This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

In this study, we examined graphical representations in several mathematics, science, and engineering textbooks and practitioner journals with the goal of identifying similarities and differences across these sources. To do this, we drew from the extant research on students interpreting graphs and reasoning covariationally to develop a framework…

In March 2020, near the onset of the COVID-19 related lockdowns, quarantine, and isolation measures being taken worldwide, we noticed an increasing number of graphs, diagrams, images and mathematical models relating to the pandemic posted on our Facebook walls. For the purposes of this paper, we selected a number of these Facebook posts to discuss…

The ability to use numerical information in different contexts is a major goal of mathematics education. In health risk communication, outcomes of a medical condition are frequently expressed in probabilities. Difficulties to accurately represent probability information can result in unfavourable medical decisions. To support individuals with…

This article comments on mathematics textbooks for lower secondary schools. Authors do not focus on texts in the books but on the nonverbal elements instead. A possible system of categories which enables mapping and classifying of such elements is suggested in this article. As a result of that, it is possible to evaluate and compare the textbooks…

This paper presents the results of a research, which proposes the introduction of the teaching by Research and Study Paths (RSPs) into Argentinean secondary schools within the frame of the Anthropologic Theory of Didactics (ATD). The paths begin with the study of "Q[subscript 0]: How to operate with any curves knowing only its graphic…

Since ancient times mathematicians and geometricians have used visualisations to describe, discuss, study and teach mathematics. In mathematics education, visualisations are still used whenever possible to support teaching, to inspire students and feed their need to actually see abstract mathematical facts. In our times, virtual reality presents a…

Presents concrete graphing experiences from the United States. (Author/CCM)

Presented are two computer programs which can be used to minimize the effort and time necessary to graph several individual functions. (TG)

Describes the use of glyphs, simple pictures or graphs whose parts represent information about a given subject, in a second-grade classroom. Includes many examples. (MKR)

Differing treatments of graphs in mathematics and science are discussed. A teaching sequence to develop contrasts between real and ideal data is suggested. (MP)

Gives a multi-lesson project exploring multiplication arrays. Students are given opportunities to model multiplication tables with rectangular arrays, develop and extend ideas about patterns, organize and present visual patterns symbolically in tables, and represent visual patterns graphically. (MKR)

A graph is an example of a symbol system which encodes information through the juxtaposition of marks in a two dimensional plane; decoding the meaning of a graph uses specific attributes of the human visual system. This study was undertaken to identify some variables critical to graph interpretation as a first step in designing better curriculum…

Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…