Hattie and Timperley (2007) distinguish four levels of feedback messages that address different aspects of students’ learning: task, process, self-regulation and self. This blog post outlines how the four levels are useful for the different steps in mathematical problem-solving and mathematical reasoning.

Figure 1 shows all four levels of feedback and the bubbles give examples of how these are linked to clues about the mathematical reasoning process. Domain-specific feedback can address simple errors in the reasoning process – for example, task feedback: ‘You made a mistake in the calculation.’ Feedback could also involve cueing to guide the search for a better solution or relationship without stating directly the correct answer – for example, process feedback: ‘What step is needed next in the reasoning process?’ Feedback may include comments to students about how they are self-monitoring their progress towards a goal – for example, self-regulation feedback: ‘Have you checked all the steps needed for the argumentation?’ Last, feedback at the self level consists of feedback responses based on the student’s character traits – for example, self feedback: ‘You are an excellent mathematician.’

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Figure 1: Hypothetical relationships between feedback levels, according to Hattie and Timperley (2007), and the steps of mathematical reasoning

According to Hattie and Timperley, the first three levels – task, process, self-regulation – are most beneficial for student learning. Based on observations in English classrooms, Brooks et al. (2019) suggested a model for learners at different stages of competence. A novice, for example, requires feedback on the task, while learners who are already proficient benefit more from process or self-regulatory feedback. Educators and researchers mostly look at the impact of these four levels on students’ learning, in general, but not on specific phases of learning in specific subjects (Harris et al., 2015; Hattie & Gan, 2011). In our multi-method study (Smit et al., 2023), feedback levels derived from the feedback model of Hattie and Timperley were used in conjunction with feedback that was related to subject-specific content; here, mathematical reasoning tasks in primary school.

We see describing and justifying as mathematical reasoning at the primary level. However, the preliminary steps of the reasoning process – such as understanding the situation, applying strategies, and carrying out operations – are necessary building blocks in order to be able to draw conclusions, and so complete the train of thought of argumentation (Lithner, 2000). Accordingly, the reasoning process, in addition to argumentation, also contains the steps of finding an approach and operationalisation (see figure 1). In addition to these three steps, argumentation can also be carried out by non-linguistic means as visual representations (such as number lines), free drawings or tables (Boonen et al., 2016).

Based on the analyses of videos and questionnaires of 44 teachers of 5th and 6th grade primary school classes (N=804), we demonstrated that feedback for finding an approach and operationalisation were related to feedback on the task, while feedback on the process connected to approach and argumentation. We further showed that feedback at the task level predicted students’ achievement in mathematical reasoning via students’ interest in mathematics.

‘Our analysis demonstrated that feedback for finding an approach and operationalisation were related to feedback on the task, while feedback on the process connected to approach and argumentation.’

It might be concluded that the four levels of feedback should be applied by teachers in such a way that they focus on the current problem that is occurring while the student is solving a task. Researchers in other subject areas should examine this assumption to ensure its validity. Teachers in other subjects may have a need-to-know which level of feedback is optimal for a specific phase of the learning process; for example, the process of scientific inquiry or the writing process during language instruction might come to mind. For physical education, feedback in the cognitive, associative and autonomous phases could be studied. As an inspiration in this regard, a study of Australian football showed that feedback on the task level by the coach increases when a game is going negatively, while process and self-regulation feedback tends to occur during winning phases (Mason et al., 2020). We leave it to the reader to now think of derivations for the classroom.

This blog post is based on the article ‘Feedback levels and their interaction with the mathematical reasoning process’ by Robbert Smit, Patricia Bachmann, Heidi Dober and Kurt Hess, published in the Curriculum Journal.

References

Boonen, A., Reed, H., Schoonenboom, J., & Jolles, J. (2016). It’s not a math lesson – we’re learning to draw! Teachers’ use of visual representations in instructing word problem solving in sixth grade of elementary school. Frontline Learning Research, 4(5), 34–61. https://doi.org/10.14786/flr.v4i5.245

Brooks, C., Carroll, A., Gillies, R. M., & Hattie, J. (2019). A matrix of feedback for learning. Australian Journal of Teacher Education, 44(4), 14–32. http://dx.doi.org/10.14221/ajte.2018v44n4.2

Harris, L. R., Brown, G. T. L., & Harnett, J. A. (2015). Analysis of New Zealand primary and secondary student peer- and self-assessment comments: Applying Hattie and Timperley’s feedback model. Assessment in Education: Principles, Policy & Practice, 22(2), 265–281.  https://doi.org/10.1080/0969594X.2014.976541

Hattie, J., & Gan, M. (2011). Instruction based on feedback Handbook of research on learning and instruction (pp. 263–285). Routledge.

Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112. https://doi.org/10.3102/003465430298487

Mason, R. J., Farrow, D., & Hattie, J. A. C. (2020). An analysis of in-game feedback provided by coaches in an Australian Football League competition. Physical Education and Sport Pedagogy, 25(5), 464–477. https://doi.org/10.1080/17408989.2020.1734555 

Smit, R., Bachmann, P., Dober, H., & Hess, K. (2023). Feedback levels and their interaction with the mathematical reasoning process. Curriculum Journal. Advance online publication. https://doi.org/10.1002/curj.221