Teachers’ diagnostic judgment regarding the difficulty of fraction tasks: A reconstruction of perceived and processed task characteristics

The selection and modification of mathematical tasks requires teachers to adequately judge task difficulty. Despite such importance, little is known about teachers’ cognitive processes that underlie these judgments. Considering possible interrelations with teaching experience and specific aspects of PCK/PK, this study reconstructs teachers’ perception and processing of task characteristics while judging task difficulty for students. In the field of fraction calculation, the tasks’ difficulty is varied systematically by modifications in the tasks’ instructional design (according to cognitive load theory; e.g., split-attention vs. integrated format) and by adjusting the fractions’ complexity (e.g., like vs. unlike fractions). The study was conducted with 55 pre- and 35 in-service mathematics teachers. The results suggest that both groups predominantly perceive and process mathematical, but only rarely instructional task characteristics. Contrary to expectations, the findings indicate that participants’ specific PCK/PK concerning difficulty-generating task characteristics is high in both areas – fraction and instructional design.