The aim of this study is to investigate Norwegian primary school students' multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8-9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as…

This study investigated upper elementary teachers' framings of their students' mathematical thinking in written across the three component skills of noticing. Drawing on a situated perspective, the research examines the influences of teachers' culturalhistorical backgrounds, attitudes, dispositions, interactions with students, and other situated…

The purpose of this study is to investigate the reflections that arise during the implementation of mathematical modeling activities with third-grade primary school students. To achieve this goal, a case study methodology was employed. The study consisted of 9 third-grade students (average age 8), selected through purposive sampling from a public…

This study describes how 24 third graders (8-9 years old) relate and represent the relationships between variables when working with a functional thinking problem. This aspect contributes to providing insights about how elementary school students attend properties and relationships between covarying quantities rather than isolated computations.…

In this exploratory descriptive study, changes in one cohort's responses to an authentic statistical investigation at the commencement of years 3 and 4 were analysed. Forty-four students made predictions by interpreting a data table of historical monthly temperatures, represented these data and explained their reasoning. An Awareness of…

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 theoretical model describing young students' (Grade 3) arithmetic-algebraic structure sense was formulated and validated empirically (n = 130), hypothesizing that young students' arithmetic-algebraic structure sense consists of five distinct but correlated factors; structure in numerical equivalence and word-problem modeling, structure in…

In this study, we examine students' mathematical reasoning within a technological environment designed to support understanding of relationships between quantities with adjustable measuring units. In particular, we provide a cross-sectional snapshot of how 30 elementary students (Grades 3-5) engaged in a series of fraction-as-measurement tasks…

The aim of this research is to determine the mental processing strategies used by 3rd grade primary school students in addition and subtraction using the empty number lines. The model of the research is a case study, one of the qualitative research methods. The participants consist of 143 students; 75 girls and 68 boys, attending the third grade…

The National Council of Teachers of Mathematics's "Principles to Actions" (NCTM, 2014) cites posing purposeful questions and eliciting and using evidence of student thinking as effective mathematics teaching practices. Interviewing students creates opportunities for teachers to develop these practices. Through interviewing, they can try…

This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

This study examined how word-problem characteristics influenced students' learning and retention of word-problem knowledge during and after an intervention. The participants were 221 fourth-grade students (average age at pretest = 8.8 years) who experienced word-problem difficulties (WPD) and had received a word-problem intervention in third…

How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…

Students in grades 3-5 are undergoing significant cognitive growth and beginning to understand what fairness and equity mean in a diverse and interconnected world. "Modern Math Tasks to Provoke Transformational Thinking" presents carefully crafted tasks that nurture multi-disciplinary literacies, including ecological and cultural…

Mathematics, being a very ancient discipline, is usually seen as a formal subject that must be learned for school purposes, which is very far from creativity and fun. Also, mathematical skills are often considered a talent, so students are easily divided into gifted and not gifted, with a focus on speed and accuracy rather than encouraging the…