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…

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…

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…

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 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.…

Several detours prompted me to find time in an overcrowded school day to incorporate important, powerful, daily, whole-class application of fact strategies. A few years ago, I embarked on a journey with my second graders, a journey through the strategies for mental computation of addition and subtraction facts. The focus of that journey was to…

In this article, the authors illustrate how the practice of number strings--used regularly in a classroom community--can simultaneously support computational fluency and building conceptual understanding. Specifically, the authors will demonstrate how a lesson about multi-digit addition (CCSSM 2NBT.B.5) can simultaneously serve as an invitation to…

In this article, I (a) illustrate how the K-2 CCSSM reflect the major findings from research studies carried out over the last 30 years on early mathematical abilities that indicate these standards are developmentally appropriate for young children, and (b) offer insights into some types of instructional strategies (e.g., student-centered…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

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?"

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

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…

This paper reports on a study to examine mental computation strategies used by Year 1, Year 2, and Year 3 students to solve addition and subtraction problems. The participants in this study were twenty five 7 to 9 year-old students identified as excellent, good and satisfactory in their mathematics performance from a school in Penang, Malaysia.…

How this teacher develops composition of ten with second graders was dramatically reshaped by the 2006 release of NCTM's "Curriculum Focal Points." The release of "Curriculum Focal Points"--particularly the suggestion that number sense and computation be focal areas in the second-grade mathematics curriculum--resulted in positive changes in this…

This article describes one teacher's journey to improve her teaching of mathematics by conducting classroom-based inquiry to meet the specific mathematical needs in her second grade classroom. Her process to develop and improve computational fluency through research-based methods is detailed. (Contains 9 figures.)