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