Making mathematical thinking visible

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Funding year: 
2 years
University of Auckland - Te Whare Wānanga o Tāmaki Makaurau
Cross sector
Project start date: 
January 2016
Project end date: 
March 2018
Principal investigator(s): 
Dr. Caroline Yoon and John Moala
Research team members: 
Phil Kane, Peter Radonich, Julie De Saedeleer, Robyn Gandell, Alan delos Santos, Dimitri Leemans, James Sneyd, Vivien Kirk
Research partners: 
Northcote College and Papatoetoe High School, Unitech Institute of Technology and University of Auckland


Project Description

This project designs reporting tools for documenting the mathematical thinking that emerges during non-standard mathematics tasks called modelling activities.  These tools will raise the visibility of mathematical thinking in modelling activities, addressing the often-heard criticism: 'these are fun problems, but where's the maths?'

Why is this research important?

Modelling activities encourage students to develop 21st C mathematical competencies such as communication, problem solving, and teamwork.  Yet current measures of mathematical learning are inadequate for describing the complexity of mathematical thinking that occurs during modelling activities.  Consequently modelling activities are often marginalised in upper-secondary and tertiary curricula, compared to easy-to-measure basic skills. Well-designed reporting tools can redress this imbalance by raising the visibility of the complex mathematical thinking that occurs during modelling activities. 

The aim of this research

The aim is to capture and describe student mathematical thinking in a way that raises the visibility while retaining and respecting its complex nature.  The project addresses two research questions:

  1. What reporting tools will document, measure and describe the mathematical thinking of students working on modelling activities in a way that makes their complex mathematical thinking visible to researchers, teachers, and students?
  2. What theoretically justifiable analytical framework can be used to capture and describe rigorously the complex mathematical thinking of students working on modelling activities, in order to inform the design of practical reporting tools?

What we will do

We will design reporting tools and the underlying theoretical framework for these tools over twelve design cycles within six research sites.  The research will be conducted according to a design based research methodology, which involves the twin development of theory and practical tools:

  • Within each cycle, students will work on four modelling activities.
  • Researchers will design reports of the mathematical thinking students demonstrate during these modelling activities.
  • These reports will then be critically evaluated by teachers, researchers, and the students themselves, to determine how well they raised the visibility of hte mathematical thinking.
  • Feedback from the testing will inform revisions to the theoretical framework, which will then inforthe design of the reporting tools in the subsequent cycle.


Contact details

Associate Professor Caroline Yoon
Department of Mathematics
The University of Auckland
Private Bag 92061
Symonds Street 1150
09 923 874