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Learning and doing algebra

Learning and doing algebra (ME322) 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 in the pedagogy (learning and teaching) of algebra, such as the progressions from number to algebra and the importance for learners of expressing and interpreting relationships in words, diagrams and graphs. You’ll learn ways to identify and analyse your own and others’ algebraic reasoning. If you work or plan to work within education, this module is an important step towards achieving your aims.

Modules count towards OU qualifications

OU qualifications are modular in structure; the credits from this undergraduate module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

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Module code




  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.

Study level

Across the UK, there are two parallel frameworks for higher education qualifications, the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ) and the Scottish Credit and Qualifications Framework (SCQF). These define a hierarchy of levels and describe the achievement expected at each level. The information provided shows how OU module levels correspond to these frameworks.
Level of Study
3 10 6

Study method

Module cost

Entry requirements

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What you will study

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 your 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 the choices we make 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 to notice different ways in which 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 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 makes connections between algebra and geometry, supporting progression to Learning and doing geometry (ME321).

You can find the full content list on the Open mathematics and statistics website.

You will learn

You’ll learn to:

  • apply ideas from the field of mathematics education for analysing algebraic thinking and learning, specialising in the algebraic content and processes relevant to 11–16-year-olds
  • apply a range of approaches to algebraic problems in your own mathematics and in interpreting learners’ algebraic activity
  • formulate approaches to teaching
  • communicate algebraic thinking, including adapting problems to suit learners
  • formulate a personal perspective on issues covered in the module and reflect on developments in your thinking
  • use graphing software to support the learning of algebra.

Vocational relevance

This module is relevant to those who wish to pursue a career in education. It’s excellent preparation for undertaking a Postgraduate Certificate in Education (PGCE), particularly if studied as part of the BSc (Honours) Mathematics and its Learning (Q46) or as part of a degree alongside other mathematics or education modules.

Teaching and assessment

Support from your tutor

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

  • Marking your assignments (TMAs) and providing detailed feedback for you to improve.
  • Guiding you to additional learning resources.
  • Providing individual guidance, whether that’s for general study skills or specific module content.
  • Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.


The assessment details for this module can be found in the facts box.

Future availability

Learning and doing algebra (ME322) starts once a year – in October.

This page describes the module that will start in October 2024.

We expect it to start for the last time in October 2029.


As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Student Policies and Regulations website.

Course work includes:

3 Tutor-marked assignments (TMAs)
End-of-module assessment

Entry requirements

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.

Preparatory work

The free course Teaching mathematics is good preparation for this module, particularly Weeks 4 and 5.


Start End Fee
- - -

No current presentation - see Future availability

This module is expected to start for the last time in October 2029.

Additional Costs

Study costs

There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

If your income is not more than £25,000 or you are in receipt of a qualifying benefit, you might be eligible for help with some of these costs after your module has started.

Ways to pay for this module

Open University Student Budget Account

The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

You pay the OU through OUSBA in one of the following ways:

  • Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.
  • Pay by instalments – OUSBA calculates your monthly fee and number of instalments based on the cost of the module you are studying. APR 5.1% representative.

Joint loan applications

If you feel you would be unable to obtain an OUSBA loan on your own due to credit history or affordability issues, OUSBA offers the option to apply for a joint loan application with a third party. For example, your husband, wife, partner, parent, sibling or friend. In such cases, OUSBA will be required to carry out additional affordability checks separately and/or collectively for both joint applicants who will be jointly and severally liable for loan repayments.

As additional affordability checks are required when processing joint loan applications, unfortunately, an instant decision cannot be given. On average the processing time for a joint loan application is five working days from receipt of the required documentation.

Read more about Open University Student Budget Accounts (OUSBA).  

Employer sponsorship

Studying with The Open University can boost your employability. OU courses are recognised and respected by employers for their excellence and the commitment they take to complete. They also value the skills that students learn and can apply in the workplace.

More than one in ten OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the module you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees. 

  • Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.
  • You won’t need to get your employer to complete the form until after you’ve chosen your module.  

Credit/debit card

You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module. 

We accept American Express, Mastercard, Visa and Visa Electron. 

Mixed payments

We know that sometimes you may want to combine payment options. For example, you may wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Account (OUSBA).

Please note: your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fee information provided here is valid for modules starting before 31 July 2024. Fees normally increase annually. For further information about the University's fee policy, visit our Fee Rules

This information was provided on 30/11/2023.

Can you study an Access module for free?

In order to qualify, you must:

  1. be resident in England
  2. have a personal income of less than £25,000 (or receive qualifying benefits)
  3. have not completed one year or more on any full-time undergraduate programme at FHEQ level 4 or above, or completed 30 credits or more of OU study

How to apply to study an Access module for free

Once you've started the registration process, either online or over the phone, we'll contact you about your payment options. This will include instructions on how you can apply to study for free if you are eligible.

If you're unsure if you meet the criteria to study for free, you can check with one of our friendly advisers on +44 (0)300 303 0069 or you can request a call back.

Not eligible to study for free?

Don't worry! We offer a choice of flexible ways to help spread the cost of your Access module. The most popular options include:

  • monthly payments through OUSBA
  • part-time tuition fee loan (you'll need to be registered on a qualification for this option)

To explore all the options available to you, visit Fees and Funding.

What's included

You’ll have access to a module website, which includes:

  • a week-by-week study planner
  • course-specific module materials
  • audio and video content, filmed in schools
  • independent study readings from the OU Library
  • free educational software
  • assignment details and submission section
  • online tutorial access.

We’ll also provide you with three printed algebra task booklets, each covering 2–3 units of study.

Computing requirements

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS (11 'Big Sur' or higher).

Any additional software will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.

If you have a disability

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.