Mathematical Modelling content for Mathematics Curriculum Companion

The challenge

Mathematical modelling – the solving of real-world problems – has always been a key part of mathematics in the Victorian Curriculum. In 2023, the Victorian Curriculum Foundation to Level 10 (F-10), Maths Version 2.0 was launched with a focus on processes of mathematics, of which mathematical modelling is one. The Years 7-10 curriculum has a ‘strengthened emphasis on mathematical modelling … [that] helps students recognise, connect and apply mathematical structures to real-world’.

The Mathematics Curriculum Companion (MCC) is a suite of learning and teaching resources aligned to the Victorian Curriculum. It has been developed in consultation with Victorian primary and secondary teachers. Resources are organised by strand, sub-strand and level and incorporate the proficiencies: understanding, fluency, problem solving and reasoning. These resources unpack the mathematics content descriptions to provide teachers with relevant content knowledge, online resources and suggested teaching and learning ideas.

Project overview

The project team will develop content for 19 new MCC webpages to align with the Victorian Curriculum Maths Version 2.0. This work is nested within a program of inquiry aimed at answering the research question, ‘What are the issues and challenges in translating curriculum descriptors into classroom-ready approaches to, and understanding of, mathematical modelling in Years F-10?’

The project involves several phases.

Phase 1: Examine and analyse the 19 content descriptors through the lens of the development of mathematical modelling.

Phase 1 will consider such questions as:

• What are the expectations across the year levels?
• At what year level is [estimation/formation/justification …] expected?

A Wisdom of Practice document will be developed from this analysis. This document will form the basis of overall teaching advice. Implementing mathematical modelling requires teachers to step back and allow students to make decisions, get stuck and make errors. The Wisdom of Practice document will outline to teachers what is best practice during modelling and why – specifically for the requirements of the Victorian Curriculum. This document will explain mathematical modelling, describe the role of the teacher during modelling and the expectations and role of student mathematical modellers.

The Wisdom of Practice document will follow the approach of modelling as content where modelling is valued in its own right (rather than as a vehicle to learn some other mathematics). Every modelling experience, irrespective of whether the real-world problem is solved, has the potential to increase student capacity to model and enhance student understanding of their world and the value of mathematics. The Wisdom of Practice document will form the basis of the details provided to teachers on each webpage, particularly the ‘teaching context’.

Phase 2: Development of the webpages

In this phase the team will begin development of the content for the 19 webpages.

Phase 3: Expectations of learners

In this phase the team will focus on the development of modelling practices to ensure these are consistently described, introduced and developed. Are essential aspects of mathematical modelling being introduced, and subsequently expected to be used?

Phase 4: Focus on language

In this phase the team will focus on the language of mathematical modelling and how this is developed across the webpages.

As mathematical modelling is a process, the teaching approach must be considered. As described in the curriculum.

Mathematical processes refer to the thinking, reasoning, communicating, problem-solving and investigation skills involved in working mathematically. Opportunities to learn process skills have been embedded across the strands, building in sophistication across the levels. Mathematical problem-solving and investigation draws on the processes of mathematical modelling…

Mathematical models are used to gain insight into and make predictions about real-world phenomena, to inform judgements and make decisions in personal, civic and work life. In the modelling process students formulate a real-world problem mathematically by making assumptions; recognise, connect and apply mathematical structures; analyse and solve the mathematical model; and interpret, generalise and communicate their results in response to the real-world situation. Mathematical modelling is an essential dimension of the contemporary discipline of mathematics and is key to informed and participatory citizenship.

Thus, teachers must work toward, students being active learners to meet the aims of the Victorian Curriculum. Teachers are expected to provide opportunities for students to engage in the mathematical activities associated with mathematical ways – increasingly across the Years F-10.

Outcomes

This applied research project developed content for 19 new Mathematics Curriculum Companion webpages, and addressed the question:

‘What are the issues and challenges in translating curriculum descriptors into classroom-ready approaches to, and understanding of, mathematical modelling in Years F-10?’