University of Queensland, Australia

This course will be concerned with conceptual complexity and its effect on cognition in infants and children. Cognitive development will be seen as ability to process more complex concepts. The core question will be: How do we define complexity? A conceptual complexity metric based on representational rank will be used as the main organising idea. Rank is the number of entities that are bound into a representation, and is related to the number of dimensions, which is a measure of complexity. Each rank corresponds to a class of neural nets. The ranks, the typical concepts which belong to them, and the typical median ages of attainment are:

• Rank 0, elemental association, all ages;
• Rank 1, content-specific representations and configural associations, 6 months or earlier;
• Rank 2, unary relations, class membership and variable-constant bindings, one year;
• Rank 3, binary relations, proportional analogies, two years;
• Rank 4, ternary relations, transitivity and hierarchical classification, five years;
• Rank 5, quaternary relations, proportion and the balance scale, eleven years.
• Rank 6, quinary relations, minority of adults.

Rank 0 can be performed by 2-layered nets, rank 1 by 3-layered nets, and ranks 2-6 by symbolic nets (e.g. nets based on tensor products of the corresponding number of vectors). All animals with nervous systems perform rank 0, vertebrates perform rank 1, nonhuman primates perform rank 2-3, but ranks 4-6 are uniquely human.

Required readings:

Halford, G.S., Wilson, W.H. & Phillips, W. (1998) Processing capacity defined by relational complexity: Implications for comparative, developmental and cognitive psychology. Behavioral Brain Sciences, 21(6), 803-864. Sections 1, 2 and 3.

Required readings:

Cowan, N., Nugent, L.D., Elliott, E.M., Ponomarev, I & Saults, J.S. (1999) The role of attention in the development of short-term memory: Age differences in the verbal span of apprehension. Child Development, 70(5), 1082-1097.

Halford, G.S., Wilson, W.H. & Phillips, W. (1998) Processing capacity defined by relational complexity: Implications for comparative, developmental and cognitive psychology. Behavioral Brain Sciences, 21(6), 803-864. Section 6.2.

Optional readings:

Halford, G.S. (1993) Children's Understanding: The Development of Mental Models. Hillsdale, N.J.: Erlbaum. Chapter 3, pp. 75-142. Note that, due to a computer error, in the subject index only, page numbers 2-20 should be reduced by 1; e.g. p. 19 should be read as 18, etc. Page numbers 31-477 should be reduced by 11; e.g. p. 233 should be 222, etc. The author index needs no correction.

Required readings:

Halford, G.S. (1993) Children's Understanding: The Development of Mental Models. Hillsdale, N.J.: Erlbaum, Chapter 7, pp. 277-297; Chapter 8, pp. 339-364.

Required readings:

Call, J. & Tomasello, M. (1999) A nonverbal false belief task: The performance of children and great apes. Child development, 70(2), 381-395.

Frye, D., Zelazo, P.D. & Palfai, T. (1995) Theory of mind and rule-based reasoning. Cognitive Development, 10(4), 483-527.

Halford, G.S. (1993) Children's Understanding: The Development of Mental Models. Hillsdale, N.J.: Erlbaum, Chapter 8, pp. 364-412.

Optional readings:

Astington, J. W. (1993) The Child’s Discovery of the Mind. MA: Harvard University Press (for general reading – not required).

English, LD and Halford, GS, (1995) Mathematics Education: Models and Processes. Hillsdale, NJ.: Erlbaum. Chaper 3, pp. 57-96; Chapter 4, pp. 97-143. Recommended for applications to education, but not required.

Required readings:

Baillargeon, R. (1995) A model of physical reasoning in infancy. In C. Rovee-Collier & LP Lipsitt (Eds) Advances in Infancy Research, Vol 9. Norwood, NJ: Ablex.

Marcovitch, S. and Zelazo, P.D. (1999) The A-Not-B Error: Results from a logistic meta-analysis. Child Development, 70(6), 1297-1313

Rivera, S.M., Wakeley, A. & Langer, J. The drawbridge phenomenon: Representational reasoning or perceptual preference? Developmental psychology, 1999, 35(2), 427-435.

Wynne, K. (1995) Origins of numerical knowledge. Mathematical cognition , 1 (1), 35-60.

Small Groups

Group discussions, work in groups on experimental design and interpretation of results. The main aim will be to consider how an experiment could be designed to test an issue identified in the lectures. Controversial topics will be discussed.

Assessment

Participant wishing to get credits for this course should write a paper on a topic on development, selected by consultation with the lecturer.

Graeme Halford was born in Sydney, Australia. He obtained a PHD from the University of Newcastle in 1969. He was awarded a personal chair at the University of Queensland in 1989. He conducts research on cognitive development and adult cognitive processes, and is specially interested in the role of learning and information processing limitations in shaping children's cognitions. He is currently working on the influence of relational complexity on processing load in adults and children. He has published approximately 80 technical works, including The Development of Thought (Erlbaum, 1982), Children's Understanding: The Development of Mental Models (Erlbaum, 1993), Mathematics Education: Models and Processes (with L. English, Erlbaum, 1995) and Developing Cognitive Competence: New Approaches to Process Modeling (Edited with Tony Simon, Erlbaum, 1995). He is a consulting editor of The Psychological Review and a member of the editorial boards of Cognitive Science and Cognitive Development.