ACADEMIC DEPTH AND RIGOUR IN THE B.ED

FEB 12 2014, NWU

Hamsa Venkat, SA Numeracy Chair, Wits

Why do we need to focus on this?

Widespread evidence of gaps in discipline-related knowledge base of teachers in the system – at the levels of CK and PCK (Taylor & Vijnevold, 1999 > Spaull, 2013)

Leading, two decades into democracy, to questions about what is happening within pre-service teacher education

Anecdotal evidence, and emerging research evidence of significant differences in content across institutions, and in whether disciplinary content is dealt with in ‘integrated’ or ‘stand-alone’ ways

Teachers’ mathematical knowledge in SA

Carnoy, Chisholm et al (2008) – G6 teachers scoring at around 60% mark on test focused on G5-related CK and PCK items

Taylor (2011) – G4 and 5 teachers taking 5 items drawn from G6 curriculum content: ‘Two-thirds of the teachers could answer only three questions, and just 12% could answer all five’.

Van der Berg et al (2011 ) – large differences in measures of teacher knowledge did not seem to play out as differences in learner scores: ‘may be that the ability to teach students well at a Grade 6 level is more dependent on the teacher’s ability to convey knowledge.’

Theorizing teacher educationContent Knowledge

Methodology

OR

Content Knowledge Methodology

PCK

Theorizing teacher knowledge

Deborah Ball and colleagues: ‘Mathematical knowledge for teaching’

Knowledge of content & students

Knowledge of content & teaching

Knowledge of curriculum

Specialized content knowledge

Common content knowledge

Horizon knowledge

CK PCK

Mathematical knowledge for teaching

Knowledge of content & students

Knowledge of content & teaching

Knowledge of curriculum

Specialized content knowledge

Common content knowledgeHorizon knowledge

CK PCK

Mathematical knowledge for teaching

Knowledge of content & students

Knowledge of content & teaching

Knowledge of curriculum

Specialized content knowledge

Common content knowledge

Horizon knowledge

CK PCK

Specialized content knowledge

Presenting mathematical ideas

Responding to students’ “why” questions

Finding an example to make a specific mathematical point

Recognizing what is involved in using particular representations

Linking representations to underlying ideas and to other representations

Connecting a topic being taught to topics from prior or future years

Appraising and adapting the mathematical content of textbooks

Modifying tasks to be either easier or harder

Giving/evaluating mathematical explanations

Evaluating the plausibility of students’ claims

Choosing and developing useable definitions

Asking productive mathematical questions

Anecdotes from maths teaching

Halving’ is the topic being dealt with in a Grade 2 class. The task in focus is working out ‘Half of 26’.

Each pair in the class is asked to make 26 balls from clay – which they do. The teacher’s explanation proceeds as follows: ‘I want us to count to 13, and move those balls aside. How many balls are on the other side? 13 as well. So 13 is half of 26.

Anecdotes from maths ed

Is a square a rectangle or is a rectangle a square? Confusion among some 4th year secondary maths B Ed students.

‘Radians, yes, 2π = 360° and π = 180° HV: Yes, so what are radians? These things we are talking about? PGCE sec maths students: No answer

Priorities for maths teacher education

PCKCCK with an SCK orientation

‘Practical theory’

General methodology

CCK with an SCK orientation

627 × 34 =

‘I can think about this as (600 + 20 + 7) × (30 + 4). I do this because …. [multiples and powers of 10 are easy numbers to multiply by]

‘I can represent this multiplication as an area:

600 20 4 30 4

600 x 30 20 x 304 x 30

600 x 4 20 x 4 4 x 4

Emphasis (and possible critique)

learner object of learning

teacher

Ways forward

Opening up discussion around differences at the level of content and orientation within disciplines across different tertiary institutions – JET study could kick this off.

Establishing forums where these issues can be debated, collaborative monitoring instituted, and a basis for greater shared foundations for what we believe and want our children to be able to do, and how we think about a teacher education that aligns with these goals.

AMESA and SAERA conferences – possible places to start

Ways forward

Opening up discussion around differences at the level of content and orientation within disciplines across different tertiary institutions – JET study could kick this off.

Establishing forums where these issues can be debated, collaborative monitoring instituted, and a basis for greater shared foundations for what we believe and want our children to be able to do, and how we think about a teacher education that aligns with these goals.

AMESA and SAERA conferences – possible places to start

Thank

you!