How pedagogical content knowledge sharpens prospective teachers’ focus when judging mathematical tasks: an eye-tracking study

IF 3.4 2区教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH Educational Studies in Mathematics Pub Date : 2023-12-19 DOI:10.1007/s10649-023-10281-6

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Abstract

Teachers’ ability to accurately judge difficulties of mathematical tasks is an essential aspect of their diagnostic competencies. Although research has suggested that pedagogical content knowledge (PCK) is positively correlated with the accuracy of diagnostic judgments, experimental studies have not been conducted to investigate how PCK affects perception and interpretation of relevant task characteristics. In an intervention study with a control group, 49 prospective mathematics teachers judged the difficulty of 20 tasks involving functions and graphs while an eye tracker tracked their eye movements. Some of the tasks included characteristics well known to be difficult for students. Participants’ domain-specific PCK of typical student errors was manipulated through a three-hour intervention, during which they learned about the most common student errors in function and graph problems. We found that the process of perception (relative fixation duration on the relevant area in the tasks) was related to judgment accuracy. Pre-post comparisons revealed an effect of the intervention not only on participants’ domain-specific PCK of typical student errors but also on their perception and interpretation processes. This result suggests that domain-specific PCK of typical student errors allowed participants to focus more efficiently on relevant task characteristics when judging mathematical task difficulties. Our study contributes to our understanding of how professional knowledge makes teachers’ judgment processes of mathematical tasks more efficient.

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教学内容知识如何使准教师在判断数学任务时更加专注：一项眼动追踪研究

摘要教师准确判断数学任务难度的能力是其诊断能力的一个重要方面。尽管有研究表明，教学内容知识（PCK）与诊断判断的准确性呈正相关，但尚未开展实验研究来探讨 PCK 如何影响对相关任务特征的感知和解释。在一项有对照组的干预研究中，49 名未来的数学教师在眼动跟踪器跟踪下对 20 个涉及函数和图形的任务的难度进行了判断。其中一些任务包括众所周知对学生来说比较困难的特征。通过三小时的干预，学员们了解了学生在函数和图形问题中最常见的错误，从而操纵了他们对学生典型错误的特定领域 PCK。我们发现，感知过程（任务中相关区域的相对固定时间）与判断准确性有关。前后比较显示，干预不仅对参与者关于典型学生错误的特定领域 PCK 有影响，而且对他们的感知和解释过程也有影响。这一结果表明，对典型学生错误的特定领域 PCK 使参与者在判断数学任务难度时更有效地关注相关任务特征。我们的研究有助于我们理解专业知识如何使教师对数学任务的判断过程更有效率。

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来源期刊

Educational Studies in Mathematics EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

5.60

自引率

9.40%

发文量

期刊介绍： Educational Studies in Mathematics presents new ideas and developments of major importance to those working in the field of mathematics education. It seeks to reflect both the variety of research concerns within this field and the range of methods used to study them. It deals with methodological, pedagogical/didactical, political and socio-cultural aspects of teaching and learning of mathematics, rather than with specific programmes for teaching mathematics. Within this range, Educational Studies in Mathematics is open to all research approaches. The emphasis is on high-level articles which are of more than local or national interest.? All contributions to this journal are peer reviewed.