Sheila Henderson University of Dundee

Transcription

1 Uniwersytet Łódzki Why the journey to mathematical excellence may be long in Scotland s primary schools Sheila Henderson University of Dundee The 6th Annual Conference of Teacher Education Policy in Europe 17th 19th May 2012, Warsaw, Poland T E P E 2012

2 Reasons for the paper Theoretical context Wydział Nauk o Wychowaniu Structure of presentation Mathematics achievement in Scotland Radical reform or business as usual? A three-pronged solution

3 Reasons for paper New curriculum introduced in Scotland Curriculum for Excellence (CfE) Ongoing concerns about levels of achievement in mathematics Previous studies on student primary teachers levels of mathematics competence and confidence (Henderson & Rodrigues 2008; Henderson 2012) Review of teacher education in Scotland (Donaldson 2010)

4 Constructivism Theoretical context reform pedagogies around the world mathematical thinking v procedural mathematics increasing teacher autonomy does this deskill teachers? (Henderson & Cunningham 2011) Mathematics knowledge for teaching SMK and PCK (Shulman 1986; 1987) KCS and KCT (Ball et al. 2008) Both require sound subject knowledge

5 Mathematics achievement in Scotland Scottish Survey of Achievement (SSA) Percentage of children who have well established or very good skills at expected 5-14 levels P3 87% of children have well-established or very good skills at the expected 5-14 levels P7 47% S2 30% (Scottish Government 2009a)

6 Scotland s mathematics achievement internationally Trends in International Mathematics and Science Survey (TIMSS) Scale average of 500 used (Number) P5 481 (significantly lower) Yet 56% of time devoted to number (50% avge) S2 489 (significantly lower) Yet 36% of time devoted to number (24% avge) Advanced benchmark of 625 P5 significantly lower than 1995 S2 significantly lower than 2003 (IEA 2008)

7 Radical reform or business as usual? See handout

8 Table progression of rounding numbers Level B Level C Level D Level E Level F Round 2-digit whole numbers to the nearest 10 Round 3 digit whole numbers to the nearest 10 (e.g. when estimating) Round any number to the nearest appropriate whole number, ten or hundred Round any number to one decimal place Round to a required number of decimal places and significant figures Adapted from SOED (1991), SEED (1999)

9 Table 2 CfE progression of rounding numbers First Level I can share ideas with others to develop ways of estimating the answer to a calculation or problem, work out the actual answer, then check my solution by comparing it with the estimate. Second Level I can use my knowledge of rounding to routinely estimate the answer to a problem then, after calculating, decide if my answer is reasonable, sharing my solution with others. Third Level I can round a number using an appropriate degree of accuracy, having taken into account the context of the problem. Adapted from Scottish Government (2009b)

10 Advised pedagogies Table 3

11 1. Qualifications More advanced qualifications don t equal teaching effectiveness (Askew et al. 1997a; Ma 1999) More advanced qualifications don t equal greater competence or confidence (Henderson & Rodrigues 2008; Henderson 2012) More in-depth understanding of primary curriculum needed instead? (Burghes 2009)

12 2. Initial Teacher Education Anecdotal evidence English approach University of Dundee approach Online Maths Assessment Review of teacher education (Donaldson 2010)

13 3. Continuing Professional Development Maths focused CPD is best (DMTPC?) Longer sessions have more impact Who attends these? (Askew et al. 1997b) MaST programmes Current economic climate

14 Ambitious aims of CfE Opportunities and challenges Conclusions Success dependent on sound subject knowledge Finally teachers, in spite of courses and workshops, are most likely to teach maths just as they were taught (Ball 1988)

15 Questions? Paper to be published in Scottish Educational Review May 2012

16 References Askew, M., Brown, M., Rhodes, V., Johnson, D. and Wiliam, D. (1997a). Effective Teachers of Numeracy: Final Report. London: King's College. Askew, M., Brown, M., Rhodes, V., Johnson, D. and Wiliam, D. (1997b). The contribution of professional development to effectiveness in the teaching of numeracy. Teacher Development, 1, 3, Ball, D. L. (1988) Unlearning to teach mathematics. For the Learning of Mathematics, 8 (1), Ball, D.L., Thames, M.H. & Phelps, G. (2008) Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), Burghes, D. (2009). A radical change? The right teachers, the right system. In S. Lawlor(ed), Teachers Matter: Recruitment, Employment and Retention at Home and Abroad, The Report of the Politeia Education Commission. London: Politeia, Donaldson, G. (2010). Teaching Scotland s future: report of a review of teacher education in Scotland. Edinburgh: Scottish Government. Heaton, R. M. (1992). Who is minding the mathematics content? A case study of a fifth-grade teacher, The Elementary School Journal, 93, 2, Henderson, S. & Rodrigues, S. (2008). Scottish student primary teachers levels of mathematics competence and confidence for teaching mathematics: Some implications for national qualifications and initial teacher education, Journal of Education for Teaching, 34, 2, Henderson, S. (2012). Student primary teachers improving their mathematics subject knowledge: cognition and affect intertwined, Journal of Education for Teaching, 38, 5, (in press). Henderson, S. & Cunningham, E. (2011). Curriculum Reform in Scotland: Principles and Practice. In B. Hudson & M Meinart(eds.). Beyond Fragmentation: Didactics, Learning and Teaching in Europe. Leverkusen-Opladen: Barbara Budrich Publishers. IEA (2008). Trends in Mathematics and Science Survey Lynch School of Education, Boston College: International Association for the Evaluation of Educational Achievement. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum. Scottish Government (2009a) Scottish Survey of Achievement: Mathematics and Core Skills. Available online at Scottish Government (2009b) Curriculum for Excellence: Numeracy and mathematics experiences and outcomes. Available online at: SEED (1999). National Guideline 5-14: Mathematics Level F. Edinburgh: Scottish Executive Education Department. Shulman, L. S. (1986). Those who understand: Knowledge growth for teaching, Educational Researcher, 15, Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform, Harvard Educational Review, 57, 1, SOED (1991). National Guidelines 5-14: Mathematics. Edinburgh: Scottish Office Education Department.