1. Oxford Learning Institute Lecturing for Learning Maths May 15 th 2007

2. Oxford Learning Institute TeachingLearning

3. Oxford Learning Institute Learning From Lectures: An Explanatory Model

4. Oxford Learning Institute Practical Implications of the Model Lecturing is a two-way process which involves the students. Ideas and facts being presented must be capable of being easily assimilated into existing knowledge and understanding. Both lecturers and students have intentions for the lecture, and those intentions may not be aligned. Taking their intentions into account, or making yours explicit may be productive (especially with first years) Getting some feedback from students and/or peers may be beneficial in revealing aspects of this process from your own perspective. You must ensure that you gain and retain the students’ attention.

5. Oxford Learning Institute What students do during the lecture While lecturing, students are not attending to what is being said 40% of the time (Pollio, 1984, p 11) The majority of students (84%) felt that they could only attend to a lecture for a maximum of 20-30 minutes (MacManaway, 1970, pp 321-329)

6. Oxford Learning Institute

7. Notional effect of interruptions on attention

8. Oxford Learning Institute Examples of tasks – checking and planning 'Take two minutes to look at your notes. Check them, fill in gaps, make sure you understand them‘ 'Swap notes with the person next to you and see what they have written about. You may spot things you could add to your notes when you get them back'. 'Take two minutes to plan out what further work you need to do on this topic -- what you need to read, try out, get practice on...’

9. Oxford Learning Institute Examples of tasks – engagement 'Tackle this problem I am displaying on the overhead projector'. 'I've presented one theory or model. Offer one critique or counter example.‘ 'I've presented one theory or model. Suggest one way in which it could be tested empirically'.

10. Oxford Learning Institute Examples of tasks - questions 'I'd like you to write down one or two questions you have at this point in the lecture. Get the question exactly right so that it addresses what you are really interested in or confused about'. 'Take the questions you have written down and ask them of the people all around you until you have satisfactory answers'. 'What would be a good question which would test your understanding of what I've said so far?'

11. Oxford Learning Institute Diversity Language Culture Knowledge/Understanding Learning Difficulties (e.g dyslexia) Disabilities (e.g impaired vision or hearing) http://ltsn.mathstore.ac.uk/access/index.shtml Levels of intellectual development (students’ understanding of what knowledge is). See William Perry, 1978. Ways of thinking

12. Oxford Learning Institute Encouraging ‘Deep Learning’ (Ramsden, 2003) Factors that encourage a student to take a ‘deep approach’ to learning include: Interest in the material being presented A perception that the material is relevant/important Contextualisation – real world applications or broader implications of the material being presented A reasonable workload – too much material can overwhelm students Beginning from a point of student understanding Asking students to apply/manipulate information

13. Oxford Learning Institute Some Strengths of Mathematics Lecturing: Lectures allow subject experts the opportunity to ‘model’ disciplinary thinking. “The teacher, as a speaker of the specialist discourse, is able to ‘lend’ students the capacity to frame meanings that they cannot yet produce independently.” (Northedge, 2003: 173) Lecturers can model the solution of a problem for students if they “dar[e] to model learning in action, not learning as passive acquisition” (Lacoss, 1998).

14. Oxford Learning Institute Some Strengths of Mathematics Lecturing: The traditional ‘chalk and talk’ approach allows one to set a reasonable pace for the lecture. Lectures allow students to set aside an amount of time in which to consider the material in a focused and structured way. The expertise of the lecturer often means that a great deal of material can be conveyed in a concise manner which makes it easier to comprehend. Lectures can provide different approaches to a topic, up-to-date research and introduce a personal experience.

15. Oxford Learning Institute What you do after…(getting feedback) Use eye contact and check for body language (formative) Ask for questions at key moments (formative) ‘Instant questionnaires’ - ask for questions/key points/learning at the end (summative) Ask a sample of students to allow you to see their lecture notes (summative) Be observed (peer review - summative) Video yourself (self-evaluation – summative)

16. Oxford Learning Institute What students do after…(not very much?!) Although every student surveyed intended to do follow-up work based upon a particular set of lecture notes, 87% did not subsequently even read the notes! (Hartley and Cameron, 1967, pp 30-33) Approximately 60% of a lecture is likely to be forgotten within 24 hours unless reinforced in some way (McCleish, 1976)

17. Oxford Learning Institute Conclusions Lecturing is a two-way process which has to take account of the student. The best lecturing begins with a consideration of the student and is responsive to students More variety in a lecture helps to sustain attention and this may well have a knock-on effect on both assimilation of information and recall. Lectures should aim to encourage ‘deep learning’ by ensuring that the material is relevant, interesting, at the right level, in the right quantities and well structured.

18. Oxford Learning Institute Conclusions (cont’d) Students need to be encouraged to work on lecture material after the lecture to aid recall and understanding. Lecturers should be aware of student diversity and methods for helping students to engage with lecture material. Feedback should be obtained in order to improve and adapt lectures.