Improving Maths in Key Stage 2 & 3

References

  1. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.; Coe, R., Aloisi, C., Higgins, S., & Major, L. E. (2014). What makes great teaching? Review of the underpinning research. London: The Sutton Trust; Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Tsai, Y.-M. (2010). Teachers' Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress. American Educational Research Journal, 47(1), 133-180. doi:10.3102/0002831209345157
  2. http://tdtrust.org/about/dgt
  3. Dowker, A. (forthcoming). Review of Mathematics Education Programmes. London: The Education Endowment Foundation.
  4. Higgins, S., Katsipataki, M., Coleman, R., Henderson, P., Major, L.E., Coe, R. & Mason, D. (2018). The Sutton Trust-Education Endowment Foundation Teaching and Learning Toolkit. London: Education Endowment Foundation.
  5. Elliott, V. et al (2016). A marked improvement? A review of the evidence on written marking. London: Education Endowment Foundation.
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  7. More information about the common misconceptions and misunderstandings which students develop in different mathematical topics can be found in the following texts.
  8. Ibid.
  9. 9 Hansen, A. (Ed.) (2017). Children's Errors in Mathematics (4th ed.). London: Sage.; Ryan, J., & Williams, J. (2007). Children’s mathematics 4-15: Learning from errors and misconceptions. McGraw-Hill Education.; Hart, K. M., Brown, M. L., Kuchemann, D. E., Kerslake, D., Ruddock, G., & McCartney, M. (1981). Children’s understanding of mathematics: 11-16. London: John Murray.
  10. Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380.
  11. NCETM curriculum glossary https://www.ncetm.org.uk/public/files/17308038/ National+Curriculum+Glossary.pdf
  12. Carbonneau, K. J. et al. (2013)
  13. Nunes, T. et al. (2009)
  14. Carbonneau, K. J. et al. (2013)
  15. Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183-198. doi: 10.1016/j.learninstruc.2006.03.001
  16. Ainsworth, S. (2006)
  17. Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http:// ies.ed.gov/ncee/wwc/publications_reviews.a...
  18. Gersten, R. et al (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies. ed.gov/ncee/wwc/publications/practiceg...
  19. Siegler, R. et al (2010). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE #2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from whatworks.ed.gov/ publications/practiceguides.
  20. Brown, J. S., & Van Lehan, K. (1982). Towards a generative theory of 'bugs'. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and Subtraction: A cognitive perspective. Hillsdale, NJ: Lawrence Erlbaum
  21. Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 433-463.; Hembree, R., & Dessart, D. J. (1986). Effects of hand-held calculators in precollege mathematics education: A meta-analysis. Journal for research in mathematics education, 17(2), 83-99
  22. Ruthven, K. (1998). The Use of Mental, Written and Calculator Strategies of Numerical Computation by Upper Primary Pupils within a 'Calculator-Aware' Number Curriculum. British Educational Research Journal, 24(1), 21-42
  23. Siegler et al. (2010)
  24. Ibid.
  25. Nunes, T., Bryant, P., & Watson, A. (2009). Key understandings in mathematics learning. London: Nuffield Foundation.
  26. Jones, I., & Pratt, D. (2012). A Substituting Meaning for the Equals Sign in Arithmetic Notating Tasks. Journal for Research in Mathematics Education, 43(1), 2-33.
  27. Nunes, T. et al. (2009)
  28. Muijs, D. et al (forthcoming), Evidence review for the EEF metacognition review. London: Education Endowment Foundation.
  29. The EEF will publish a guidance report on self-regulation and metacognition in 2018.
  30. Lai, E. R. (2011). Metacognition: A literature review. Always learning: Pearson research report.
  31. Wittwer, J., & Renkl, A. (2010). How effective are instructional explanations in example-based learning? A meta-analytic review. Educational Psychology Review, 22(4), 393-409.
  32. Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281-310.
  33. Rittle-Johnson, B., Loehr, A. M., & Durkin, K. (2017). Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM, ZDM Mathematics Education, 49 (4), pp. 1-13599–611
  34. Ellis, A. K., Denton, D. W., & Bond, J. B. (2014). An analysis of research on metacognitive teaching strategies. Procedia-Social and Behavioral Sciences, 116, 4015-4024.
  35. Kyriacou, C. and Issitt, J. (2008) What characterises effective teacher-initiated teacher-pupil dialogue to promote conceptual understanding in mathematics lessons in England in Key Stages 2 and 3: a systematic review. Technical report. In: Research Evidence in Education Library. London: EPPI-Centre, Social Science Research Unit, Institute of Education, University of London.
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  38. Greany, T., Barnes, I., Mostafa, T., Pesniero, N., & Swenson, C. (2016). Trends in Maths and Science Study (TIMSS): National Report for England. London: Department for Education
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  41. Petronzi. D. (2016). The Development of the Numeracy Apprehension Scale for Children Aged 4-7 Years: Qualitative Exploration of Associated Factors and Quantitative Testing. University of Derby: Ph.D. Thesis.
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  43. Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp 319-369). Charlotte, NC: Information Age Publishing).
  44. Higgins, S., Xiao, Z. and Katsipataki, M. (2012) The Impact of Digital Technology on Learning: A Summary for the Education Endowment Foundation. London: Education Endowment Foundation. https://educationendowmentfoundation.org.uk/public... The_Impact_of_Digital_Technologies_on_Learning_(2012).pdf
  45. Evaluations of interventions can be found in the upcoming EEF review of mathematics programmes, on the projects section of the EEF website, or in the Evidence 4 Impact database maintained by the Institute for Effective Education.
  46. Dowker, A. (forthcoming). Review of Mathematics Education Programmes. London: The Education Endowment Foundation.
  47. Gersten, R. et al (2009).
  48. Dowker, A. (2009). What Works for Children with Mathematical Difficulties? The Effectiveness of Intervention Schemes. London: Department of Children, Schools and Families. Kaufmann, L., Mazzocco, M. M., Dowker, A., von Aster, M., Göbel, S. M., Grabner, R. H., Henik, A., Jordan, N., Karmiloff-Smith, A. D., Kucian, K., Rubinsten, O., Szucs, D., Shalev, R., & Nuerk, H. C. (2013). Dyscalculia from a developmental and differential perspective. Frontiers in Psychology 4: 516
  49. Brown, M., Askew, M., Hodgen, J., Rhodes, V., Millett, A., Denvir, H., & Wiliam, D. (2008). Individual and cohort progression in learning numeracy ages 5-11: Results from the Leverhulme 5-year longitudinal study. In A. Dowker (Ed.), Mathematical Difficulties: Psychology and Intervention (pp. 85-108). Oxford: Elsevier.Higgins, S., Katsipataki, M., Coleman, R., Henderson, P., Major, L.E., Coe, R. & Mason, D. (2018). The Sutton Trust-Education Endowment Foundation Teaching and Learning Toolkit. London: Education Endowment Foundation
  50. Higgins, S., Katsipataki, M., Coleman, R., Henderson, P., Major, L.E., Coe, R. & Mason, D. (2018). The Sutton Trust-Education Endowment Foundation Teaching and Learning Toolkit. London: Education Endowment Foundation.