This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children's subtraction by addition strategy use (SBA; e.g., 712 - 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied…

Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

We present an innovative educational design for basic arithmetic that responds to students' documented difficulties with adding and subtracting single-digit positive and negative numbers. The design utilizes MOVES, a technological architecture that combines floor- and wall-projected interactive interfaces. Students enact arithmetic operations,…

Our work investigated how six primary school students used a non-traditional method for adding and subtracting: the ABN method, a Spanish acronym for Open (method) Based on Numbers. Commognitive theory [Sfard, A. 2008. "Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing." New York: Cambridge…

Early mathematics education presents middle-school students with the challenge of adding and subtracting negative integers. This paper reports on results from the experimental implementation of a proposed educational design for integer arithmetic that utilized the number-line (NL) form as a resource for students to enact simple addition and…

Students with learning disabilities in mathematics often struggle with the underlying concepts of multidigit addition and subtraction. To help students build a conceptual understanding of these computations, teachers can utilize evidence-based practices such as the concrete-semi-concrete-abstract framework and the use of multiple visual…

Adults shift their attention to the right or to the left along a spatial continuum when solving additions and subtractions, respectively. Studies suggest that these shifts not only support the exact computation of the results but also anticipatively narrow down the range of plausible answers when processing the operands. However, little is known…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

This study examined adults' frequent, efficient and adaptive use of direct subtraction (DS) and subtraction by addition (SBA) in mental multi-digit subtraction with the choice/no-choice method. Participants were offered subtractions in one choice condition (choice between DS and SBA) and two no-choice conditions (mandatory use of either DS or…

As national and international assessments continue to show students struggle with rational concepts, which are seen as a major stumbling block for future career in STEM fields, we used the certainty of response index (CRI) as a method of analysis to investigate a group of 40 United Arab Emirates (UAE) seventh grade students' understanding of basic…

Adaptive teachers use student data to guide instruction. Learn about using an anecdotal record form to support adaptive teaching. In this article, the authors describe how teachers can use learning trajectories to make adaptive decisions to meet the needs of their students. They provide an example using the U .S. Math Recovery Council's learning…

A converging body of evidence from neuroimaging, behavioral, and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in…

The objective of this study was to evaluate and characterize the argumentation patterns used by seventh-grade students in the context of algebraic addition and subtraction problems. A qualitative case study was conducted using the Claim-Evidence-Reasoning (CER) model (McNeill & Krajcik, 2008) and argument quality framework. To describe the…