Durham University
Programme and Module Handbook

Postgraduate Programme and Module Handbook 2018-2019 (archived)

Module EDUC43630: Representation and Reasoning in Mathematics

Department: Education

EDUC43630: Representation and Reasoning in Mathematics

Type Tied Level 4 Credits 30 Availability Not available in 2018/19 Module Cap
Tied to X9KC14
Tied to X5K207
Tied to X5K307
Tied to X9K907
Tied to X9A602
Tied to X9A102
Tied to X9KD07


  • None.


  • None.

Excluded Combination of Modules

  • None.


  • To introduce students to the theoretical notions of ‘representation’ and ‘reasoning’ in mathematics education.
  • To promote critical understanding of, and reflection on, aspects of teaching and learning in mathematics education.
  • To introduce students to mathematics education from a research-based perspective.
  • To provide an opportunity for an in-depth investigation of a specific aspect of mathematics education.
  • To provide the opportunity for students to develop their own understanding of mathematics.


  • The topics upon which the lectures will be based are:
  • The notion of representation in mathematics education;
  • Supporting learning with mathematical representations;
  • Representations and learning theories;
  • Computer-based representations of mathematics;
  • The empty number line;
  • Representations of fractions;
  • Other key representations for the mathematics classroom (primary or secondary)
  • Visual representations of complex concepts;
  • Making sense of large numbers;
  • Representations and reasoning in mathematics education.

Learning Outcomes

Subject-specific Knowledge:
  • On completion of this module, students will be able to:
  • LO1: To have a critical understanding of the notion of representation’ and ‘reasoning’ in students;
  • LO2: To have a critical understanding of current paradigms informing mathematics education practice;
  • LO3: To have a critical understanding of the use of specific representations in primary or secondary mathematics.
Subject-specific Skills:
  • LO4: To be able to analyse critically mathematics education as a subject area;
  • LO5: To critically analyse research relating to mathematics education and then apply this knowledge to solve specific problems relating to practice in a school-related context.
Key Skills:
  • LO6: Critical analysis of research literature;
  • LO7: Presentation skills;
  • LO8: Academic writing and communication skills;
  • LO9: Critical reflective analysis.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • The lectures will introduce a particular topic linked to the notion of ‘reasoning’ and ‘representations’, with readings and tasks for the following week. [LO1, LO2, LO3]
  • The seminar will then follow up this lecture, with presentations and discussions of the research and problem-based approach to exploring the relevant issues. [LO4, LO5, LO6, LO7, LO9] The tutorials will be individual small group tutorials designed to provide support for the assignment. [LO4, LO5, LO6, LO9]
  • The assignments will be a portfolio examining the use of a particular mathematical representation in the classroom (30%) [LO8]; 3500 word assignment relating theory to practice in schools with implications for teaching (70%). [LO8, LO4, LO5, LO6, LO9]

Teaching Methods and Learning Hours

Activity Number Frequency Duration Total/Hours
Lectures 10 1.5 15
Seminars / worshops 10 1.5 15
Tutorials 5 1.5 7.5
Directed tasks (via study guide & DUO) 8 1 8
Preparation & reading 254.5
Total 300

Summative Assessment

Component: Assignment Component Weighting: 100%
Element Length / duration Element Weighting Resit Opportunity
Written assignment 3500 words 70%
Portfolio 2000 30%

Formative Assessment:

Verbal feedback is given to students' contribution during class teaching sessions. Staff can be contacted for individual help. Written formative feedback is provided for the academic outline of the written assignment, and explored in more depth in the tutorials. Formative feedback on mathematical subject knowledge provided during seminars and tutorials.

Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University