This study investigates the nature of student errors in the context of problem solving and Dynamic Math Environments. This led to the development of the Problem Solving Action Identification Framework; this framework captures and defines all activities and errors associated with problem solving in a dynamic math environment. Found are three…

Introduction: Students are daily exposed to a variety of assessment tasks in the classroom. It has long been recognized that students' perceptions of the assessment tasks may influence student academic achievement. The present study aimed at predicting academic achievement in mathematics from perceptions of the assessment tasks after controlling…

This research aimed to examine the application of two-valued and fuzzy logics teaching in better understanding the precise approximate concepts of chapter 4 of Sixth grade mathematics. Participants of this study were 30 Sixth grade mathematics students from an elementary school in Sari (a city in the north of Iran) in the academic year of…

In this study, we administrated dynamic geometry activities which provide students opportunities to explore and estimate geometric figures to connect measurement estimation with geometry. The aim of the study is to investigate effects of using dynamic geometry activities on eighth graders' achievement levels and estimation performances in…

This article analyses lesson study as a mode of professional learning, focused on the development of mathematical problem solving processes, using the lens of cultural-historical activity theory. In particular, we draw attention to two activity systems, the classroom system and the lesson-study system, and the importance of making artefacts…

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fourth-grade level through visualization, play, and…

This paper examines the learning by students who were participating in a project designed to promote persistence while working on mathematical tasks. We examined their learning of mathematics concepts and learning about the processes of engaging in mathematical tasks. There were substantial increases in students' knowledge of angles and also…

Research that has explored students' interpretations of graphical representations has not extended to include how students apply understanding of particular statistical concepts related to one graphical representation to interpret different representations. This paper reports on the way in which students' understanding of covariation, evidenced…

In this article, Derek Hurrell, points out that while it's easy to fall into the impression that the proficiency strand "Fluency" is all about knowing basic number facts in all its many and splendid ways. He add it is easy to overlook, that within Fluency there are requirements that are based in Algebra; Measurement and Geometry; and…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants' mathematical foundations,…

The solving of structured multi-step word problems has been a dominant practice in schools and is seen as a way to develop students' mathematical reasoning abilities. Unfortunately, it is limited in scope and does not provide opportunities for eliciting deeper reasoning as they are neither rich enough nor anchored in authentic data that resemble…

This paper outlines a framework to explain the early development of place-value understanding based on an analysis of data from 84 five- to seven-year-old children from diverse cultural and linguistic backgrounds. The children were assessed individually on number knowledge tasks (recalled facts, subitizing, counting, place-value understanding) and…

Shrinking the achievement gap in mathematics is a tall order. One way to approach this challenge is to think about how the achievement gap manifests itself in the classroom and take concrete action. For example, opportunities to participate in activities that involve mathematical reasoning and argumentation in a safe and supportive manner are…

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. We contribute to these efforts by expanding the constructs in Cobb and Yackel's (Educational Psychologist 31:175-190, 1996) interpretive framework that allow for coordinating social and individual…