MEMA533: Innovations through lesson study: Teaching and Learning Mathematics for Understanding.


This module aims through discussion, group activities, reading and seminar presentations to:

  1. consider what is meant by teaching and learning mathematics with understanding
  2. Ÿuncover what is meant by “mathematical thinking”.
  3. Ÿdevelop an appreciation of the inherent beauty of mathematics
  4. Ÿencourage understanding through reflection and communication
  5. Ÿexplore the nature and purpose of collecting data as evidence of mathematical thinking and understanding within the classroom.
  6. Ÿconsider the nature of classroom tasks, the role of the teacher and the social culture of the classroom in designing a classroom where understanding is the primary goal
  7. Ÿunderstand the misconceptions made by pupils and students in key mathematical topics, concepts and notation
  8. Ÿidentify and critically examine how applications and contexts can enhance the teaching of mathematics
  9. Ÿidentify ways of improving professional and educational practice in the teaching of mathematics through extension, enrichment and practical activities designed for different abilities
  10. Ÿdemonstrate enquiry, insight and analytical capability with regard to their own professional development of mathematical skills, knowledge and understanding

ASSESSED LEARNING OUTCOMES: At the end of a module the learner will be expected to be able to:

  1. identify, select, critically analyse and evaluate ideas, perspectives, theories or data relevant to an appropriate area of study;  undertake a critical, imaginative and ethical investigation; relate theory to practice; formulate a coherent set of aims and objectives which effectively utilise available resources;  organise and manage the study.
  2. locate work within a broader context, usually through ideas, perspectives and theories from appropriate literature.
  3. adopt a questioning, reflective and critically aware stance throughout the study.
  4. choose and implement appropriate media and processes in relation to ideas, aims, intentions and context; select and apply appropriate methodologies to stated objectives and utilise them competently and methodically.
  5. show clarity and coherence in structure, writing conventions, style, presentation of evidence and argument; ensure the work is readable, accessible to its intended audience and effectively communicates the intended meaning.
  6. generate ‘new’ ideas and connections, apply existing material to new contexts or reappraise or critique familiar material; further, combine or resolve uncertainties, identify similarity, difference and interconnection, take risks and use rational and intuitive thinking.

Apply these generic abilities and qualities to one of the specific PGDip assessment modes – Critical Review of a Body of Knowledge, Developing Practice through a Project, Data Collection & Analysis, Critical Reflection on Practice, Making an Argument