Cover, Copy, Compare (CCC) has been shown to be an effective intervention at improving single-digit multiplication fluency within the academic intervention literature. The application of the three-term contingency trial embedded within CCC provides the intervention with several key components of evidence-based interventions. Given that teachers…

This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

Educational apps can help children develop their early numeracy skills, but only if they incorporate certain pedagogical features. AppLINOU is an early numeracy app that was co-designed by a multidisciplinary team to be compatible with the way numeracy is taught in France's preschools. This study of whether incorporating AppLINOU into classroom…

Student engagement in math and science courses decreases starting in middle school and continues throughout high school (Museus, et al., 2011). This lack of engagement results in students taking only the required math and science coursework and not advanced coursework that would help prepare them for future careers in science, technology,…

Counting is fundamental to early mathematics. Most studies of teaching counting focus on teachers observing children count. The present study compares mathematical ideas that 12 PK, transitional kindergarten (TK), and kindergarten teachers noticed from observing their own students count during a classroom session of Counting Collections with ideas…

This study presents a teaching experiment in which second-grade primary school students compared a city and a town according to population estimates. The activities were presented to them as Fermi problems and required an analysis of the reality to identify sub-problems that students could deal with. The students' products were analyzed from the…

Potential benefits of providing elementary school students experiences with coding robots are well-documented. These include building skill sets related to logical thinking, problem solving, persistence, collaboration, and communication (Harrell 2015). The authors embrace the value of coding in helping elementary school students develop these…

We examined the effect of distributed practice on the mathematical performance of third and seventh graders (N = 213) in school. Students first received an introduction to a mathematical topic, derived from their curriculum. Thereafter, they practiced in one of two conditions. In the massed condition, they worked on three practice sets in 1 day.…

This observation study documents the amount and quality of mathematics instruction provided to students with intellectual and developmental disabilities in kindergarten through second grade in self-contained special education settings. We observed six special education teachers and their students (N = 12) during a total of 967 min allotted to…

Children's literature can provide useful contexts for teaching mathematics. In this article, the authors discuss the use of the children's book "Measuring Penny" (Leedy 1997) to support Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) related to length measurement. The authors first describe three types of misconceptions…

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual…

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

Children with cognitive delays or developmental disabilities are at elevated risk of having a persistent mathematics disability. Students who have difficulty in mathematics display trouble with awareness of numbers and numeric concepts. This is alarming because students who display lower mathematics performance early on in school make smaller…

This article encourages approaches that develop children's understandings of data representations. In particular, when children develope flexibility in their approaches to data representation and understanding, the same data can be represented in different ways. Flexible and adaptive use of representations is part of mathematics competence which…

This article describes how a teacher in Mexico City worked with two researchers on an instructional design project to help kindergartners become proficient in participating in whole-class mathematical conversations.