Children's early understanding of mathematics provides a foundation for later success in school. Identifying ways to enhance mathematical instruction is crucial to understanding the ideal ways to promote academic success. Previous work has identified mathematical language (i.e., the words and concepts related to early mathematical development such…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

This study investigated the effects of a number sense intervention in 5-year-old Italian children (n = 96) from different socioeconomic status (SES) backgrounds. We investigated whether a short-term intervention could enable low SES children to reach the same level of their middle-upper SES peers in number sense; in addition, we compared the…

According to creative writing pedagogies academic Susanne Gannon ("English in Australia, 54"(2), 43-56, 2019), and the Federal government-commissioned NAPLAN review (McGaw et al., 2020), NAPLAN has restricted how writing is taught in secondary schools. A NAPLAN-influenced structural approach to teaching writing has subsumed the…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

Baroody, Lai & Mix [2006. The development of young childrens number and operation sense and its implications for early childhood education. In B. Spodek, & O. N. Saracho (Eds.), "Handbook of research on the education of young children" (2nd Ed., pp. 187-221). NJ: Lawrence Erlbaum.] differentiate between four different learning…

Ireland's government placed a renewed focus on the teaching and learning of numeracy with the publication of a national strategy in 2011. Whole-school planning for numeracy was already a requirement for disadvantaged schools also known as Delivering Equality of Opportunity in Schools (DEIS) in Ireland. This single site case study explored how a…

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…

The overarching theme of this book can be simply stated: Building on a foundation of biologically based abilities, children construct number via sensorimotor and mental activity. In this chapter, we return to this theme, and we connect it to three additional themes that emerge across chapters: comparing competing models for conceptual change;…

The main purpose of this study was to test the effects of word-problem (WP) intervention, with versus without embedded language comprehension (LC) instruction, on at-risk 1st graders' WP performance. We also isolated the need for a structured approach to WP intervention and tested the efficacy of schema-based instruction at 1st grade. Children (n…

This study reports initial results of a larger study examining teacher practices in numeracy in the secondary sector. Survey data examined STEM teachers' confidence in mathematics topics and attitudes towards numeracy in everyday life, and the responses were compared to teachers trained in non-STEM areas. The data indicate that teachers'…

The outcomes of a longitudinal randomized number sense intervention including pre-, post- and follow-up tests are reported. The intervention was conducted in Grade 0 when children were six years old. Using Concrete-Representational-Abstract principles, a structured explicit 10-week program focusing on numbers and collective reasoning about…

Background/Context: Despite the surge in efficacy studies, a recent meta-analysis indicates that the relative effectiveness of any two math interventions is largely unknown (Nelson & McMaster, 2019). Additionally, policy makers rarely choose educational programs based on an assessment of costs and cost-effectiveness (Hollands et al., 2016;…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

Conceptualizing numbers as discursive constructs generated in, and for the sake of, communication, we investigated the development of the numerical discourse of Milo, a boy who was 2 years and 8 months old when we first met him and whom we then followed for 18 months. Our analyses of the child's evolving responses to the question "Where is…