1. Transition and Mathematics Education Friday 2 nd March 2012 Chancellors, University of Manchester

2. Aim of today To consider  issues arising from research of learners and mathematics in transition  how to ensure what we know might make an impact

3. Agenda 1:30 - 2:00pmWelcome and Introduction 2:00 - 3:15pmTransitions into Higher Education 3:15 - 4:00pmTransitions into and through post-16 study 4:00 to 4.30pmTea/coffee 4.30 - 5.30pmTransitions into and through post-16 study (continued) 5:30 - 6:30pmAcademic and professional perspectives on impact

4. TransMaths overview: Issues in understanding learners and mathematics in transition

5. Transition and Mathematics Education Investigators: Julian Williams (PI), Laura Black, Pauline Davis, Birgit Pepin and Geoff Wake Research Associates: Valerie Farnsworth, Paul Hernandez-Martinez, Maria Pampaka Associate Research Fellow: Diane Harris Associate Research Students: Kamila Jooganah and Irene Kleanthous Research Statistician: Graeme Hutcheson Administrator: Tim Millar

6. The Study of Mathematics England allows participation in mathematics education by post-16 students to be optional which has the following consequences: the vast majority of students elect to opt out of studying mathematics approximately 50% of students in England might be considered capable of studying mathematics beyond the age of 16 just over 10% of students in England choose to take the first year of a course in A-level mathematics in preparation for study in HE.

7. Transition The transition period for students seems crucial as they move into advanced study of mathematics. Deeper understanding of mathematics seems particularly important as we seek to develop a ‘workforce’ that is prepared to ensure effective participation in the high-tech world of the 21st century. Achieving this outcome requires high standards of student performance but before this can be achieved, students must be disposed towards and engaged with mathematics.

8. Programme (1 st year of A Level) Institution (college) Classroom culture Teacher Student Background & experiences Aspirations Methodology Longitudinal series of interviews Learning outcome measures Surveys Case study Lesson observations & videos Teacher survey instrument Interviews

10. The two major longitudinal studies

11. Aims of the two major Projects TLRP: 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) AS Mathematics Vs AS Use of Mathematics TransMaths: To understand how 6th Form and Further Education (pre-university) 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, e.g. Medicine and Education)

12. Key issues Learners -positive discourse of challenge and opportunity -growing independence with students relishing becoming someone “new”. -developing “understanding” and becoming increasingly more “responsible” for their own learning.

13. Key issues Learners -the development of self-directing skills needs support.

14. Key issues Mathematics -a widespread belief that mathematics is an “unsociable” subject (e.g. in mathematics “you work on your own”) -transmissionist teaching practices (“spoon- feeding” focussed on routine use of procedures rather than understanding).

15. Key issues -learners’ dispositions to study mathematics are in steady decline through the two year period of ‘advanced’ study, but this decline is exacerbated by ‘transmissionist pedagogy’ (Pampaka et al., 2010); -different classroom experiences relate to distinct mathematical identities (Williams et al. 2009);

16. Key issues -a leading identity, e.g. becoming an engineer, can be important in shaping a student’s motives for mathematical activity (Black et al. 2010).

17. Measures (of course outcomes) -disposition to study in Higher Education -disposition to study mathematics further -and self efficacy in using AS mathematics, in addition to the -teachers’ self-report of teaching practices.

18. Measuring Dispositions during the two projects Disposition to go into HE Disposition to finish chosen course in HE Disposition to study more mathematics (Maths disposition) Background Variables: Course, Gender, Ethnicity, Language of first choice, EMA, LPN, First generation into HE Background Variables: Course (Math, Science/Engineering, Other) Gender, Ethnicity, Language of first choice, Country of origin, First generation into HE Background Variables: Course (Math, Science/Engineering, Other) Gender, Ethnicity, Language of first choice, Country of origin, First generation into HE

19. Some key findings (TLRP): Students’ dispositions to go into HE overall are increasing during their AS year and this continues until the middle of their A2s. Students’ dispositions to study more mathematics decrease over time. (TLRP: AS Trad students reported statistically significant higher disposition at all times. Even though the drop is consistent for the two groups during the AS year UoM students seem to report higher disposition during their A2 year).

20. Some key findings (Transitions into HE): The disposition of students to finish their chosen course does not change very much over time: there is a very weak decreasing trend but this varies when different subgroups of students are compared. As far as students’ disposition to study more mathematics in the future, it seems that the trend is again declining, however not as steeply as found in the TLRP project.

21. Some key findings (Transitions into HE): Mathematical perceived self efficacy: two sub-measures related to pure and applied mathematics, the Use of Mathematics programme is effective in promoting increased self-efficacy over the period of the course.

22. Measuring pedagogy Transmissionist teaching practices tend to be teacher driven with learners being told how things are with the intention that they assimilate given knowledge. In mathematics the student activity that results is often restricted to practising rules and procedures. Connectionist teaching practices fundamentally value relational above procedural understanding of mathematics and seeks to highlight connections both within mathematics and to the non-mathematical world. This often results in social learning with students working with each other.

23. Different classroom experiences lead to the development of distinct mathematical identities Programme design makes a difference – for example, AS Use of Maths with the requirement for coursework led to different student experiences

24. Key findings

25. Transitions into Higher Education