This case study involves one public school in a suburb of a major metropolitan area, focusing on one classroom of first grade students selected from a pool of volunteer classrooms. The first grade class of students, during their regular mathematics instruction, were given three tasks by their teachers designed to elicit a productive struggle…

Learning mathematics involves abstract thinking and the use of symbols. To be successful in a mathematics classroom, students must master what symbols mean and how they work. Much prior work has focused on the nature of the external representations used in mathematics instruction, including manipulatives and symbolic representations. In this work,…

For schools implementing Response-to-Intervention, it is important to understand how to efficiently intensify interventions. Treatment intensity, or intervention design, is a critical yet overlooked and understudied aspect in math. More frequent dosage results in greater student gains. However, questions remain regarding how teaching episodes…

Cognitively Guided Instruction (CGI) is a mathematics instructional strategy that focuses on students using problem-solving strategies to construct their own understanding. Little research has been conducted to help determine what CGI could look like in other subject areas. The purpose of this study was to investigate ways to apply CGI to a…

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded…

This article reports from a Teacher-led Innovation Fund project that investigated connecting practices and resources for mathematical learning between a kindergarten and the first year of school. Teachers at both sites were teacher-researchers in the 2-year project. Our results highlighted expected and unexpected aspects of connections and…

Whereas some evidence exists that math anxiety may interfere with math performance from the very beginning of primary school, no study to date has attempted to investigate whether math anxiety may also interfere with early math learning (i.e., the encoding of new math knowledge) and not only with recalling already mastered contents in test…

Mastering the ability for learning to learn is the most ambitious goal of modern educators. A distinction is made between two relatively independent components of this expertise: (a) the reflective component of the learning to learn ability that allows a person comprehend what knowledge and skills he or she lacks to act in the new situation; (b)…

This paper contributes to the Symposium: "Research Methods Involving Children's Drawings in Mathematical Contexts" by exploring the use of digital pens as a data gathering tool. The availability of digital recording devices has been a boon to researchers wanting to capture the real-time dynamics of a research situation. When capturing a…

Foundation phase teachers in South African schools follow a socio-constructivist approach to the teaching and learning of mathematics, which entails that learners experiment freely with concepts and are encouraged to communicate and share their thoughts and ideas. In an effort to understand the impact that the physical learning environment, such…

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…

Among the practical applications of statistics is the collection of data from manufacturing processes. Often collected in the form of a time series, data collected from a series of measurements show the variation in those measurements, such as mass of a product manufactured. Limits are set for quality control and if these are exceeded then a…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…