The purpose of this analysis was to assess whether effects of first-grade mathematics intervention apply across the range of at-risk learners' initial skill levels. Students were randomly assigned to control (n = 213) and two variants of intervention (n = 385) designed to improve arithmetic. Of each 30-minute intervention session (48 over 16…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

Learning the content of entrepreneurship arithmetic is an extension of social arithmetic that focuses on mathematical calculations in business or creative economy. Most teachers do not link students' daily activities to classroom teaching and learning on traditional markets around the environment. This significantly affects the interest in…

Traditional houses are part of the culture of every country. Indonesia is a country that has a variety of traditional houses. The traditional Banyuwangi house is known as the "Using" house. This house can be explored in terms of ethnomathematics and used as part of learning mathematics. This research is focused on knowing and describing…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children's…

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD,…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…

The present study examined phonological processing skills (phonological memory, phonological awareness, and rapid automatised naming, RAN) in relation to early Chinese reading and early Chinese mathematics for young children. Early Chinese reading was assessed with single character reading and multi-character word reading, and early mathematics…

Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured…

This study investigated the longitudinal associations between children's early mathematics and their home numeracy environment (HNE). Chilean children from families who varied widely in socioeconomic status were assessed at the beginning and end of prekindergarten in 2016 (N = 419, M[subscript age] = 4:7 [years:months]), and at the end of…

What constitutes effective teaching of arithmetical skills in early school years is still uncertain. Finger use could play a crucial role in this acquisition, but some children do not use them spontaneously and studies would be necessary to know if it is possible to teach them. This research assesses the impact of a teacher-implemented…

Overall mathematics proficiency of fourth graders in the U.S. continues to be poor and students falling at or below the 25th percentile display declining performance (NCES, 2017), which suggests the need for schools to provide supplemental intervention supports as soon as skill gaps are observed. Unfortunately, there is a paucity of small group…

People's everyday lives offer plenty of situations where complex processing of information takes place, in which information needs to transfer across modalities to achieve a behavioral goal. The study examined the differential effects on object detection by a visual, verbal, or auditory cue held in working memory (WM), and the role of concurrent…