What is the effect of self-efficacy on students’

participation? Investigators: Julian Williams (PI), Laura Black, Pauline Davis, Birgit Pepin and Geoff WakeResearch Associates: Valerie Farnsworth, Paul Hernandez-Martinez, Maria PampakaAssociate Research Fellow: Diane HarrisAssociate Research Students: Kamila Jooganah and Irene KleanthousResearch Statistician: Graeme HutchesonAdministrator: Tim Millar

Professor Bandura has written the following onthe distinction between self-efficacy and confidence

“ Perceived self-efficacy refers to belief in one's agentive capabilities, that one can produce given levels of attainment. A self-efficacy assessment, therefore, includes both an affirmation of a capability level and the strength of that belief. Confidence is a catchword rather than a construct embedded in a theoretical system. Advances in a field are best achieved by constructs that fully reflect the phenomena of interest and are rooted in a theory that specifies their determinants, mediating processes, and multiple effects. Theory-based constructs pay dividends in understanding and operational guidance. The terms used to characterize personal agency, therefore, represent more than merely lexical preferences."

Self-Efficacy: The Exercise of Control, 1997, p. 382

•Self-efficacy (SE) beliefs “involve peoples’ capabilities to organise and execute courses of action required to produce given attainments” and perceived self-efficacy “is a judgment of one’s ability to organise and execute given types of performances…” (Bandura 1997, p. 3)

• "a situational or problem-specific assessment of an individual's confidence in her or his ability to successfully perform or accomplish a particular maths task or problem" (Hackett & Betz, 1989, p. 262)

What is Mathematics Self-Efficacy?

Why self efficacy is interesting?

• Important in students’ decision making (sometimes more than actual test scores)

• Positive influence on students’ academic choices, effort and persistence, and choices in careers related to maths and science.

• How to measure? • Contextualised questions

Sept-Nov2006

April-June2007

Sept-Dec2007TIME

Cohort’s Educational

LevelStart of AS End of AS Start of A2

Data Point

DP1 DP2 DP3

July-Sept2008

Feb-May2008

Oct 2009 – Jan 2010

End of A2Pre-HE

Mid First Year HE

Start of Second year HE

DP1[DP4]

DP2[DP5]

DP3[DP6]

TLRP project TransMaths project Two of the Projects and Samples

Total 1779 1076 604

AS Trad 1285 (72%)

730(68%)

459(76%)

UoM 494(28%)

346(32%)

145(24%)

1778 875 901

AS Trad: A traditional mathematics A-level UoM: a ‘modelling’-based programme intended to widen participation in mathematics through use of technology and coursework.

Measuring Mathematics Self Efficacy

Sept-Nov2006

April-June2007

Sept-Dec2007TIME

Cohort’s Educational

LevelStart of AS End of AS Start of A2

Data Point

DP1 DP2 DP3

July-Sept2008

Feb-May2008

Oct 2009 – Jan 2010

End of A2Pre-HE

Mid First Year HE

Start of Second year HE

DP1[DP4]

DP2[DP5]

DP3[DP6]

TLRP project TransMaths project

MSE Instrument of 30 items:• 3 difficulty levels• 7 mathematical competences• Pure and Applied/Modelling

MSE Instrument of 10 items of different

mathematical areas

Confidence in the same 10 mathematical areas

1. Problem solving: The table below shows how the circumference of a glass varies with height. Find, using mathematics, the height to which you would need to fill the glass so that you have half a glass of

beer.

Not confident at all Not very confident Fairly confident Very confident

Example ‘Applied’ Item(common in both studies)

Measuring Self Efficacy - TLRP

Investigation of these items shows that those easier for AS traditional students are items defined earlier as ‘pure’ whereas, in contrast, items easier for the Use of Mathematics (UoM) group are more ‘applied’ items. One Overall measure (MSE),

And two useful sub-scales:• Pure MSE

• Applied MSE

What we found regarding MSE

• consistent positive relationships of MSE with students’ prior mathematical attainment

• male students were more self-efficacious

• AS traditional students score consistently higher in the pure MSE aspect, and the difference increases with time

• UoM students also increase their scores in the applied dimension considerably over the AS course.

MSE changing during the AS course

MSE and Learning Outcomes:A logistic regression model of drop-out

The probability of dropout reduces when MSE increases (controlling for the other variables in the model)

MSE and Other Learning Outcomes (Dispositions - TLRP)

• Linear Model of Maths Disposition at DP2

The reported MSE of the students at the beginning of their MSE programme has a positive effect on their dispositions to continue with mathematically demanding subjects (which is directly relevant to particular career choices)

Another model…

MSE and Other Learning Outcomes (Dispositions - TransMaths

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.09392 0.18271 -0.514 0.60745 MdispDP4 0.55988 0.03998 14.004 < 2e-16 *** International[T.Yes] 0.32724 0.20001 1.636 0.10243 MSE_DP4 0.13673 0.04514 3.029 0.00257 ** sen[T.Yes] -0.87557 0.31291 -2.798 0.00533 ** subjectarea1[T.Mathematics] 0.10701 0.19822 0.540 0.58952 subjectarea1[T.Medicine] -0.42762 0.22413 -1.908 0.05696 . subjectarea1[T.Other] 0.57756 0.56679 1.019 0.30869 subjectarea1[T.OtherScience] 0.32010 0.23499 1.362 0.17375 subjectarea1[T.SocialSciences] -0.87239 0.33791 -2.582 0.01011 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 1.423 on 513 degrees of freedom (3035 observations deleted due to missingness) Multiple R-squared: 0.5681, Adjusted R-squared: 0.5605 F-statistic: 74.97 on 9 and 513 DF, p-value: < 2.2e-16

A consistent association of MSE with changing mathematics dispositions during first year university study

MdispDP4 effect plot

MdispDP4

Md

isp

DP

5

-4

-3

-2

-1

0

1

2

3

-6 -4 -2 0 2 4 6

International effect plot

International

Md

isp

DP

5

0.2

0.4

0.6

0.8

No Yes

MSE_DP4 effect plot

MSE_DP4

Md

isp

DP

5

-1

-0.5

0

0.5

1

-4 -2 0 2 4 6

sen effect plot

sen

Md

isp

DP

5

-1

-0.5

0

0.5

No Yes

subjectarea1 effect plot

subjectarea1

Md

isp

DP

5

-1

-0.5

0

0.5

1

1.5

2

EngineeringMathematicsMedicine OtherOtherScienceSocialSciences

SEN

Dis

po

sitio

n to

Stu

dy

Fu

rth

er

Ma

ths

at

DP

5

Dis

po

sitio

n to

Stu

dy

Fu

rth

er

Ma

ths

at

DP

5

Engineering Maths Medicine OtherScienceOther SocialSciences

Subject Area

MdispDP4 effect plot

MdispDP4

Md

isp

DP

5

-4

-3

-2

-1

0

1

2

3

-6 -4 -2 0 2 4 6

International effect plot

International

Md

isp

DP

5

0.2

0.4

0.6

0.8

No Yes

MSE_DP4 effect plot

MSE_DP4

Md

isp

DP

5

-1

-0.5

0

0.5

1

-4 -2 0 2 4 6

sen effect plot

sen

Md

isp

DP

5

-1

-0.5

0

0.5

No Yes

subjectarea1 effect plot

subjectarea1

Md

isp

DP

5

-1

-0.5

0

0.5

1

1.5

2

EngineeringMathematicsMedicine OtherOtherScienceSocialSciences

MdispDP4 effect plot

MdispDP4

Md

isp

DP

5

-4

-3

-2

-1

0

1

2

3

-6 -4 -2 0 2 4 6

International effect plot

International

Md

isp

DP

50.2

0.4

0.6

0.8

No Yes

MSE_DP4 effect plot

MSE_DP4

Md

isp

DP

5

-1

-0.5

0

0.5

1

-4 -2 0 2 4 6

sen effect plot

sen

Md

isp

DP

5

-1

-0.5

0

0.5

No Yes

subjectarea1 effect plot

subjectarea1

Md

isp

DP

5

-1

-0.5

0

0.5

1

1.5

2

EngineeringMathematicsMedicine OtherOtherScienceSocialSciences

Disposition to Study Further Maths at DP4 Maths Self Efficacy at DP4

Dis

posi

tion

to S

tudy

Fur

ther

Mat

hs a

t DP

5MdispDP4 effect plot

MdispDP4

Md

isp

DP

5

-4

-3

-2

-1

0

1

2

3

-6 -4 -2 0 2 4 6

International effect plot

International

Md

isp

DP

5

0.2

0.4

0.6

0.8

No Yes

MSE_DP4 effect plot

MSE_DP4

Md

isp

DP

5

-1

-0.5

0

0.5

1

-4 -2 0 2 4 6

sen effect plot

sen

Md

isp

DP

5

-1

-0.5

0

0.5

No Yes

subjectarea1 effect plot

subjectarea1

Md

isp

DP

5

-1

-0.5

0

0.5

1

1.5

2

EngineeringMathematicsMedicine OtherOtherScienceSocialSciences

International Student

A final point – from TransMaths• MSE measure highly correlated with

‘confidence’ measure• We only measure MSE at the beginning, but

confidence at all data points (up to the 2nd Year at University)

• How is confidence changing during University?

TransMaths ‘ mathematics confidence’Plot of Means

TransLong$DP

mea

n of

Tra

nsLo

ng$M

athC

onf

0.0

0.5

1.0

1 2 3

TransLong$BroadAreas

MathematicsOtherScienceEngin

Course

Pre/Start of Uni [DP1]

End of Year 1 [DP2]

Year 2[DP3]

Co

nfi

de

nc

e i

n M

ath

em

ati

cs

(L

og

its

)

Pre/Start of Uni [DP1]

End of Year 1 [DP2]

Year 2[DP3]

Co

nfi

de

nc

e i

n M

ath

em

ati

cs

(L

og

its

) Gender

Plot of Means

TransLong$DP

me

an

of T

ran

sLo

ng

$M

ath

Co

nf

0.0

0.5

1.0

1 2 3

TransLong$BroadAreas

MathematicsOtherScienceEngin

Plot of Means

TransLong$DP

mea

n of

Tra

nsLo

ng$M

athC

onf

0.2

0.4

0.6

0.8

1.0

1.2

1 2 3

TransLong$gender

FemaleMale

Course

Pre/Start of Uni [DP1]

End of Year 1 [DP2]

Year 2[DP3]

Co

nfi

de

nc

e i

n M

ath

em

ati

cs

(L

og

its

)

Pre/Start of Uni [DP1]

End of Year 1 [DP2]

Year 2[DP3]

Co

nfi

de

nc

e i

n M

ath

em

ati

cs

(L

og

its

) Gender

Conclusions• due to the significant role of mathematics self-

efficacy in students’ future career choices, teachers, educational policy-makers and practitioners should endeavour to promote and develop students’ mathematics self-efficacy.

• Use of Mathematics seems to benefit students to increase their MSE, (especially on students with low mathematics self-efficacy).