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…

Early mathematics plays an important role in introducing foundational concepts for number sense in children. One of the critical areas of learning is the establishment of a linear view of numbers. It is essential to create opportunities for young children to understand that numbers are equally spaced on the number line and that they increase in…

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…

Play allows young children to acquire and practice mathematics skills and concepts while engaging in meaningful and enjoyable activities (Bobis, 2010; Reed & Young, 2018). In particular, open-ended play provides children opportunities to discover materials, explore concepts, and solve problems (Rosli & Lin, 2018) and in the process,…

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…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

This article asks the question: is the "Last Banana" game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by…

In this article, the authors explain how they leveraged the popularity of the "Star Wars" franchise to introduce a task steeped in popular culture as a fun way to engage their students in investigating complex mathematics that have real-life connections to careers in toy design and engineering design in general. The authors share various…

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…

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…

We use number sense in our daily lives to make decisions about quantities. This number sense is connected to our mental number line, in which we draw on our understanding of physical number lines. We often use number lines in the elementary grades for counting and to represent mathematical operations, such as addition and subtraction. Such tasks…

According to NCTM's "Principles and Standards for School Mathematics" (2000), the act of estimating is reflective of students' mathematical intuition and number sense. Students with more developed number sense are better able to judge the reasonableness of their results. To promote estimation, Jennifer Marshall explored incorporating…

This article focuses specifically on the inclusion of meaningful (but potentially messy) real-world mathematics tasks in the middle school classroom. Real-world tasks provide students with learning opportunities allowing mathematics to be used to understand the world, strengthen mathematical knowledge, and offer opportunities for students to use…

This article discusses how technology, in conjunction with carefully designed tasks and orchestrated discussions, has the potential to both reveal students' mathematical practices and to provide opportunities to shape those practices. Four specific mathematical practices that tend to be associated with problem-solving situations are examined: (1)…