Building on Transmaths: TeLePriSM

Teaching and Learning Practices in Secondary Mathematics

Maria Pampaka2nd March 2012

Formal ESRC Title: “Mathematics teaching and learning in secondary schools: the impact of pedagogical practices on important learning outcomes” (RES-061-25-0538)

TeLePriSM

Overall aim: to show how we built on TransMaths to develop Teleprism

- Aims and design- Analytical Framework- Instrumentation- Teleprism: some preliminary findings from

the first data point

Outline

The TransMaths projects: Design and Aims

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)

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

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

Teachers’Survey

Teleprism

TeLePriSM

Aim: To map secondary students’ learning outcomes and choices, including dispositions and attitudes, together with the teaching they are exposed to.

Surveys for students from Years 7 to 11 (3 times) and also for their mathematics teacher (twice).

Case studies in a small number of schools with lesson observations and interviews with students and teachers.

Inst 1a Inst 2Inst 1

Inst 2aInst 2 Inst 3

Inst 3aInst 3 Inst 4

Inst 4aInst 4 Inst 5

Inst 5aInst 5 Inst 6

Y8 Y9 Y10Y7 Y11

COHORT Y9 COHORT Y11

COHORT Y10COHORT Y8

COHORT Y7

Teleprism: Design and Aims

TeLePriSM

(i) to understand how learners’ dispositions to study Mathematics develop through Secondary School (i.e. KS3 and KS4)

(i) to understand how mathematics pedagogies vary across different situations and contexts,

(ii) to understand how different pedagogies, programmes and school contexts influence learning outcomes, including dispositions, and

(iii) to solve a series of measurement and analytical challenges involving a synthesis of longitudinal and cross-sectional analyses, and dealing with missing data.

Teleprism: Detailed Aims

Inst 1a Inst 2Inst 1

Inst 2aInst 2 Inst 3

Inst 3aInst 3 Inst 4

Inst 4aInst 4 Inst 5

Inst 5aInst 5 Inst 6

Y8 Y9 Y10Y7 Y11

COHORT Y9 COHORT Y11

COHORT Y10COHORT Y8

COHORT Y7

Instrument Development

Measures’ Construction and Validation(Rasch Model)

Model Building(Multiple Regression, GLM)

respondto RQs

A common analytical framework

Figure 1: Analytical Framework

RESOLVING METHODOLOGICAL

CHALLENGES RQ3

MEASURES CONSTRUCTION & VALIDATION (Rasch Model)

RQ1

MODEL BUILDING(GLM, Multilevel Modelling)

RQ2

INSTRUMENT DEVELOPMENT

TeLePriSM

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

Teachers’Survey

UoMAS

APR/MAY 2012 DP2

OCT/DEC 2011DP1

OCT/DEC 2012DP3

INSTRUMENT 4

END Y EARSTART YEAR

CO

HO

RT

Y11

CO

HO

RT

Y10

CO

HO

RT

Y9C

OH

OR

TY8

CO

HO

RT

Y7

SUMMER HOLIDAYS

START Y EAR

INSTRUMENT 1

INSTRUMENT 2 INSTRUMENT 3

INSTRUMENT 1a INSTRUMENT 2

INSTRUMENT 4a

INSTRUMENT 5a

INSTRUMENT 6[TLRP-DP1]

INSTRUMENT 5

GCSE

GCSE

GCSE

“New” Qualifications [Functional Maths, New GCSE, Use of Maths AS]

“Traditional” Qualifications [Current GCSE, AS Maths]

Key for Student/Classroom Group:Traditional Examinations

Key for “Testing” condition:

“New” Experimenal Examinations

INSTRUMENT 3a

INSTRUMENT 2a

INSTRUMENT 3 INSTRUMENT 4

INSTRUMENT 5

3750-6250 surveys x 3

Average 15000

Average 15000

Average 15000

Average 15000

DATASTUDENT SURVEY DESIGN

SURVEY 1 SURVEY 2

TEACHERS SURVEY DESIGN DATAAverage

3000

TeLePriSM

What have we measured? DISPOSITIONS

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

What are we measuring?

Disposition to go into HE Disposition to complete HE course

Disposition to study more mathematics (Maths disposition)

Teleprism:• A measure of dispositions / attitudes• We also have questions about disposition to go into HE (possibly)

TeLePriSM

• TransMaths instruments (left) were consideredBUT…

• complicated for younger students

• PLUS more instruments on literature on attitudes, affect

Maths Dispositions / Attitudes…

TeLePriSM

How much do you agree or disagree with the following statements?

Measurement question:

Can we get a ‘unified’ measure of disposition/attitude towards maths out of this?

Preliminary findings: promising

TeLePriSM

What have we measured? 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

What are we measuring?

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

Teleprism:• A measure of mathematics self efficacy• Some common items with TLRP

TeLePriSM

Contextualised items…TLRP (applicable for Year 11, 10,…)Measuring Maths Self Efficacy

Example: How confident are you to interpret complex or unfamiliar graphs and charts such as:

TeLePriSM

From…Previous exam papers (2006 to 2009)– AQA – Edexcel – GCSE – GCSE F – MALT – OCR – SATS

More items for younger students…

TeLePriSM

Bank of 217 itemsPiloted 35 items (only

Years 7 to 10)Used 56 items for main

study

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

What have we measured? “Teaching Mathematics What are we measuring?

Teachers’Survey Students’ perception of pre-

university pedagogy

Students’ perception of university pedagogy

Teleprism:• Measures of teachers’ self report teaching• Students’ perception of teaching• Common items between the two as well as between TransMaths

www.transmaths.org

TLRP teacher survey TransMaths Students’ SurveyTeleprism: We tried to keep these common

TeLePriSM

The survey design…Data Point 1 (DP1)

UoMAS

APR/MAY 2012 DP2

OCT/DEC 2011DP1

OCT/DEC 2012DP3

INSTRUMENT 4

END Y EARSTART Y EAR

CO

HO

RT

Y11

CO

HO

RT

Y10

CO

HO

RT

Y9C

OH

OR

TY8

CO

HO

RT

Y7

SUMMER HOLIDAYS

START Y EAR

INSTRUMENT 1

INSTRUMENT 2 INSTRUMENT 3

INSTRUMENT 1a INSTRUMENT 2

INSTRUMENT 4a

INSTRUMENT 5a

INSTRUMENT 6[TLRP-DP1]

INSTRUMENT 5

GCSE

GCSE

GCSE

“New” Qualifications [Functional Maths, New GCSE, Use of Maths AS]

“Traditional” Qualifications [Current GCSE, AS Maths]

Key for Student/Classroom Group:Traditional Examinations

Key for “Testing” condition:

“New” Experimenal Examinations

INSTRUMENT 3a

INSTRUMENT 2a

INSTRUMENT 3 INSTRUMENT 4

INSTRUMENT 5

3750-6250 surveys x 3

Average 15000

Average 15000

Average 15000

Average 15000

DATASTUDENT SURVEY DESIGN

SURVEY 1 SURVEY 2

TEACHERS SURVEY DESIGN DATAAverage

3000

TeLePriSM

DP1 – Participating schools and studentsAge range Boys only Girls only Mixed Total 11-16 0 2 13 15

11-18 1 5 19 25

Total 1 7 32 40

Year 7 3749

Year 8 2883

Year 9 2560

Year 10 1991

Year 11 1681

Total 12444

TeLePriSM

DP1 – Some preliminary findings

Top 10 favourite and least favourite topics

TeLePriSM

Key Strongly disagree Disagree Unsure Agree Strongly agree

Item name Frequency bars Mathematics is important to me.

Maths is one of the most interesting school subjects.

Learning maths is enjoyable for me.

I have a mathematical mind.

I can get good results in maths.

I am interested in learning new things in maths.

I can learn maths even if it is hard.

I like using familiar maths rather than new maths topics.

I am more worried about maths than any other subject.

I often need help with maths.

Compared to my classmates, I am good at maths.

I never want to take another mathematics course.

I would prefer my future studies to include a lot of maths.

I would look forward to studying more mathematics after school.

I would like to be a mathematician.

Maths is important for my future (after school)

Students’ attitudes to mathematics

TeLePriSM

Key Never Rarely Sometimes Always

Item name Frequency bars The teacher asks us questions.

The teacher tells us which questions/activities to do.

The teacher asks us to explain how we get our answers.

We listen to the teacher talk about the topic.

The teacher expects us to remember important ideas learnt in the past.

We copy the teacher's notes from the board.

The teacher gives us problems to investigate.

The teacher asks us what we already know about a lesson topic.

We discuss ideas with the whole classroom.

The teacher uses the computer to teach some topics.

We talk with other students about how to solve problems.

We work through exercises from the textbook.

We use calculators.

We ask other students to explain their ideas.

We explain our work to the whole class.

The teacher tells us to work more quickly.

The teacher tells us what value the lesson topic has for future use.

We work together in groups on projects.

What we learn is related with our out-of-school life.

We learn that mathematics is about inventing rules.

We get assignments to research topics on our own.

The teacher starts new topics with problems about the world.

We use computers.

We do projects (assignments) that include other school subjects.

We learn how mathematics has changed over time.

We use other things like newspapers, magazines, or video.

Students’ report of teaching practices

Our current ‘impact’ dilemma:

Reporting back to schools DP1: To who? What? How?

Thank you! Q&A

www.teleprism.com