<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>An important aspect of mathematics teachers’ diagnostic competences is the ability to judge the difficulty of a mathematical task. The process of judging task difficulty includes the perception and interpretation of task characteristics that are potentially challenging for students. Such judgement processes are often quick and difficult to assess. Most previous studies described these processes on the basis of teachers’ verbal reports. A more recent approach to tap into cognitive processes is eye tracking. However, there is no firm knowledge yet whether eye tracking allows for a reliable assessment of teachers’ judgements of mathematical task difficulty. The present study aims at filling this gap. We asked <italic>N</italic> = 55 prospective mathematics teachers to judge the difficulty of 20 tasks on linear functions, some of which included characteristics that are well known to be challenging for students. Participants viewed the tasks on a computer screen while their eye movements were recorded with an eye tracker. Our analyses of various eye-tracking parameters suggest that “fixation duration”, “fixation duration average” and “number of fixations” were the most reliable measures of participants’ perception and interpretation processes across a set of tasks. These measures were also correlated with participants’ judgement accuracy. Using qualitative analyses of two participants’ eye-tracking data, we illustrate when and how they processed the relevant task characteristics. In conclusion, eye tracking may be considered a suitable method for assessing how teachers detect task difficulty. We discuss implications for the use of eye tracking in further research on teachers’ diagnostic competences.</p>
</abstract>

An important aspect of mathematics teachers’ diagnostic competences is the ability to judge the difficulty of a mathematical task. The process of judging task difficulty includes the perception and interpretation of task characteristics that are potentially challenging for students. Such judgement processes are often quick and difficult to assess. Most previous studies described these processes on the basis of teachers’ verbal reports. A more recent approach to tap into cognitive processes is eye tracking. However, there is no firm knowledge yet whether eye tracking allows for a reliable assessment of teachers’ judgements of mathematical task difficulty. The present study aims at filling this gap. We asked N = 55 prospective mathematics teachers to judge the difficulty of 20 tasks on linear functions, some of which included characteristics that are well known to be challenging for students. Participants viewed the tasks on a computer screen while their eye movements were recorded with an eye tracker. Our analyses of various eye-tracking parameters suggest that “fixation duration”, “fixation duration average” and “number of fixations” were the most reliable measures of participants’ perception and interpretation processes across a set of tasks. These measures were also correlated with participants’ judgement accuracy. Using qualitative analyses of two participants’ eye-tracking data, we illustrate when and how they processed the relevant task characteristics. In conclusion, eye tracking may be considered a suitable method for assessing how teachers detect task difficulty. We discuss implications for the use of eye tracking in further research on teachers’ diagnostic competences.

How prospective teachers detect potential difficulties in mathematical tasks – an eye tracking study

Research in Subject-matter Teaching and Learning (RISTAL)

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.

An important aspect of mathematics teachers’ diagnostic competences is the ability to judge the difficulty of a mathematical task. The process of judging task...

How prospective teachers detect potential difficulties in mathematical tasks – an eye tracking study

Published Online: Jul 11, 2022

Page range: 109 - 126

DOI: https://doi.org/10.23770/rt1845

Keywords
Diagnostic competences, diagnostic processes, judgement, eye tracking, functions and graphs, typical student errors

© 2021 Kirsten Brunner et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.

How prospective teachers detect potential difficulties in mathematical tasks – an eye tracking study

Published Online: Jul 11, 2022

Page range: 109 - 126

DOI: https://doi.org/10.23770/rt1845

KeywordsDiagnostic competences, diagnostic processes, judgement, eye tracking, functions and graphs, typical student errors

© 2021 Kirsten Brunner et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords
Diagnostic competences, diagnostic processes, judgement, eye tracking, functions and graphs, typical student errors