The ability to generalize previous knowledge to new contexts is a key aspect of human cognition and relational learning. A well-known learning maxim is that breadth of training predicts "breadth of training predicts breadth of transfer." When examples vary in their surface features, this provides evidence that only the common relational…

Recent research seeks to develop more comprehensive learner models for adaptive learning software. For example, models of reading comprehension built using data from students' use of adaptive instructional software for mathematics have recently been developed. These models aim to deliver experiences that consider factors related to learning beyond…

We explore how different components of an Automatic Short Answer Grading (ASAG) model affect the model's ability to generalize to questions outside of those used for training. For supervised automatic grading models, human ratings are primarily used as ground truth labels. Producing such ratings can be resource heavy, as subject matter experts…

Automatic short answer grading is an important research direction in the exploration of how to use artificial intelligence (AI)-based tools to improve education. Current state-of-the-art approaches use neural language models to create vectorized representations of students responses, followed by classifiers to predict the score. However, these…

Pedestrian skills are important for children with intellectual disabilities to continue their daily lives independently. The aim of this study is to determine the effectiveness of virtual reality in the acquisition and maintenance of pedestrian skills for children with intellectual disabilities. In addition, the effect of virtual reality on…

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…

Structural thinking skills should be developed as a prerequisite for a young person's future mathematical understanding and a teachers' understanding of mathematical structure is necessary to develop students' structural thinking skills. In this study, three secondary mathematics pre-service teachers (PSTs) learned to notice structural thinking…

The development of students' mathematical problem-solving skills is contingent upon the approaches and methods employed by primary school teachers. This research endeavors to scrutinize the effectiveness of primary school teachers in their roles within the problem-solving process, with particular attention directed toward their inquiry techniques,…

Measuring similarity of educational items has several applications in the development of adaptive learning systems, and previous research has already proposed a wide range of similarity measures. In this work, we provide an experimental evaluation of selected similarity measures using a large dataset. The used items are alternate-choice questions…

This study investigated how 155 pre-service teachers solved three pattern generalization problems in a two-part written test and sequenced them for teaching purposes to demonstrate their curricular noticing. Participants' solutions were analyzed using inductive content analysis, which showed that only 8.4% of PSTs produced correct answers to all…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

Computational activity is increasingly relevant in education and society, and researchers have investigated its role in students' mathematical thinking and activity. More work is needed within mathematics education to explore ways in which computational activity might afford development of mathematical practices. In this paper, we specifically…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

In this study, we explored enacted task characteristics (ETCs) that supported students' quantitative reasoning (QR). We employed a design-based methodology; we conducted a teaching experiment with eight secondary school students. Through ongoing and retrospective analyses, we identified ETCs which supported students' quantitative reasoning. The…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…