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

2. To understand how 6 th 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) Project Aim

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

6. Items / MeasuresDP4DP5DP6 Reasons for choosing University and course Experiences that influence choice of Uni Programme Disposition to complete chosen course Preparedness and Usefulness of ways of studying Transitional Experiences Mathematics Dispositions Perceived Pedagogic Practices at Pre-uni (maths) experience Perceived Pedagogic Practices at Uni (maths) Mathematics Self Efficacy Confidence with Mathematics Usefulness of Mathematics Perceived Mathematical support at Uni Relevance of mathematics The Instruments and Measures

7. 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) Background – What is Mathematics Self Efficacy

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

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 Items A ‘pure’ item

15. Example Items An ‘applied’ item

16. ‘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 Constructing the measure Measurement methodology

17. Sample

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

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

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

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

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

27. Similar Model from our previous TLRP project DP1: Beginning of AS DP2: End of AS

28. 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 Conclusions