Functions and graphs are fundamental mathematical concepts in mathematics and are vital to helping students comprehend the relationship between variables and other advanced topics in higher-level mathematics. Research has shown that students continually possess misconceptions and inaccurate thinking about functions and function representations.…

Research shows that though some students can easily find the correct solutions to the problem(s) at hand, the algorithms that these students create are not always ones that would, when implemented, produce the correct solution(s). Towards shedding light on this phenomenon, the present study explicates a mechanism--accounting for features of the…

The Dijkstra's algorithm is an algorithm that determines the shortest paths needed to go from a starting node to any node in a graph. In this article, the process and results of an activity that included route formation among the provinces in the Aegean region using Dijkstra's algorithm are shared. The activity was designed based on a mathematical…

The purpose of this study was to investigate the misperceptions and performance of king Saud University students' about concept and finding the limit of same partial functions given in the form of both graphical and symbolic. In the collection of the data, the researcher employed the open-ended question test consisted of four items. Firstly,…

Participants were pretrained and tested on mutually entailed trigonometric relations and combinatorially entailed relations as they pertained to positive and negative forms of sine, cosine, secant, and cosecant. Experiment 1 focused on training and testing transformations of these mathematical functions in terms of amplitude and frequency followed…

Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)

Provides an activity as an example of how matrices can be introduced from finite graphs and how finite graphs can be analyzed by examining their matrix representations. Presents the materials, objectives, prerequisites, directions, extension activities, answers, and worksheets. (YP)

Describes a five-step graphing method for various trigonometric periodic functions. Emphases is on teaching constants and functions. (YP)

This project aimed to quantitatively measure the ability of first year science students to transfer their mathematical skills and knowledge to a physical context. An instrument used in earlier studies to measure transfer of mathematical knowledge was modified for this project, and tested with 49 student volunteers. This paper presents the Transfer…

Solves the problem of defining a smooth piecewise linear approximation to a given function. Discusses some alternative approaches to the problem. (YP)

Outlines differences between classical statistics and exploratory data analysis. Provides examples in the use of the exploratory techniques. (YP)

Discussed are assumptions about technology and classroom equipment, teaching methods, getting started, pitfalls, and the role of algebra and calculus. Suggestions are given for implementing the spirit and vision of the standards. (YP)

Discusses the use of the symbolic manipulator which helps students solve equations one step at a time. Recommends features to look for in algebra tools. Compares 14 programs on general, graphic, numeric, and symbolic manipulation and provides short reviews of each. (MVL)