Assessment of teaching quality in a thinking classroom in upper-secondary mathematics

Reflection on teaching practices in an upper-secondary school

Abstract

Thinking classroom (Liljedahl, 2020) is a teaching methodology that revolves around creating a space where thinking is required, a space where students engage in tasks to build up understanding of new concepts and ideas, a space where students seek understanding through dialogue with peers and the teacher. In this research, the teaching of one mathematics teacher in an Icelandic upper-secondary school was observed. The objective of this research was to provide the teacher with feedback on the quality of his own teaching when teaching according to the methodology of a thinking classroom in mathematics education and to gain insight into the teacher’s self-reflection on the results. This research was conducted collaboratively by a teacher and an external researcher, combining both action research (where the teacher investigated his own practice) and a classroom study (which the external researcher implemented).

In mathematics education in both upper- and lower-secondary schools, traditional teaching methods prevail, where instruction begins with the teacher’s input, followed by individual student practice and exercises based on that input (Anna Helga Jónsdóttir et al., 2014; Ingvar Sigurgeirsson et al., 2018; Þóra Þórðardóttir & Unnar Hermannsson, 2012). Emphasis is placed on individual work, and on learning specific methods to solve particular types of problems (Birna Svanbjörnsdóttir et al., 2023; Guðný Helga Gunnarsdóttir & Guðbjörg Pálsdóttir, 2015; Savola, 2010). These methods seem to lead to a lack of focus on critical thinking, understanding, discussions, and reasoning (Anna Helga Jónsdóttir et al., 2014). Teachers sometimes struggle to maintain standards of analytical thinking during class, and it is common for them to reduce the challenge of activities (Jóhann Örn Sigurjónsson & Berglind Gísladóttir, 2020).

Thinking classroom, however, presents an alternative to traditional teaching methods. It emphasises collaboration among students in small groups of two to three, all working on the same task. The focus shifts to thinking, understanding, and student autonomy. Students actively seek information and support from their peers, and the teacher asks thought-provoking questions to stimulate their thinking.

Data were collected with audio recordings and observations during three mathematics lessons with a group of upper-secondary school students. These lessons were part of a course covering integration, differential equations, sequences, and series. Thirteen to fourteen students attended each lesson, ranging in age from 17 to 22. The mathematics teacher in this study began teaching according to the methodology of thinking classroom two years prior. During data collection, the teacher taught according to the first three toolkits of four in a thinking classroom.

Quality of teaching was evaluated using the PLATO framework (Grossman, 2015), using two of its overarching factors: disciplinary demand and instructional scaffolding. Under disciplinary demand, subcategories include intellectual challenge and classroom discourse. Instructional scaffolding encompasses modelling and use of models, feedback, and strategy use and instruction.

Key findings reveal that disciplinary demand was generally scored at higher levels. However, instructional scaffolding factors were evaluated at both higher and lower levels. Examples of modelling and use of models, and strategy use and instruction were observed at the highest level while feedback never scored at the highest level.

These results demonstrate that thinking classroom can be effectively used in the Icelandic context to create a learning environment where students collaboratively tackle challenging tasks that encourage analytical thinking. The teacher had the flexibility to request explanations and reasoning, thus giving students the opportunity to deepen their understanding of the task and the solution process. Discussions were based on students’ responses, allowing opportunities for explanation and active listening. Thinking classroom seems to provide good opportunities for feedback, which the teacher could have taken better advantage of. The feedback provided was often brief praise where deeper explanations were needed so that students would see their strengths and weaknesses in their work or solutions. The results highlight the potential of group discussions after students work with mathematical concepts rather than more traditional approaches that introduce concepts before students work on them. Results show that in these group discussions both modelling and classroom discourse scored at the highest level.

It should be noted that this study is based on a single group of students taught by one teacher and an active teaching method was used, which could potentially be assumed to align well with some of the assessment criteria that were used. The student group was small and consisted of students who had chosen a study programme that requires mathematics courses on calculus. Therefore, the generalisability of the results is limited but, for an Icelandic school context, it serves as an existence proof (Schoenfeld, 2007).