Science Technology Engineering Mathematics and Environmental Education Research Group
Re-imagining futures in STEME
Assessing Mathematical Reasoning
Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false, and when they compare and contrast related ideas and explain their choices.
The Assessing Mathematical Reasoning resources provide teachers with a suite of tools to assess reasoning. It builds teachers’ understanding of the nature of mathematical reasoning and its assessment.
“Well, the kids were constantly having to explain, because they worked with partners which meant they could make their thinking out loud, you could always hear them justifying, thinking about other reasons why things won’t work, or the reasons why things do work” (Year 3/4 Primary school teacher).
The resources include a Teachers’ Guide and eight exemplar tasks demonstrating the application of a rubric co-developed by the project teachers and researchers. The exemplars are ready for classroom use and include a description of a task and the aspects of mathematical reasoning which the task especially supports.
In order to assess a students’ reasoning, we need to be able to see and/or hear their reasoning, and we need to know what to notice. The rubric outlines what to notice, and these ideas are illustrated in the exemplars provided with these resources. Annotated work samples are provided to illustrate practical use of the Assessing Mathematical Reasoning Rubric and to give concrete examples of students’ reasoning. Teachers used the text in the rubric when assessing a student’s work.
“He can explain the meaning of the rule using one example, and he can add to the pattern, and he can communicate a single property and repeated components” (Year 6 Primary school teacher).
The Teachers’ Guide provides support for teachers in developing their understanding of mathematical reasoning. It is explains the reasoning actions analysing generalising and justifying and provides a learning trajectory for each along with prompts to encourage higher order mathematical thinking. A poster summarising these prompts are summarised is available along with a set of prompt cards which can be laminated.
A focus of these resources is on students constructing, sharing, and comparing their solutions to the tasks in small groups and in whole-class discussions. The resources assist teachers to emphasise reasoning in any lesson and to recognise different levels of the reasoning actions, applicable across all primary year levels and all mathematics content.
The materials were developed by Colleen Vale, Sandra Herbert, Leicha Bragg, Esther Loong and Wanty Widjaja of Deakin University. They were extensively trialled in Victorian primary schools.
The Assessing Mathematical Reasoning Special Topic is available at: https://www.resolve.edu.au/assessing-mathematical-reasoning