A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

This article addresses why instructors choose to not use inquiry-oriented instructional practices (IO-IPs) even if they believe the practices are beneficial. A national sample of undergraduate mathematics instructors (N = 269) responded to questionnaires on their use of IO-IPs, beliefs on student learning, and recognition of professional…

Building on the work of Professional Noticing of Children's Mathematical Thinking, we introduce the Curricular Noticing Framework to describe how teachers recognize opportunities within curriculum materials, understand their affordances and limitations, and use strategies to act on them. This framework builds on Remillard's (2005) notion of…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, analysis of video, interviews with teachers, and analysis of textbooks, we define categories of knowledge and practices of teaching for understanding and assessing teachers'…

Quantitative and qualitative analyses of 37 first-graders' solutions to addition problems were conducted to re-examine inconsistencies in children's progress from counting-all to counting-on. The authors applied the constructivist's participatory-anticipatory stage distinction as a tool for fine-grained assessment. Among solutions given by…

Selection bias is a problem for mathematics education researchers interested in using observational rather than experimental data to make causal inferences about the effects of different instructional methods in mathematics on student outcomes. Propensity score methods represent 1 approach to dealing with such selection bias. This article…

This article examines 3 models for developing and analyzing culturally responsive teaching in mathematics teacher education. The models were developed from and are illustrated by findings from a series of exploratory research studies conducted to evaluate various methods for preparing preservice teachers to address the educational implications of…

This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated…

The "Descriptor for Individualized Instruction" described here is a paradigm developed for use in describing individualized instruction and conceptualizing related research. The paradigm concerns itself with aspects of aims, instruction, and management. (SD)

Describes a three-tiered teaching experiment in which teachers were studied over a protracted period of time as they attempted to understand and improve their approaches to one-to-one tutoring. Documents the initial and revised strategies of the teachers. Reports various indices of teacher change. Discusses strengths and limitations of the…

Tested a structural model of mathematics achievement and attitude with a probability sample of 3,116 adolescents from the Longitudinal Study of American Youth. Concluded that prior achievement and home environment influenced subsequent achievement most powerfully and that previous attitude had the most powerful influence on subsequent attitude.…

Discusses constructivist teaching, students' mathematical knowledge, activating prior knowledge, hypothetical learning trajectory, and reflection in teaching mathematics, all in reaction to Simon's model of constructivist pedagogy. (24 references) (MKR)

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…