Ideas to enliven:
Further Mechanics
Abstract
• This session will be based upon the
oversubscribed session from the 2009 MEI
conference ‘Stretching Students: Mechanics in
Further Mathematics’.
• It will include suggestions for using reflective
learning, STEP questions, ‘Gems’ questions,
Mechanics in Action, contextualised questions
and simulations/investigations
• This session will be of interest to all those
teaching further mathematics mechanics units.
Stephen Lee
It should be said that…
1. STEP questions
…No two groups of students are alike
• Useful information/links at:
www.maths.cam.ac.uk/undergrad/admissions/step/
• Need to consider each situation on its
own merits
• Consider having a range of different ‘exercises’
at your disposal
• Hopefully this session will provide you with some
ideas which you can relate to your own cases
• Past papers and solutions:
STEP questions
Reflective Learning
• Should be considered for use, even if
students are not sitting the STEP exams
Provide students with:
• a (suitable) question
• A mark scheme
And/or
• Worked Solution
• Examiners report/comments
• See mechanics examples used for tutoring
students on a distance learning STEP
course
www.admissionstests.cambridgeassessment.org.uk/adt/step/Test+Preparation
1
Reflective Learning
Ask students to undertake the following:
• Read through the whole question, to get a ‘feel’
for it
• Then, before attempting the question, try and
determine what they think the solution strategy
will be and what the key things to note (e.g.
information given and/or information needed to
be obtained) are in each part of the question
• Attempt to solve the question
Reflective Learning
• Read through the mark scheme/example
solution/examiners report
• Consider additional questions about what you have just
undertaken.
– Did the solution strategy that you noted turn out to be
appropriate or did it prove that you needed to revise your
strategy part way through?
• If so, was this unavoidable, i.e. is it actually feasible to prepare the
perfect strategy before you begin the question?
– Was the information you identified as being key BEFORE
starting the question necessary and sufficient or was it inevitable
that further key information not initially considered would arise
whilst undertaking the question?
2. Mechanics in Action
Mechanics in Action
• 1990s publication of above name to
accompany a ‘Leeds Mechanics Kit’
• Contained 53 worksheets, with additional
notes
• Many relevant activities that can be used
to enliven your teaching
• Examples include:
(Difficult to get hold of a hard copy, but available
online at: http://stem.org.uk/rx324 and teachers
guide: http://stem.org.uk/rx327)
– High road and low road (sheet 26)
– Wind up (sheet 38)
– A stop-go phenomenon (sheet 39)
– The superball as a deadly weapon (sheet 53)
• (Mechanics in action: Practical Mechanics
session D 17.00-18.00)
3. Gems questions
4. Contextualised examples
• At previous MEI conferences there has been
sessions on ‘6 gems in mechanics’
• Obviously very useful to have questions
that are set in context
• These are excellent questions/ideas for students
to look at and consider
• See handout (or MEI website)
(E.g. Q1, Q2, Q4)
• A suggestion may be to consider the use
of undergraduate books/materials
– See handout from ‘Engineering Mathematics
through Applications’ Kuldeep Singh
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Contextualised examples
5. Simulations/Investigations
Materials also available via nrich site:
• M1: http://nrich.maths.org/7099
• M2: http://nrich.maths.org/7100
• M3: http://nrich.maths.org/7101
• M4: http://nrich.maths.org/7102
• M5: http://nrich.maths.org/7103
• Open ended problems
• Well designed simulations and
investigations can often lead to students
develop their own thinking of how to look
at a topic/idea
• E.g. Escape from Planet Earth
Real Life Golf Problem
•
19th
Simulations/investigations
Hole at Legends Golf Course has been
designed to involve teeing off from a cliff onto a
green in the shape of South Africa at the foot of
the cliff
• Ideal situation to consider by using modelling
from Mechanics units
• Could use an interactive Geogebra file and
additional exploratory/investigatory worksheet(s)
• Students could investigate real values (or
teachers could provide them…)
• Virtual Physical Laboratory
www.vplab.co.uk
(Free if attend a training session)
• Mechanics-online.com
M1 and M2
(costs £100-175 for school subscription)
Simulations/Investigations
Session re-cap
• Additional ‘soft’ skills can also be developed
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• Creating posters
• Presentations based around an experiment
• Exemplars document
(Mechanics in the real world?)
STEP questions
Mechanics in Action
‘Gem’ questions
Contextualised examples
Simulations/investigations
• Participants’ experiences
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