Having students solve shape puzzles, such as with pattern blocks or tangrams, is a popular way to encourage students to compose shapes in different ways and talk about the effects of different compositions (Clements et al., 2004; Clements & Sarama, 2009; Sales, 1994), meeting Common Core geometry standards in kindergarten through second grade…

During the past few years, the social interactions of students have been limited. The act of social distancing has not only exacerbated developmental gaps in social and emotional learning (SEL) (Vaillancourt et al. 2021) but also interrupted mathematics instruction (Lewis et al. 2021). Teachers are searching for strategies that promote…

Usable Math available at https://usablemath.org/ is being designed as an open online tutor for elementary school math students and teachers in the USA. It provides interactive problem solving for 3rd through 6th grade students who are learning mathematical reasoning and computation skills through word problems. Using the system, students and…

The author presented a math task asking all his 3rd graders to find ways to count seven sets of eight donuts, arranged in grids of two-by-four. He hoped this task would lead students toward fluency in single-digit multiplication, albeit in a manner that was inherently personalized learning, with students choosing their own methods to reach an…

Computational thinking has been taught in elementary classrooms in other countries for many years, but in the United States this has only been a focus recently due to the drastic shortage of computer scientists. Early exposure to computational thinking has been shown to motivate students to pursue STEM careers, especially computer science (Jin,…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Using an example of a grade 3 science unit about population changes during competition for resources, we describe how we integrated computational thinking (CT) into existing curriculum identifying three levels of depth of integration: identifying connections that already exist, enhancing and strengthening connections, and extending units to…

In this article, the authors present a brief description of the different views of the "nature of mathematics" (NOM), share a five-point view of NOM that undergirds the teaching profession's guiding documents, and describe ways of providing opportunities for teachers and students to have conversations in the classroom that build…

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical…

Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…

This article proposes a latent variable regression four-level hierarchical model (LVR-HM4) that uses a fully Bayesian approach. Using multisite multiple-cohort longitudinal data, for example, annual assessment scores over grades for students who are nested within cohorts within schools, the LVR-HM4 attempts to simultaneously model two types of…

This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have "hands-on" experiences that support their understanding of "number". The teaching "aid" might be unfashionable in…

Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

Ever since "mental arithmetic" was updated to "mental calculation," official documents have succeeded in perpetuating several basic misconceptions and misunderstandings about this topic. This situation does not augur well for the successful teaching of mental calculation strategies to young children. In this article, the author…

This summary of nine studies provides information about evidence-based practices for Tier 2 interventions and how to use Response to Intervention (RTI) in mathematics. It gives a critical technical analysis and review of research on RTI and multi-tiered instructional systems. In an earlier Center on Instruction publication, the authors described…