities which move along the concrete-to-abstract continuum. (MP)

Guessing is seen in all forms to be a creative and critical process which has practical and scientific utility. The goal of science in early childhood is viewed as having children make better guesses. Ways of instruction that create and develop an atmosphere for guessing are detailed. (MP)

The teaching of mathematics as a science to elementary school children is promoted. Use of the scientific method in learning is presented as a form of experiential or discovery teaching. (MP)

Presents a study to determine whether computer use in guided-discovery learning episodes would enhance the problem-solving ability of secondary school students (n=147). Results indicate interaction between low- and middle-level students' mathematical achievement and treatment groups, while high-level students performed well regardless of approach.…

Describes examples of student-centered activities for exploring mathematical induction using BASIC programs or spreadsheets. Discusses the advantages of using this medium to teach the concept and provides computer programs for the activities. (MDH)

Describes three components of a seminar in mathematical problem solving for preservice mathematics teachers: (1) a cognitive component that accents particular phases of problem solving; (2) an affective component that allows for observation of skillful problem solvers; and (3) an investigative component that provides for independent study and…

Described is a study that used LOGO to improve the proportional reasoning ability of students enrolled in mathematics classes for students poorly prepared for college-level mathematics. Included are the methodology, procedures for using logo, and a discussion of the results. (KR)