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Learning and doing geometry

Examine how people learn geometry and the nature of geometric thinking. You’ll both do some geometric tasks and learn about the pedagogy (learning and teaching) of geometry. Including how to use ideas introduced to analyse geometric reasoning. This module is for those interested in mathematics education – particularly those who work, or plan to work, in the sector.

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 core units and a final optional unit. Each unit has mathematical content and pedagogical content.

Unit 1: Organising and classifying
Mathematical content: triangles and quadrilaterals; shape properties (perpendicular sides, parallel sides, equal sides and angles).
Pedagogical content: properties – organising and classifying (shape definition; discrete and inclusive classifications); Van Hiele levels of geometric reasoning; emphasising and ignoring; figural concept.

Unit 2: Conjecturing and convincing
Mathematical content: triangles and quadrilaterals; congruence and similarity: symmetry; proving.
Pedagogical content: conjecturing and convincing (examples and non-examples; emphasising and ignoring; conventions in geometric notation).

Unit 3: Static and dynamic representations of geometric figures
Mathematical content: drawing and constructing geometric figures using squared paper, ruler and compasses and paper folding; constructing geometric figures using Dynamic Geometry Software; using measures of sides and angles to justify shape properties (and understand this is different from proof).
Pedagogical content: static and dynamic representations; soft and robust constructions.

Unit 4: Invariance and change
Mathematical content: lengths, angles, areas, volumes; Pythagoras theorem.
Pedagogical content: Invariance and change (conventions; another and another (examples))

Unit 5: Representing abstract concepts in geometry
Mathematical content: concrete manipulatives, diagrams, co-ordinates, Dynamic Geometry Software (DGS), mental imagery, verbal; constructions of figures; plans and elevations; coordinates; properties (and representations) of 3D shapes; reflecting on what geometric thinking is being worked on and how we recognise it?
Pedagogical content: representing abstract concepts (organising and classifying); learner constructed examples; conjecturing and convincing; generalising; doing and undoing; invariance and change; figural concept (Fischbein); concept image (Tall and Vinner).

Unit 6: Transforming shapes in two and three dimensions
Mathematical content: reflections, rotations, translations, enlargements; tiling patterns (infinity).
Pedagogical content: transformations (doing and undoing plus previous pedagogic ideas).

Unit 7: Circles, reasoning and proving
Mathematical content: use of diagrams both static and dynamic; angles subtended on a chord; cyclic quadrilaterals.
Pedagogical content: circles and circle theorems (say what you see; DGS: invariance and change; convince: use of diagrams and isosceles triangles).

Unit 8: Trigonometry
Mathematical content: ratio; similarity; graphing trig functions; unit circle to generate trig values.
Pedagogical content: trigonometry (representations; solving physical problems; context).

Unit 9: Geometry and algebra – making the connection
This unit provides optional study focusing on the links between algebra and geometry.
Mathematical content: links to algebra (algebraic equations; trig functions and identities; Pythagorean triples).

Pedagogical content: work linking the geometry and algebra modules.

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

You will learn

  • Become familiar with the field of geometry and the use of analytic frameworks for understanding geometric thinking and learning.
  • Apply a range of approaches to geometric problems in your own mathematics and in interpreting learners’ geometrical activity.
  • Formulate approaches to teaching and critically evaluate evidence from observations.
  • Communicate geometric thinking, including adapting problems to suit different learners and purposes.
  • Develop a personal perspective on issues covered in the module and reflect on developments in your thinking.
  • Communicate and write accurately and clearly, using the conventions of academic writing.
  • Use dynamic geometry software to support the learning of geometry.

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.

All tutorials are held online using Adobe connect. There are seven tutorials throughout the module; four support you preparing for the assignments and three address module content.


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

Future availability

Learning and doing geometry (ME321) starts once a year – in October.

This page describes the module that will start in October 2023.

We expect it to start for the last time in October 2028.


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
    No residential school

    Entry requirements

    There are no formal entry requirements or pre-requisite study. However,

    • you should be over 18
    • your own level of mathematics should be at least GCSE Grade C (or equivalent)
    • you do need to have a reasonable standard of spoken and written English
    • to complete the assessment, you'll need to work with a learner or learners who will be pleasantly challenged by secondary school-level mathematics. It is possible for friends or family members to act as your learners. You will learn most if you work with children aged 11-14.

    Find out more details about our mathematics education modules.

    If you’re not sure you’re ready, contact us and talk to an advisor.

    Preparatory work

    We recommend you study Mathematical thinking in schools (ME620) before this module.


    Start End England fee Register
    07 Oct 2023 Jun 2024 £1731.00

    Registration closes 07/09/23 (places subject to availability)

    This module is expected to start for the last time in October 2028.

    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 08/06/2023.

    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
    • assignment details and submission section
    • online tutorial access.

    We’ll also provide you with three printed geometry task booklets, each covering three 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 ME321 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.