Explored the differential application of a self-regulatory strategy on mathematics performance among three eighth-graders with learning disabilities and diverse planning abilities. Found that all students improved on fraction probes as a function of using a cue card strategy. The student with high planning ability demonstrated consistent…

This study examined the arithmetic computation performance of 229 normally achieving students (ages 9 to 14) and 101 students with learning disabilities. Results found that the students with learning disabilities performed at lower levels and that their progress from one age to another was extremely limited. (Author/CR)

Describes how the card game Numero helps students improve their knowledge of basic number facts while having fun. Suggests ways in which Numero can best be used in the classroom. (ASK)

Novices and experts used the same metaphors to understand and solve problems with negative numbers. Results suggest that the metaphors used by both the children and the adults are central to understanding arithmetic. (Author/MM)

We examined the relation between self-explaining and encoding among kindergartners. For 5 days, children (n = 27) took turns solving addition problems with an adult expert who always used an advanced addition strategy. During the game, children explained the expert's answers (Explain-Expert), explained their own answers (Explain-Novice), or did…

This study argues that maximizing early childhood educators' abilities to create social opportunities for co-construction of knowledge rests on two understudied assumptions, one theoretical and one empirical. Theoretically this study rejects the notion of language as an impartial conveyor of knowledge in favor of one in which math and language…

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students…

The main goal of this study was to examine possible socioeconomic status (SES) differences in 4- and 5-year-old children's informal mathematical knowledge. One hundred and two children, 32 from lower, 39 from middle, and 31 from upper SES families participated in the study. Each participant was given a clinical interview involving several addition…

In this paper I argue that children have a right to basic numeracy and that studies of adult numeracy suggest that this right is being denied to many in British schools. Because of the way that maths education discourses are structured, we do not have a separately defined discourse around numeracy teaching, and this has implications for young…

Clinical interviews administered to third- to sixth-graders explored children's conceptualizations of rational number and of certain extensive physical quantities. We found within child consistency in reasoning about diverse aspects of rational number. Children's spontaneous acknowledgement of the existence of numbers between 0 and 1 was strongly…

The aim of this study was twofold. First, it evaluated the developmental changes on frequency of use, efficiency, and choice of counting strategies from childhood to adulthood. Second, it determined the adaptation of the counting strategies to the structural features of the task. Participants in seven age groups ranging from 5-year-old to…

This book sets out a constructivist, inquiry-based approach to instruction. The approach builds on clear understandings of children's current levels of knowledge, where their learning should progress to, and the means by which children learn early numeracy topics. The methods presented in this book have been used extensively by practitioners in…

The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…

The basic theory of Rasch measurement applies to situations where a person has a certain level of a trait being investigated, and this level of ability is what determines (to within a measurement error) how well the person does on each item in a test. This paper responds to frequent suggestions from colleagues that the use of Rasch measurement…

Age-related changes in children's performance on simple division problems (e.g., 6 divided by 2, 72 divided by 9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children.…