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Learning and doing algebra

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.

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

Module code

ME322

Credits

Credits

  • 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.
30

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
OU SCQF FHEQ
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 .

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 counts towards the mathematics degree content required to start secondary mathematics teacher training. It can be studied as part of the BSc (Honours) Mathematics and its Learning (Q46), on its own, or alongside other mathematics or education modules.

Teaching and assessment

Support from your tutor

You’ll get help and support from an assigned tutor throughout your module.

They’ll help by:

  • marking your assignments and offering detailed feedback to help you improve
  • providing individual guidance, whether that’s for general study skills or specific module content
  • guiding you to additional learning resources
  • facilitating online discussions between your fellow students in the dedicated module and tutor group forums.

Online tutorials run throughout the module. Where possible, we’ll make recordings available. While they’re not compulsory, we strongly encourage you to participate.

Assessment

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 2025.

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

Regulations

As a student of 快猫视频, you should be aware of the content of the academic regulations which are available on our 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 in our Help Centre.

Preparatory work

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

Register

Start End England fee Register
04 Oct 2025 Jun 2026 拢1946.00

Registration closes 11/09/25 (places subject to 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 receive 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

快猫视频 Student Budget Accounts Ltd (OUSBA) offers a convenient &/courses/modules/me322/39;pay as you go&/courses/modules/me322/39; option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that 快猫视频 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 .

Employer sponsorship

Studying with 快猫视频 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.

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 .


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 2026. Fees typically increase annually. For further information about the University&/courses/modules/me322/39;s fee policy, visit our .

This information was provided on 04/04/2025.

Can you study an Access module for free?

Depending on eligibility and availability of places, you could apply to study your Access module for free.

To qualify, you must:

  1. be resident in England
  2. have a household income of not more than £25,000 (or be in receipt of a qualifying benefit)
  3. have not completed one year or more on any full-time undergraduate programme at FHEQ level 4 or above or successfully completed 30 credits or more of OU study within the last 10 years

How to apply to study an Access module for free

Once you&/courses/modules/me322/39;ve started the registration process, either online or over the phone, we&/courses/modules/me322/39;ll contact you about your payment options. This will include instructions on how you can apply to study for free if you are eligible and funded places are still available.

If you&/courses/modules/me322/39;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&/courses/modules/me322/39;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&/courses/modules/me322/39;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

  • Primary device – A desktop or laptop computer. It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device.
  • Peripheral device – Headphones/earphones with a built-in microphone for online tutorials.
  • Our OU Study app operates on supported versions of Android and iOS.
  • Operating systems – Windows 11 or latest supported macOS. Microsoft will no longer support Windows 10 as of 14 October 2025.
  • Internet access – Broadband or mobile connection.
  • Browser – Google Chrome and Microsoft Edge are recommended. Mozilla Firefox and Safari may be suitable.

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 .