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academic depth and rigour in the B.ED Feb 12 2014, NWU

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?.

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academic depth and rigour in the B.ED Feb 12 2014, NWU

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  1. academic depth and rigour in the B.EDFeb 12 2014, NWU Hamsa Venkat, SA Numeracy Chair, Wits

  2. 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

  3. 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.’

  4. Theorizing teacher education Content Knowledge Methodology OR Content Knowledge PCK Methodology Methodology Content knowledge Methodology Content knowledge

  5. Theorizing teacher knowledge CK PCK Knowledge of content & students Common content knowledge Specialized content knowledge Knowledgeof curriculum Horizon knowledge Knowledge of content & teaching Deborah Ball and colleagues: ‘Mathematical knowledge for teaching’

  6. Mathematical knowledge for teaching CK PCK Knowledge of content & students Common content knowledge Specialized content knowledge Knowledgeof curriculum Horizon knowledge Knowledge of content & teaching

  7. Mathematical knowledge for teaching CK PCK Knowledge of content & students Common content knowledge Specialized content knowledge Knowledgeof curriculum Horizon knowledge Knowledge of content & teaching

  8. 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

  9. 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.

  10. Anecdotes from mathsed • 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

  11. Priorities for maths teacher education CCK with an SCK orientation PCK General methodology ‘Practical theory’

  12. 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 4 x 30 600 x 30 20 x 30 600 x 4 20 x 4 4 x 4

  13. Emphasis (and possible critique) teacher learner object of learning

  14. 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

  15. 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!

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