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

Biza, I. & Nardi, E. (2019). Scripting the experience of mathematics teaching: The value of student teacher participation in identifying and reflecting on critical classroom incidents International Journal for Lesson and Learning Studies, 9(1), 43-56. 

Kayali, L., & Biza, I. (2019). ‘Balancing’ the ‘live’ use of resources towards the introduction of the iterative numerical method. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education, (pp. 3648-3655). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME. 

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.


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