For mathematics teaching to be considered of good quality, it is necessary to uphold a certain level of cognitive activation and academic rigour in the classroom. In the PLATO framework, intellectual challenge captures „the academic rigour of activities, assignments and teacher questions“ (Grossman, 2019, p. 32). One of the challenges that arise when analysing this teaching quality element from video is when students are working individually on problem sets in textbooks, either in silence or with indistinguishable chatter. This textbook-work instructional pattern is the most common one in mathematics classrooms in Iceland according to previous reports on the lower and upper secondary level (Jónsdóttir et al., 2014; Þórðardóttir & Hermannsson, 2012). The same instructional pattern was commonly found in the video data for this study. It is, however, a challenge to measure cognitive activation in classrooms where activities and assignments are not made explicit in whole-class instruction, but strictly referred to as numbered problems in textbooks. To address this challenge in obtaining an accurate measure of cognitive activation, not only must the teacher questions be analysed from the video data, but also the tasks themselves that students are set to be solving in the lesson. Results are presented from a study where the cognitive demand of mathematical tasks was analysed in addition to the coding of video data according to the PLATO framework. Employed in this study was the Task Analysis Guide, in which mathematical tasks are divided into four categories: two of low cognitive demand and two of high cognitive demand (Stein, 2009). This multi-layered approach has both strengths and weaknesses. The weakness to this approach is that it still does not measure what students notice and direct attention to when working silently. However, its strength is that it does measure the cognitive demand of tasks that the teacher chooses for the students to engage in as well as the volume of tasks. To include an analysis of tasks in addition to analysis of classroom activity observable from video provides important contextual information for a more thorough and reliable measure of cognitive activation in the classroom. The results reveal opportunities for further research and additional methodological challenges to be addressed.

Grossman, P. (2019). PLATO 5.0: Training and Observation Protocol. Stanford, CA: CSET. Jónsdóttir, A. H., Briem, E., Hreinsdóttir, F., Þórarinsson, F., Magnússon, J. I., & Möller, R. G. (2014). Úttekt á stærðfræðikennslu í framhaldsskólum. Reykjavík. Stein, M. K. (2009). Implementing standards-based mathematics instruction: A casebook for professional development (2nd ed.). Reston, VA: National Council of Teachers of Mathematics. Þórðardóttir, Þ., & Hermannsson, U. (2012). Úttekt á stærðfræðikennslu á unglingastigi grunnskóla. Reykjavík.