Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected…

Recent work reveals a left digit effect in number line estimation such that adults' and children's estimates for three-digit numbers with different hundreds-place digits but nearly identical magnitudes are systematically different (e.g., 398 is placed too far to the left of 401 on a 0-1000 line, despite their almost indistinguishable magnitudes;…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

We discuss the limits of the equation of the period of a simple pendulum, T[subscript s] = 2[pi][square root]l/g, frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one,…

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…

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…

This study aims to examine the differences in numerosity estimation on a right-to-left number line between second- to fourth-grade students and undergraduate students, together with whether number-line estimation is related to basic arithmetic tasks (addition and subtraction). Hence, 53 Arabic-speaking children and 63 Arabic-speaking adults…

Research Findings: The aim of this study was to investigate U.S. preschool teachers' math teaching knowledge in a specific content domain: counting and numbers. One hundred in-service and pre-service teachers participated in the study; they completed a questionnaire that is composed of learning scenarios and scenario-based math teaching questions.…

Units of measure are critical in many scientific fields. While instructors often note that students struggle with units, little research has been conducted about the nature and extent of these difficulties or why they exist. We investigated calculus students' unit use in area and volume computations. Seventy-three percent of students gave…

Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we…

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

Inspection of thousands of student responses to computer-marked assessment questions has brought insight into the errors made by adult distance learners of science. Most of the questions analysed were in summative use and required students to construct their own response. Both of these things increased confidence in the reliability of the…

This article explores the configural weighted average (CWA) hypothesis suggesting that extension biases, like conjunction and disjunction errors, occur because people estimate compound probabilities by taking a CWA of the constituent probabilities. The hypothesis suggests a process consistent with well-known cognitive constraints, which…

This study extends the debate concerning the mathematical skills deficit of bioscience undergraduates towards a deeper understanding of their mathematics learning, since only through the latter can appropriate and effective explicit teaching be implemented. Three hundred and twenty-six first-year bioscience undergraduates, from three pre- and four…

The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…