Interdisciplinary teaming in middle schools has increased dramatically over the past few decades (McEwin, Dickinson & Jensen, 2003); nevertheless, students have rarely been consulted as important sources of insight into this practice (Dickinson & Erb, 1997) of two or more teachers sharing the responsibility for instruction, curriculum, and…

Describes one pattern of reasoning observed in a mathematical activity with students in a grade 5 class and discusses ways in which the pattern is or is not mathematical. Describes patterns of reasoning in terms of ways of reasoning and degree of formulation of the reasoning. Distinguishes between mathematical reasoning and scientific reasoning in…

Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…

Introduces crossdisciplinarity as a strategy for highlighting the discrete notions of learning that psychology thus far has succeeded in coherently articulating. This strategy positions teachers to consult their own values, interests, and strengths in defining their own teaching priorities while at the same time marshaling accessible, theory-based…

Considers the potential of reform-oriented curricula to promote equity. Presents two studies in which middle school and high school teachers using reform-oriented mathematics curricula achieved a reduction in linguistic, ethnic, and class inequalities in their schools. Suggests relational analyses of equity as critical to go beyond the curriculum…

Explores challenges of learning to think about data as signal and noise. Examines the signal/noise metaphor in the context of three different statistical processes: (1) repeated measures; (2) measuring individuals; and (3) dichotomous events. Makes several recommendations for research and instruction on the basis of this analysis. (Author/KHR)

Examines preschool children's understanding of the mathematical significance of unit size through problems that involve making judgments about the number of larger objects versus the number of smaller objects. Elicits children's judgments about the effects of object size both before and after the presentation of a series of demonstration trials.…

Discusses fairness and equity in mathematics assessment. Illustrates these issues with two studies of teachers' informal classroom assessment practices and their interpretation and evaluation of students' formal written mathematical texts. Indicates that different teachers could interpret similar work differently. Discusses and critiques…

Presents research produced by the Standard Impact Research Group (SIRG), a research agenda for studying the influence and impact of Principles and Standards for School Mathematics. (Author/KHR)

Investigates the arithmetical and algebraic problem-solving strategies and skills of preservice primary and secondary school teachers in Flanders, Belgium. Compares aspects of preservice teachers' own problem-solving behavior with the way in which they evaluated students' arithmetical and algebraic solutions to problems. Discusses teachers' use of…

Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

Examines in-service secondary school mathematics teachers' conceptions of proof. Suggests that teachers recognize the variety of roles that proof plays in mathematics. Noticeably absent, however, was a view of proof as a tool for learning mathematics. Many of the teachers held limited views of the nature of proof in mathematics and demonstrated…

Describes a novel assessment method used to examine Japanese and American teachers' ideas about what constitutes effective mathematics pedagogy. Evaluates American and Japanese mathematics lessons and classifies teachers' comments into over 1600 idea units. Suggests that U.S. teachers have culturally sanctioned options for teaching mathematics;…

Explores what is involved in the teacher's work of engaging students in producing a proof. Analyzes what teachers do to create a task in which students can produce a proof and what teachers do to get students to prove a proposition. Indicates that traditional, formal, two-column proofs place contradictory demands on teachers regarding how ideas…

Uses situated abstraction to understand nurses' conceptions of intensive quantity of drug concentration. Explores nurses' conceptions to undertake a pointed examination of the degree of situatedness of nurses' knowledge and reasoning. Demonstrates that nurses' conceptions were abstracted within their practice when they coordinated mathematical…