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.

6

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

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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.

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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).

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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.

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Fre

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Fre

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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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