Transition and Mathematics Education

Friday 2nd March 2012Chancellors, University of Manchester

Aim of todayTo consider issues arising from research of learners and mathematics in transitionhow to ensure what we know might make an impact

Agenda1:30 - 2:00pm Welcome and Introduction 2:00 - 3:15pm Transitions into Higher Education3:15 - 4:00pm Transitions into and through

post-16 study4:00 to 4.30pm Tea/coffee 4.30 - 5.30pm Transitions into and through

post-16 study (continued)5:30 - 6:30pm Academic and professional

perspectives on impact

TransMaths overview:Issues in understanding learners

and mathematics in transition

Transition and Mathematics Education

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

The Study of MathematicsEngland 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.

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.

Programme(1st year of A Level)

Institution(college)

Classroom culture

Teacher Student

Background & experiences

Aspirations

Methodology

Longitudinal series of interviewsLearning outcome measuresSurveys

Case study

Lesson observations & videos

Teacher survey instrument

Interviews

The two major longitudinal studies

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

Aims of the two major ProjectsTLRP: 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)

Key issuesLearners-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.

Key issuesLearners-the development of self-directing skills needs support.

Key issuesMathematics-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) .

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);

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).

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.

Measuring Dispositions during the two projects

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

Disposition to go into HEDisposition to go into HE Disposition to finish chosen course in HEDisposition to finish chosen course in HE

Disposition to study more mathematics (Maths disposition)Disposition to study more mathematics (Maths disposition)

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).

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.

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.

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.

• 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

Key findings

Transitions into Higher Education