Research and reading

All of the CA publications, indeed the whole of Cognitive Acceleration, are the result of many years of research. The first project of this nature, CASE (Cognitive Acceleration through Science Education) began some 22 years ago, at King's College, London, and was directed by Professor Michael Shayer and Professor Philip Adey.

The aim of this page is to highlight some of the research publications relating to CA and to provide these papers for public consumption, also to indicate some reading material around some of the wider issues raised by What is CA? to learning and professional development.

If you want to read a selection of articles (both published and unpublished) written by practitioners teaching CA and developing a CA approach in their schools, see our Practitioner's Perspective page.

Key CA texts
Classroom practice and professional development
Research on effects of CA intervention
Cognitive development theory background to CAME
Mathematics curriculum background to CAME
Related reading - how What is CA? fits with current initiatives in education
CA in the press - recent related articles

Key CA texts

Adey, P & Shayer, M (1994) Really Raising Standards. London: Routledge
Adhami, M (2002) Cognitive Acceleration in Years 5 and 6: problems and challenges. In Learning Intelligence, (Eds. M Shayet and P Adey) Open University Press, 2002, pp99-117
Shayer, M, & Adey, P (Eds) (2002) Learning Intelligence: Cognitive Acceleration Across the Curriculum from 5 to 15 Years. Milton Keynes: Open University Press
Shayer, M & Adhami, M (2004). Realising the cognitive potential of children 5-7 with a mathematics focus. International Journal of Educational Research 39, 743-775
Shayer, M & Wylam, H (1978) The distribution of Piagetian stages of thinking in British middle and secondary school children II: 14-16 year olds and sex differentials. British Journal of Educational Psychology, 48, 62-70
Shayer, M & Adhami, M (2007) Fostering cognitive development through the context of mathematics: results of the CAME project, Educational Studies in Mathematics, pp 256-291

Classroom practice and professional development

Adey, P, Hewitt, G, Hewitt, J, & Landau, N (2004) The Professional Development of Teachers: Practice and Theory. Dordrecht: Kluwer Academic
Adhami, M., Johnson, D.C. & Shayer, M. (1995). Cognitive Acceleration through Mathematics Education - Towards a theory of instruction and instruction. Paper presented at the British Congress of Mathematics Education (BCME) July 1995
Adhami, M., Johnson, D.C. & Shayer, M. (1996). Theory-based lessons as a focus for professional development. Paper presented at the 8th International Congress for Mathematical Education (ICME-8), July 1996
Adhami, M., Johnson, D.C. & Shayer, M. (1998). Cognitive development and classroom interaction: A theoretical foundation for teaching and learning. In D. Tinsley & D. Johnson (Eds) School Mathematics in the World of Communication Technologies. London: Chapman & Hall, 205-214
Adhami, M. (1999). The challenge of whole class teaching. Equals, 5 (2), 5-9. London, Mathematics Association
Adhami, M. (2000). Where Do Good Questions Come From? Equals, 6 (2), London, Mathematics Association, pp14-17
Adhami, M. (2001). Three thinking questions, Equals, 7 (2), London, Mathematics Association, pp 4-5
Adhami, M. (2003). From lesson objectives to lesson agenda: flexibility in whole class lesson structure, in Thompson, I. (2003) Enhancing primary mathematics teaching, Open University Press pp 65-77
Adhami, M. (2001). Responsive Questioning in a Mixed Ability group, Support For Learning 16.1 NASEN, pp 28-34
Adhami, M. (2000). Peer Evaluation of Whole Class Teaching. In Proceedings of the British Society for Research into Learning Mathematics Day Conference, University of Loughborough, 6 May 2000. London: BSRLM, 42-48
Adhami, M. (2000). Framing investigation for whole class teaching. Mathematics in Schools, 29 (3). Mathematics Association, 15-19
Adhami, M. (2001). Two Cheers for the National Numeracy strategy, Equals 7 (1), London, Mathematics Association, pp 8-10
Adhami, M., Johnson, D.C. & Shayer, M.(1999). Tensions in Planned Mathematics Lessons. In Proceedings of the British Society for Research into Learning Mathematics Day Conference, University of Warwick, 13 November 1999. London: BSRLM, 35-41
Adhami, M., Johnson, D.C. & Shayer, M (1995). Cognitive Acceleration Through Mathematics Education: An Analysis of the Cognitive Demands of the National Curriculum and Associated Commercial Schemes for Secondary Mathematics. In Proceedings of the Joint Conference of the British Society for Research into Learning Mathematics, BSRLM, and the Association of Mathematics Education Tutors, AMET, Loughborough, 19-20 May 1995. London: BSRLM, 1-6.
Adhami, M (2003) First steps in handling data. Equals, London, Mathematics Association. 9(3), pp12-15
Johnson, D.C., Hodgen, J and Adhami, M.(2003) Professional Development from a Cognitive and Social Standpoint. In Millet, A, Brown, M. Askew, M. (Eds.), Primary Mathematics and the Developing Professional. Kluwer Academic Publishers. pp 2-208
Zongyi, D (2007) Transforming the subject matter: examining the intellectual roots of pedagogical content knowledge. The Ontario Institute for Studies in Education of the University of Toronto

Research on effects of CA intervention

Adey, P., Robertson, A., & Venville, G. (2002). Effects of a cognitive stimulation programme on Year 1 pupils. British Journal of Educational Psychology, 72, 1-25
Shayer, M. (1999). Cognitive acceleration through science education II: its effects and scope. International Journal of Science Education, 21, (8), 883-902
Johnson, D.C., Adhami, M. & Shayer, M. (1998). Does CAME work? Summary report on phase 2 of the Cognitive Acceleration in Mathematics Education, CAME, project. In Proceedings of the British Society for Research into Learning Mathematics Day Conference, Bristol, 15 Nov. 1997. London: BSRLM, 26-31
Shayer, M., Johnson, D.C. & Adhami, M. (1999). Does CAME work (2)? Report on Key Stage 3 results following the use of the Cognitive Acceleration in Mathematics Education, CAME, project in Year 7 and 8. In Proceedings of the British Society for Research into Learning Mathematics Day Conference, St. Martin's College, Lancaster, 5 June 1999. London: BSRLM, 79-84
Shayer, M. & Adhami, M. (2006). Fostering Cognitive Development through the context of Mathematics: Results of the CAME Project. Accepted for publication by Educational Studies in Mathematics
Shayer, M., (1999). Cognitive acceleration through science education II: its effects and scope. International Journal of Science Education, 21, (8), 883-902

Cognitive development theory background to CAME

Baddely, A. (1990). Human Memory: Theory and Practice, Hove: Erlbaum
Black, P., Harrison, C. Lee, C., Marshall, B. & Wiliam, D. (2003). Assessment for Learning: Putting it into practice. Maidenhead: Open University Press
Bloom, B.S. (Ed.) (1956) Taxonomy of educational objectives: The classification of educational goals: Handbook I, cognitive domain. New York: Longmans, Green
Bruner, J. (1967). Towards a Theory of Instruction. New York: W.W. Norton
Bryant, P. (1974). Perception and Understanding in Young Children. London: Methuen
Butterworth, B, (1999). The Mathematical Brain. London: Macmillan
Case, R. (1992). The mind's staircase. Hillsdale, NJ: Erlbaum
Collis, K.F. (1978). Chapters 7 & 8 in, Keats, J.A., Collis, K.F.,& Halford, G.S. (Eds). Cognitive Development: Research based on a Neo-Piagetian approach. New York: John Wiley & Sons
Dehaene, S, (1997). The Number Sense. London: Allen Lane
Dehaene, S, Dehaene-Lambertz, G., & Cohen, L.(1998). Abstract representations of numbers in the animal and human brain. Trends in Neuroscience, 21, 355-361
Demetriou, A., Platsidou, M., Efklides, A., Metallidou, Y. & Shayer M. (1991). The development of quantitative-relational abilities from childhood to adolescence: structure, scaling, and individual differences. Learning and Instruction, 1, 1, 19-43
Duncan,J.; Seitz, R. J.; Kolodny, J.; Bor, D.; Herzog, H.; Ahmed, A.; Newell, F. N.; Emslie, H.(2000). A neural basis for general intelligence. Science 289(5478): 457-60, 2000
Epstein, H. T., (1986). Stages in human brain development. Developmental Brain Research, 30, 114-119.
Feuerstein, R. , Rand, Y., Hoffman, M., & Miller, M.(1980). Instrumental Enrichment: an intervention programme for cognitive modifiability, Baltimore: University Park Press
Gelman, G. & Gallistel, G.R. (1978). The Child's Understanding of Number. London: Harvard University Press
Halford, G.S.(1982). The development of thought. Hillsdale, NJ: Erlbaum
Houde, O. & Tzourio-Mazoyer, N.(2003). Neural foundations of logical and mathematical cognition. www.nature.com/reviews/neuro June 2003
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. London: Routledge
Nunes, T. (1999). The role of systems of signs in reasoning. Paper presented at the Jean Piaget Society, Mexico
Piaget, J. (1950). The psychology of intelligence. London: Routledge
Piaget, J. (1953). The Origin of Intelligence in the Child. London: Routledge
Piaget, J.,& Szeminska, A.(1941; 1952). The Child's Conception of Number. London: Routledge
Resnick, L., Bill, V. Lesgold, S. & Leer, M. (1991). Thinking in Arithmetic Class. in B. Means, C. Chelmer & M.S..Knapp (Eds.). Teaching advanced skills to at-risk students: Views from research and practice. San Francisco: Jossey-Bass
Resnick, L.B., Bill, V. & Lesgold, S. (1992). Developing thinking abilities in arithmetic class. In A. Demetriou, M. Shayer & A. Efklides (Eds.). Neo-Piagetian theories of cognitive development. London: Routledge
Shayer, M (2008) Intelligence for education: as described by Piaget and measured by psychometrics. British Journal of Educational Psychology, 78, 1-29
Shayer, M. (2003). Not just Piaget; not just Vygotsky, and certainly not Vygotsky as alternative to Piaget. Learning and Instruction 13, 465-485
Shayer, M., & Adey, P. S. (1981). Towards a Science of Science Teaching. London: Heinemann Educational Books
Shayer, M., Coe, D., Ginsburg, D. (2007). Thirty years on – a large anti-Flynn effect? The Piagetian test Volume and Heaviness norms 1975-2003 British Journal of Psychology, 77, 25-41
Shayer, M., & Beasley, F. (1987). Does Instrumental Enrichment work? British Educational Research Journal, 13, 2, 101-119
Shayer, M., Demetriou, A., & Pervez, M..(1988). The structure and scaling of concrete operational thought: three studies in four countries. Genetic, Social and General Psychological Monographs, 309-375
Shayer, M., Ginsburg, D. (2009) Thirty years on – a large anti-Flynn effect(II): 13- and 14-year-olds. Piagetian tests of formal operations norms 1976–2006 British Journal of Psychology, 79, 409-418
Shayer, M., Kuchemann, D. E., & Wylam, H. (1976). The distribution of Piagetian stages of thinking in British middle and secondary school children. British Journal of Educational Psychology, 46, 164-173
Shayer, M. & Gamble, R. (2001). Bridging from CASE to Core Science. Hatfield: Association for Science Education. ISBN 0 86357 3320 The Association for Science Education College Lane, Hatfield, Herts, AL10 9AA, Tel: 01707 283000, Fax: 01707 266532 Booksales...booksales@ase.org.uk
Smith, L. (2002). Reasoning by Mathematical Induction in Children's Arithmetic. Oxford: Elsevier Science
Spearman, C. (1927). The abilities of man: their nature and measurement. London: Macmillan
Tanner, J.M. (1978). Foetus into Man: Physical growth from Conception to Maturity. London: Open Books
Vergnaud (1997). The Nature of Mathematical Concepts. Chapter 1 in T. Nunes & P. Bryant (Eds.). Learning and Teaching Mathematics: an International Perspective. Hove: Psychology Press
Vygotsky, L.S. (1986) (Ed. A. Kozulin). Thought and Language. Cambridge, MA: MIT Press
Wright, B.J. & Stone, M.H.(1979). Best Test Design: Rasch Measurement. Chicago: MESA Press

Mathematics curriculum background to CAME

Adhami, M ( 2003). By the pan or by the person. Equals, London, Mathematics Association, 9 (1) pp 21-23
Adhami, M ( 2003). Strategy Games, Equals, London, Mathematics Association. 9(2), PP6-7
Adhami, M. (1999). Playing with Numbers: a Route for Rapid Improvement of Number Skills for Children with Learning Difficulties/Disabilities. A review of Turkish research. Equals, 6 (1), London, Mathematics Association, 5-6
Adhami, M. (2002). Infant Numeracy Matters Equals, , London, Mathematics Association, 8 (2) pp 4-8, and 8 (3) pp 14-16
Adhami, M. (2002). The Paradox of the Textbook, Equals, 8 (1), London, Mathematics Association, pp19-20
Adhami, M. (Series editor) (1998-99). Maths Direct. Secondary School Textbooks (A-F), Teacher's Packs 1-3( also in CDs), and Course Guide. London: Collins Educational
Brown, M. (1989). Graded Assessment and Learning Hierarchies in Mathematics-an alternative view. British Educational Research Journal, 15, 2, 121-128
Brown, M. (Project director) (1992) Graded Assessment in Mathematics: Teacher's Guide; Activities volumes 1-4, Topic criteria; Topic Tasks; Student Activities; Cross referencing guide and record sheets. Thomas Nelson and Sons Ltd
Cable, J., (1997). A Constructivist theory of Quantities or In Praise of Ratio. PhD: University of London
Hart, K (Ed), (1981). Children's Understanding of Mathematics: 11- 16. London: John Murray
Kornilaki, K. (1999). Young children's understanding of multiplication: A psychological approach. PhD, University of London
Noelting, G. (1980). The development of proportional reasoning and the ratio concept. Part I- differentiation of stages. Educational Studies in Mathematics, II, 217-253
Nunes, T. & Bryant, P. (1996). Children Doing Mathematics. Oxford: Blackwells
Vergnaud, G. (1983). Multiplicative Structures. Chapter 5 in Richard Lesh & Marsha Landau, Eds. Acquisition of Mathematics Concepts and Processes. New York: Academic Press.

cognitive acceleration

DEVELOPING CHILDREN'S THINKING