A first-year algebra student's curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics. In this article, the authors, math teachers in Massachusetts, examine how to solve for factorials of negative numbers and discuss how they taught…

This study aims to develop a learning trajectory to help students understand concept of subtraction of integers using multimedia in the fourth grade. This study is thematic integrative learning in Curriculum 2013 PMRI based. The method used is design research consists of three stages; preparing for the experiment, design experiment, retrospective…

This study is focused on the structure of equivalence problem to probe the evolution from operational to relational view of students' understanding of the equals sign. We propose a modified construct map which incorporates the intermediate levels in such a transition which were previously ignored. Our findings suggest that the structure of number…

The aim of this study is to examine the number sense skills of preservice elementary school mathematics teachers. This study was conducted by using the survey model among descriptive research methods. A total of 111 preservice teachers studying at second and third grades in the elementary school mathematics teaching program at a state university…

One of the basic science process skills, number and space relation, is used to transform a twodimensional object into a three-dimensional shape or express symmetry axis of the objects. The aim of this research was to determine the number and space relation skills of pre-service science teachers in order to train more qualified science teachers…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

In education, the use of information, computers, and the Internet as a form of blended technology has been receiving increased attention and consideration. Additionally, increasing attention is being paid toward a scaffolding mechanism that can be integrated into science classrooms in order to solve technological challenges. This work describes a…

We address the question: How can a student's conceptual transition, from attending only to singleton units (1s) given in multiplicative situations to distinguishing composite units made of such 1s, be explained? We analyze a case study of one fourth grader (Adam, a pseudonym) during the course of a video recorded cognitive interview. Adam's case…

This research aims to produce a learning trajectory that can assist students in studying decimals. The method used in this research is design research with the initial stage at preparing for an experiment, the second stage of the design experiment and the final stage of retrospective analysis. The learning approach used is Indonesian Realistic…

The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students' (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early…

The purpose of this study is to describe Mathematical Literacy (ML) of Prospective Elementary School Teachers with attention to aspects of mathematical skills and gender. The type of research is qualitative with the research design of Case Study. Respondents are assigned 12 Prospective Elementary School Teachers, consisting of 6 men and 6 women.…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

This action research study employed a mixed-method design to examine the impact of a number talks intervention on the number sense development and mathematical proficiency of students in one third-grade mathematics class. The number talks strategy was also studied to determine its impact on third-grade students' development of a productive…

In this chapter, we review two approaches for understanding these national differences in math abilities. The first approach attempts to link cross-national differences in educational input to cross-national differences in test scores. A tacit assumption of this approach is that children's performance on tests of mathematics is a direct effect of…

Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions--rational numbers between 0 and 1 expressed in the place-value symbol system. The results…