In this paper, we present data from two iterative teaching experiments involving students' constructions of four basic counting problems. The teaching experiments were designed to leverage the generalizing activities of relating and extending to provide students with opportunities to reflect on initial combinatorial activity when constructing…

Computational activity is increasingly relevant in education and society, and researchers have investigated its role in students' mathematical thinking and activity. More work is needed within mathematics education to explore ways in which computational activity might afford development of mathematical practices. In this paper, we specifically…

We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. The arguments can be…

Studies have acknowledged computational thinking (CT) as an efficient approach for problem-solving particularly required in digital workplaces. This research aims to identify indicators for a holistic CT assessment instrument for undergraduate students. A three-round fuzzy Delphi study has been conducted to gain comprehensive opinions and…

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

Researchers are strongly encouraged to accompany the results of statistical tests with appropriate estimates of effect size. For 2-group comparisons, a probability-based effect size estimator ("A") has many appealing properties (e.g., it is easy to understand, robust to violations of parametric assumptions, insensitive to outliers). We review…

Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students'…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (a; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw…

This paper presents a simple method for calculating Clebsch-Gordan coefficients for the tensor product of two unitary irreducible representations (UIRs) of the rotation group. The method also works for multiplicity-free irreducible representations appearing in the tensor product of any number of UIRs of the rotation group. The generalization to…

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…