Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about parity arguments for sums of evens and odds, as well as underlying…

In this meta-analysis of 54 longitudinal studies with over 58,000 students in kindergarten through 12th grade, we examined the predictive nature of early numeracy measured at or before the first year of formal schooling in relation to later mathematics. Results showed that early numeracy significantly predicted mathematics measured after 6 months…

This study aims to determine the effect of the cognitive conflict approach on the elimination of misconceptions in square root numbers. For this purpose, this study was conducted with 8th-grade students of a secondary school in a region of Turkey. A three tiered diagnostic test was used to determine the impact of the 5-step cognitive conflict…

To date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly…

Place value is a foundational competency for primary school mathematics and for this reason we have sought to investigate what the recent and current academic conversations are around this important concept. In this paper we present a survey of literature presented in the Australasian, European and Southern African contexts through a review of…

This study aimed to reveal the solutions of pre-service teachers to contextual problems related to number bases other than the base ten. Furthermore, it was intended to investigate which issues pre-service teachers discussed about their learning in the problem-solving process, including context, and about student learning in their future teaching…

Traditionally, various meanings of "10" are systematically ignored in early childhood curriculum and children's understanding of numbers is restricted within the solitary mapping between the symbol "10" and quantity concept of "ten." This may be problematic for other ways that mathematics is used, both in modern life…

We make a "prima facie" case for identifying a single pathway in the learning of Hindu-Arabic numerical symbols and discuss why this ability may be a critical gateway concept in developing mathematical competencies. A representative sample of English and Scottish children was assessed using a number symbol identification paradigm in the…

The integer is a basic concept in studying arithmetic and algebra. However, students still frequently experience misconceptions, especially in negative integer, count operations. Traditional games are activities that are often carried out by students in coastal areas so that they are relevant to be used as a tool to construct learning trajectories…

The current study was conducted with the goal of helping to address the research gap of improving preservice teachers' pedagogical knowledge about probability by investigating how preservice teachers explored concepts of probability during aleatoric music composition, as well as their contemplation process during follow-up reflections focused on…

The use of different registers to represent mathematical concepts enhances understanding. For example, rational numbers can assume pictorial, symbolic and natural language representations and this kind of change improves learning. Based on these assumptions, a teaching experiment for the learning of rational numbers by 2nd grade students was…

In this article we show how students' productive struggle on a mathematical task can lead to collective mathematical creativity. We use observable (co)actions and interactions from a video record that features three Grade 6 students in a problem-solving session to document the emergence of collective creativity leading to a solution. We discuss…

Learning progressions (LPs) have seen a growing interest in recent years due to their potential benefits in the development of formative assessments for classroom use. Using an LP as the backbone of an assessment can yield diagnostic classifications of students that can guide instruction and remediation. In operationalizing an LP, assessment items…

This study is a series of Didactical Design Research in prospective analysis stage to comprehensively identify some obstacles in learning negative integer in order to capture how the learning process used by teachers and how the impact on students in understanding the concept of negative numbers. This research is a case study administered to…

Knowledge components (KCs) define the underlying skill model of intelligent educational software, and they are critical to understanding and improving the efficacy of learning technology. In this research, we show how learning curve analysis is used to fit a KC model--one that was created after use of the learning technology--which can then be…