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Eye tracking is an increasingly popular method in mathematics education. While the technology has greatly evolved in recent years, there is a debate about the specific benefits that eye tracking offers and about the kinds of insights it may allow. The aim of this review is to contribute to this discussion by providing a comprehensive overview of the use of eye tracking in mathematics education research. We reviewed 161 eye-tracking studies published between 1921 and 2018 to assess what domains and topics were addressed, how the method was used, and how eye movements were related to mathematical thinking and learning. The results show that most studies were in the domain of numbers and arithmetic, but that a large variety of other areas of mathematics education research was investigated as well. We identify a need to report more methodological details in eye-tracking studies and to be more critical about how to gather, analyze, and interpret eye-tracking data. In conclusion, eye tracking seemed particularly beneficial for studying processes rather than outcomes, for revealing mental representations, and for assessing subconscious aspects of mathematical thinking.
Mathematics teachers’ motivational and emotional orientations regarding digital tools in mathematics classrooms are key aspects influencing whether and how technology is used to teach mathematics—making the support of those characteristics one central goal for teacher education. In this article we investigated if and how a workshop-based in-service teacher training can foster teachers’ perceived value of digital media in mathematics education, their self-efficacy, and their anxiety towards teaching mathematics with digital tools. In an intervention study with N = 83 in-service teachers with varying teaching experience, we used cluster analysis based on their experience, value, self-efficacy, and anxiety before the intervention to determine three different teacher orientations regarding teaching mathematics with digital tools. Paired sample t-tests with pretest and posttest data revealed that for two of three clusters these beliefs, motivation, and emotions changed in a positive way during the intervention while for the third no change was found. Our study sheds light on the role of motivational and emotional orientations for the implementation of digital tools in mathematics education: it shows that these orientations can be utilized to cluster teachers on this topic and illustrates that these orientations can be successfully fostered—while individual differences may exist in the effect and success of interventions.
Abstract
Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.