Describes a student's unique perspective on the algorithm for finding equations of non-vertical lines given one point and the slope. Indicates that students had a better understanding of what they were doing. (KHR)

Explores developing a concept image of functions. Includes assessment items, describes students' responses to these items, and interprets those responses. (KHR)

Classroom discourse can nurture students' appreciation of mathematics as a community activity by involving students in defining the curriculum, engaging in authentic mathematical inquiry, and using the history of mathematics to understand how mathematical thought develops in society. (MKR)

The problem of solving mathematical equations can be quite tough for some students hence they face a great difficulty when applying ideas to the actual process. Students in algebra classes are taught coding in which they write down what they will need to do to solve the equation and this coding makes the students more adept at solving equations…

The need for students of engineering to acquire the rational, methodical approaches identified with the "mathematical way of thinking" is discussed. The skill areas in mathematics most critical to engineering majors are pointed out, with proper shaping of student attitudes seen as an important role secondary school mathematics must play.…

Five basic skill areas needing more attention in standard high school geometry are discussed. Levels of student mental development in geometry and a need for less emphasis on formal proofs are reviewed. (MP)

Presents research findings related to students' intuitive ideas about the concepts of chance to inform teachers how students form their concepts of probability and statistics. Discusses adolescents' conceptions of uncertainty, judgmental heuristics in making estimates of event likelihood, the conjunction fallacy, the outcome approach, attempts to…

Discusses the use of feedback from students and the analysis of students' error patterns to understand why students develop misconceptions in mathematics. Looks at learning vis-a-vis the abstract nature of mathematics and the students' cognitive development. (MDH)

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

Compared are the van Hiele levels of geometric thinking and the geometry curriculum recommended by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Activities which illustrate the various levels are provided by grade level with procedures. (CW)

Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)

The intuitive simplicity of probability can be deceiving. Described is a dialogue that presents arguments for conflicting solutions to a seemingly simple problem determining the probability of having two boys in a two-child family knowing that one child is a boy. Solutions contain multiple arguments and representations. (MDH)

Great care must be taken when making the jump from the finite to the infinite. The concept of infinity is explored through a series of examples from infinite sequences, presenting potential contradictions that could occur from a natural extension of finding the fraction form of a repeating decimal. (MDH)

Discussed is why students have the tendency to apply an "add the numerators and add the denominators" approach to adding fractions. Suggested is providing examples exemplifying this intuitive approach from ratio, concentration, and distance problems to demonstrate under what conditions it is applicable in contrast to the addition algorithm. (MDH)

This analysis synthesizes the research on characteristics of the mathematically gifted and describes some ways in which programs can be designed to address those characteristics. (MNS)