Donna Kotsopoulos

Pre-service teacher research: an early acculturation into a research disposition

This study examines the role of pre-service teacher research in facilitating early and meaningful links between research and practice. Results from this mixed methods study show that pre-service teacher research is a promising method of early acculturation. However, despite a programme-wide emphasis on research as a mechanism for learning to teach and about education, challenges continue to exist. One notable contribution to the existing literature is the importance of principals taking a leadership role in school-based research.

The Case of Mitchell's Cube: Interactive and Reflexive Positioning During Collaborative Learning in Mathematics

Using positioning theory as a guiding framework, this qualitative research examined the experiences of students who appeared to be marginalized from collaborative learning in mathematics in a middle school setting. Positioning theory describes the discursive process whereby people are located in conversations as observably and subjectively coherent participants in jointly produced story lines. Interactive positioning describes when one or more persons position another individual. Reflexive positioning describes the positioning of oneself. In this research, I examined instances of (mis)alignment between interactive and reflexive positioning during collaborative learning. Factors potentially contributing to (mis)alignment are considered as well as implications for students, learning, and instruction.

A Pair-Wise Analysis of the Cognitive Demand Levels of Mathematical Tasks Used During Classroom Instruction and Those Assigned for Homework

This research compared the cognitive demand levels of mathematical tasks engaged in during classroom instruction to paired mathematical tasks assigned for homework. The research took place in an eighth-grade classroom over the course of one school year. In total, the cognitive demand levels of 66 mathematical tasks were evaluated using the IQA Academic Rigor: Mathematics Rubric for the Potential of the Task (Boston & Smith, 2009). Results from this research showed that approximately two thirds of the time the mathematical tasks assigned for homework differed in levels from the tasks used during classroom instruction. Implications for student learning, classroom instruction, homework, and further research are discussed.RésuméCette étude compare le niveau d’exigence cognitive des tâches mathématiques accomplies en classe et celui des tâches mathématiques données en devoir à faire à la maison. L’étude a été réalisée au cours d’une année scolaire, dans une classe de huitième année. Au total, le niveau d’exigence cognitive de 66 tâches mathématiques a été évalué au moyen du test d’évaluation de la qualité de l’enseignement de Boston et Smith (IQA Academic Rigor: Mathematics Rubric for the Potential of the Task, 2009). Les résultats montrent que, dans environ les deux tiers des cas, les tâches mathématiques données en devoir étaient d’un niveau différent de celui des tâches accomplies en classe pendant les cours. Les implications de cet état de fait sur l’apprentissage, l’enseignement en classe, les devoirs et la recherche future sont ensuite analysées.

Gesturing about number sense

Gestures such as finger counting, pointing, and touching have been found to facilitate mathematical development in preschool and school-aged children. However, little is known about the types of mathematically related gestures used by parent–toddler dyads to facilitate early mathematics learning during the first 3 years of life. A total of 24 children (12 boys and 12 girls) between 18 and 25 months of age and their parents participated in a recorded 30-minute play session at home. After the play session, each child completed a task to ascertain his or her counting ability from one to five. Parents initiated significantly more instances of mathematically related gestures than did the children. In contrast, children responded with more gestures to mathematically related talk than did their parents. The most frequent types of gestures produced are collecting/grouping of items in an array, counting objects while enumerating, tapping/touching, holding up, and pointing at an item. A total of 13 children demonstrated some understanding of the five counting principles except the cardinality principle proposed by Gelman and Gallistel. Our findings suggest that parents use specific types of mathematically related gestures during play with their toddlers.

Electronic portfolios in grades one, two and three: a cautionary tale

Some electronic portfolios (EPs) developers are proposing that EPs are suitable for implementation in primary education (i.e. kindergarten to grade three). Yet, empirical research evaluating the implementation and efficacy of EPs used in primary school settings at both the teacher and the student level is scarce. In this research, the authors attempted to implement EPs in grades one, two and three (approximate ages 6 through 8). EPs were reviewed to make the EP selection and in-depth collaborative planning with the teachers ensued. The main challenges for teachers and students were at the user interface level. Results from this cautionary tale suggest that implementation of EPs in primary education may be premature. While much potential exists in EPs, it has yet to be realised. Recommendations for improving EPs are suggested.

Gender Differences in Toddlers’ Visual-Spatial Skills

ABSTRACT The purpose of the present study was to determine whether there are visual-spatial gender differences in two-year-olds, to investigate the environmental and cognitive factors that contribute to two-year-olds’ visual-spatial skills, and to explore whether these factors differ for boys and girls. Children (N = 63; Mage = 28.17 months) were assessed on their visual-spatial skills and on measures related to visual-spatial skills: intelligence, quantitative reasoning, working memory, and home spatial activity engagement. Children’s mothers were assessed on mental rotation ability. Results found no difference between boys’ and girls’ visual-spatial skills at age two. Quantitative reasoning contributed the most to girls’ visual-spatial skills. No variables were predictive for the boys, though boys with higher spatial activity frequency had higher visual-spatial skills. The differential predictors have implications for the development and fostering of visual-spatial skills, particularly for girls, who may be at a disadvantage in this area when they are older.

In any way, shape, or form? Toddlers’ understanding of shapes

Using the intermodal preferential looking paradigm, two-year-old childrens ability to discriminate valid (typical and atypical) squares, rectangles, triangles, and circles from invalid distractors was examined. The cognitive and environmental factors that might predict this ability were also investigated. Two-year-old children (N=33) were able to discriminate squares, triangles, and circles, but not rectangles. No significant cognitive or environmental predictors of this ability were found. The results suggest that the ability to shape discriminate at age two is under considerable development and that other factors may be responsible for childrens ability to discriminate shapes.

Number Knowledge and Young Children's Ability to Measure Length.

AbstractResearch Findings: In this research we explore the relationship between young children’s number knowledge and their measurement of length. First, we examined 4- to 5-year-olds’ (kindergartners’) understanding of and preference for using standard or nonstandard units to measure length. Second, we investigated whether the following tasks were related to children’s understanding of using standard (i.e., rulers) and nonstandard (i.e., blocks) units to measure length: (a) counting and written number identification knowledge, (b) symbolic or nonsymbolic number magnitude comparison ability, and (c) approximate number line estimation ability. Third, we examined whether understanding these number tasks predicted understanding how to measure length for both standard and nonstandard units. Our results show that young children prefer to use standard units of measurement when given a choice, and some of these children use a ruler correctly. Our results also show an important relationship between children’s und...

Mathematics and Language in the Home Environment

By 4 years of age, differences in children’s early mathematical competence have emerged; this underscores the importance of providing an enriched home environment for young children to acquire foundational mathematical concepts prior formal schooling. Hence, this chapter focuses on why adult mathematical talk—numeracy and spatial—is important for early mathematical development and how parents can make mathematical talk happen during everyday activities in their home environment. Providing an enriched home environment may often be easier said than done as it is influenced by factors such as culture, mathematics anxiety, and socio-economic status. We discuss instructional strategies and activities through purposeful play and everyday routines that can foster and scaffold early mathematics development.