The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

The ideas of computational thinking (CT) and computer science (CS) are increasingly being integrated into K-12 education. Yet, insufficient attention exists regarding access and exposure of CT and CS for students with disabilities. In this Technology in Action, the authors sought to present an argument--as well as actual activities--for teachers…

Tangible programming tools (TPTs) are promising teaching aids in programming courses due to their interactivity and ability to enhance early childhood students' computational thinking, spatial reasoning, and executive function skills. However, it remains unclear whether TPTs support these skills simultaneously. This study examines the impact of…

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…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…

The Birthday Paradox problem can be investigated either with a carefully constructed spreadsheet (for greatest precision) or a calculator process (for reasonable precision). A number of ways of approaching this problem as a class activity are provided.

Recently a teacher friend enquired about the S-I-R equations for disease spread, and what follows was stimulated by that exchange. COVID-19 provides an opportunity to put mathematical flesh on verbal bones such as "self-isolation", "lockdown", "herd immunity", "flattening the curve", "closed…

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

This book provides prospective and practicing teachers with research insights into the mathematical difficulties of students with learning disabilities and classroom practices that address these difficulties. This linkage between research and practice celebrates teachers as learners of their own students' mathematical thinking, thus contributing…

A second-grade class visits Saint John's Food Pantry each year and spends the morning learning about the needs of the community. Then students pitch in and help the staff for a few hours. When the children return to school, they create signs advertising a canned food drive, and they place collection boxes at various locations around the school.…

Computational thinking--a set of mental and cognitive tools applied to problem solving--is a fundamental skill that all of us (and not just computer scientists) draw on. Educators have found that computational thinking enhances learning across a range of subjects and reinforces students' abilities in reading, writing, and arithmetic. This book…

When asked to determine the number of tens in twenty-five, most second graders who have had instruction on place value can quickly provide the correct answer of two. However, when asked to show how the numeral 2 is represented in a set of twenty-five objects, many children struggle to draw a connection between the digit 2 and twenty objects in the…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

Computational thinking can provide a basis for problem solving, for making evidence-based decisions, and for learning to code or create programs. Therefore, it is critical that all students across the K-12 continuum--including students in the early grades--have opportunities to begin developing problem solving and computational thinking skills.…