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1
“Can extension work and methods usually aimed at a small proportion of high ability students be
used to motivate mixed ability classes studying A2 level Physics?”
Dr Eliza McIntosh (The Perse School)
Abstract
The research investigates whether extension work and methods usually aimed at a small proportion
of high ability students can be used to motivate mixed ability classes studying A2 Physics. Six lessons
were spent on extension activities, using material from the Senior Physics Challenge (SPC), a four day
academically selected residential summer school held annually at the University of Cambridge
Physics department. The students’ response to the extension sessions was assessed by
questionnaires at the start and end of the programme, interviews with students from across the
ability range and observations of the classes. While the approach of exams was a key factor in
changes in the working practice of students during the study, the extension sessions did play a role
in motivating the study group. There were no appreciable negative effects of the extension sessions
on students from across the ability range and the most able students in particular were stimulated
by their interest in and the challenge of the extension sessions.
Context
To facilitate different combinations of subjects during Sixth Form studies, high ability students are
necessarily taught in mixed ability sets. In the academic year 2013-14 one additional 40 minute
period in each fortnightly timetable cycle for each Sixth Form subject was introduced at The Perse,
reducing time pressure and providing the opportunity for extension sessions within timetabled
lessons.
While extension Physics classes outside the normal timetable are run at the Perse during the Lent
term of Year 12 and the Michaelmas term of Year 13, only the most able students committed to
studying PEM (Physics, Engineering and Mathematics) subjects at University and those seeking to
gain Oxbridge offers usually attend. Pre-U Physics has also recently been introduced at The Perse as
an alternative to Physics A-level for students intending to study PEM students at University; in Pre-U
lessons extension material of a more mathematical nature is more routinely included. In the current
Year 13 cohort, 11 students study CIE Pre-U compared to 26 OCR B Physics A-level. At The Perse in
2013, 8 out of 27 A-level Physicists attained an A* grade and a further 11 an A grade.
A benefit to the Physics department exists in assessing the impact of extension classes on students
across the ability range and in developing or adapting resources. In addition, with the introduction
of the A* grade at A-level in 2010, there is renewed pressure on schools to achieve the top grade.
The A* proportion at The Perse declined from 2012 to 20131, with a key factor thought to be a lack
of motivation for students to work hard for an A* grade if an A grade will suffice to meet a University
1 In Physics at the Perse, the A* proportion in Physics reduced from 54% of entries in 2012 to 30% in 2013 (or
49% in 2013 if A-level and Pre-U equivalent grades are both included). In the school as a whole, the proportion of A* grades reduced from 42% in 2012 to 33% in 2013.
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offer. Compulsory extension sessions may motivate students to work harder and therefore achieve
a higher proportion of A* grades.
The debate as to whether or not A-level Physics adequately prepares students to study PEM subjects
at University has recently been revived with the establishment of the Rutherford Schools Physics
Partnership (RSPP) which provides web resources, school workshops and residential courses offering
support and activities in Physics problem solving to teachers and students to encourage key
transitions to Sixth Form and University Physics. The Senior Physics Challenge (SPC), directed at Year
12 students at the end of the AS year, is run annually by the Department of Physics at the University
of Cambridge and has recently been incorporated into the RSPP. The SPC offers approximately 70
academically selected students the opportunity to spend a week tackling extension theoretical and
experimental Physics. It is from resources used at the SPC that the majority of the extension
material used in the present study was taken, and as the project base for the SPC expands with the
creation of the RSPP the present research also provides an opportunity to assess the suitability of
the resources used on the course for mixed ability classes.
Background
Pupil motivational effort in has been identified as an important psychological factor in education
(Aronson, 2002). A number of definitions of motivation emerge with a common theme that
motivation affects pupils’ levels of engagement with a task, their enjoyment of activities, how and
when they learn and their performance (Smith, 2005). Factors identified as affecting motivation in
Physics and Mathematics specifically include pupils’ self-identification as learners, choice of
activities, the role of the teacher and the use of praise and assessment (Alderman, 2004; Harlena
and Deakin Crick, 2002; Kyriacou and Goulding, 2006; Dweck, 2004). As Smith et al. (2005) note,
‘motivation is not a simple or binary concept’.
The concept of ability remains controversial. As in previous CamSTAR research (Hedgeland, 2013),
rather than enter an argument about the concept of ability, we will accept that some members of a
class will inevitably engage more quickly with tasks and progress more easily to higher levels of
learning than others. The merits of ability grouping and its link to self-concept and motivation have
been widely discussed (Boaler et al., 2000; Ireson and Hallam, 2005; Kulik and Kulik, 1982; Slavin,
1986, 1990) and White et al. (2003) suggested that wherever possible enrichment activities should
be embedded within the curriculum. A wide body of literature on ‘high ability’, ‘academically
talented’ or ‘gifted and talented’ students in Physics and Mathematics also exists (e.g. Lynch, 1992;
Benbow and Minor, 1986), and we note as relevant here that mathematically talented students of
both genders tend to have more favourable attitudes towards science, particularly Physics.
In 2013 there were 35,569 students studying Physics at A level, only 4.2% of the total number of A
levels that year (JCQ, 2013), considerably lower than typical figures in the 1980s (Sainsbury of
Turville, 2007). In response to concerns about low post-16 participation rates in Mathematics and
Physics arising from economic modelling (HM Treasury, 2004), a number of projects have sought to
investigate and address the issue (Rodd et al., 2013).
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The Targeted Initiative on Science and Mathematics Education (TISME) identified a lack of awareness
of the transferability or usefulness of science qualifications as a key issue in the post-16 transition,
with pupils more likely to continue with PEM subjects at post-16 level if they perceive that the
subject stands them in good stead for achieving a well-paid and interesting job (Muitbal and Reiss,
2012). Attainment is also important, with Department for Education figures from 2013 indicating
that 43% of students with an A* grade at GCSE Physics continue to AS level, compared to 30% with A
grades and 16% with B grades. Rodd et al. (2013) propose that identification with a key adult is also
an important element in an individual’s participation, but found no evidence that the sorts of
innovation typically designed to increase Physics uptake, for example fun projects or competitions,
had been key with respect to a desire to read Physics at University.
Gender has also previously been identified as a key factor in post-16 Physics participation rates, with
7.9% of males who sat A-levels taking Physics in 2013 compared to 1.4% of females, an imbalance
which continues into Science, Technology, Engineering and Mathematics (STEM) subjects at
University. The small sample size in the present work makes it impractical to consider the effect of
gender on post-16 Physics motivation; the interested reader is referred to works by Benbow and
Minor (1986), Gillibrand (1999) and Halpern et al. (2007).
Existing studies highlighting good practice when teaching advanced topics to pre-University Physics
students include work by Ireson (2000, 2006) and Manton (2013). Recently Cheung and Warner
(2012) published ‘A Cavendish quantum mechanics primer’, representing an expansion of lectures
given at the SPC and designed to stretch ‘seriously able’ students at the end of their AS year and to
‘introduce essential ideas while emphasising skills and the solving of problems.’ In addition to the
RSPP, other projects exist to address transitions from school to PEM subjects at University including
i-want-to-study-engineering.org and the Cambridge Mathematics Education Project.
Finally, we note that while extension work may help to motivate learners, the potential negative
impacts on learners’ confidence and self-efficacy should also be considered (Bond, 2009, Boaler et
al., 2006, Bandura 1986).
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The research question
In seeking to answer our main research question,
“Can extension work and methods usually aimed at a small proportion of high ability
students be used to motivate mixed ability classes studying A2 level Physics?”,
we note that, as previously discussed, the extension activities in the present study were adapted
from those used at the SPC. The following aspects of motivation have been considered in the
present work:
• Students’ interest in and enjoyment of the subject
• Students’ perception of the relevance and future use of subject material
• The challenge posed by the work and whether the students consider it appropriate
• Time spent by students on independent study outside of the classroom.
Finally, we note that while the A2 Physics classes in the present study were mixed ability within the
full range of students at The Perse, compared to the national average they actually comprised a
relatively narrow and high ability range, with a mean ALIS test score of 122 and standard deviation
of 10.
Methods
Two classes, each comprising eight Year 13 students studying A2 Physics (the study group), spent six
40 minute lessons at fortnightly intervals on extension material during the Lent term 2014 as
outlined in Table 1. The difficulty of the material covered in the sessions and the level of
mathematics included generally increased over the course of the term. Students completed
questionnaires to assess their perception of A-level Physics and extension material before and after
the series of extension lessons in order that changes could be mapped accurately. A further class of
nine Year 13 students at the Perse (the control group) taught by different members of staff and not
formally exposed to the same extension material also completed the questionnaires.
To enable quantitative comparison of the ability range of the ‘mixed ability’ classes in the study with
the ‘small proportion of high ability students’ usually exposed to such extension material, taken here
to be participants in the 2013 SPC, the study group completed the 30 mark mathematics test used
during the selection process for the 2013 SPC, designed to test students’ ability to apply
mathematical skills to problem solving in Physics. The marks in the mathematics test were used to
select four students spanning the ability range with whom interviews were conducted during and
after the series of extension sessions to explore issues from the questionnaires in more detail. A
Physics undergraduate also observed some of the extension sessions and provided his thoughts on
the response of the students to the extension material.
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Session Methods Source of material 1 Introduction
and tracking data collection
Introduction to the extension lessons. Discussion of general advice for problem solving in Physics. Students complete questionnaire 1 and SPC maths test under exam conditions.
2013 SPC admission test
2 Estimation Teacher introduction to Fermi-style estimation in Physics with example problem worked through as a class. Students work on up to 5 further estimation questions in groups of 2 or 3, with teacher input to groups where necessary.
Questions from 2013 SPC estimation session
3 Frames of reference
Teacher introduction to the use of the zero-momentum frame in Physics to solve problems involving collisions in one-dimension. Students work on (mainly symbolic) questions involving the use of different frames of reference to solve problems involving collisions in groups of 2 or 3, or individually, with teacher input to groups where necessary.
Problems from 2012 Part IA dynamics problem sheet (University of Cambridge)
4 Potential wells Teacher introduction to classical potential wells in Physics Students work individually on similar problems in groups of 2 or 3, or individually, with teacher input to groups where necessary. Teacher introduction to the relation of classical potential wells to quantum mechanics.
Problems from 2013 SPC dynamics problem sheet
5 Quantum mechanics 1
Teacher introduction to observables, operators and eigenequations in quantum mechanics. Students work individually or in pairs on exercises 2.1 and 2.2. Class discussion of results and findings. Discussion on the postulates of quantum mechanics and how to solve the Schrodinger equation for an infinite square well potential.
Problems from the Cavendish Quantum
Mechanics Primer 2nd
edition (also used during 2012 and 2013 SPC quantum mechanics classes
6 Quantum mechanics 2
Teacher introduction to de Broglie wavelength and the uncertainty principle. Students work individually or in pairs on some of exercises 2.4-2.11 with teacher input where needed. Teacher demonstration of how to solve the Schrodinger equation for a finite square well and class discussion of implications of tunnelling.
Problems from the Cavendish Quantum
Mechanics Primer 2nd
edition (also used during 2012 and 2013 SPC quantum mechanics classes
Table 1: Summary of extension session content, methods and source material.
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SPC
Mat
hs
Test
Sco
re (
/30
)
Findings
Ability of the study group
Table 2 summarises some relevant background academic statistics for the study group and Table 3
compares the performance of the study group in the SPC maths test with applicants for the 2013
SPC. The relationship between ALIS baseline test scores and the SPC mathematics test results of the
study group was also considered (Figure 1), but no significant correlation was found.
Total number
of students
Grade at AS level Grade students hope to
achieve at A2 level2
Offer for STEM
subject at University
Offer for PEM
subject at University
Offer for PEM
subject at Oxbridge
A B C A* A A/B
16 11 2 3 8 4 1 12 (75 %) 7(44 %) 1 Table 2: Background academic statistics for the 16 members of the study group.
Study group
Study group
and planning to study PEM
subject
Study group and
planning to study STEM
subject
Study group
and not planning to study
STEM subject
2013 SPC
applicants
2013 SPC
participants
Number of students 16 7 12 4 276 71 Percentage scoring 23+ 31 43 42 0 54 100 Percentage scoring 26+ 6.3 14 8.3 0 22 76
Mean mark 18.8 20.1 19.5 16.5 22.2 26.9 Standard deviation 5.4 4.8 5.6 4.5 4.6 1.5
Table 3: Comparison of marks (/30) in the SPC maths test used for admissions to the 2013 summer school.
30
25
20
15
10
5
0
90 100 110 120 130 140 150
ALIS Test Score
Figure 1: Relationship between ALIS test score and SPC Maths test score for overall ALIS scores (blue crosses), ALIS maths score (red circles) and ALIS non-verbal score (green squares).
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4 students declined to answer this question
7
Fre
qu
en
cy
Students were asked to indicate how helpful they had found the mathematics they had studied to
date for A-level Physics, on a scale from 1 to 5 where 1 represents ‘not at all useful’ and 5 ‘extremely
useful’. The mean score awarded by the students, grouped by their mathematics course, is shown in
Table 4.
Mathematics course Mean score Number of students None 2 1 Maths 3.9 1
AS Further Maths 4.8 5 Further Maths 3.9 8
Table 4: Mean scores from 15 responses given to the question ‘Has the maths you have studied been helpful for A-level Physics?’ in questionnaire 1. Responses were given on a scale from 1 to 5, where 1 = ‘not at all useful’ and 5 =
‘extremely useful’. Results are grouped by the level of mathematics studied at Sixth Form level. ‘Maths’ refers to students who will take 6 Mathematics modules during Year 12 and Year 13 to be awarded an A-level in Mathematics. AS
Further Mathematics students at The Perse take 9 modules to be awarded an A-level in Mathematics and an AS in Further Mathematics, and Further Maths students 13 leading to the award of an A-level in Mathematics and an A-level
in Further Mathematics. The total number of students taking each course is also given. The student choosing not to complete the question studied no Mathematics at A-level.
9
8
7
6
5
4
3
2
1
0
None Maths AS Further Maths
Further Maths
5 (extremely useful)
4
3
2
1 (not at all useful)
Figure 2: Students' perceptions of how helpful the maths they have studied previously has been for A-level Physics,
from 16 responses in questionnaire 1. Responses were on a scale of 1 to 5 (1 = ‘not at all useful’, 5 = ‘extremely useful’) and are grouped according to the mathematics course studied.
Motivation to study Physics
Table 5 summarises the reasons given by members of the study group for choosing to study A-level
Physics.
Needed to make up number of A-
level subjects
Enjoyed Physics at GCSE
Interested in Physics
Needed for University course
Other (please specify)
3 11 11 9 0 Table 5: Reasons given for studying A-level Physics, from 16 responses from the study group to questionnaire 1. Each
respondent was permitted to select as many reasons from the list as they felt applied.
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To facilitate linking responses from the questionnaire to the research question, students were also
asked what they understand by the term ‘motivation’. The 14 responses to this question are listed
in Table 6.
Category Responses Frequency
Wanting to do something
• How inclined you feel to work to do well at something / in a subject
• How much you feel that you want to do something
• Energy and inclination to commit to a task
• The want to do / learn more
• That you want to do well for a reason, something to work towards
• Willing to work to achieve something
• Desire to do well
• What makes you get up in the morning
8
Mental determination
• Possessing the determination to accomplish tasks
• Having the mental drive to work towards an ultimate goal
• Having initiative, strong willed
3
Drive to achieve • Drive to achieve
• Pushing yourself to do something
2
Doing things • Working to complete activities 1
Table 6: Students' understanding of the term 'motivation', as given in questionnaire 2.
Changes in students’ perceptions and working practice during the study
In both questionnaires, students asked to report the number of hours of independent study (outside
lessons) they carried out each week (Table 7) so that any changes could be assessed. Students were
also asked to rank the five main types of activities used in A-level Physics teaching at The Perse in
order of preference from 1 (favourite) to 5 (least favourite). To enable the influence of the
extension sessions to be assessed, results from both the study and control groups are shown in
Figure 3 with changes in the mean rank of the components summarised in Table 8.
Mean no. of hours per
week
Standard deviation
(hours)
Minimum (hours)
Maximum (hours)
AS level 2.7 1.3 0.5 6 A2 level – start of Lent term 2.3 0.9 1 4 A2 level - end of Lent term 2.5 1.0 1 5 Table 7: Number of hours of independent work (outside lessons) which students indicated they completed at three
different points during the A-level course: during the AS year (from 16 responses from questionnaire 1), during the A2 year up to January (from 16 responses from questionnaire 2) and at the end of the Lent Term during the A2 year (from
15 responses from questionnaire 2).
9
16 a) 14
12 Study group, 10
questionnaire 1 8 6 4 2 0
b) 16 14
Study group, 12 10
questionnaire 2 8 6 4 2 0
c) 6 5
Control group, 4
questionnaire 1 3
2
1
0
Practicals Theory lessons
Practicals Theory lessons
Practicals Theory
lessons
Working in your own
time
Working in your own
time
Working in your own time
Completing
practice questions
Completing
practice questions
Completing
practice questions
5
4
3
2
Coursework 1
5
4
3
2
Coursework 1
5
4
3
2
Coursework 1
d) 6 5
Control group, 4
questionnaire 2 3
2
1
0
Practicals Theory
lessons
Working in
your own time
Completing
practice questions
5
4
3
2
Coursework 1
Figure 3: Responses indicating students’ order of preference for five types of activities on a scale from 1 (favourite) to 5
(least favourite). a) shows responses from questionnaire 1 for the 15 members of the study group completing both questionnaires and b) responses from questionnaire 2. Similarly, results for the 6 out of 9 members of the study group
who completed both questionnaires are shown in c) (questionnaire 1) and d) (questionnaire 2).
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Re
leva
nce
of
AS/
A2
P
hys
ics
Inte
rest
in A
S/A
2 P
hys
ics
Use
fuln
ess
of
AS/
A2
P
hys
ics
Ch
alle
nge
fro
m A
S/A
2
Ph
ysic
s
Study Control Before After Change Before After Change
Practicals
2.3
2.1
-0.2
2.5
3.2
+0.7
Theory lessons
2.7
2.4
-0.3
3.5
2.0
-1.5
Working in your own time
3.5
3.7
+0.3
3.2
3.7
+0.3
Completing practice questions
3.6
3.4
-0.2
2.3
2.5
+0.2
Coursework
3.1
3.4
+0.3
3.5
3.7
+0.2
Table 8: Changes in the mean preference for different activities from the A-level course, where a rank of 1 represents ‘favourite’ and 5 ‘least favourite’. Results are given for the 15 respondents from the study group and 6 from the control group completing both questionnaires. Shading has been used to aid interpretation of the data, with green showing an overall increase in preference and red an overall decrease in preference. The darker the shade, the greater the change.
Figure 4 shows the students’ interest in the Physics course, the challenge they feel is posed by the
course and the perceived relevance and usefulness of the course on a scale from 1 ‘extremely’ to 5
‘not at all’. The blue bars indicate opinions of the AS course, the red bars opinions of the A2 class at
the start of the study and the green bars opinions of the class after the extension classes.
a) b) 1
2
3
4
5
0 2 4 6 8 10
Frequency
c) d)
1
2
3
4
5
0 2 4 6 8 10
Frequency
1 1
2 2
3 3
4 4
5 5
0 2 4 6 8 10
Frequency
0 2 4 6 8 10
Frequency
Figure 4: Opinions of students in the study group of the AS Physics course (blue, from questionnaire 1), the A2 Physics
course before the extension lessons (red, from questionnaire 1) and of the A2 course after the extension lessons (green, from questionnaire 2), on a scale from 1 to 5 where 1 represents ‘extremely’ and 5 ‘not at all’. Only data for the 15
students who completed both questionnaires has been included.
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Enjo
yme
nt
of
exte
snio
n
wo
rk
Students’ responses to extension material
In the first questionnaire, students were asked how much they enjoyed extension work and
responses are shown in Figure 5, with 1 representing ‘very much’ and 5 ‘not at all’.
1
2
3
4
5
0 2 4 6 8 10
Frequency
Figure 5: Students' opinions of how much they enjoyed extension work in Physics from responses questionnaire 1, on a scale from 1 ‘very much’ to 5 ‘not at all’. Again, only data from the 15 students who completed both questionnaires is
included.
In questionnaire 2, students were asked to give their responses to each of the extension sessions.
Table 9 summarises the responses, giving the mean value of the response for each criteria and each
session, while Figure 6 shows the distribution of responses. As previously, students’ responses were
given on a scale from 1 to 5, where 1 was the highest positive response as specified in Table 8.
How much did you enjoy the
session?
How interesting
did you find the session?
How challenging did you find the session?
Was the level of challenge appropriate?
Was the amount of
maths in the session
appropriate? 1 on scale represents
A lot
Extremely
Extremely Very
appropriate
Not enough
5 on scale represents
Not at all
Not at all
Not at all
Not at all
Far too much
1 - Maths test
3.4
3.7
3.1
2.5
3.3
2 – Estimation
2.9
2.9
3.1
2.0
2.5
3 - Frames of reference
2.9
2.2
2.7
1.9
2.8
4 - Potential wells
3.1
2.6
2.1
2.6
3.1
5 - Quantum mechanics 1
2.8
2.4
1.8
3.0
3.5
6 - Quantum mechanics 2
2.7
2.6
1.6
3.2
3.3
Table 9: Mean values of responses to questions probing students' perceptions of each of the extension sessions, from 15 responses of the study group to questionnaire 2. The top row shows the question asked, and the second and third
rows the indicators on the scale from 1 to 5 which students were asked to use to respond.
12
Ap
pro
pri
ate
mat
hs
Ch
alle
nge
of
sess
ion
En
joym
en
t o
f se
ssio
n
Inte
rest
in s
ess
ion
A
pp
rop
riat
e c
hal
len
ge
a) b)
1 1
2 2
3 3
4 4
5 5
0 5 10
Frequency
c) d)
0 5 10
Frequency
1 1
2 2
3 3
4 4
5 5
0 5 10
Frequency
0 5 10
Frequency
e) f)
1
2
3
4
5
0 5 10
Frequency
Figure 6: Frequency of responses to questions probing students' perceptions of each of the extension sessions, from 15 responses of the study group to questionnaire 2. a) How much did you enjoy the session? (1 = ‘a lot’, 5 = ‘not at all’); b)
How interesting did you find the session? (1 = ‘extremely interesting’, 5 = ‘not at all’); c) How challenging did you find the session? (1 = ‘extremely challenging’, 5 = ‘not at all’); d) Was the level of challenge of the session appropriate? (1 = ‘very appropriate’, 5 = ‘not at all appropriate’); e) Was the amount of maths in the session appropriate? (1 = ‘not enough’, 5 =
‘far too much’); f) Colour key to distinguish sessions in plots a) to e).
13
The relation between students’ responses to each extension session and their abilities as indicated
by their ALIS test scores and performance in the SPC mathematics test were assessed. The
statistically significant correlations are listed in Table 10. A small number of absences from some
sessions mean that the sample size, n, varies slightly between tests.
Ability indicator
Response
Session
n =
r Significance
level Summary
SPC maths test score
Enjoyment
4 - Potential wells
14
-0.474
0.1
Higher SPC maths score,
enjoyed more SPC maths test score
Interest
2 - Estimation
15
0.451
0.1
Higher SPC maths score,
lower interest SPC maths test score
Interest
4 - Potential wells
14
0.458
0.1
SPC maths test score
Interest
5 – Quantum mechanics 1
12
-0.537
0.1
Higher SPC maths score,
higher interest ALIS
combined
Challenge
1 – SPC Maths test
15
0.444
0.1
Higher ALIS score, lower
challenge
ALIS combined
Challenge
5 – Quantum mechanics 1
12
0.621
0.05
ALIS maths
Challenge
5 – Quantum mechanics 1
12
0.571 0.1
ALIS combined
Challenge
6 – Quantum mechanics 2
14
0.483
0.1
ALIS maths
Challenge
6 – Quantum mechanics 2
14
0.505
0.1
Table 10: Statistically significant correlations between ability indicators and students' perception of the extension sessions from responses to questionnaire 2. n gives the sample size for each test. r is the correlation coefficient found
by Pearson's Product Moment, and the significance level of the test is given in the final column.
Finally, the overall changes in students’ motivation and perception of Physics during the Lent term
were assessed and results are shown in Figure 7. Students were invited to choose as many
responses to each question as they thought applied. Responses to a further question: ‘Has the
session changed your attitude to Physics in any way? If so, how? If not, why not?’ are summarised
in Table 11.
14
Fre
qu
en
cy
Fre
qu
en
cy
Fre
qu
en
cy
Fre
qu
en
cy
a) Has the amount of work you have done outside of Physics lessons increased during the term? 9 8 7 6 5 4 3 2 1 0
No Yes, due to Yes, as exams Yes, due to the Yes, as my Yes, but due to normal ‘on
syllabus’ Physics lessons
are getting closer
extension classes
maths has improved
throughout the year
another factor
b) Do you now consider maths to be more important in Physics than you did at the start of term? 9 8 7 6 5 4 3 2 1 0
No Yes, due to Yes, as exams Yes, due to the Yes, as my Yes, but due to normal ‘on
syllabus’ Physics lessons
are getting closer
extension classes
maths has improved
throughout the
another factor
c) Has your motivation to succeed at Physics increased? year
9 8 7 6 5 4 3 2 1 0
No Yes, due to
Yes, as exams Yes, due to the
Yes, as my
Yes, but due to
normal ‘on syllabus’
Physics lessons
are getting closer
extension classes
maths has improved
throughout the year
another factor
d) Do you think that you have a better understanding of skills that would be useful for a PEM degree? 9 8 7 6 5 4 3 2 1 0
No Yes, due to normal ‘on
syllabus’ Physics lessons
Yes, as exams are getting
closer
Yes, due to the extension
classes
Yes, as my maths has improved
throughout the year
Yes, but due to another factor
Figure 7: Changes in the motivation and working practice of students based on 15 responses from the study group (blue)
and 7 from the control group (red) to questionnaire 2. Students were allowed to select multiple responses.
15
Session Comments in response to question ‘has the session changed your attitude to Physics in any way? If so, how? If not, why not?
2 - Estimation ‘Was the most fun session’ ‘Yes, can work out stuff by using estimation questions’
3 – Frames of reference
‘Yes, interesting to have an alternative method of doing momentum calculations’ ‘Strange concept but was useful’ ‘Interesting new and potentially easier method for collisions’ ‘Look at problems differently’
4 – Potential wells
‘ Very theoretical’
5 – Quantum mechanics 1
‘Good introduction’
6 – Quantum mechanics 2
‘Used stats 2 module to answer which was surprising’ ‘Yes, Uni Physics would be too hard’ ‘Made me want to look into the area as I found it very hard and wanted to understand it’
4 , 5 and 6 ‘Yes – these sessions made me think about different ways of thinking about Physics‘ ‘I’ve realised Physics is maths based’ ‘Physics has a lot of maths’
All sessions ‘Found it interesting, but (it has) not changed (my) attitude’ Table 11: Students' responses to question ‘Has the session changed your attitude to Physics in any way?’ from
questionnaire 2.
The observer’s comments on session 5 (quantum mechanics 1) provide a concise summary of the
mixed responses of the students to the harder extension material:
“With the exception of Student I (female, no maths A-level, Bio-Chemistry at University), who
had made up her mind before the lesson started that she was not interested and did not
bother to listen, everybody seemed initially interested and most people seemed to be dealing
with the concepts. Although a couple of them didn’t seem to be able to motivate themselves
to get stuck in with the problems element of the lesson...and appeared to get frustrated
towards the end of some of the lessons…about half the class seemed to really enjoy and
progress with it.”
16
Discussion
Considering first the ability of the study group, if we can assume that the score achieved on the SPC
mathematics test is an indicator of the ability of pupils to solve mathematical Physics problems, then
Table 3 shows that the ability of the study group is both more mixed and lower, on average, than
that of the SPC participants. We note, however, that while the study group completed the test
under exam conditions, SPC applicants complete the test online at home. As previously noted, the
concept of ability itself is both complex and controversial, and indeed Figure 1 shows that there
exists no clear relationship between results from the baseline ALIS test and performance in the SPC
mathematics test. The importance of mathematics for A-level Physics as well as for extension work
is, however, supported by Figure 2 and Table 4 which show that students in general found the
mathematics they had studied useful for Physics. Students’ comments also revealed they recognise
the interdependence of Physics and maths:
“I see Physics as deriving a result and maths as implementing.”
(Student J - male, AS Further Maths, Law at University)
“Basic-ish maths is useful. I’m not doing A-level maths, that’s probably why it’s difficult. I
think it would help a bit”
(Student I)
Table 5 showed that the key factors influencing students to study A-level Physics were an interest in
Physics, previous enjoyment of the subject and a requirement to study Physics for their University
course. Comments made by students when asked whether they enjoyed Physics lessons also
support the view that interest and challenge are key motivating factors:
“(Physics is) my favourite lesson – it’s most interesting. (Physics is about) stuff which is more
important. Physics is more satisfying when you don’t understand and then you do…I would
do more work if stuff was harder and less routine. I want a different take with each question
so you have to think.”
(Student K - male, Further Maths, Physics at University)
“I would spend longer on the questions if they were more interesting”
(Student A - female, AS Further Maths, Electrical Engineering at University)
While students’ interpretation of the term motivation varies (Table 6), a common theme exists in a
desire or drive to accomplish a task. As such, the number of hours of work completed by students
outside of the classroom can be taken as one indicator of motivation. Table 7 shows that while, on
average, the number of hours of independent work increased throughout the period of the study, it
was lower than that undertaken by students during the AS course. However, the differences are
small, students’ memories may not be reliable and many factors including revision for exams at the
end of the academic year, changes in the amount of work set by different teachers and the number
of subjects studied will affect the number of hours worked in addition to students’ motivation.
Figure 4 shows that changes in students’ perceptions of the Physics course during the study period
are small, although we see that students’ interest in Physics (Figure 4a) is slightly higher after the
extension classes (green) than before (red) while in Figure 4b the perceived challenge of the A2
course (red) is lower than that of the AS course (blue).
17
Clearer changes are seen in students’ preference for different types of activities during the study
period (Figure 3 and Table 8). The main changes for the study group are a trend towards median
values of preference for theory lessons and a slight overall increase, contrasted with an overall
decrease in preference of students for working in their own time and for coursework. In contrast, a
marked increase occurs in the preference of the control group for theory lessons, accompanied by a
decrease in preference for practicals. It is difficult to draw firm conclusions as to the effect of the
extension lessons from the small shifts in preference for the different activities, particularly because
sample sizes are small and the control class had a change of teacher at the start of the Lent term
which may have been responsible for the significant increase in preference for theory lessons.
Comparing students’ opinions of how much they enjoyed extension work in Physics before the
extension classes (Figure 5) with how much they enjoyed each individual extension session (second
column of Table 9 and Figure 6a), we find that the students’ overall enjoyment of extension material
changed very little as a result of the extension sessions, and as such any negative effects of the
extension work on students were minimal. The quantum mechanics sessions had the most variation
in students’ enjoyment. With the exception of the first extension session comprising the
mathematics test, students generally found the sessions of similar interest except frames of
reference (green bars in Figure 6b) which they found most interesting. Frames of reference was the
extension topic most closely linked to on-syllabus material from the A2 course and so was perhaps
most conceptually accessible to the students. As expected, students found the sessions increasingly
challenging but, on the whole, felt the level of challenge was appropriate, although most students
considered the level of challenge of the second quantum mechanics session to be on the hard side of
appropriate. Figure 6e indicates that while students generally felt the amount of mathematics
included in the sessions was appropriate, some students thought that the potential well and
quantum mechanics sessions contained too much mathematics.
Students with higher baseline ALIS scores reported a lower level of challenge from the maths test
and quantum mechanics sessions (Table 10), as perhaps expected given that they were the most
challenging sessions and of the most mathematical nature. In contrast, the higher the SPC
mathematics test score the less interest students had in the (mathematically simpler) estimation and
potential well sessions, implying an association between the perceived level of challenge and
interest in a session, at least for the most mathematically able students. Indeed a positive
correlation, significant at the 0.1 level, was found in addition between the perceived challenge and
interest in the session for quantum mechanics 2, indicating that the higher the perceived challenge,
the higher the interest in the session.
Changes in students’ motivation and perception of Physics during the Lent term were shown in
Figure 7. Figure 7a shows that some students in the study group felt that the amount of work they
had done outside of Physics lessons had increased during the term as a result of normal Physics
lessons as well as because exams were approaching, in contrast to the control group who only cited
the approach of exams as a factor. In both groups of students, the predominant factor for an
increase in motivation to succeed at Physics was that exams are getting closer (Figure 7c), perhaps
related to generally disappointing results in a mock exam which students sat at the start of the Lent
term with a mean improvement of 6.4% in a second mock sat two weeks later. Student K
commented: “My first mock in January was not good so I need to do more rather than coasting ….I
hate losing and failure so want to avoid it.” There is also some evidence that the extension classes
18
showed students that mathematics and Physics at University level are linked, with a higher
proportion of students in the study group considering maths to be more important after than before
the extension classes, with 5 out of 15 citing the extension classes, and the quantum mechanics
sessions in particular, as an important factor (Figure 7b). Students’ comments support this view,
with the five students in Figure 7b who considered mathematics more important in Physics at the
end of term than at the start all citing the quantum mechanics extension classes as a specific reason.
Very little evidence was found for any negative effects on learners’ confidence in or enjoyment of
Physics arising as a result of the extension sessions. One student (Student B - male, Further Maths,
Medicine at University) commented that the sessions had made him realise that “Uni Physics would
be too hard.” Although Student I reported that she had ‘not really’ enjoyed the extension sessions
“as (I) can’t do them”, she was “not put off” and noted that “as I have worked harder (at Physics) I
have understood it more so enjoyed it more.” Positive effects of the extension classes were more
usually noted, for example:
“Overall they (the extension lessons) have made me more confident in my Physics. They have
had a positive effect – I understood most topics and it’s given me a degree of confidence in
my ability.”
(Student J)
While we have shown that being challenged by subject material is crucial for students’ interest and
enjoyment, we note that the level of challenge does need to be appropriate so as to not be off
putting:
“The last two (sessions) were harder so I enjoyed them less, but they were on the limits of
what I could do – but that is why I want to do Physics at University to be able to do questions
like that.”
(Student K)
We note that although Student I chose to opt out of the first quantum mechanics extension session
as she found the level of mathematical challenge too high no other students did, strongly suggesting
that they enjoyed the sessions.
Finally, we compare the responses of the Perse students in the present study with trends from the 2013 SPC (Table 12). Far more participants in the SPC rated the quantum mechanics problem sessions as too hard than the dynamics sessions (which included frames of reference and classical potential wells), although a high proportion still rated their interest in the sessions as ‘high’, commensurate with the high proportion of Perse students who found the quantum mechanics sessions hard but were still interested.
Interest Difficulty
High
Medium
Low
Too hard About right
Too easy
Dynamics 56 11 0 13 50 2 Quantum Mechanics 49 16 1 51 14 1
Table 12: Response of SPC participants to dynamics and quantum mechanics problem sessions. Data taken from SPC end of course participant questionnaire 2013, used with permission of the course directors.
19
Recommendations emerging
We conclude that the use of extension work and methods usually aimed at a small proportion of
high ability students at the SPC can play a role in motivating mixed ability classes studying A2
Physics, although the main reason for changes in students’ working practices throughout the study
period appears to be the approach of exams. Students did look forward to the extension lessons
and at least to that extent the extension work served to motivate the study group. Negative effects
on students across the ability range from the extension classes were minimal while the
(mathematically) more able students were definitely interested in and challenged by exposure to the
extension material. In particular, students found that the quantum mechanics sessions illustrated
the presence of mathematics in advanced Physics. While isolating factors contributing to students’
exam performance is extremely difficult, an additional point of interest will be to assess whether the
extension classes impact on the proportion of students gaining an A* grade at A2 level.
We suggest therefore that extension material as used in the present research can be used
successfully with mixed ability classes, but that teachers should be aware of the need for
‘appropriate challenge’ and tailor the content of the extension sessions to the mathematical fluency
of the students. Extension sessions for mixed ability classes would perhaps be especially useful for
students at the end of Year 12 to better inform their University choices and understanding of the
requirements of PEM degrees. While extension practical work was not included in the present study
due to time constraints, this aspect of extension work could be considered in a future study. We
further suggest that future studies of the impact of extension work on A-level Physics classes be
conducted during the Michaelmas term or after exams in the summer term, so that impending
exams preoccupy students to a lesser extent.
Acknowledgements
The author would like to thank the Physics Department at The Perse for their suggestions and
support and Dr Anne Bowker for her advice on background literature. In addition, the author is
grateful to Jamie Muirhead for his comments on the sessions he observed and to Dr Lisa Jardine-
Wright and Prof. Mark Warner, co-directors of the SPC and Principal Investigators for the Rutherford
Schools Physics Partnership for allowing resources from the SPC to be used in the classroom setting.
20
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