This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We…

The purpose of this paper is to highlight issues related to students' personal inferences that arise when students verbally explain their justification for calculus statements. We conducted clinical interviews with three undergraduate students who had taken first-semester calculus but had not yet been exposed to formal proof writing activities…

Automated scoring of free drawings or images as responses has yet to be used in large-scale assessments of student achievement. In this study, we propose artificial neural networks to classify these types of graphical responses from a TIMSS 2019 item. We are comparing classification accuracy of convolutional and feed-forward approaches. Our…

Graphical model validation techniques for linear normal models are often used to check the assumptions underlying a statistical model. We describe an approach to provide "instant experience" in looking at a graphical model validation plot, so it becomes easier to validate if any of the underlying assumptions are violated.

The maximum power theorem is a useful extension to work on EMF and internal resistance at school level. Furthermore, a very simple physical collision model can be used to show equivalent mathematical patterns to those found with the maximum power theorem and to emphasize fundamental links to ideas of impedance matching. (Contains 2 tables and 6…

This article discusses the role of assessment in a response-to-intervention model. Although assessment represents only 1 component in a response-to-intervention model, a well-articulated assessment system is critical in providing teachers with reliable data that are easily interpreted and used to make instructional decisions. Three components of…

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…

Methods that have been employed in McGill University's (Montreal, Quebec) program of research into the nature of learning are described. The methods illustrate four phases of inquiry: conceptualization or model-building; data gathering techniques; data representation; and data analysis. For the university's learning task project, the development…

This document presents the proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of this conference is "Navigating Currents and Charting Directions." The theme reminds us that, although we are constantly pushed to account for the quality and impact of our research, we…