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)

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…

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…

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)

Discusses research findings related to students' ability to make connections between analytical (symbolic) and graphical representations of functions in calculus. Describes graphing tasks and typical student interpretations. Implications for teaching are suggested. (Contains 17 references.) (MKR)

Describes one teacher's reflection concerning the quest to develop an understanding of school mathematics that promotes and sustains students' opportunities for exploration and conjecture. Recounts that a particular student's exploration of the features of parabolas eventually led to an understanding of the quadratic formula precisely because of…

Presents activities that use visual-geometric models to help students develop their understanding of exponents and division of powers with the same base. Presents opportunities for students to discover patterns for themselves and communicate these findings to others. (MDH)

Discussed is how the concept of equivalence can relate various segments of a mathematics program and help students develop an appreciation of the unity of mathematics. Activities and examples of equivalence at all grade levels are included. (KR)

Describes a geometry course that integrates transformation geometry into traditional high school geometry. Discussion of the scope and sequence of the course includes the topics of proof, congruence, translations, rotations, reflections, dilations, quadrilaterals, parallel lines, and similarity. (MDH)

Presents five activities to help students construct meaning for multiplying fractions through real-world problem contexts, physical or pictorial models, the recognition of patterns, and the use of calculators. In the context of a garden plot, worksheets examine various aspects of parts of plots, patterns in plots, and a maximization problem.…