We view the (real) Laplace transform through the lens of linear algebra as a continuous analogue of the power series by a negative exponential transformation that switches the basis of power functions to the basis of exponential functions. This approach immediately points to how the complex Laplace transform is a generalisation of the Fourier…

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 paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…

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…

In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…

This article provides a range of activities designed to engage students in using an early form of graphing. While the "Australian Curriculum: Mathematics" (2014) highlights understanding, fluency, problem-solving, and reasoning, the National Research Council (2001) describes five strands of mathematical proficiency, with the additional…

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

People need the idea of transformation geometry in order to understand the nature and environment they live in. The teachers should provide learning environments towards perceptual understanding in symmetry training and development practice skills of the students. In order to make up such a learning environment, teachers should have information…

This study focuses on the role of multiple solution tasks (MST) incorporating multiple learning tools and representation systems (MTRS) in encouraging each student to develop multiple perspectives on the learning concepts under study and creativity of thought. Specifically, two types of MST were used, namely tasks that allowed and demanded…

Many of us in the social sciences deal with data that do not conform to assumptions of normality and/or homoscedasticity/homogeneity of variance. Some research has shown that parametric tests (e.g., multiple regression, ANOVA) can be robust to modest violations of these assumptions. Yet the reality is that almost all analyses (even nonparametric…

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…

Students learn more when they attempt to make sense of a mathematical situation they face. For example, a question like why square root of 25 is not + or - 5. Providing the intermediate steps and the reasoning of a technique with graphs can help make better sense of mathematics.

Assessed was the performance of subjects who had been exposed to transformational geometry treatment. The performance test consisted of geometry achievement and spacial ability measures. Second and third grade subjects were randomly assigned to experimental and control groups. The experimentals received a twelve lesson treatment and the controls a…