Investigates students' conceptions and misconceptions relating to the construction of graphs. Qualitative analysis of students' responses identified three main alternative conceptions. Quantitative analyses of the data indicated that overall students did not enter the learning situation as a tabula rasa. Discusses the theoretical and practical…

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

Explores connections between mathematics, music, and movement in early childhood curriculum. Presents music activities in which mathematical concepts are embedded; focuses on activities providing experiences with time-based relationships and rhythmic patterns. Asserts that integrating movement and mathematics into music activities provides a way…

Two experiments tested claim that transparency of Korean fraction names promotes fraction concepts. Findings indicated that U.S. and Korean first- and second-graders erred similarly on a fraction-identification task, by treating fractions as whole numbers. Korean children performed at chance when whole-number representation was included but…

Described is a strategy that shows students how one mathematical concept can be connected to another. The emphasis is on both process and product and can lead to creating a learning environment where students do mathematics as mathematicians do. (KR)

The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)

Presents four examples on arithmetic mean and harmonic mean. Provides solution of each of the examples and instructional activities related to the examples. Lists eight references on mathematical problem solving. (YP)

That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a geometric view of Singular Value Theorem. Included are two theorems, one which is a pure matrix version of the above and the other that leads to the orthogonal diagonalization of certain matrices, i.e., the Spectral Theorem. Also included are proofs and remarks. (KR)

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Presented are four mathematical discoveries made by students on an arithmetical function using the Fibonacci sequence. Discussed is the nature of the role of the teacher in directing the students' discovery activities. (KR)

Reviewed is an integrated approach to teaching place-value concepts. A semi-integrated approach is proposed which may provide a more effective implementation of the technique. (CW)

A project in which students can develop their understanding of mathematical concepts through the collaborative writing of word problems is discussed. Worksheets for project requirements and daily requirements are provided. A Thanksgiving project is proposed. The use of a fashion modeling problem in the statistics classroom is described. (CW)

Presented is a lesson in which the patterns that occur within and between sequences of polygonal numbers present an opportunity for students to analyze, represent, and generalize relationships. Materials, objectives, levels, and directions for this activity are discussed. Worksheets to accompany the activities are provided. (CW)