Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

Preschool students' mastery of early numeracy skills is important, so they enter kindergarten with the necessary prerequisite skills, which are predictive of achievement in later elementary grades. The purpose of this study was to examine the effects of a concrete-representational-abstract (CRA) instructional package on the foundational early…

Competence with rational numbers is essential for mathematics proficiency in secondary mathematics. However, many students struggle with rational number concepts, and students with mathematics difficulties struggle even more. The purpose of this study was to examine the effects of an intervention that incorporated the use of explicit instruction…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

This research focuses on prospective teachers who are a group that has a key role in teaching mathematics to future generations. A qualitative approach with an ethnographic design is used to understand and explain the culture and social life of a region by relating its role as a learning resource to developing local culture-based mathematics…

Considering the negative situations faced by the migrating societies, it is known that the language and culture factors exert a stronger influence on the mathematics course than the other undesirable conditions. From this perspective, it is known that the mathematical performance of individuals is likely to increase by placing the concept of…

Background: Early numeracy interventions including basic arithmetic are crucial for young students at risk for early mathematics difficulties (MDs), yet few studies have evaluated numeracy interventions in second grade with a randomized controlled design. Aim: This pre- and post-test randomized controlled study evaluated the effects of an…

Research focusing on the home mathematics environment has shown mixed results across age groups. Using data from a large online survey, we explored parents' perceptions of the age appropriateness of home mathematics activities for their children. Children's ages ranged from one to 6 years old (N = 958). Activities spanned multiple domains of early…

Number fact knowledge spans far beyond conventional automatic mastery practices involving rote learning. Having the ability to automatically recall number facts fluently does not mean students will have strong conceptual understanding. This article provides suggestions for how number fact thinking and fluency might be developed in primary…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

A growing body of research suggests that children's understanding of mathematical language is critical for their mathematical abilities. Most of this work has been restricted to single language learners (i.e., SLLs), and used dual language learners (i.e., DLLs) as an exclusion criterion, raising questions about the generalizability of these…

This paper examines the conceptions of 'number sense' as promoted in pre-service primary mathematics education courses at 11 South African Higher Education Institutions through the texts used by academics or prescribed for students. While all the participating institutions agree that the development of primary school learners' 'number sense' is…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…