Recent research on integration has shown the importance of quantities-based meanings for integrals. However, this research body is still in need of detailed empirical accounts of "how" students develop such understandings across an entire unit on integration. This paper contributes by providing one such account, based on a…

Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

Our study on 328 five- to six-year-old kindergarteners (mainly White European living in France, 152 girls) shows that children who do not count on their fingers and undergo finger counting training exhibit drastic improvement in their addition skills from pre-test to post-test (i.e., accuracy from 37.3% to 77.1%) compared to a passive control…

The authors provide a comprehensive and practical guide to early childhood mathematics, blending research, practice, and inspiration into a resource that teachers can immediately use. Through anecdotes, illustrative videos with a comprehensive index, and detailed assessment protocols, they show how learning trajectories and formative assessment…

Proficiency in mathematics is fundamental for academic success and is linked to numerous skills that are essential for success in the real-world. Despite its importance, many students struggle with math, leading to nationwide declines in math proficiency. This decline highlights the need for effective interventions that are accessible, able to be…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

The effects of whole number computation interventions among school students with learning disabilities in Grades K to 5 were examined using a multilevel meta-analysis. Applying a correlated and hierarchical effect model of robust variance estimation, we examined the intervention effects among 15 peer-reviewed articles and dissertations (two…

As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on…

This study, which used a multiple baseline across participants' design, examines the effectiveness of a modified schema-based instructional approach to improve the mathematical word problem solving performance of three students with mild intellectual disability, two of whom had an autism spectrum disorder. Following the intervention, the three…

Student fluency in mathematics is important, as fluency supports mathematics proficiency and achievement. While fluency can be supported with flashcards and worksheets, it can be supported by games. In this exploratory study, researchers examined the relationship between students' fluency on addition with regrouping problems and playing a virtual…

Mathematical fact fluency, particularly in addition and subtraction, is crucial for students' success in later mathematical concepts and is often a focus of elementary education. Educators are exploring tools to enhance math fluency, such as Reflex Math, a digital program designed to accelerate students' fact fluency through adaptive learning…

The objective of this case study was to identify the role of finger gestures in learning mathematics informally during play, especially in sociocultural settings. A mathematical activity involving addition was qualitatively analyzed at a Japanese preschool. We explored how the process of subjectification and objectification contributed to a…

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

Nowadays, tablets and their applications are part of the children's daily lives. These digital educational activities can become a potent educational tool for efficient and effective in neurotypical as well as children with autism spectrum disorder (ASD). Tablets and their applications allow children to take advantage of new learning platforms and…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…