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161 An SH. Capturing the Chinese way of teaching: the learning-questioning and learning-reviewing instructional model. In: How Chinese Learn Mathematics: Perspectives From Insiders. Fan LH, Fan NY, Wong, Cai JF, Li SQ (eds). Singapore: World Scientific, 2014:462–482.
162 Fan L, Miao Z, Mok I. How Chinese teachers teach mathematics and pursue professional development: perspectives from contemporary international research. In: How Chinese Teach Mathematics: Perspectives from Insiders. Singapore: World Scientific, 2014:43–70.
163 Schleppenbach M, Flevares LM, Sims LM, Perry M. Teachers’ responses to student mistakes in Chinese and US mathematics classrooms. The Elementary School Journal 2007;108(2):131–47.
164 Qiong LI, Yujing NI. Dialogue in the elementary school mathematics classroom: a comparative study between expert and novice teachers. Frontiers of Education in China 2009;4(4):526–40.
165 Fang Y. The cultural pedagogy of errors: teacher Wang’s homework practice in teaching geometric proofs. Journal of Curriculum Studies 2010;42(5):597–619.
166 Biggs JB. The Paradox of the Chinese Learner. Asian Contributions to Cross-Cultural Psychology 1996:180–199.
167 Watkins DA, Biggs JB. The Chinese Learner: Cultural, Psychological, and Contextual Influences. Hong Kong/Melbourne: CERC & ACER, 1996.
168 Li J. US and Chinese cultural beliefs about learning. Journal of Educational Psychology 2003;95(2):258.
169 Rao ZH. Understanding Chinese students’ use of language learning strategies from cultural and educational perspectives. Journal of Multilingual and Multicultural Development 2006;27:491–508.
170 Deci E, Ryan R. Handbook of Self-determination Research. Rochester, NY: University of Rochester Press, 2002.
171 Wang Q, Pomerantz EM. The motivational landscape of early adolescence in the US and China: a longitudinal investigation. Child Development 2009;80:1280–96.
172 Stevenson HW, Lee SY, Chen C, et al. Contexts of achievement: a study of American, Chinese, and Japanese children. Chicago: University of Chicago Press, 1990.
173 OECD. Ready to Learn: Students’ Engagement, Drive and Self-beliefs – Volume III. Paris: OECD, 2013.
174 Zhou N, Lam SF, Chan KC. The Chinese classroom paradox: a cross-cultural comparison of teacher controlling behaviors. Journal of Educational Psychology 2012;104:1162–74.
175 Chua A. Battle Hymn of the Tiger Mother. London: Bloomsbury Publishing, 2011:29.
176 Pratt D, Kelly M, Wong S. Chinese conceptions of “Effective Teaching” in Hong Kong: towards a culturally sensitive evaluation of teaching. International Journal of Lifelong Education 1999;18(4): 241–58.
177 Reuters. Wen says rote learning must go in Chinese schools. Available in: www.reuters.com/article/us-china-education-idUSTRE67U18Y20100831; 2010.
178 Tan C. Learning from Shanghai: Lessons on Achieving Educational Success. Germany: Springer, 2013.
179 BBC News: China universities ‘must shun Western values’. Available at: www.bbc.co.uk/news/world-asia-china-31052682
180 Adams GL, Engelmann S. Research on Direct Instruction: 25 Years beyond
DISTAR. Seattle: Educational Achievement Systems, 1996.
Hattie J. Visible Learning: A Synthesis of Over 800 Meta-analyses Relating to Achievement. New York: Routledge, 2008.
181 Glaser R, Chi MT. Overview. In: The Nature of Expertise . Hillsdale: Erlbaum, 1988: xv-xxvii.
182 New to BC. Diverse British Columbia: Immigration in Western Canada. Available at: http://newtobc.ca/2015/05/diverse-british-columbia-immigration-in-western-canada
183 OECD. Ontario, Canada: reform to support high achievement in a diverse context. In: Strong Performers and Successful Reformers in Education: Lessons from PISA for the United States. Paris: OECD, 2011.
184 Statistics Canada. Immigration and Ethnocultural Diversity in Canada. Available at: www12.statcan.gc.ca/nhs-enm/2011/as-sa/99-010-x/99-010-x2011001-eng.cfm
185 If you were to be irritated by the inconsistency between China entering different regions separately and Canada entering its different provincial systems as one country, you could say Canada came sixth in 2009 and ninth in 2012 out of all the countries (were we to lump China’s scores together as one entry).
186 Entorf H, Minoiu N. What a difference immigration law makes: PISA results, migration background and social mobility in Europe and traditional countries of immigration. In: ZEW-Centre for European Economic Research Discussion Paper, (04-017), 2004.
187 National Centre for Education Statistics International Data Explorer.
188 The three territories opted not to participate in PISA, partly due to inaccessibility (there are no roads connecting communities in Nunavut, you’d have to get a plane), which excluded 1.1 per cent of Canada’s student population from the tests.
189 Despite their similarities, provinces have quite different scores, much of
which can be explained by differences in student background. This explains more of the score difference between provinces than it does between countries, which makes sense given the similarities in policy. If all the countries in the world had identical education systems, they still wouldn’t all have the same results, but most of the variation would be due to student background. So it is with Canadian provinces – their similar approaches to education mean that less of the variation in their scores can be explained by their systems, and so more is explained by the children’s home lives.
190 Neil Guppy, Professor of Sociology and author of textbook on education in Canada, interviewed by the OECD for ‘Ontario, Canada: Reform to Support High Achievement in a Diverse Context’, Lessons from PISA for the United States, (OECD, 2011).
191 Cappon P. Think Nationally, Act Locally: A pan-Canadian strategy for education and training. (2014).
192 An evaluation of Quebec’s early years programme found negative effects on five-year-olds, with the authors suggesting that this was due to the children going in too young, for too long, and to poor quality settings without sufficient qualified staff.
Lefebvre P, Merrigan P, Verstraete M. Impact of Early Childhood Care and Education on Children’s Preschool Cognitive Development: Canadian Results from a Large Scale Quasi-Experiment. In: CIPEE. Working Paper 06–36, 2006. Available at: www.cirpee.org/fileadmin/documents/Cahiers_2006/CIRPEE06-36.pdf
193 The significant growth in the proportion of five-year-olds attending kindergarten (from about a third to almost all) happened during the 1960s.
194 Cornelius-White J. Learner-centered teacher-student relationships are effective: a meta-analysis. Review of Educational Research 2007;77(1):113–43.
195 Jennifer Walner. Learning to School: Federalism and Public Schooling in Canada. Toronto: Toronto University Press, 2014:54.
196 OECD (2014). Are grouping and selecting students for different schools related to students’ motivation to learn? PISA in Focus 39. Paris: OECD.
197 Pashler, H., McDaniel, M., Rohrer, D., & Bjork, R. (2008). Learning styles
concepts and evidence. Psychological Science in the Public Interest, 9(3), 105-119. p105.
198 In Ontario they have grade-level rubrics too, but they cannot include any ‘negative language’ like you see in BC’s ‘not yet within expectations’ box. Instead they focus on what the child did achieve.
199 For a much better explanation of this idea, see Daisy Christodoulou’s blog ‘The Wing to Heaven’ in which she writes about comparative judgement.
200 In a sense, even criterion-referenced exams are based on what is normal for a particular age-group, because it is human beings deciding on the criteria, and their decision is likely to be based on what children have been able to achieve in previous years. If the scenario above actually happened, and all Grade 4 Canadian children met or exceeded the grade-level expectations, there would no doubt be criticism, or at least self-reflection, about whether the expectations were high enough. Nevertheless, there is still a clear distinction between an assessment in which children are judged against standards, and an assessment
in which they are judged against each other.
201 British Columbia Ministry of Education. Gifted Education – A Resource Guide for Teachers. Available in: www.bced.gov.bc.ca/specialed/gifted/giftedlearners.htm; accessed dates: 2nd June 2016
202 Hattie J. Visible Learning: A Synthesis of Over 800 Meta-analyses Relating to Achievement. Abingdon: Routledge, 2008.
203 Kanevsky LS. A survey of educational acceleration practices in Canada. Canadian Journal of Education 2011;34(3):153–80.
204 King LA, Burton CM. The hazards of goal pursuit. In: Chang EC, Lawrence J (eds). Virtue, Vice, and Personality: The Complexity of Behavior. Washington, DC: American Psychological Association, xxvi, 2003:53–69.
205 Dunae P. The School Inspectorate 1856 – 1973. Available in: www2.viu.ca/homeroom/content/Topics/Programs/inspect.htm
206 Hough LM, Oswald FL. Personnel selection: Looking toward the future—remembering the past. Annual Review of Psychology 2000;51:631–64.
207 Döbert H, Klieme E, Sroka W. Conditions of School Performance in Seven Countries. Waxmann Verlag, 2004.
208 Stokke A. What to do about Canada’s declining math scores. Commentary 427, CD. Howe Institute, Toronto, 2015. Available at: www.cdhowe.org/sites/default/files/attachments/research_papers/mixed/commentary_427.pdf
209 Here problem-based learning is defined after Gijbels (2005), who outlined six core characteristics: learning is student-centred; learning occurs in small groups; a tutor is present as a facilitator or guide, authentic problems are presented at the beginning of a learning sequence; the problems encountered are used as tools to achieve the required knowledge and the problem-solving skills necessary to eventually solve the problem; and new information is acquired through self-directed learning. Often the terms ‘problem based learning’ and ‘discovery learning’ are used interchangeably, although Hmelo-Silver et al. suggest that there are clear distinctions between them; that discovery based learning involves less teacher guidance and is therefore less effective. As the research quoted refers to problem-based learning, the overall lack of evidence of its effectiveness on supporting knowledge and understanding in school-aged children should therefore worry us even more.
Gijbels D, Dochy F, Van den Bossche P, Segers M. Effects of problem-based learning: a meta-analysis from the angle of assessment. Review of Educational Research 2005;75(1):27–61.
Hmelo-Silver CE, Duncan RG, Chinn CA. Scaffolding and achievement in problem-based and inquiry learning: a response to Kirschner, Sweller, and Clark (2006). Educational Psychologist 2007;42(2):99–107.
210 Kirschner PA, Sweller J, Clark RE. Why minimal guidance during instruction does not work. Educational Psychologist 2006;41(2):75–86.
211 Hattie J. Visible learning: a synthesis of over 800 meta-analyses relating to achievement. Abingdon: Routledge, 2008.
212 Echazarra A, Salinas D, Méndez I, et al. How Teachers Teach and Students Learn. Paris: OECD, 2016.
213 This is the argument that due to working memory limitations, children are limited in the extent to which they can solve problems without relevant prior knowledge – as expressed in Kirschner et al. (2006).
214 Haeck C, Lefebvre P, Merrigan P. All students left behind: an ambitious provincial school reform in canada, but poor math achievements from grade 2 to 10. Available at: SSRN 1966937; 2011.
215 Coe R, Aloisi C, Higgins S, Elliot Major L. What makes great teaching? Review of the underpinning research. Centre for Evaluation and Monitoring/The Sutton Trust, Durham, 2014.
216 Didactique has a lot in common with PCK, but it’s not quite the same thing.
Within the continental European tradition (which is the Quebecois use of diadctique comes from) it also includes issues of curriculum design, such as the relative strength and weakness of various metaphors for teaching mathematics. Examples are whether you introduce negative numbers as bank balances, temperatures, heights below sea-level, and so on. Many thanks to Dylan Wiliam for pointing out this distinction.
217 Hattie (2008): 211
218 Not every country I visited adheres to all five principles, but each principle is followed by at least four of the five top-performing systems.
219 Formby S. Children’s early literacy practices at home and in early years settings: Second annual survey of parents and practitioners. National Literacy Trust, 2014.
220 Aunio P, Aubrey C, Godfrey R, et al. Children’s early numeracy in England, Finland and People’s Republic of China. International Journal of Early Years in Education 2008;16(3):203–21.
221 Alexander R. The Education of Six Year Olds in England, Denmark and Finland: An International Comparative Study. London: Ofsted, 2003.
222 Nah KO. A comparative study of mathematics education practices in English and Korean preschools focusing on implementation of curriculum content. KEDI Journal of Educational Policy 2011;8(1):
223 Whitburn J. Contrasting approaches to the acquisition of mathematical skills: Japan and England. Oxford Review of Education 1996;22(4):415–34. Although this research was conducted in 1996, the findings are still true – Japanese preschool is still entirely play-based.
224 Bassok D, Latham S, Rorem A. Is Kindergarten the new first grade? Working Paper Series, No. 20. Available at: http://curry.virginia.edu/uploads/resourceLibrary/20_Bassok_Is_Kindergarten_The_New_First_Grade.pdf; 2015.
225 Sylva K, Nabuco M. Research on quality in the curriculum. International Journal of Early Childhood 1996;28(2):1–6.
Elkind D, Whitehurst G. Young Einsteins. Much too early: much too late. Education Matters 2001;1(2):8–21.
Dee T, Sievertsen H. The gift of time? School starting age and mental health. NBER Working Paper No. 21610, 2015. Available at: http://www.literacytrust.org.uk/assets/0002/4082/EY_Final_report_2014.pdf
Black S, Devereux P, Salvanes K. Too young to leave the nest? The effects of school starting age. The Review of Economics and Statistics 2011;93(2):455–67.
226 Kavkler M, Tancig S, Magajna L, Aubrey C. Getting it right from the start? The influence of early school entry on later achievements in mathematics. European Early Childhood Education Research Journal 2000;8(1):75–93.
McGuinness C, Sproule L, Bojke C, Trew K, Walsh G. Impact of a play-based curriculum in the first two years of primary school: literacy and numeracy outcomes over seven years. British Educational Research Journal 2014;40(5):772–95.
Schmerkotte H. Ergebnisse eines Vergleichs von Modellkindergarten und Vorklassen in Nordrhein-Westfalen Results from a comparison of typical kindergartens and preschools in North Rhine-Westphalia. Bildung und Erziehung 1978;31:401–11.
227 Marcon R. Moving up the grades; relationship between pre-school model and later school success. Early childhood Research and Practice 2002;4(1):517–30.
Suggate S, Schaughency E, Reese E. Children learning to read later catch up to children reading earlier. Early Childhood Research Quarterly 2013;28:33–48.
228 Aunio P, Aubrey C, Godfrey R, Pan Y, Liu Y. Children’s early numeracy in England, Finland and People’s Republic of China. International Journal of Early Years Education 2008;16(3):203–21.
229 Heckman JJ. Schools, skills, and synapses. Economic Inquiry 2008;46(3):289–324.
230 ibid.
231 Aunio, et al. (2008).
232 Ee J, Wong K, Aunio P. Numeracy of Young Children in Singapore, Beijing Helsinki. Early Childhood Education Journal 2006;33(5).
233 Nurturing Early Learners: A curriculum for kindergartens in Singapore. Numeracy. Available from: www.moe.gov.sg/docs/defaultsource/document/education/preschool/files/nel-edu-guide-numeracy.pdf
234 OECD (2015). Helping Immigrants Succeed at School – and Beyond. Available from: https://www.oecd.org/education/Helping-immigrant-students-to-succeed-at-school-and-beyond.pdf
235 Bransford JD, Brown AL, Cocking RR. How People Learn: Brain, Mind, Experience, and School. Washington DC: National Academy Press, 1999.
236 I have drawn heavily on the work of Tim Oates (2010) and Schmidt and Prawat (2006) for
this section, and recommend their work for further reading.
Oates T. Could Do Better. Cambridge: Cambridge Assessment, 2010.
Schmidt WH, Prawat RS. Curriculum coherence and national control of education: issue or non_issue? Journal of Curriculum Studies 2006;38(6):641–58.
237 NB. Having a national curriculum needn’t mean it is designed by the government – it could be a national non-governmental body. The important thing is that it is credible to teachers.
238 Van de Werfhorst HG, Mijs JJ. Achievement inequality and the institutional structure of educational systems: a comparative perspective. Annual Review of Sociology 2010;36:407–28.
239 Thanks to Tim Oates for pointing out this distinction.
240 PISA finds that, after accounting for socio-economic status and performance in reading and mathematics, immigrant students are 44 per cent more likely than non-immigrant students to be enrolled in vocational programmes. The systematic tracking of disadvantaged immigrants into vocational tracks and less-demanding courses not only limits the academic skills they may acquire, but also creates an additional barrier into high-status professional occupations later on.