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…

Simplified, reductionist approaches to curriculum design and delivery are pervasive in science education. In ecological curricula--particularly in, but not limited to K-12--biomes, ecosystems, habitats, and other units of study are simplified and presented as static, easily identified and described entities. Characteristics, components, 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…

Young children love opportunities to build, discover, and solve problems. Teachers can take advantage of these natural tendencies by introducing students to aspects of engineering design while they engage in classroom activities. Engineering also lends itself to supporting students in developing disciplinary literacy practices such as learning…

The authors illustrate how using design thinking allows learners to empathize with the perspectives of others, engage in collaborative problem-solving, practice communicating effectively, and respond to struggle or failure throughout the process.

This paper reports on a project that sought to enhance problem-solving practices within a cluster of primary schools. In-service teachers' description of their approach to problem-solving suggested it was treated as an isolated practice that occurred after concepts had been taught; often focusing on teaching particular problem-solving strategies…

We present in this paper a pair of approaches to support mathematics educators and learners in formulating original tasks. In particular, we facilitate the posing of rich mathematical problems by using two novel methods that were created by a mathematics department at a K-12 school in the United States, and further developed alongside our students…

In this article, the authors introduce the "Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II): A Framework for Statistics and Data Science Education" report. This report, which was published by the American Statistical Association (ASA) and endorsed by the National Council of Teachers of Mathematics…

In the second edition of "Data-Driven Dialogue: A Facilitator's Guide to Collaborative Inquiry," authors Bruce Wellman and Laura Lipton provide strategies that transform school culture through data-driven inquiry. By applying a three-phase model and a host of process tools to facilitate collaborative data analysis, K-12 school and…

Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, the authors share a process for revising them using Universal Design for Learning (UDL). Outlined in detail here are problems for kindergarten, grades 5 and 7, and high school (algebra).

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.

The sandwich problem described in this article would likely be considered more appropriate for third grade or above. However, as members of the research team for a lesson study involving teachers from kindergarten through fourth grade, the authors saw kindergarten students rise to the challenge. The authors invite readers to review two scenarios,…

Myths about early education abound. Many beliefs people hold about early math have a grain of truth in them, but as a whole are not true--they are largely myths. But the myths persist, and many harm children. In this article, we address ubiquitous math myths that may be negatively affecting many young students. We conclude that avoiding the myths…

Young students starting school for the first time (e.g., kindergarteners) often benefit from more than typical intensity of behavioral support. Learning new social expectations, routines, and interaction patterns can be daunting. This is an important concern for schools implementing positive behavioral interventions and supports (PBIS). Learning a…

Complex problem solving is an effective means to engage students in disciplinary content while also furnishing critical non-cognitive and life skills. Despite increased adoption of complex problem-solving methods in K-12 classrooms today (e.g., case-, project-, or problem-based learning), we know little about how to make these approaches…