Active learning strategies are purported to be effective in enhancing students' understanding of concepts that would otherwise be difficult to master through other strategies of mediating learning. This study forms part of a bigger study where pre-service teachers' errors and misconceptions in transformation geometry were identified, analyzed and…

This study reports the classroom mathematical practices proposed in an instructional sequence grounding on the principles of inquiry-based learning (IBL) through the use of the dynamic geometry software (DGS) in learning to teach geometric transformations. A 5-week instructional sequence consisting of IBL activities that were guided by the…

Learning and teaching function transformation has a significant place since it provides new opportunities for learners to use, reflect and discover knowledge related to the concept of function. This study's main goals related to the importance of learning function transformation are to examine pre-service mathematics teachers' (PMTs) mental…

Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM)…

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the probability density function and cumulative distribution…

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…

Integration (here visualized as a pounding process) is mathematically realized by simple transformations, successively smoothing the bounding curve into a straight line and the region-to-be-integrated into an area-equivalent rectangle. The relationship to Riemann sums, and to the trapezoid and midpoint methods of numerical integration, is…

When irreducible representations are given in diagrammatic form, it is possible to show direct products pictorially. By giving a similar description of the electric vector associated with a light wave, group-theoretical selection rules (the requirement of a totally symmetric direct product) can also be shown in pictorial form. The [upsilon](CO)…

The logarithmic transformation is often used in regression analysis for a variety of purposes such as the linearization of a nonlinear relationship between two or more variables. We have noticed that when this transformation is applied to the response variable, the computation of the point estimate of the conditional mean of the original response…

The objective of the present paper is to provide a simple approach to statistical inference using the method of transformations of variables. We demonstrate performance of this powerful tool on examples of constructions of various estimation procedures, hypothesis testing, Bayes analysis and statistical inference for the stress-strength systems.…

Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…

It is shown that the bisector of a segment of a geodesic and the bisector of an angle in hyperbolic geometry can be expressed in terms of points which are equidistant from the end points of the segment, and points that are equidistant from the rays of the angle, respectively. An important tool in the approach is that the shortest distance between…

This research explored students' views of geometric objects through the implementation of a curriculum module that allowed them to explore the relationships between transformational geometry and linear algebra. The majority of the students were middle and secondary mathematics education majors enrolled in a one-semester geometry course that is…