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Lecturing for Learning
Maths
May 15th 2007
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Teaching
Learning
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Learning From Lectures: An Explanatory
Model
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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.
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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)
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Notional effect of interruptions on
attention
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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 . . .’
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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'.
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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?'
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Diversity
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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
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Encouraging ‘Deep Learning’ (Ramsden,
2003)
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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
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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).
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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.
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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)
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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)
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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.
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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.