It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…

The goal of the present study was to describe fraction-calculation errors among 4th-grade students and determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low- vs. average- vs. high-achieving). We…

Given the dearth of research on early numeracy interventions in low- and middle-income countries, this paper presents the instructional methodology and impact results of the Tayari program. Tayari is a preprimary intervention in Kenya (2014-2019) that prepares children aged four and five for entry into primary school by providing materials for…

There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…

The present research focuses on the psychometric properties of the Birthday Party measure for ages 3-5. The Birthday Party was developed to provide a reliable, valid, and engaging measure of early mathematical content--Number and Operation, Shape, Space, and Pattern--that can be given in either a short or a long form to English and Spanish…

This paper focuses on kindergarten teachers' interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers' roles and actions in these activities and extend considerations of teachers' orchestrations current in the research literature with regard to agency and…

Detailing is a linguistic tool for mathematical argumentation in which given mathematical information is operationalized through one's warrants to support a claim. Recent literature suggests that students' detailing is related to their early algebraization. This study examined 168 elementary students' use of detailing in two mathematical…

Learning the sequence of number words in English up to 30 is not a simple process. In NSW government schools taking part in "Early Action for Success," over 800 students in each of the first 3 years of school were assessed every 5 weeks over the school year to determine the highest correct oral count they could produce. Rather than…

Recent research has suggested that the Piraha, an Amazonian tribe with a number-less language, are able to match quantities greater than 3 if the matching task does not require recall or spatial transposition. This finding contravenes previous work among the Piraha. In this study, we re-tested the Pirahas' performance in the crucial one-to-one…

Does speaking more than one language help a child perform better on certain types of cognitive tasks? One possibility is that bilingualism confers either specific or general cognitive advantages on tasks that require selective attention to one dimension over another (e.g. Bialystok, [Bialystok, E., 2001]; Hilchey & Klein, [Hilchey, M.D.,…

Representations are often used in instruction to highlight key mathematical ideas and support student learning. Despite their centrality in scaffolding teaching and learning, most of our understanding about the tasks involved with using representations in instruction and the knowledge requirements imposed on teachers when using these aids is…

This study investigates whether number dissimilarities on subject and object DPs facilitate the comprehension of subject- and object-extracted centre-embedded relative clauses in children with Grammatical Specific Language Impairment (G-SLI). We compared the performance of a group of English-speaking children with G-SLI (mean age: 12;11) with that…

We report a multidimensional test that examines middle grades teachers' understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers' and students' reasoning in this content…

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that…

This study was situated in a semester-long classroom teaching experiment examining prospective teachers' understanding of number concepts and operations. The purpose of this paper is to describe the learning goals, tasks, and tools used to cultivate prospective teachers' understanding of addition and subtraction with whole numbers. Research…