Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

This paper shows how the variance and standard deviation can be represented graphically by looking at each squared deviation as a graphical object--in particular, as a square. A series of displays show how the standard deviation is the size of the average square.

Used software environment to examine algebra students' attempts to reformulate narratives using verbal and iconic lexical sets. Described how natural language text turns into a script of events and processes, how the qualitative graphic description of the script is sketched using iconic notations, and how the graph turns into a subject for…

In this paper, we give a detailed account of the design principles and construction of activities designed for learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. Our approach is model-based, that is, it focuses attention on the idea that students constructed their own models--in the…

This article examines a "calculus graphing schema" and the triad stages of schema development from Action-Process-Object-Schema (APOS) theory. Previously, the authors studied the underlying structures necessary for students to process concepts and enrich their knowledge, thus demonstrating various levels of understanding via the calculus…

This study reports the cognitive processing of a Year 8 female student (Kerri) during a test, and during her subsequent homework as she consolidated as part of abstracting; a topic of recent research interest. This case adds to the body of knowledge about how constructing and consolidating can occur simultaneously. The analysis captured the…

Examines bar models as graphical representations of rational numbers and presents related real life problems. Concludes that, through pairing the fraction bars with ratio tables and other ways of teaching numbers, numeric strategies become connected with visual strategies that allow students with diverse ways of thinking to share their…

U.S. mathematics education has been criticized for being too broad. This article examines ways middle school students use simple problems and situations to foster a deeper understanding of underlying concepts. Presents a sample area and perimeter problem, describes extending the problem using tiles to determine minimum perimeter, and discusses…

This report summarizes the work of a two-year project which focused primarily on the problems that students have with algebra in general, and graphs in particular. The first of two major sections in the document deals with the use of computer software to assist in the teaching of graphing. It concludes that thoughtful design and use of graphing…

A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…