What can we learn by comparing students' diagram-construction processes with the mathematical conceptions inferred from their explanations with completed diagrams? (original) (raw)

Science and engineering students’ use of diagrams during note taking versus explanation

Educational Studies, 2013

The use of diagrams in learning and communication is generally considered efficacious and an important skill to cultivate, especially among science students. At the same time, previous research has revealed many problems in student diagram use, including a lack of spontaneity in such use, but the extent to which these problems persist into the tertiary level had not been investigated. The present study examined science and engineering university students’ use of diagrams in note taking to learn information from a written passage, and in a subsequent task of constructing an explanation of that information for another person. The results showed that the students used significantly fewer diagrams in explaining compared to when they were note taking, suggesting that many students may lack awareness of the usefulness of diagrams in effectively communicating information to others. The results also revealed that the students used significantly more diagrams in taking notes from and explaining a passage with higher imageability (i.e. easier to visually imagine) compared to one with lower imageability. Educational implications of the findings are discussed.

Mental Representations of Diagrams, Views about Diagrams, and Problem Solving

palm.mindmodeling.org

This study investigated people's mental representations of diagrams and whether these related to views about diagrams and problem solving performance. The participants were 93 undergraduate students who were asked to complete a questionnaire which included free writing on the topic of diagrams, and problem solving. Analysis of the statements and ideas that the students wrote revealed four categories through which diagrams may be mentally represented: uses/purposes, exemplars, personal opinions, and structure. Personal opinions responses were found to negatively correlate with views about the usefulness of diagrams, and with experiences and confidence in using diagrams. In contrast, responses about the uses/purposes of diagrams positively correlated with confidence in using diagrams. Evidence was also found suggesting that, among students studying math, greater knowledge about the uses/purposes of diagrams facilitated better problem solving performance.

To use or not to use diagrams: The effect of drawing a diagram in solving introductory physics problems

AIP Conference Proceedings, 2013

Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solution. We conducted an investigation in which 111 students in an algebra-based introductory physics course were subjected to two different interventions during recitation quizzes throughout the semester. They were either (1) asked to solve problems in which the diagrams were drawn for them or (2) explicitly told to draw a diagram. A comparison group was not given any instruction regarding diagrams. We developed a rubric to score the problem-solving performance of students in different intervention groups. We investigated two problems involving electric field and electric force and found that students who draw expert-like diagrams are more successful problem solvers and that a higher level of detail in a student's diagram corresponds to a better score.

A Practice-Based Approach to Diagrams

Visual Reasoning with Diagrams, 2013

In this article, I propose an operational framework for diagrams. According to this framework, diagrams do not work like sentences, because we do not apply a set of explicit and linguistic rules in order to use them. Rather, we become able to manipulate diagrams in meaningful ways once we are familiar with some specific practice, and therefore we engage ourselves in a form of reasoning that is stable because it is shared. This reasoning constitutes at the same time discovery and justification for this discovery. I will make three claims, based on the consideration of diagrams in the practice of logic and mathematics. First, I will claim that diagrams are tools, following some of Peirce's suggestions. Secondly, I will give reasons to drop a sharp distinction between vision and language and consider by contrast how the two are integrated in a specific manipulation practice, by means of a kind of manipulative imagination. Thirdly, I will defend the idea that an inherent feature of diagrams, given by their nature as images, is their ambiguity: when diagrams are 'tamed' by the reference to some system of explicit rules that fix their meaning and make their message univocal, they end up in being less powerful.

Cognitive Factors and Representation Strategies In Sketching Math Diagrams

2015

Previous research has shown sketching to be useful to students solving math problems. The present study examines which aspects of middle school students’ sketching are related to, or predict, successfully answering math problems. The effects of individual differences in cognitive factors – working memory, spatial ability, and prior math knowledge – on answer accuracy are also analyzed. Stepwise regression analysis indicates that prior math knowledge and the inclusion of numerical representations of key problem relationships in sketches positively predict answer accuracy, whereas including irrelevant relationships in a sketch is associated with lower answer accuracy. Methodological implications for future research are discussed.

Diagrams in Mathematics: To Draw or Not to Draw?

2012

This paper describes the use of diagrams as self-explanatory tools. It considers the use of diagrams, in general, and more specifically, examines research that is currently being undertaken in the broad field of visualisation. The research participants referred to in this article were Advanced Certificate of Education students and the paper attempts to analyse their responses to questions based on simple area problems in mathematics. The outcome of this research underscores the strategic use of diagrams when dealing with problem solving. While this is an ongoing research project, the paper attempts to capture the current status of research on the use of diagrams.

Diagrams in Essays: Exploring the Kinds of Diagrams Students Generate and How Well They Work

Diagrammatic Representation and Inference

Using appropriate diagrams is generally considered efficacious in communication. However, although diagrams are extensively used in printed and digital media, people in general rarely construct diagrams to use in common everyday communication. Furthermore, instruction on diagram use for communicative purposes is uncommon in formal education and, when students are required to communicate what they have learned, the usual expectation is they will use words – not diagrams. Requiring diagram inclusion in essays, for example, would be almost unheard of. Consequently, current understanding about student capabilities in this area is very limited. The aim of this study therefore was to contribute to addressing this gap: it comprised a qualitative exploration of 12 undergraduate students’ diagram use in two essays (in which they were asked to include at least one diagram). Analysis focused on identifying the kinds of diagrams produced, and the effectiveness with which those diagrams were use...