Bogota, Colombia, 22 November 06 The preparation and professional development of mathematics...

Bogota, Colombia, 22 November 06

The preparation and professional development of mathematics

teachers

Challenges, initiatives and innovations in post-apartheid South

Africa

Professor Jill AdlerChair of Mathematics Education

Marang Centre for Mathematics and Science EducationUniversity of the Witwatersrand. South Africa.


OVERVIEW

• Mathematics teacher education• Challenges (across contexts)• Education in post apartheid South Africa• Examples from institutional initiatives for

pre- and in-service (professional deevelopment) mathematics teacher education – Curriculum innovation and restructuring


Mathematics teacher education research and practice

• Relatively young research and development field

• We now “know” some things (includes knowing what we don’t yet know or understand)culture and pedagogyTeacher education Teaching Learning


Central dilemmas

• What to select in from mathematics, mathematics education, general education– How much? “More” math quality teaching– What kind? PCK? Integration?

• How are prospective teachers best taught? Methods?

• Where - learning in and from practice• When - Professional development lifelong and

continuous


Challenges - multifaceted

• Recruitment and retention– Relative status of profession– Recruitment from other countries - drifts

• Preparing and supporting teachers for– Demands on them in a reform context

• New technologies and competencies

– Changing classroom conditions in schools• Composition – diversity, poverty• Migration to cities

– Magnets of hope; contexts of alienation


Education in South Africa

• Complex conditions– Pervasive legacies of apartheid– Post apartheid reform

• Extensive policy change• Rapid implementation


Legacy of apartheid education• Deep systemic inequalities

• Co-existance of rich and poor - unevenly spread across country; majority of poor also rural

• Gross under-development of mathematics and science in ‘black’ schooling

• Perverse language-in-education policy• Key factor in mathematics performance (TIMSS)

• Teacher education - colleges, 3 year diplomas• Poor orientation to subject (e.g. math)• Under and un-qualified teachers in system• Shortages (quality and quantity) in mathematics

Redress, repair and reform


Post-apartheid education reform

First democratic government 1994 – 12 years ‘young’

• Rationalisation into single system• New curriculum policy and curricula for schooling

– new knowledge and applied competencies (integrated knowing … learner-centred pedagogies)

– New technologies• Radical change in classroom composition - demographic,

cultural and linguistic• New language-in-education policy (politics of access to

English)• New ‘norms and standards’ - policy for teacher education• Implementation scale and time scale - political imperatives• Context of multiple, competing social demands, and onset

and spread of HIV-AIDS


New School Mathematics Curriculum• Gr 0 -9 (GET); Gr 10 - 12 (FET)• New topics and orientations to mathematics

knowledge and know-how– Knowledge, skills and values– Aligns with strands of mathematical “proficiency”

• Introduction of Mathematical Literacy Gr 10 – 12 (Compulsory)

• Mathematics for ‘science’ and for ‘citizenship’


For teacher education

Restructuring of Higher Education (HEIs)• Closure of numerous ‘apartheid” colleges of education• Location of teacher education and formal upgrading in

Universities

New teacher qualifications• Four year UG B Ed for primary and secondary teachers

– Specialisations at levels and in subjects• Upgrading diplomas and degrees

– Partnerships between private funding, NGOs and HEIs

• Demands on tertiary institutions to meet this

challenge


A (mathematical) problem of Teaching

A negative times a negative gives a positive

Why?

How would you convince learners?

Knowledge of mathematics

Metaphors, contexts, associated obstacles


Another (math) problem of teaching

The sum of three consecutive even numbers is 60. Find the three numbers. Expected response:2x + (2x + 2) + (2x + 4) = 60

Learner's response:

Let numbers be x, x + 2, x + 4then x + x + 2 + x + 4 = 60 3x = 54 Numbers are 18, 20, 22

Mathematical work of teaching Why does a definition of

" x, x + 2, x + 4" work? Will this definition always work

for problems like this? What if we changed 60 to:

64, 54, 600? Why can't we express the

general sum of 3 consecutive even numbers as

"x + x + 2 + x + 4"?


And one more

Task set for Gr 10 - Sept 2006

How many diagonals are there in a 700 sided polygon?

Reponse 1. 350

Explain? I divided by 2

Reponse to 1: I took four sides - its easier with smaller number of sides and 2 is right


What kind of math work is this?• Provoking, interpreting and responding to

learners’ mathematical thinking– Setting up tasks (nature of task, selection of examples -

numbers …)– Representing, rescaling – Defining, explaining– Probing - questions (Ball & Bass)

• Current research suggests its topic specific• Where is this math problem-solving taught?

learned?


Overview of B.Ed Programme:Snr/FET Maths

• Components– Mathematical content

• 2 compulsory maths courses • 8 elective courses in maths

– Methodology • 2 courses in maths methodology

– Practice of teaching• 24 weeks in schools, approx 15 weeks of

maths


Overview of B.Ed Programme:Snr/FET Maths

Year Courses for Snr/FET Maths teachers

1 Functions and algebra Geometry and trigonometry

2 Introductory calculusIntroductory vector and matrix algebra 1st methodology course

3 Mathematical modellingStatistics

4 Mathematical connectionsFinancial mathematics 2nd methodology course


Issues

Covering content versus developing a mathematical discourse community

Integration versus separation of content and methodology

Preparing students for the practice of maths teaching


Coverage of content versus developing a mathematical discourse community

• We cannot separate what maths is learnt from how it is learnt – investigating mathematical ideas– learning mathematical practices– developing mathematical habits of mind– learning to talk about own mathematical ideas– critiquing the arguments of fellow students

– reflecting on own learning


Coverage of content versus developing a mathematical discourse community

• Challenging students’ notions of what mathematics is, and how it is best taught and learnt

• More effective to do this in content courses than in methods courses


Given conditions in post apartheid mathematics teacher education in South Africa, mathematics for teaching needs specific attention in UG and formal inset, within mathematics courses -

where benefits for teaching about teaching mathematics are tied to what and how students do

maths, and reflect on this doing and learning.

In conclusion …


Thank you Ngiyabonga

Bogota, Colombia, 22 November 06 The preparation and professional development of mathematics...

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