Previous research has investigated the representational translation practices of high school students, high school teachers, and college preservice teachers in various mathematical contexts including linear functions. Findings from qualitative research has frequently led to new notions about participant work and understanding. Many quantitative…

The findings reported in this paper were generated from a case study of teacher leaders at a state-level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…

Recognizing and responding to students' thinking is essential in teaching mathematics, especially when students provide incorrect solutions. This study examined, through a teaching scenario task, elementary preservice teachers' interpretations of and responses to a student's work on a task involving reflective symmetry. Findings revealed that a…

Methods of determining probabilities of various outcomes of the game Yahtzee are described. (SD)

Definitions of estimating and approximating are given and areas where these skills are used (such as practical situations, problem solving, and measurement) are discussed. Nine activities which range from second to twelfth-grade level are suggested. (MK)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Examples of mathematical problems which arise outside the classroom situation are presented. The author suggests that the conceiving and solving of such problems by students would be a good way to provide the students with applications of the mathematics they learn. (JP)

Tables of life expectancy can provide data for use in a great variety of problems related to probability theory. (SD)

Describes an instructional method in secondary school mathematics applicable to physics instruction, to develop conceptual understanding of motion word problems. Distance, rate, and time are defined, used as variables and considered with relative motion as a unifying concept. (JM)

Graph theory is presented as a tool to instruct high school mathematics students. A variety of real world problems can be modeled which help students recognize the importance and difficulty of applying mathematics. (MP)

Provides a discussion and an example of a problem which occurs in mathematical contests or entrance examinations and deals with the question of the magnitude of exponentials. Includes additional illustrative examples. (RT)

As calculators and computer use increases in mathematics education, more educators are recognizing a shift in emphasis from computation to problem solving. Ways to generate problems that can be used to develop pupil creativity and insight are suggested, and process-oriented instruction is promoted. (MP)