Mathematical maturity: How can it inform teaching and learning of mathematics?
About the project
The mathematical community considers mathematical maturity an important characteristic to have to develop as a mathematician however it is currently poorly defined. In this project the team aimed to better define the concept and also to investigate if mathematical maturity can be used for the teaching and learning of mathematics. The particular focus was on students who are not seeking to major in mathematics, but who take mathematics courses as part of their degree requirements.
The team undertook a review of the literature around mathematics education. Data from the review informed a survey that was conducted internationally and was designed to probe professional mathematician’s’ ideas about mathematical maturity and if and how it could be taught.
The study was carried out within Aotearoa/New Zealand with its unique, bicultural heritage influencing the tertiary teaching environment. However, a more generic approach means that the study informs tertiary mathematics education in general, not just within the Aotearoa/New Zealand tertiary context.
Findings about mathematical maturity
As a concept, mathematical maturity has considerable similarity with the general concept of expertise. Experts display characteristics such as fluency in the topic, being able to quickly recognise patterns, and transfer knowledge from one area to the next. The data in the study also identified a person with mathematical maturity as having these characteristics.
A wide range of responses to the teaching for mathematical maturity also identified techniques that are both general good pedagogical practices, and techniques to help students become more expert-like
Conclusion and recommendations
Mathematical maturity is not a meaningful construct to use in the design of teaching and learning in tertiary mathematics. It is too nebulous a construct to be operationalised in a way that can inform classroom practice. From an educator’s perspective, a more fruitful conversation would be about what educators want students to understand and to be able to do as they progress through curriculum in mathematics.
Consequently, the team strongly caution against the use of mathematical maturity as a formal or informal prerequisite for tertiary mathematics (or statistics) courses.
Mathematical maturity in the sense of expertise has its place in teaching. This is not just through the obvious required content knowledge to teach the subject material, but in particular through expert modelling. Teachers, in their own teaching behaviours, can be explicit in showing students how an expert mathematician thins about and approaches mathematical problems, allowing students to learn to think like a mathematician.
- Dr Maarten McKubre-Jordens (Project Lead) (University of Canterbury)
- Dr Erik Brogt (University of Canterbury)
McKubre-Jordens, M. & Horton, A. (2016). Mathematical maturity: How can it inform teaching and learning of mathematics?. Presentation at Ako Aotearoa Southern Hub Projects Colloquium IV, Christchurch. (14 November).
|This report from this project is published under the Creative Commons 3.0 New Zealand Attribution Non-commercial Share Alike Licence (BY-NC-SA). Under this licence you are free to copy, distribute, display and perform the work as well as to remix, tweak, and build upon this work noncommercially, as long as you credit the author/s and license your new creations under the identical terms.|