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Accessibility statement
This module examines the nature of algebra and how children learn. It develops your awareness of choosing and using symbols and your ability to express general mathematical statements. You’ll meet ideas about learning and teaching algebra, such as the progressions from number to algebra and the importance of communicating and interpreting relationships in words, diagrams and graphs. You’ll also learn ways to identify and analyse your own and others’ algebraic reasoning. This module is a step towards qualifying and developing as a secondary or primary mathematics teacher, teaching assistant, tutor or parent educator.
The module comprises eight units:
Unit 1: The nature of algebra
You’ll meet some definitions of school algebra and algebraic thinking. You’ll tackle problems that approach algebra as a way of exploring and expressing generality. And read about moving between well-chosen examples and generalisations, and appreciating the role of freedoms and constraints. Additionally, you’ll develop algebraic expressions for simple numerical problems and encounter ideas from research and classroom practice about learning to interpret and treat algebraic symbols.
Unit 2: Representing structural relationships
You’ll tackle problems involving making algebraic conjectures and convincing yourself when these are true. Taking an approach that algebra is a way of noticing underlying structure, you’ll meet a range of early-algebraic representations used in classrooms, such as bar models and Cuisenaire rods. You’ll read about choosing algebraic representations and work on problems with a learner.
Unit 3: The power of symbolising
This unit focuses on the power of using algebra symbols and the difficulties people experience. You’ll reflect on our choices when symbolising and how symbols help create convincing proofs. Additionally, you’ll meet the module idea ‘Manipulate, Get a sense of, Articulate’ that connects learning progression with choice of representations.
Unit 4: Equivalence and the equals sign
You’ll read and tackle problems that help you notice different ways numeric and algebraic expressions can be equivalent, including how learners use the equals sign. You’ll meet two new module ideas: ‘Doing and undoing’ underpins some widely used methods of solving linear equations; ‘Productive lingering’ describes how teachers take time over small steps of algebraic reasoning. You’ll also undertake a project where you adapt a given task and work on it with your learner.
Unit 5: Invariance and change
You’ll focus on algebraic thinking as noticing change and, amidst this change, expressing properties or relationships that stay the same. You’ll tackle problems that require you to organise and represent change in one or more variables, particularly sequences problems. Additionally, you’ll create a presentation that identifies invariance and change in your algebraic reasoning.
Unit 6: Covariant relationships
This unit focuses on covariation: how two or more variables change in relation to one another. You’ll tackle problems involving algebraic expressions and graphs. You’ll also learn to use Cornerstone Maths and GeoGebra, two digital environments designed for education, to depict covariant relationships and reflect on the affordances of different representations.
Unit 7: Exploring functions and graphs
You’ll focus on functions, including the properties and contexts that give rise to linear, quadratic and exponential functions. Then, having now met all the module ideas, you’ll choose appropriate ones to identify algebraic thinking in your own mathematics and that of your learner. This forms the basis of your end-of-module assessment.
Unit 8: Progressing to geometry
This final unit connects algebra and geometry, supporting progression to Learning and doing geometry (ME321).
The full content list is on the Open mathematics and statistics website.
There is no formal pre-requisite study, but we recommend that you study Mathematical thinking in schools (ME620) before or alongside this module.
The ability to write reports in good English is needed for the assignments. You can find support developing academic English in our Help Centre.
The free course Teaching mathematics is good preparation for this module, particularly Weeks 4 and 5.
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Course work includes:
You’ll have access to a module website, which includes:
Additionally, the website includes:
We also provide physical:
The OU strives to make all aspects of study accessible to everyone, and this Accessibility Statement outlines what studying ME322 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.
To find out more about what kind of support and adjustments might be available, contact us or visit our Disability support website.
Learning and doing algebra (ME322) starts once a year – in October.
It will next start in October 2026.
We expect it to start for the last time in October 2029.
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