The notion that mental arithmetic is associated with shifts of spatial attention along a spatially organised mental number representation has received empirical support from three lines of research. First, participants tend to overestimate results of addition and underestimate those of subtraction problems in both exact and approximate formats.…

The authors assessed a battery of number skills in a sample of over 500 preschoolers, including both monolingual and bilingual/ multilingual learners from households at a range of socio-economic levels. Receptive vocabulary was measured in English for all children, and also in Spanish for those who spoke it. The first goal of the study was to…

In this paper, the researchers report an experimental study on conceptual knowledge learning and application through embodied interactions, expecting that bodily movements would facilitate learning in a positive manner. The intervention was enabled by Unity3D and Kinect V2, and taught novice adult learners the concepts of and conversions between…

Estimation is an essential competence with a developmental role in the learning of various mathematical topics. Yet, as previous studies highlight, this competence is either excluded or ambivalently included in intended curricula around the world. The current study investigates the estimation-related opportunities in the primary curricula of three…

The purpose of this mixed methods study was to investigate the implementation of a researcher-created numberless word problem instructional unit designed to introduce second-grade students to word problems in the semantic category of "compare with the word more, smaller unknown." The 10-day instructional unit incorporated three elements:…

Teacher quality in primary schools in South Africa is a serious concern, and how best to prepare teachers in initial teacher education--with regard to mathematics--remains an open and vexing question. There is a confluence of challenges facing the mathematics education community in South Africa: poor conceptual understanding of mathematics amongst…

The present study aimed to test the effect of the problem-posing instruction experimentally based on the extended active learning framework on the development of Turkish middle school sixth-grade students' (N = 19) problem-posing and -solving skills with whole-number operations. The training programme was completed in 13 lessons over a seven-week…

Research has identified that children differ in the extent to which they spontaneously focus on numerical aspects of the environment (Spontaneous Focusing on Numerosity, SFON) and that this correlates with their mathematics achievement. It is assumed that the mechanism underpinning this relationship is that children who spontaneously focus on…

Instructional routines, like "Number Talks" and "Notice and Wonder," engage students in doing and then talking about their mathematical thinking. Number Talk routines are short mathematical discussions where students mentally solve and share the strategies they used to make sense of the problem. In comparison, the Notice and…

This study examines the conceptual understanding of numbers and operations among 372 fifth-grade students, based on their responses to an online three-tier test designed to assess their number sense, declarative knowledge, explanatory knowledge, and confidence. The results showed that most students had low performance and low number sense, with…

Integers present a global challenge for students due to their abstract nature and complex operations. To delve into the challenge students encountered, error analysis served as an alternative method to investigate errors diagnostically. This study aimed to explore error patterns related to integer addition and subtraction among seventh-grade…

Seventh graders from a STEM school performed poorly with rational number concepts in the yearly standardized test. This research investigated the impact of a three-day professional development intervention focused on improving math teachers' self-efficacy when teaching rational numbers. The study employed a concurrent mixed-method research design…

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be…

A common measure of number word understanding is the give-N task. Traditionally, to receive credit for understanding a number, N, children must understand that N does not apply to other set sizes (e.g. a child who gives three when asked for 'three' but also when asked for 'four' would not be credited with knowing 'three'). However, it is possible…

In this paper, drawing on semi-structured interviews with generalist teachers of year-one children in England and Sweden, we examine comparatively the influence of the intended curriculum (teachers in both countries work within mandated national curricula) and the received curriculum (the collectively assumed efficacious practices and goals handed…