The KeyMath-3 Diagnostic Assessment (KM-3) is an individually-administered math assessment used in educational placement and diagnostic decisions. It includes 10 subtests making up Basic Concepts, Operations, and Applications indexes and a "Total Test" composite that measures overall math ability. Here, covariances among subtests from…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve nonroutine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic…

Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…

To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children's…

The way mathematics teaching and learning activities are presented to learners can make them hate or like the subject. The question of accomplishing the mathematics education of the learner from primary to post-secondary school levels is one which necessarily tasks, not only the teacher's stock of mathematical knowledge but also his skill, his…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

This experience has taken place at the School of Education of the Universidad Complutense de Madrid. The goals of the subjects considered are to show how the computer can help in the teaching-learning process in Primary and/or Secondary Education and to clarify and strengthen the mathematical concepts of our students. Mastering a specific…

The present study focused on the lack of knowledge of the double use of brackets in arithmetic expressions and the difficulty in the operatively of expression for mathematics application at the school level. Learning the other rules and formulas of mathematics involves learning the use of a bracket. Binding is useful in both arithmetic and…

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children's…

This case study investigates, at three Swedish schools, primary school students' knowledge of the equal sign. The schools were chosen as representatives of schools whose students have different socioeconomic backgrounds. The data consist of Grade 3 and 6 students' responses to an assessment form based on Matthews et al. ("JRME,"…

This commentary summarizes emerging research into fractions instruction for students who are at risk for failure. Each of the three articles emphasizes a measure conception of fractions. Teaching fractions as measurement helps students learn the magnitude of rational numbers. However, measurement is only part of the way that students should…

This article draws on some ideas explored during and after a writing workshop to develop classroom resources for the reSolve: Mathematics by Inquiry (www.resolve.edu.au) project. The project develops classroom and professional learning resources that will promote a spirit of inquiry in school mathematics from Foundation to year ten. The…

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…