Identifying key visual-cognitive processes in students’ interpretation of graph representations using eye-tracking data and math/machine learning based data analysis

We present a mathematical and computational analysis, partially based on machine learning techniques, of the visual scan-paths obtained during a graph interpretation task which allows us to identify when the problem solver succeeds in solving the problem with a fair degree of accuracy, and helps to understand the visual-cognitive processes at work during the problem solving task.Peer reviewe

Scanning Signatures: A Graph Theoretical Model to Represent Visual Scanning Processes and A Proof of Concept Study in Biology Education

In this article we discuss, as a proof of concept, how a network model can be used to analyse gaze tracking data coming from a preliminary experiment carried out in a biodiversity education research project. We discuss the network model, a simple directed graph, used to represent the gaze tracking data in a way that is meaningful for the study of students’ biodiversity observations. Our network model can be thought of as a scanning signature of how a subject visually scans a scene. We provide a couple of examples of how it can be used to investigate the personal identification processes of a biologist and non-biologist when they are carrying out a task concerning the observation of species-specific characteristics of two bird species in the context of biology education research. We suggest that a scanning signature can be effectively used to compare the competencies of different persons and groups of people when they are making observations on specific areas of interests

Scanning Signatures: A Graph Theoretical Model to Represent Visual Scanning Processes and A Proof of Concept Study in Biology Education

In this article we discuss, as a proof of concept, how a network model can be used to analyse gaze tracking data coming from a preliminary experiment carried out in a biodiversity education research project. We discuss the network model, a simple directed graph, used to represent the gaze tracking data in a way that is meaningful for the study of students’ biodiversity observations. Our network model can be thought of as a scanning signature of how a subject visually scans a scene. We provide a couple of examples of how it can be used to investigate the personal identification processes of a biologist and non-biologist when they are carrying out a task concerning the observation of species-specific characteristics of two bird species in the context of biology education research. We suggest that a scanning signature can be effectively used to compare the competencies of different persons and groups of people when they are making observations on specific areas of interests

Editorial : Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers

This LUMAT special issue is a collection of selected papers from the 24th international conference of mathematical views that was held on August 20–22, 2018 in Helsinki, Finland. The conference was a wonderful opportunity to elaborate issues related to mathematics-related affect among colleagues interested in this area of research. The keynote at the conference was given by Reinhard Pekrun with a title: “Achievement emotions in mathematics”. Out of the 25 conference presentations, 12 were submitted as a manuscript for peer review. We had one reviewer selected among MAVI 24 participants, and another reviewer was invited among mathematics affect researchers who were not at the conference. After the review and revisions, we ended up with eight articles that you can read in this special issue.Non peer reviewe

Application of mathematical and machine learning techniques to analyse eye tracking data enabling better understanding of children’s visual cognitive behaviours

In this research, we aimed to investigate the visual-cognitive behaviours of a sample of 106 children in Year 3 (8.8 ± 0.3 years) while completing a mathematics bar-graph task. Eye movements were recorded while children completed the task and the patterns of eye movements were explored using machine learning approaches. Two different techniques of machine-learning were used (Bayesian and K-Means) to obtain separate model sequences or average scanpaths for those children who responded either correctly or incorrectly to the graph task. Application of these machine-learning approaches indicated distinct differences in the resulting scanpaths for children who completed the graph task correctly or incorrectly: children who responded correctly accessed information that was mostly categorised as critical, whereas children responding incorrectly did not. There was also evidence that the children who were correct accessed the graph information in a different, more logical order, compared to the children who were incorrect. The visual behaviours aligned with different aspects of graph comprehension, such as initial understanding and orienting to the graph, and later interpretation and use of relevant information on the graph. The findings are discussed in terms of the implications for early mathematics teaching and learning, particularly in the development of graph comprehension, as well as the application of machine learning techniques to investigations of other visual-cognitive behaviours.Peer reviewe

Phases of collaborative mathematical problem solving and joint attention : a case study utilizing mobile gaze tracking

Given the recent development of mobile gaze-tracking devices it has become possible to view and interpret what the student sees and unravel the associated problem-solving processes further. It has also become possible to pinpoint joint attention occurrences that are fundamental for learning. In this study, we examined joint attention in collaborative mathematical problem solving. We studied the thought processes of four 15-16-year-old students in their regular classroom, using mobile gaze tracking, video and audio recordings, and smartpens. The four students worked as a group to find the shortest path to connect the vertices of a square. Combining information on the student gaze targets with a qualitative interpretation of the context, we identified the occurrences of joint attention, out of which 49 were joint visual attention occurrences and 28 were attention to different representations of the same mathematical idea. We call this joint representational attention. We discovered that 'verifying' (43%) and 'watching and listening' (35%) were the most common phases during joint attention. The most frequently occurring problem solving phases right after joint attention were also 'verifying' (47%) and 'watching and listening' (34%). We detected phase cycles commonly found in individual problem-solving processes ('planning and exploring', 'implementing', and 'verifying') outside of joint attention. We also detected phase shifts between 'verifying', 'watching and listening', and 'understanding' a problem, often occurring during joint attention. Therefore, these phases can be seen as a signal of successful interaction and the promotion of collaboration.Peer reviewe

Advancing video research methodology to capture the processes of social interaction and multimodality

In this reflective methodological paper we focus on affordances and challenges of video data. We compare and analyze two research settings that use the latest video technology to capture classroom interactions in mathematics education, namely, The Social Unit of Learning (SUL) project of the University of Melbourne and the MathTrack project of the University of Helsinki. While using these two settings as examples, we have structured our reflections around themes pertinent to video research in general, namely, research methods, data management, and research ethics. SUL and MathTrack share an understanding of mathematics learning as social multimodal practice, and provide possibilities for zooming into the situational micro interactions that construct collaborative problem-solving learning. Both settings provide rich data for in-depth analyses of peer interactions and learning processes. The settings share special needs for technical support and data management, as well as attention to ethical aspects from the perspective of the participants' security and discretion. SUL data are especially suitable for investigating interactions on a broad scope, addressing how multiple interactional processes intertwine. MathTrack, on the other hand, enables exploration of participants' visual attention in detail and its role in learning. Both settings could provide tools for teachers' professional development by showing them aspects of classroom interactions that would otherwise remain hidden.Peer reviewe

Exploring collaboration during mathematics problem solving in the classroom with multiple mobile eye tracking

Conference on Embodied Design in Interaction, October 30-31, 2017, Utrecht University, UtrechtNon peer reviewe

Scanning Signatures: A Graph Theoretical Model to Represent Visual Scanning Processes and A Proof of Concept Study in Biology Education

In this article we discuss, as a proof of concept, how a network model can be used to analyse gaze tracking data coming from a preliminary experiment carried out in a biodiversity education research project. We discuss the network model, a simple directed graph, used to represent the gaze tracking data in a way that is meaningful for the study of students’ biodiversity observations. Our network model can be thought of as a scanning signature of how a subject visually scans a scene. We provide a couple of examples of how it can be used to investigate the personal identification processes of a biologist and non-biologist when they are carrying out a task concerning the observation of species-specific characteristics of two bird species in the context of biology education research. We suggest that a scanning signature can be effectively used to compare the competencies of different persons and groups of people when they are making observations on specific areas of interests

Identifying subgroups of CERME affect research papers

Research in mathematics related affect uses a variety of theoretical frameworks. Three different dimensions have been suggested as significant to characterize concepts in this area: (1) emotional, motivational, and cognitive aspects of affect, (2) state and trait aspects of affect, and (3) physiological, psychological, and sociological level of theorizing affect. In this study, we used the information in reference lists and graph theory to identify Graph Communities (coherent clusters) of research papers published in the affect groups of CERME conferences. The four main Graph Communities identified in the analysis were Foundation (beliefs, attitudes, emotions), Self-Efficacy, Motivation, and Teacher Development. There were six smaller Graph Communities that may suggest emerging new frameworks: Academic Emotions, Metacognition, Teacher Beliefs, Resilience, Meaning, and Identity. These results suggest that of the three possible dimensions to structure the area, the distinction between cognition (beliefs), motivation, and emotions is the most important one.Peer reviewe