Unconscious processing in children : developing mathematical concepts through mathematical puzzles : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in Psychology at Massey University
The degree of occurrence of unconscious versus conscious processing of information in children is unclear. Also unclear is knowledge of mechanisms and reasons for selective transference of unconsciously processed sensory and perceptual information into conceptual, conscious and verbal awareness. Examples of unconscious processing were evidenced in the difficulty some children experienced verbalising processes and naming classifications after solving some mathematical puzzles. Correct solutions indicated children had clear conceptual understanding of the structure of the task. A series of personally designed junior mathematical puzzles utilising environmental materials to aid development of pre-mathematical concepts of classification, patterning, seriation, ideas of conservation and one to one correspondence in five and six year old New Zealand primary school children were used, and extended to incorporate mathematical concepts taught to twelve year old children at New Zealand intermediate school Form 2 level. These senior puzzles incorporated concepts of set theory, probability, matrices, tessellations, and rotational patterning and ordering, with some puzzles developed to adult difficulty levels. Some adults had difficulty with some junior puzzles, and found senior puzzles as difficult as the twelve year olds they were designed for. Mathematically able six year old children solved some senior puzzles successfully. A hypothesis developed that children could master mathematical concepts considered beyond their age ability defined by the current school curriculum, provided concepts were presented in manipulable and visual form. This was supported in the present study in 1985-1986 where 92 six to ten year old junior and senior children with the highest and lowest mathematical ability or special learning difficulties in three primary schools researched the puzzles. Schools selected senior children from national age normed Progressive Achievement Tests (P.A.T.) mathematics results. Junior children were teacher assessed. Unexpected findings included unconscious processing of some unfamiliar concepts with difficulties verbalising unfamiliar and familiar concepts, contrasting conscious deliberation required for multiple concepts, transfer of learning and use of strategy, indicating ability, especially in conjunction with speed, novel approach, use of symmetry and a younger age of child. Puzzles were diagnostic in detecting and in remediating mathematical understanding of single concepts. The formal mathematics of some remedial and extension children improved, suggesting unconscious transfer of concepts, and some children who previously disliked mathematics or school in general developed a liking for both. No gender performance differences emerged. P.A.T. performance did not correlate with puzzle performance, emphasising differences between P.A.T. formal verbal mathematics and nonverbal visual spatial logic puzzle mathematics, or predominantly left versus right brain mathematical processing respectively, possibly explaining difficulties children had verbalising nonverbal actions. Two P.A.T. average children included with extension children performed above the highest P.A.T. children. Lack of P.A.T. correlation indicates formal mathematics alone may be inadequate to identify all mathematically able children, to remediate all having difficulties, or to extend those needing lateral enrichment. As pre-mathematical concepts incorporated into junior puzzles are prerequisites for formal mathematics, mathematical concepts incorporated into senior puzzles may aid unconscious transfer into formal mathematics through conscious awareness from verbal introspection, providing useful remediation and enrichment if embedded within future curricula.