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Learning and doing geometry

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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.

Entry requirements

There are no formal entry requirements.

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

Preparatory work

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

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 a desktop or laptop computer with an up-to-date version of 64-bit Windows 10 (note that Windows 7 is no longer supported) or macOS and broadband internet access.

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.

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.

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.

Future availability

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

This page describes the module that will start in October 2021.

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

Course work includes:

3 Tutor-marked assignments (TMAs)
End-of-module assessment
No residential school