Mathematical Thinking Mathematical Thinking

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In this strand we explore teachers’ mathematical knowledge and their gravitation towards certain types of pedagogy and didactical practices. In the Tasks of this strand we invite teachers to: solve a mathematical problem; examine a (fictional yet research- and practice-informed) solution proposed by one student (or more) and, in some versions, a (fictional yet research- and practice-informed) teacher response to the student; and, describe the approach they themselves would adopt in this classroom situation. Teacher engagement with these Tasks, have allowed us to access a range of teacher knowledge and beliefs (epistemological and pedagogical). For example, we engage with questions such as: What is the role of visualisation in mathematics and mathematical learning? Is a graph-based argument an acceptable argument in the mathematics classroom? Do teachers prioritise mathematical, pedagogical or curricular considerations when they make decisions about their teaching? You can find examples of Tasks and publications from this strand below.


Inequalities [pdf]

Modulus [pdf]

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Factorisation [pdf]

Quadratic equations [pdf]

[More materials] [More materials]

Quadratic using factorisation [pdf]

Quadratic using the formula [pdf]

[More materials] [More materials]

Problem Solving -  Equal shares [pdf]

L-shaped garden [pdf]

Reasoning task [pdf]

 Definite integral [pdf]


[More materials]

Problem solving - Angles [pdf]

Rounding [pdf]

Iteration [pdf]

Differential Equations [pdf]

[More materials]  

Rectanglular card [pdf]


Latest Publications Latest Publications

Kayali, L., & Biza, I. (2018). Micro-evolution of documentational work in the teaching of the volume of revolution. PME42, Vol. 3, pp. 195-202.

Nardi, E., Healy, L., Biza, I., & Fernandes, S.H.A.A. (2018). ‘Feeling’ the mathematics of disabled learners: Supporting teachers towards attuning and resignifying in inclusive mathematics classrooms. In R. Hunter, M. Civil, B. Herbel-Eisenmann, N. Planas, & D. Wagner (Eds.), Mathematical discourse that breaks barriers and creates space for marginalized learners, (pp. 147-170). SENSE Publications.

Biza, I., Nardi, E., & Zachariades, T. (2018). Competences of mathematics teachers in diagnosing teaching situations and offering feedback to students: Specificity, consistency and reification of pedagogical and mathematical discourses. In T. Leuders, J. Leuders, & K. Philipp (Eds.), Diagnostic Competence of Mathematics Teachers. Unpacking a complex construct in teacher education and teacher practice, (pp. 55-78). New York: Springer.

Biza, Irene (2017) “Points”, “slopes” and “derivatives”: Substantiations of narratives about tangent line in university mathematics students’ discourses. CERME (pp. 1993-2000).

Kayali, L., & Biza, I. (2017). “One of the beauties of Autograph is … that you don’t really have to think”: Integration of resources in mathematics teaching. CERME, (pp. 2405-2413).

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