Judith Wylie

Individual differences in trajectories of arithmetical development in typically achieving 5- to 7-year-olds

The arithmetical performance of typically achieving 5- to 7-year-olds (N=29) was measured at four 6-month intervals. The same seven tasks were used at each time point: exact calculation, story problems, approximate arithmetic, place value, calculation principles, forced retrieval, and written problems. Although group analysis showed mostly linear growth over the 18-month period, analysis of individual differences revealed a much more complex picture. Some children exhibited marked variation in performance across the seven tasks, including evidence of difficulty in some cases. Individual growth patterns also showed differences in developmental trajectories between children on each task and within children across tasks. The findings support the idea of the componential nature of arithmetical ability and underscore the need for further longitudinal research on typically achieving children and of careful consideration of individual differences.

Assistive Software Tools for Secondary-Level Students with Literacy Difficulties

The present study assessed the compensatory effectiveness of four assistive software tools (speech synthesis, spellchecker, homophone tool, and dictionary) on literacy. Secondary- level students (N = 93) with reading difficulties completed computer-based tests of literacy skills. Training on their respective software followed for those assigned to the Assistive Software and the Microsoft Word Control groups. Posttests revealed an improvement for the Assistive Software group on reading comprehension, homophone error detection, spelling error detection, and word meanings. The Microsoft Word Control group also improved on spelling error detection and word meanings, but performed worse on homophone error detection. A Full Control group showed no significant improvements on any of the measures. Overall, results indicate a significant assistive value of the four software tools (from the software package Read & Write Gold, 2002) across several domains of literacy.

Phonological awareness and mathematical difficulty: A longitudinal perspective

The present longitudinal study sought to investigate the impact of poor phonology on childrens mathematical status. From a screening sample of 256 five-year-olds, 82 children were identified as either typically achieving (TA; N = 31), having comorbid poor phonology and mathematical difficulties (PDMD; N = 31), or having only poor phonology (phonological difficulty, PD; N = 20). Children were assessed on eight components of informal and formal mathematics achievement at ages 5-7 years. PD children were found to have significant impairments in some, mainly formal, components of mathematics by age 7 compared to TA children. Analysis also revealed that, by age 7, approximately half of the PD children met the criteria for PDMD, while the remainder exhibited less severe deficits in some components of formal mathematics. Childrens mathematical performance at age 5, however, did not predict which PD children were more likely to become PDMD at age 7, nor did they differ in terms of phonological awareness at age 5. However, those PD children who later became PDMD had lower scores on verbal and non-verbal tests of general ability.

Children's Thinking about Air Pollution: a systems theory analysis

Summary A methodology for probing systems thinking was developed and used to investigate the way children think about the natural environment. Thirty five primary school children (aged 8 and 11 years) participated in semi‐structured interviews about air pollution. The analytical framework consisted of cycles (of inputs, processes and outputs), interventions, outcomes and links. Differences between the groups were found for the numbers of complete cycles, inputs, outputs and longest chain of linked cycles about which the children could talk. Although more of the older children showed evidence of a high level of systemic thinking — cycles with interventions and their likely outcomes — than the younger children, a large proportion of the 8‐year‐olds demonstrated that they were capable of this kind of thinking. The results suggest that children can engage in systemic thinking earlier than predicted by traditional developmental research.

How Children Solve Environmental Problems: Using computer simulations to investigate systems thinking

Two computer simulations were developed and used to investigate systems thinking and environmental problem solving in children. Ninety-two primary school children (aged 8 years and 11 years) interacted with computer simulation of either a deforestation problem or a water depletion problem. The childrens task was to manipulate the simulation thereby enabling it to run for as long as possible before resources—water or trees—were exhausted. This could be achieved via a number of strategies and their use by the two groups of children was compared. Through efficient use of resources and recycling strategies, the older children outperformed the younger children. Magical thinking was more prevalent among the 8-year-olds. The results also suggest that seemingly isomorphic environmental problems may not be interpreted as such.

Mathematical Prerequisites for Learning Statistics in Psychology: Assessing Core Skills of Numeracy and Mathematical Reasoning among Undergraduates

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology—calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylies (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge, likely to hamper the learning of statistics.

Proofreading Using an Assistive Software Homophone Tool: Compensatory and Remedial Effects on the Literacy Skills of Students With Reading Difficulties

The present study investigated the effects of using an assistive software homophone tool on the assisted proofreading performance and unassisted basic skills of secondary-level students with reading difficulties. Students aged 13 to 15 years proofread passages for homophonic errors under three conditions: with the homophone tool, with homophones highlighted only, or with no help. The group using the homophone tool significantly outperformed the other two groups on assisted proofreading and outperformed the others on unassisted spelling, although not significantly. Remedial (unassisted) improvements in automaticity of word recognition, homophone proofreading, and basic reading were found over all groups. Results elucidate the differential contributions of each function of the homophone tool and suggest that with the proper training, assistive software can help not only students with diagnosed disabilities but also those with generally weak reading skills.

Strategic development in exact calculation: Group and individual differences in four achievement subtypes

This longitudinal study sought to identify developmental changes in strategy use between 5 and 7 years of age when solving exact calculation problems. Four mathematics and reading achievement subtypes were examined at four time points. Five strategies were considered: finger counting, verbal counting, delayed retrieval, automatic retrieval, and derived fact retrieval. Results provided unique insights into childrens strategic development in exact calculation at this early stage. Group analysis revealed relationships between mathematical and/or reading difficulties and strategy choice, shift, and adaptiveness. Use of derived fact retrieval by 7 years of age distinguished children with mathematical difficulties from other achievement subtypes. Analysis of individual differences revealed marked heterogeneity within all subtypes, suggesting (inter alia) no marked qualitative distinction between our two mathematical difficulty subtypes.

Developing children's thinking: A tale of three projects

The paper identifies recent trends in instructional research which point to changing viewpoints on how to develop childrens thinking skills. Three current projects at Queens University Belfast, consistent with these viewpoints, are described. The ACTS project (Activating Childrens Thinking) is a wide ranging initiative to promote the development of thinking skills in Northern Ireland classrooms. The second project, SMILES (Simulated Methods for Interactive Learning of Environmental Systems), is analysing childrens understanding of environmental concepts within a systems framework, with a focus on computer-aided instruction. The final project on mathematics education is the result of a long-standing research programme and has been recently associated with the production of a set of commercially available textbooks called Oxford Mathematics.

Mathematics and reading difficulty subtypes: minor phonological influences on mathematics for 5-7-years-old.

Linguistic influences in mathematics have previously been explored through subtyping methodology and by taking advantage of the componential nature of mathematics and variations in language requirements that exist across tasks. The present longitudinal investigation aimed to examine the language requirements of mathematical tasks in young children aged 5–7 years. Initially, 256 children were screened for mathematics and reading difficulties (RDs) using standardized measures. Those scoring at or below the 35th percentile on either dimension were classified as having difficulty. From this screening, 115 children were allocated to each of the mathematical difficulty (MD; n = 26), MDRD (n = 32), RD (n = 22) and typically achieving (n = 35) subtypes. These children were tested at four time points, separated by 6 monthly intervals, on a battery of seven mathematical tasks. Growth curve analysis indicated that, in contrast to previous research on older children, young children with MD and MDRD had very similar patterns of development on all mathematical tasks. Overall, the subtype comparisons suggested that language played only a minor mediating role in most tasks, and this was secondary in importance to non-verbal skills. Correlational evidence suggested that children from the different subtypes could have been using different mixes of verbal and non-verbal strategies to solve the mathematical problems.