Intellectual Challenge In Mathematics Teaching In Lower Secondary Schools

The aim of this study was to assess the level of intellectual challenge offered to students in lower secondary mathematics in Iceland as it appears in mathematical tasks and in the enactment of tasks in the classroom. The national curriculum explicitly states that students should learn to explain their thoughts to others and engage with mathematical tasks in which both critical and analytical thinking is required (Mennta- og menningar-malaraouneytio, 2012 (Ministry of Education, Science and Culture). Previous research has shown that teachers generally have a positive view towards cognitively demanding tasks, but such tasks are scarce in Icelandic textbooks (Johann Orn Sigurjonsson & Jonina Vala Kristinsdottir, 2018). How teachers enact tasks in the classroom with the aim of developing students' competency in critical and creative thinking has not been the object of much study in Iceland.Ten Icelandic lower secondary schools participated in the study. Schools were purposefully chosen with the aim of establishing heterogeneity of the sample and included different school types in terms of location, size, and students ' background. Three to four consecutive mathematics lessons were video recorded in 8th grade in each school, in total 34 lessons. Two frameworks were used to analyse the data. The Protocol for Language Arts Teaching Observations (PLATO) was used to analyse the level of intellectual challenge offered to students in the classroom on a 4-point scale in 15 minute segments (Bell et al., 2019; Grossman, 2019). The Task Analysis Guide (TAG), was used to analyse whether the solution of mathematical tasks required analytical thinking (Stein et al., 2009).For the study 144 mathematical tasks were analysed. The tasks were identified from both the videos and lesson plans. Findings showed that the majority of tasks involved procedures without connections to underlying mathematical concepts, or 64%. The tasks that involved procedures with connections counted 33% and only four tasks were in the highest category and involved doing mathematics or 3%. No tasks were in category 1 that involves only memorization.In a majority of segments, or 63%, intellectual challenge was at the 2-level which indicates limited evidence of intellectually challenging activities. A common reason for segments scoring at the 2-level was that teachers reduced the challenge of activities in their assistance to students. Teachers commonly told students exactly how to solve tasks and, in some cases, told them the answers. About 20% of segments scored at the 3 or 4-level, which require teachers to provide activities that to some extent prompt high level analytic and inferential thinking. Only in two schools did the intellectual challenge of activities reach the 4-level in some segments. In those cases, teachers advanced the intellectual challenge by asking students questions where explanation and reasoning was emphasized to develop conceptual understanding.The results show that mathematics teaching in Iceland focuses mostly on tasks where procedures for how to solve the tasks are either fully explained by the teacher or by examples in the learning materials. In lessons where intellectual challenge was found to be at a high-level, students worked in pairs and the whole class was working on the same tasks, giving room for mathematical discussions among students. However, in a large portion of the observed lessons, students worked individually on a variety of different tasks at their own pace with limited interactions with other students.The findings of this study indicate that there are opportunities to improve intellectual challenge in mathematics teaching in Icelandic classrooms by organizing lessons with specific tasks or learning goals in mind. Such a lesson structure seems to create richer opportunities for student reasoning and explanations. Lessons where the goal is to develop procedural fluency, for example in solving equations and simplifying expressions, may be of some benefit to students but it is imperative to place emphasis on conceptual understanding. The results of this study and previous studies on mathematics teaching in Iceland show that too much time is devoted to procedural lessons at the cost of critical thinking, intellectual challenge and classroom discourse.