Expert Blind Spot in Pre-Service and In-Service Mathematics Teachers: Task Design moderates Overestimation of Novices' Performance

Expert Blind Spot in Pre-Service and In-Service Mathematics Teachers: Task Design moderates Overestimation of Novices’ Performance Katharina Hellmann (katharina.hellmann@ezw.uni-freiburg.de) Matthias Nuckles (matthias.nueckles@ezw.uni-freiburg.de) University of Freiburg, Department of Educational Science, Instructional and School Research Rempartstrase 11, 79098 Freiburg, Germany Abstract To act efficiently in the classroom, teachers need to be able to judge the difficulty of problems from a novice’s perspective. However, research suggests that experts use their own knowledge as an anchor, adjust estimations for others to their own knowledge and thus underestimate the difficulty that a problem may impose on novices. Similarly, experts should underestimate the benefit for novices of task designs derived from Cognitive Load Theory (CLT), as – following the expertise reversal effect – these should be rather disadvantageous for experts. We investigated pre-service and in-service teachers’ competencies in estimating the difficulty of mathematical tasks for novices. Thirty-four pre-service teachers and thirteen experienced teachers solved tasks that varied in instructional design (optimized for novices following CLT versus non-optimized). Participants solved each task and then estimated how many students of a fictional 9 th grade class would be able to solve that task. Solution frequencies were collected from fifty-two 9 th grade students. In both expert groups, overestimation was clearly more pronounced for non-optimized than optimized tasks, suggesting an expert blind spot that can be explained in terms of an expertise-reversal effect. The experts failed to adequately take into account the benefits of didactic task variation for novice learners. However, whereas pre-service teachers’ overestimations of student performance were large and significant both for non-optimized and optimized tasks, in-service teachers’ overestimations were generally small and failed to approach statistical significance. In contrast to pre- service teachers, in-service teachers seem to have a better mental model of what a student is able to achieve, thus making better judgments of student performance. Keywords: expert blind spot; perspective taking; expertise reversal effect. Theoretical Background Expert Blind Spot Peoples’ judgements of others are very often based on their self-assessment and are therefore cognitively biased (e.g. Tversky & Kahneman, 1974). In line with this, research in the area of expertise has repeatedly shown that experts tend to misjudge novices’ knowledge, achievement, or time on task, amongst others, to a certain degree (e.g. Herppich, Wittwer, Nuckles & Renkl, 2010; Hinds, 1999; Lentz & de Jong, 2006). This effect has also been found to apply to teachers (e.g. Nathan & Koedinger, 2000). Teachers, usually referred to as being domain experts in their content area, as they possess a high level of specialized knowledge, are considered to be prone to an expert blind spot (Nathan & Petrosino, 2003) when evaluating the difficulty of mathematical problems for students. Following Nickerson’s (1999) anchoring model, teachers may be inclined to use their specialized knowledge as an anchor when assessing the difficulty of problems for students. As a result, they are not able to take the student perspective adequately. Figure 1: The process of perspective taking through anchoring and adjustment (adapted from Nickerson, 1999) According to Nickerson (1999, see Figure 1), people tend to build an inaccurate mental model of the potential knowledge of general or specific others. They fail to take into account the specificity or exclusivity of their own knowledge, therefore unconsciously using it as an anchor when estimating other persons’ knowledge. As a result, teachers might underestimate the difficulty that a problem will impose on a student, and overestimate students’ performance. However, the ability to adequately assess the difficulty of tasks for students is a crucial aspect of teaching expertise. It is necessary for communicating efficiently with students as well as for adapting teaching behaviour in and outside the classroom (e.g. selecting problems for homework, lessons or exams). Teachers should be able to take a novice’s perspective and judge task attributes independently of their own perception of difficulty or effortlessness (Helmke, Hosenfeld & Schrader, 2004). Cognitive Load Theory Cognitive Load Theory (CLT; e.g. Sweller, 2005; Sweller, van Merrienboer & Paas, 1998) can help to understand how and why experts and novices differ in their perceptions of