Our study on 328 five- to six-year-old kindergarteners (mainly White European living in France, 152 girls) shows that children who do not count on their fingers and undergo finger counting training exhibit drastic improvement in their addition skills from pre-test to post-test (i.e., accuracy from 37.3% to 77.1%) compared to a passive control…

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…

In their recent article on teachers' proportional reasoning, Copur-Gencturk et al. (2022) draw attention to a type of strategy that they call "relative", lodged right between additive and multiplicative thinking. This strategy raised interest in our research team, as it aligned well and helped give stronger meaning to some strategies…

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…

This study is an examination of 79 elementary prospective teachers' (PSTs') capacity for recognizing the core ideas involved in modeling fraction addition problems and their difficulties in solving and presenting the process of fraction addition using area, length, and set models. PSTs completed a written task in which they represented the process…

The level of arithmetic knowledge of a high school student was explored when solving additive word problems considering the semantic structure and syntactic component. The methodology was qualitative and developed in four stages: the first is the selection of the participant, the second is the design of a questionnaire with twenty additive…

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…

The exploration of children's drawings as mathematical representations is a current focus in early years mathematics education research. This paper presents a qualitative analysis of 72 kindergarten to Grade 3 (5 to 8 years old) children's drawings produced during problem-solving tasks centred on multiplicative strategies. Existing frameworks for…

After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

Proficiency in mathematics is fundamental for academic success and is linked to numerous skills that are essential for success in the real-world. Despite its importance, many students struggle with math, leading to nationwide declines in math proficiency. This decline highlights the need for effective interventions that are accessible, able to be…

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…

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…

Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have…

Students encounter mathematics word problems as early as kindergarten and continue to see them throughout their schooling experience. Schema instruction with an attack strategy can support students to successfully navigate word-problem solving. Schemas help students categorize word problems by similar characteristics. To better support students…