This module examines how people learn geometry and the nature of geometric thinking. You'll complete geometric tasks and learn about the learning and teaching of geometry, including how to use ideas introduced to analyse geometric reasoning. This module is for those interested in mathematics education – it’s a step towards qualifying and developing as a secondary or primary mathematics teacher, teaching assistant, tutor or parent educator.
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.
Pedagogical content: Invariance and change (conventions; another and another (examples))
Unit 5: Representing abstract concepts in geometry
Mathematical content: concrete manipulatives, diagrams, coordinates, 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
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.
The full content list is on the Open mathematics and statistics website.
Entry requirements
There are no formal entry requirements or prerequisite study. However,
your own level of mathematics should be at least GCSE Grade 4 (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.
Preparatory work
We recommend you study Mathematical thinking in schools (ME620) before this module.
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 forums.
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Assessment
Course work includes:
3 Tutor-marked assignments (TMAs)
End-of-module assessment
For this module, we may use an assessment verification process to meet the requirements of relevant accrediting, professional, statutory or regulatory bodies. As part of this process, you may be asked to attend a short post-assessment video discussion, lasting around 15 minutes. During the discussion, you’ll need to show a photo ID and talk through your answers to a small number of questions with a tutor or a member of the module team. The discussion is not graded and is only used to confirm that you completed the assessment yourself.
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
assessment details and submission section
online tutorial access
access to student forums.
We also provide physical:
geometry task booklets.
Computing requirements
Primary device – A desktop or laptop computer with at least 8 GB of RAM and a quad-core processor (2.4 GHz minimum speed). 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.
Operating systems – Windows 11 or the latest supported macOS.
Internet access – Broadband or mobile connection.
Browser – Google Chrome and Microsoft Edge are recommended; Mozilla Firefox and Safari may be suitable.
Our OU Study app operates on supported versions of Android and iOS.
Software – Any additional software will be provided or is generally available for free.
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.
Future availability
Learning and doing geometry (ME321) starts once a year – in October.
It will next start in October 2027.
We expect it to start for the last time in October 2028.