The effects of informational complexity and working memory on problem-solving efficiency

This study investigated the influence of informational complexity and working memory capacity on problem-solving efficiency. We examined two predictions of thesituational efficiency hypothesis, which states that the efficiency of problem solving varies as a function of situational constraints. One prediction is that informational complexity affects problem-solving efficiency. A second prediction is that working memory capacity affects problem-solving efficiency. Students completed a working memory task and solved abstract and concrete syllogisms. Participants solved abstract syllogisms more accurately than concrete syllogisms and spent more time solving abstract syllogisms. Thus participants demonstrated greater problem-solving efficiency when solving concrete syllogisms. Results indicate that there is a trade-off between problem-solving accuracy and problem-solving time when information differs with respect to informational complexity, a phenomenon we refer to as theefficiency paradox. Working memory capacity did not affect accuracy or efficiency. The results support the conclusion that problem-solving efficiency is situational and a function of the complexity of information. Educational implications and directions for future research are suggested.     

Teachers’ perceptions of assessments of their mathematical knowledge in a professional development course

The purpose of the project reported in this article was to evaluate how assessing teachers’ mathematical knowledge within a professional development course impacted from the teachers’ perspective their learning and their experience with the course. The professional development course consisted of a 2-week summer institute and the content focus was geometry. We had decided to assess the mathematical learning of the teachers during this professional development course for various accountability reasons, but were concerned about possible negative by-products of this decision on the teachers and their participation. Thus, we worked to design assessment in ways that we hoped would minimize negative impacts and maintain a supportive learning environment. In addition, we undertook this evaluation to examine the impacts of the assessment, which included homework, quizzes, various projects, and an examination for program evaluation. Seventeen grade 5–9 teachers enrolled in the course participated in the study by completing written reflections and by describing their experiences in interviews. We learned that while our original intent was “to do no harm,” the teachers reported that their learning was enhanced by the assessment. The article concludes by describing the various properties of the assessments that the teachers identified as contributing to their learning of the geometry content, many of which align with current recommendations for assessing and evaluating grade K-16 mathematics students.

A randomized controlled trial of a home-visiting intervention aimed at preventing relationship problems in depressed mothers and their infants

This study examined the effect of a mother–baby intervention on the quality of mother–child interaction, infant–mother attachment security, and infant socioemotional functioning in a group of depressed mothers with infants aged 1–12 months. A randomized controlled trial compared an experimental group ( n = 35) receiving the intervention (8–10 home visits) with a control group ( n = 36) receiving parenting support by telephone. There were assessments pre, post, and follow-up after 6 months. The intervention had positive effects on the quality of mother–infant interaction. Infants in the experimental group had higher scores for attachment security and for one aspect of socioemotional functioning, namely, competence. The intervention proved successful in preventing deterioration of the quality of mother–child interaction.     

Factors influencing early adolescents’ mathematics achievement: High-quality teaching rather than relationships

This study used data from the Assessment Tools for Teaching and Learning project, which involved data on the academic performance of more than 90,000 New Zealand students in six subjects (i.e. reading, writing and mathematics in two languages). Two sub-samples of this dataset were included for detailed re-analysis to test the general applicability of the Australian model of Quality of School Life (Ainley et al. 1986) in the New Zealand context. The first sample comprised 336 year 8 students from elementary schools and the second sample consisted of 272 year 10 students from high schools. Furthermore, two structural equation models were developed and tested, expressing relationships between students’ quality of school life perceptions, students’ attitudes to mathematics, and their effects on mathematics achievement. The quality of school life questionnaires scales [Ainley and Bourke, in Res Pap Educ 7(2):107–128, 1992] were used as indicators of students’ perceptions regarding learning, teachers and peer relationships. The model proposed that perceived quality of school life would affect students’ attitudes of liking and confidence in mathematics, which would in turn affect their academic performance. After controlling for other variables in the model, students’ perception about their self-efficacy to learn mathematics was more directly related to outcomes than to perceptions of teacher quality or peer involvement. Data analyses revealed no apparent relationships of these factors to mathematics achievement. Moreover, results for both samples led to the conclusion that the perceived quality of learning is connected with ‘confidence in’ and ‘liking mathematics’, which in turn predict students’ mathematics achievement.