OAME presentation documents and links (May 2025)
session descriptor: The tasks we give to our students shape their idea of mathematics and how mathematics relates to the world we live in. Though it is clear that our students need to do more than just be good calculators, it is not yet clear what it is that we as math educators want them to be good at as citizens, workers, entrepreneurs and critical thinkers. Through this short presentation/workshop I hope to clarify quality numeracy tasks (which are much more than just word problems) as a distinct form of mathematical task, and show how this perspective can improve assessments at all levels of the curriculum, bring struggling students into mathematical discourse, and help us as teachers bring meaning to the mathematics that we are teaching.
The presentation takes Sfard’s (2000) perspective on Thinking as Communication, which conceptualizes knowledge as participation in discourse, as a starting point and leads to a conceptualization of numeracy tasks as a distinct type of mathematics task.
For Sfard, knowing mathematics means participating in communication in the discourse of mathematics. This is not the current state of our mathematics curriculum in elementary, secondary and most post-secondary settings. Our curriculum typically takes a knowledge transmission approach. Numeracy interventions in math education fare no better. We present a word problem for illustrative purposes.
Danylo’s problem – a task posed in a grade 11 math test (quadratic equations unit) in Ontario – is not inviting the student into the mathematics discourse. What is it about? What sort of thinking is it provoking?
(Dahl et al. 2023) suggest three types of tasks presented in mathematics classrooms:
– Tasks that are internal to mathematics (to mathematical discourse) and set in abstract world
– Tasks that are internal to mathematics and set in concrete (real) world
– Tasks that are external to mathematics – set in concrete (real) world context
Does Danylo’s problem fit into any of the above? Given the teacher’s assessment, I suggest this is a poorly written example of a task that is set in the concrete (CD sales) but actually internal to mathematics in that it is meant to provoke the use of quadratic functions not help the storekeeper with CD sales.
Below is a slide showing examples of each of the three types of tasks.
Numeracy Tasks are those that are External to mathematics. They aim to provoke transfer, which we conceptualize as the shifting between concrete and abstract thinking spaces (Blum, 2009). They do not aim to provoke numeracy discourse (i.e. discussions about math education related to transfer).
How do we assess the degree to which tasks are able to engage the discourse important to numeracy tasks? We use the numeracy task rubrics developed by us in Gula and Lovric (2024) and described here.
References:
Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of mathematical modelling and application, 1(1), 45-58.
Dahl, B., Hüttel, H., Rasmussen, J. G., & Rasmussen, M.G. (2023). Contextualisation in university level problem-based learning. For the Learning of Mathematics, 43(3), 27–31.
Gula, T, & Lovric, M. (2024) Quality Numeracy Tasks: Development and Stress Test of Three Rubrics for Teachers and Designers. Adults Learning Mathematics: An International Journal. link
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944