Two experiments involving 67 elementary school and 439 high school students show that students present solutions to many unsolvable problems without showing realistic reactions. Results are discussed with respect to the quality of word problems in teaching mathematics, the culture of teaching and learning, and the issue of social rationality in…

Tested three models of children's mathematics word-problem solving based on developmental differences in quantitative conceptual structures: (1) quantitative relations represented as ordered array of mental objects; (2) numbers represented on two tentatively coordinated mental number lines; and (3) numerical operations represented as objects on…

Presents a project that explored student choice of a solution method for quadratic inequalities. Students were first instructed in the use of the case, critical-number, and graphical methods using the graphing calculator. The majority of students chose graphical methods of solution. (DDR)

Argues that encouraging talking among young learners in the classroom is one of the best ways to foster learning. Presents incidents which illustrate that children naturally use language to report on experiences, collaborate toward agreed ends, project into the future, focus on causal and dependent relationships, create and discuss problems,…

Examines changes in the problem posing strategies of a group of elementary preservice teachers as they posed problems to pupils. Indicates that the teachers' problem posing practices were changed from posing traditional single steps and computational problems to multiple approaches and solutions with open-ended and exploratory problems.…

Describes the process of mathematical modeling, an extensive teacher's guide, and a student modeling activity to improve the efficiency of soft-drink packaging. (KHR)

Describes one pattern of reasoning observed in a mathematical activity with students in a grade 5 class and discusses ways in which the pattern is or is not mathematical. Describes patterns of reasoning in terms of ways of reasoning and degree of formulation of the reasoning. Distinguishes between mathematical reasoning and scientific reasoning in…

Describes a variation on a problem from the history of mathematics in which the class is divided into cooperative learning groups of four students each. Each group is challenged to find a procedure for resolving the situation with several solutions emerging. Emphasizes the importance of examining "incorrect" answers and discussing the…

Describes strategies for using literature to teach number sense and problem solving. Reports that the rich class discussions reflected some of the students' thinking, gave students opportunities to share their approaches and understandings, and gave the teacher additional insights into students' thinking. (JRH)

Explores the working group model for mathematics teacher education and presents group investigations from the areas of number theory, probability, and geometry. Argues that by working in groups, sharing ideas, and making and testing conjectures, prospective teachers gain confidence in their own ability to do mathematics and develop a variety of…

Explores the various cultural perspectives present in mathematics education in China. States that the Chinese mathematics education has hidden problems and can learn from the Western mathematics education that utilizes approaches such as problem solving and constructivism. States that ethnomathematics should have an active role. (CMK)

Assesses the effects of explicitly teaching for transfer by broadening the categories by which students group problems requiring the same solution methods and prompting students to search novel problems for these broad categories. This transfer treatment was combined with instruction on solution methods. Improvement on immediate- and near-transfer…

Introduces an activity, Equation Telephone, designed to improve students' ability to interpret written information and recognize equivalent forms of an equation. Discusses the activity in detail and presents examples of student responses. (KHR)

Examines the extended effects of an instructional program designed to enhance schema development. Uses non-goal specific problems to teach geometry to high school students who need remedial tuition. Indicates that participants in the non-goal specific group showed greater improvements. Includes references. (CMK)

Examines the performance of deaf and hearing-impaired students in Queensland, Australia when solving arithmetic word problems. Subjects' solutions of word problems confirmed trends for learning students but their performance was delayed in comparison. Confirms other studies in which deaf and hearing-impaired students are delayed in their language…