The role of probability in curricula for children has fluctuated greatly over the past several decades. Recently, some countries have removed probability from their preschool and primary curricula, and others have retained it. One reason for such lack of agreement is that theory about early probability learning is still relatively new and under development. The purpose of this report is to sketch a tentative theoretical structure with the potential to anchor curricular decisions and inform further research on early probability learning.
Students with learning disabilities display a diverse array of factors that interplay with their mathematical understanding. Our aim in this paper is to discuss the extent to which one case study elementary school child with identified learning disabilities (LDs) made sense of composite units and unit fractions. We present analysis and results from multiple sessions conducted during a teaching experiment cast as one-on-one intervention.
During the last three decades, scholars have proposed several conceptual structures to represent teacher knowledge. A common denominator in this work is the assumption that disciplinary knowledge and the knowledge needed for teaching are distinct. However, empirical findings on the distinguishability of these two knowledge components, and their relationship with student outcomes, are mixed. In this replication and extension study, we explore these issues, drawing on evidence from a multi-year study of over 200 fourth- and fifth-grade US teachers.
We share here results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3–5.
The purpose of this study was to identify affordances and limitations of using order and value comparison tasks versus number placement tasks to infer students’ negative integer understanding and growth in understanding. Data came from an experiment with kindergarteners (N = 45) and first graders (N = 48), where the experimental group played a numerical linear board game and the other group did control activities, both involving negative integers.
In this chapter we discuss some of the affordances and constraints of using online teaching simulations to support reflection on specific pedagogical actions. We share data from a research project in which we implemented multiple iterations of a set of simulated teaching experiences in an elementary mathematics methods course. In each experience, preservice teachers contrasted the consequences of different pedagogical choices in response to a particular example of student thinking.
Professional learning experiences (PLEs) provide teachers with opportunities to improve their understanding of mathematics content and teaching practices. However, PLEs are often conducted in person and in small groups—hence costly and localized. The purpose of the current study was to explore different ways for teachers to engage in PLEs and how these approaches might enable the field to scale up these efforts in a sustainable manner.