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…

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

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)

Analyzed are textbook word problems that are typically used as applications of mathematics and shows some of the difficulties in making these problems realistic. A discussion and examples of sources of genuine mathematical applications in real life follows. (MN)

Provides guidelines for developing and implementing lessons using selections from children's literature as meaningful and appropriate contexts for solving word problems. Selection procedures, materials for constructing the characters, and two sample problems are provided. Lists 15 references. (YP)

Presented is a calculation for the probability of a athletic event. Assumptions, computations, and questions to be considered in the solution of this problem are discussed. (CW)

Outlines a plan of action designed to enhance growth in problem-posing skills. The "blueprint" provides a model for teachers and teacher educators who wish to integrate more problem posing into their curriculum. Specific activities and instructional strategies are cited to illustrate the development of problem posing as a process in the classroom.…

Investigated the effect of the choice of a model's medium (algebraic expression or computer program) on the performance of students. Student programers did not transfer the qualities of a computer program approach to their algebraic models. Provides items for five tests. (YP)

Presents examples of word problems that can be used to illustrate the distributive property for preservice teachers. Includes examples involving extended sums, volume, area, prealgebra, place value, long multiplication, fractions, decimals, and algebra. (MDH)

Reports a study to examine secondary school students' (n=200) responses to two figurally and spatially similar problems from mathematics and science that require different responses before and after instruction. Results indicated that most students gave the same response to both questions. Reasons for this pattern are discussed. (MDH)

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