Given the importance of modelling in mathematics classrooms, and despite the extensive body of research on teacher support for promoting the mathematical modelling cycle in the classroom, authors have overlooked how teacher support for argumentation can contribute to this cycle. This study is aimed at characterizing teacher support for…

The Verhulst model can be used to forecast the sequence, which is characterized as non-monotone and fluctuant sequence or saturated S-form sequence. According to the situation of national enrollment scale of college, this paper forecasts the quantity of students taking entrance examination to college with a Verhulst model with remedy based on data…

Several varieties of perceptual independence are investigated, including sampling independence, dimensional orthogonality, stimulus separability and integrality, and performance parity. A general multivariate perceptual theory is developed, and a precise definition of perceptual independence is offered. (Author/LMO)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

The stochastic interactive activation and competition (SIAC) model of perception is presented and tested using several data sets from previous research. The asymptotic predictions of the SIAC model are compared with those of the fuzzy logical model of perception (FLMP). Evidence favoring the FLMP is reviewed. (SLD)

A technique and mathematical model--the "Catch Model"--for identifying a face previously seen are presented. Three experiments, involving a total of 38 American and 30 Israeli college students, supported the model for identification of a target face. Practical implications are discussed. (SLD)

A visual model of fractions, the tower of bars, is used to discover patterns. Examples include equalities, inequalities, sums of unit fractions, sums of differences, symmetry, and differences and products. Infinite sequences of numbers, infinite series, and concepts of limits can be introduced. (DC)

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)

Described is a learning activity that requires students to observe, read, and interpret graphs and organize and describe data. Included are the grade level, materials, objectives, prerequisites, directions, answers to questions, and copies of handouts. (KR)

Discusses the use of computer visualization to motivate and support mathematical dialogues. Describes the "Scientific Visualization Software Suite," a set of public domain visualization tools from the National Center for Supercomputing Applications. (Author/MDH)