Theories in the Learning and Teaching of Mathematics
Included in Study
PhD Programme in Engineering and Science
Language of instruction
Students joining this course will normally have achieved a high level of performance in a master´s course in mathematics education or similar programme. Students without a master´s qualification in mathematics education will be required to provide evidence that their knowledge and skills reaches the required standard before commencing.
On successful completion of the course, the student should be able to:
Judge the coherence of the theory within which published research is framed.
Critically evaluate the consistency within theoretical arguments in the field of teaching and learning mathematics.
Organise theoretical arguments from different sources to synthesise new ideas especially in relation to their own research goals.
Further develop and gain a level of mastery of discussing, explaining, and critically evaluating and interpreting the theories of learning and teaching in the field of mathematics education.
Develop and integrate within their own value system a consistent theory of learning and teaching mathematics, and explain and interpret their own research goals within their beliefs and value system.
The course will include content from the following:
the nature of mathematics and of mathematical activity and thinking;
what it means to learn and to teach mathematics;
learning theories - behaviourism, constructivism, sociocultural theory and other related theories;
the work of Piaget and Vygotsky and their associates and followers;
examples of learner´s activity and thinking; use of theories as lenses to explain and situate learning as we see it;
analysis of learning through classroom observation and interview, tests and experiments;
questions about teaching and how teaching is related to learning;
relationship between approaches to teaching and teachers´ perspectives on mathematics and on the learning of mathematics;
how theories of learning inform teaching;
the process of teaching and how might this be seen to relate to the education of teachers of mathematics;
how current theories provide insights into teaching processes and ways in which teaching can develop;
how theories of teaching inform the practice of teaching so that students learning mathematics can have a richer, more fruitful and successful learning experience;
what can be regarded as successful learning and teaching;
how is successful teaching reflected in students´ perfomance;
the sociocultural, economic and political questions that form the basis of the evaluation of performance of teaching.
Teaching and learning will be through exposition (lecture), teacher and student led discussion, workshops, guided reading and reflection, student presentations, seminars. Students are expected to take a full part in the whole course and undertake the prescribed reading. Attendance at all classes is a basic requirement. In special circumstances students may, in consultation with the course leader, be absent from no more than 20% of classes, additional reading tasks will be assigned.
All students will be required to undertake a course task which is the compiling a list of about 20 references (in APA format) of research papers that relate theories of learning and teaching to the students own declared research interest, together with a presentation in class of the contents of a small sample from this list.
Assessment methods and criteria
The course will be assessed on a piece of written work (~ 4000 words) which should be a forerunner of the theory, or literature review, chapter of your thesis. Students will be required to give an appropriate title.
The person responsible for the course decides, in cooperation with student representative, the form of student evaluation and whether the course is to have a midway or end of course evaluation in accordance with the quality system for education, chapter 4.1.