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…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

A follow-up of a cluster-randomized trial evaluated the long-term impacts of a scale-up model composed of 10 research-based guidelines grounded in learning trajectories. Two treatment groups received the intervention during the prekindergarten year, and one of these groups received follow-through support in kindergarten and first grade.…

A theoretical model describing young students' (Grades 1-3) functional-thinking modes was formulated and validated empirically (n = 345), hypothesizing that young students' functional-thinking modes consist of recursive patterning, covariational thinking, correspondence-particular, and correspondence-general factors. Data analysis suggested that…

Although considerable literature illustrates how students' experiences and identities are racialized in mathematics education, little attention has been given to Asian American students. Employing ethnographic methods, this study followed 10 immigrant Chinese-heritage families to explore how the racial narrative of the model minority myth was…

This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…

In this study, I examined the relationship between teachers' mathematical knowledge and instruction. Twenty-one K-8 teachers who were enrolled in a master's program were followed for 3 years to study how their mathematical knowledge and teaching changed over time. The results of multilevel growth models indicated that gains in teachers'…

The release of the Common Core State Standards for Mathematics and their adoption across the United States calls for careful attention to the alignment between mathematics standards and assessments. This study investigates 2 models that measure alignment between standards and assessments, the Surveys of Enacted Curriculum (SEC) and the Webb…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…

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…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

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…