During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

In this study, we explore four, second graders' performances on integer addition problems before and after analyzing contrasting cases involving integers. The students, as part of a larger study, participated in a pretest, small group sessions, one short whole-class lesson on integer addition, and a posttest. Based on their integer mental models…

Script writing by learners has been used as a valuable pedagogical strategy and a research tool in several contexts. We adopted this strategy in the context of a mathematics course for prospective teachers. Participants were presented with opposing viewpoints with respect to a mathematical claim, and were asked to write a dialogue in which the…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) emphasize the Standards for Mathematical Practice (SMP) that describe processes and proficiencies included in the NCTM Process Standards (NCTM 2000) and in the Strands for Mathematical Proficiency (NRC 2001). The development of these mathematical practices should happen in…

Language processing plays a crucial role in language development, providing the ability to assign structural representations to input strings (e.g., Fodor, 1998). In this paper we aim at contributing to the study of children's processing routines, examining the operations underlying the auditory processing of relative clauses in children…

The purpose of this study is to develop design principles for crafting tasks that will encourage conjecturing and proving in the context of elementary number theory at the undergraduate level. From the analyses of the written work of 46 prospective mathematics teachers on a task designed according to these principles, we think that there is…

The meaning given to letters is significant for students' ability to be successful with algebraic tasks. Recent studies have noted that even when students have a sense of generalised number, they often have a natural number bias in the values they think a letter can take. This study analyses interviews from 13 students across two schools to…

This paper considers infinity as an element of professional knowledge. We assume that teachers need a wider knowledge of the topic than that they possess as mathematics students. Using three models of professional knowledge, athematics Teacher's Specialised Knowledge (MTSK), Mathematical Knowledge for Teaching (MKT), and Knowledge Quartet (KQ), we…

Number and operations serve as the "cornerstone" of the K-12 mathematics curriculum in many countries. Solving problems in the mathematical domains of algebra, geometry, measurement, and statistics is often closely connected to student knowledge of number and operation (Griffin, 2005). Although considerable knowledge exists regarding the…

This study aims to reveal prospective middle school mathematics teachers' knowledge regarding the possible misconceptions and/or errors of middle school students in describing integers. In addition to this, it aims to reveal the possible reasons underlying these from the perspective of prospective teachers. Data was qualitatively collected from 38…

Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

This report provides a description of the development process, field testing, and psychometric properties of a student mathematics test designed to assess grades K, 1, and 2 student abilities. The test was administered to 4,535 participating grade K, 1, and 2 students in 66 schools located in 9 public school districts in Florida during spring…

A critical aspect of mathematics study is developing both understanding of quantities and fluency in manipulating them. These abilities are essential for students who intend to enter technical or scientific professions. All students, however, should be exposed to methods of quantitative reasoning in order to function effectively in today's…

Today, almost all introductory physics textbooks include standardized "rules" on how to find the number of significant figures in a calculated value. And yet, 30 years ago these rules were almost nonexistent. Why have we increased the role of significant figures in introductory classes, and should we continue this trend? A look back at…

The relationship between letter and numeral identification is reviewed to determine whether early identification of these symbols impact upon both literacy and numeracy development. Numerals and letters share similar perceptual properties such as geometric features and arbitrary labels. Through early socio-cultural experiences with surrounding…