BN1.1 Mathematics Education - Material for the year 2019-2020

2019-2020
External Lecturer(s): 
Dr Nick Andrews
General Prerequisites: 

None.

Course Term: 
Michaelmas
Course Lecture Information: 

Quota: There will be a quota of approximately 20 students for this course.

Course Weight: 
1.00 unit(s)
Course Level: 
H

Assessment type:

Course Overview: 

The Mathematics Education option will be a unit, run in Michaelmas Term. The course is appropriate for all students of the appropriate degree courses, whether or not they are interested in teaching subsequently.
Final credit will be based on two examined written assignments (35% each), one of which will be submitted at the start of Hilary Term, and a presentation (30%).
Teaching will be 22 hours of contact time which will include lecture, seminar, class and tutorial formats as follows:

  1. A two-hour lecture/class per week. These will be interactive and involve discussion and other tasks as well as input from the lecturer.
  2. Four hours of tutorial workshops in small groups to review ideas from the course and preparation for written assignments.
Learning Outcomes: 
  1. Understanding:
    • the psychology of learning mathematics;
    • the nature of mathematics and the curriculum;
    • relations between teaching and learning at primary, secondary and tertiary level;
    • the role of mathematics education in society;
    • issues associated with communicating mathematics.
  2. Understanding connections between mathematics, education issues and the mathematical experience of learners.
  3. The ability to express ideas about the study and learning of mathematics in writing, verbally, and in other forms of communication.
Course Synopsis: 
  1. Introduction to mathematics education as a field of study.
    - Issues of mathematics education research: learner, content, teacher and policy; theory and practice. Introduction to course, use of library facilities and the expected forms of study.
  2. Nature of mathematics as a human endeavour
    - Mathematics as a way of making sense of the world of experience, and ways of making sense of mathematics. Mathematical use of human powers, such as the power to imagine, notice patterns, classify, conjecture and generalise. Motivation as mix of disposition, desire, purpose, utility, experience.
  3. Psychology of learning and doing mathematics
    - Psychology of templating (behaviourism) and of construing (constructivisms). Concept image and concept definition. Intuition and education. Human psyche comprising Awareness (cognition), Emotion (Affect), Behaviour (enaction) and Attention (will).
  4. Mathematical Knowledge Needed Teaching: The Case of Multiple Representations
    - Verbal; symbolic; diagrammatic; dynamic representations.
  5. Teaching and learning mathematics
    - Theories about teaching and learning. Relations between teaching and learning. Task design.
  6. The discourse of mathematics
    - Theories about the discourse of mathematics and mathematics as a discourse. Practical implications on the teaching and learning of mathematics.
  7. Mathematics education and society
    - Overview of interfaces between mathematics education and social issues. What issues are of concern and how these relate to the global political focus on mathematics?
  8. Student presentations
  9. Assessment
    1500 word written assignment (not examined) due: 5pm Friday of week 2 Michaelmas term
    2500 word written assignment (examined) due: 12 noon Monday of week 6 Michaelmas term
    Presentation (examined) week 8
    3000 word written assignment (examined) due: 12 noon Monday of week 1 Hilary term

Reading List: 

Main Texts:

  1. Tall, D. (1991) Advanced Mathematical Thinking. (Mathematics Education Library, 11). Dordrecht: Kluwer
  2. Gates, P. (ed.) (2001) Issues in Mathematics Teaching. London: RoutledgeFalmer
  3. Mason, J., Burton, L. & Stacey, K. (2010) Thinking Mathematically. Any edition by any publisher will do.
  4. Polya, G. (1957) How to Solve It. Any edition by any publisher will do.
  5. Davis, P. And Hersh, R. (1981) The Mathematical Experience. Any edition by any publisher will do.
  6. Mason, J. & Johnston-Wilder, S. (2004) Fundamental Constructs in Mathematics Education, London: RoutledgeFalmer.
  7. Carpenter, T., Dossey, J. & Koehler, J. (2004) Classics in Mathematics Education Research. Reston, VA: National Council of Teachers of Mathematics.

Important websites:

  1. https://www.ncetm.org.uk/