Building on Transmaths: TeLePriSM Teaching and Learning Practices in Secondary Mathematics Maria...
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Transcript of Building on Transmaths: TeLePriSM Teaching and Learning Practices in Secondary Mathematics Maria...
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-Dec2007
TIME
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
UoM
AS
APR/MAY 2012 DP2
OCT/DEC 2011DP1
OCT/DEC 2012DP3
INSTRUMENT 4
END Y EARSTART Y EAR
CO
HO
RT
Y1
1C
OH
OR
TY
10
CO
HO
RT
Y9
CO
HO
RT
Y8
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…
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
TeLePriSM
The survey design…Data Point 1 (DP1)
UoM
AS
APR/MAY 2012 DP2
OCT/DEC 2011DP1
OCT/DEC 2012DP3
INSTRUMENT 4
END Y EARSTART Y EAR
CO
HO
RT
Y1
1C
OH
OR
TY
10
CO
HO
RT
Y9
CO
HO
RT
Y8
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
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