The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal…

This study investigated the extent to which domain-general and domain-specific antecedents contributed to pre-algebra's initial level and growth rate among students who experience word-problem difficulty (WPD). We examined if such a profile differs for English-language learners (ELLs; n = 75) and non-ELLs (n = 55) with WPD. We assessed 130 U.S.…

The aim of this study is to determine the primary school fourth-grade students' understanding of four operation symbols, using them in arithmetic operations and word problems. Phenomenology research design, one of the qualitative research methods, was used in the research. The participants of the research consist of 123 students, attending the…

The aim of this study is to reveal the meanings that fourth grade students in elementary school attach to the four operation symbols (+, -, x, :) that are abstract, in different representations. The pattern of the study is a case study of qualitative research methods. In the study, the evaluation tool developed by the researchers was applied to…

Grades 4 and 8 students had shown slow but steady improvement in scores on the National Assessment of Educational Progress (NAEP) mathematics assessment from 1990 until 2013, but performance since then has been lower despite the introduction of the Common Core State Standards for Mathematics (CCSSM) in the early 2010s. This study examined student…

We propose to assess conceptual knowledge of mathematical notions by having recourse to isomorphic word problems. We assumed that failing to solve isomorphic problems is an indicator of lack of conceptual knowledge. To reach these conclusions, two experiments were conducted among 4th and 5th grade students. In experiment 1, each student had to…

The relationships between visuo-spatial abilities and geometry performances in school-aged children were examined. A battery of tests assessing non-verbal reasoning, visuo-spatial mental imagery, and academic achievement in geometry (i.e., geometric knowledge and geometric problem-solving competencies) was presented to 162 8-9.5-year-old pupils…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

The use of open problem-solving tasks in mathematics education challenges teachers' beliefs, knowledge and practices. This article examines the practices of two primary teachers and their 3rd to 5th grade classes during a three-year in-service teacher training project aiming to increase mathematical problem-solving in class. Three lesson videos…

Purpose: Math word problem solving, a form of reading comprehension, is complicated by mathematical lexical ambiguity (e.g., the word "difference" can mean "dissimilarity" in everyday discourse but "the answer in a subtraction problem" in math). This study examined the role of mathematical lexical ambiguity in math…

Experiential learning was introduced to support a child's concept development towards evolution scientific literacy. This study examined the effect of an experiential learning model (The Mobile Natural Science Learning -- MNSL) on the knowledge of 4th grade primary school students in Slovenia, during natural science school lessons at the seashore…

This article highlights the main ideas that underlie the differences in potential pragmatic knowledge constructs students experience when solving problems, between the zone of proximal development (ZPD) and the zone of potential construction (ZPC). This qualitative research is based on a phenomenological approach to finding the meaning of things…

The Department of Basic Education in South Africa has identified factorisation as a problem area in Mathematics teaching. Learners in earlier grades are exposed to mathematical tasks, involving concepts, such as factors of integers, fractions, equivalent fractions and prime numbers, that are easier to solve when the divisibility rules are applied.…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children's ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional…