The same and different routine offers an opportunity to build a strong foundation for future grades while also deepening the experiences of prekindergarten and transitional kindergarten students. Students have opportunities to make sense, share ideas, and engage in the ideas of others. We conjecture this type of experience supports students and…

Students, even as young as kindergarten, are natural problem solvers (Carpenter et al., 2017). Even before they learn to count, they can make sense of mathematical problems and real- world situations (National Council of Teachers of Mathematics, 2022). Kindergartners can make sense of complex story problems, including Separate Start Unknown…

Model-eliciting activities (MEAs) challenge students to interpret a problem and collaboratively create solutions using the engineering design process. This Innovation to Practice article describes how science, technology, engineering, and mathematics (STEM) teacher educators can use MEAs to build elementary teachers' understanding of computational…

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…

In this article, the authors share frameworks for problem types and students' reasoning about integers. The authors found that all ways of reasoning (WoRs) were used across grade levels and that specific problem types tended to evoke particular WoRs. Specifically, students were more likely to use analogy-based reasoning on all-negatives problems…

In this article, the authors share how gameplay with dominoes can leverage students' quantitative reasoning to promote number development and additive reasoning. This article explores three domino games (Basic Dominoes, Just Before/Just After, and Ten Train), and considers the following: (1) rules and details; (2) students' subitizing and unit…

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…

In the USA, the Common Core Standards in Mathematics for the early grades (K-3) are designed to build on and develop students' number sense as students gain understanding of the structures of addition, subtraction, multiplication and division. It is well understood in teaching circles that subtraction is notoriously more difficult for students…

The "Next Generation Science Standards" call for engaging students in practices that scientists and engineers use (NGSS Lead States 2013), but it's also important to explicitly teach thinking approaches that scientists and engineers use. One way to help children think and act like scientists and engineers is to engage them with…

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,…

This article discusses the use of number talks to engage kindergarten children in regular joyful math opportunities in the classroom. As an educator of four- and five-year-old students in a full day kindergarten (FDK) program in Ontario, Canada, I embrace inquiry-based learning to guide children's activities. Inspired by the childcare centres in…

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…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.