Recent evidence suggests that early natural number knowledge is a predictor of later rational number conceptual knowledge, even though students' difficulties with rational numbers have also been explained by the overuse of natural number concepts--often referred to as the natural number bias. Hannula and Lehtinen ("Learn Instr"…

In this paper, illustrative excerpts from mathematics lessons are analysed to examine mathematical and multilingual moves between representations within Sepedi and English medium classrooms. Duval's theory of representational registers and the literature on multilingual practices help foreground similarities within and differences between the…

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

Previous research has linked the concept of number and other ordinal series to space via a spatially oriented mental number line. In addition, it has been shown that in visual scene recognition and production, speakers of a language with a left-to-right orthography respond faster to and tend to draw images in which the agent of an action is…

This paper presents an assessment of the understanding of the decimal numeral system in students with Down Syndrome (DS). We followed a methodology based on a descriptive case study involving six students with DS. We used a framework of four constructs (counting, grouping, partitioning and numerical relationships) and five levels of thinking for…

The main purpose of this study is to determine the time-dependent learning difficulty of "solving problems that require making four operations with natural numbers" of the sixth grade students. The study, adopting the scanning model, consisted of a total of 140 students, including 69 female and 71 male students at the sixth grade. Data…

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…

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.…