Measuring Mathematics Self Efficacy of students at the beginning of their Higher Education Studies

1. Measuring Mathematics Self Efficacy of students at the beginning of theirHigher Education Studies Maria Pampaka & Julian Williams With the TransMaths group BCME 2010 - Manchester

2. Project Aim To understand how 6th Form and Further Education (6fFE) students can acquire a mathematical disposition and identity that supports their engagement with mathematics in 6fFE and in Higher Education (HE) • Focus on Mathematically demanding courses in HE (‘control’ : non mathematically demanding)

3. Project Overall Design

4. RQ1: How do different mathematics educational practices found in 6fFE/university transition interact with social, cultural and historical factors to influence students’ (a) learning outcomes, and (c) decisions in relation to learning and using mathematics? RQ2: How are these practices mediated by different educational systems (their pedagogies, policies, technologies, assessment frameworks, institutional conditions and initiatives)? The Surveys and Relevant Research Questions

5. Analytical Framework Instrument Development Measures’ Construction and Validation (Rasch Model) Model Building (GLM, Multilevel Modeling)

6. The Instruments and Measures

7. Background – What is Mathematics Self Efficacy • 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)

8. Background – Why Mathematics Self Efficacy • 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

9. Background – Why Mathematics Self Efficacy • 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

10. Background – Previous project • DP4  Links with TLRP project (DP1, DP2, DP3) • TLRP aim: To understand how cultures of learning and teaching can support learners in ways that help them widen and extend participation in mathematically demanding courses in Further and Higher Education (F&HE) • Validated measure of MSE with pre-university students

11. Result from TLRP (Overall measure, and 2 subscales) Mean plots for the three MSE measures by course and Data Point

12. The items of the Instrument The items of the scale (mathematical tasks), were constructed based on the following seven mathematical competences: (1) costing a project (2) handling experimental data graphically (3) interpreting large data sets (4) using mathematical diagrams (including plans or scale drawings) (5) using models of direct proportion (6) using formulae and (7) measuring • PLUS ‘pure items’

13. TransMaths – DP4: 10 items Instrument measuring students’ confidence in different mathematical areas: • Calculating/estimating • Using ration and proportion • Manipulating algebraic expressions • Proofs/proving • Problem solving • Modelling real situations • Using basic calculus (differentiation/integration) • Using complex calculus (differential equations / multiple integrals) • Using statistics • Using complex numbers

14. Example ItemsA ‘pure’ item

15. Example ItemsAn ‘applied’ item

16. Constructing the measureMeasurement methodology • ‘Theoretically’: Rasch Analysis • Rating Scale Model (4 point Likert scale) • ‘In practice’ – the tools: • FACETS Software • Interpreting Results: • Fit Statistics • Differential Item Functioning for ‘subject’ groups • Person-Item maps for hierarchy

17. Sample

18. Results [1] One measure? Item Fit Statistics

19. Items more relevant to AS/A2 Maths context More difficult for non maths students Results [2] Differences among student groups Differential Item Functioning

20. Results [3]Two measures? Multidimensional Scaling?

21. Results [3 cont]Fit Analysis of two measures

22. Our modeling framework Our Modeling Framework

23. Example GLMs Outcome of Year 1 (Success/Dropout…)= Entry Qualification + Dispositions + Transitional experiences + Background Variables Change of Dispositions (DP5-DP4) = Entry Qualifications + Transitional experiences + Background Variables

24. Example GLM A model of mathematics disposition at end of first year university based on variables: • Gender • International (Yes / No) • Special Educational Needs (SEN) • “Mathematical” = Mathematically demanding courses (Maths + Engineering) • Subject Area

25. Modeling Maths Disposition at DP5 Notes: SEN: Mainly Dyslexia Subject Area reference category: Engineering

27. Conclusions • We showed how a seemingly unidimensional measure of MSE was broken down into two sub-measures which may be more appropriate and productive for research in mathematics education. Two implications • Methodological (adding to current discussion about validation of measures): Our results indicate that even when a measure initially seems robust in regards to fit statistics and overall measures of reliability, care should be taken to consider how it can be used with different sub groups of the population. In our case DIF analysis flagged a possible extra dimension in our measure. This possibility has to be examined further by employing multidimensional models • Substantive (regarding the use of such measures in further modeling): Given our psychometric results so far, it may be the case that some times two measures are more useful than one, to capture the desired relationships and consequently better inform research in mathematics education. • Preliminary GLM results showed how MSE affects students mathematics dispositions