This work was developed to present constructive steps of multiple integrals using the open-source software Geogebra. The main focus was directed towards creating three-dimensional graphs of integrals through Riemann sums in two variables. Some practical examples are developed to demonstrate the reliability of the presented results, which are…

At the school level statistics begins with exploratory data analysis, or EDA. Statistical learning goes on to include statistical inference, which will be discussed in the second part of this article. In this article, the author will talk about EDA and CODAP. EDA can be thought of as looking for patterns in data using graphs and simple statistics…

Mathematics seems abstract, difficult, and uninteresting to many students, which in turn reduces their interest in learning mathematics. It has been found that the use of ICT and meaningful contexts of problem-solving tasks can make learning mathematics more enjoyable and easier to understand for students. To increase students' interest in…

Graphical analysis of the relationships between pairs of integrals and their corresponding derivatives resulted in the development of a procedure one may describe as 'pictorial integration'. The arctangent of the derivative of various functions was analysed to confirm that this accurately reports the magnitude of angles made by integral functions…

Emergent graphical shape thinking (EGST) entails conceiving a graph as being dynamically generated via the trace of a moving point constrained by two changing quantities. As such, Paoletti et al. (2023) argue that meanings for quantities within a situation and meanings for graphical representations must be connected, or bridged, to engage in EGST.…

Studying students' performance in learning differentiability is essential since it requires them to perform proceptual thinking. This case study research investigates students' proceptual thinking outcomes in learning the differentiability concept using Desmos Classroom Activities (DCA) based on the Three Worlds of Mathematics (TWM) framework. In…

In this article, the authors share activities designed to help students make a connection between the complex roots of X[superscript 2] - 2x + 5 = 0 and the graph of y = X[superscript 2] - 2x + 5. We piloted these activities in three precalculus classes. The activities involved both concrete and technological representations of the mathematical…

Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…

The aim of this research is to advance in the teaching-learning process of representing quadratic functions, both with pencil and paper and with a technological tool. For this purpose, a didactic experience is presented. Firstly, it is explained in the traditional way how to graph a quadratic function; secondly, students are introduced to the…

In this paper, we investigate how a research mathematician conjectures and proves when conducting her research. To be precise, the aim of this study is to achieve a comprehensive understanding of the way this research mathematician develops these mathematical practices and thus gain insight to improve the teaching and learning of these two…

This paper focuses on the emergence of abstraction through the use of a new kind of motion detector--WiiGraph--with 11-year-old children. In the selected episodes, the children used this motion detector to create three simultaneous graphs of position vs. time: two graphs for the motion of each hand and a third one corresponding to their…

The authors described the influence of the GeoGebra based environment on students' achievements in the field of functions with parameters, during collaborative learning. Functions with parameters are important because of their application in science. Students had to choose different values for parameters and to examine the properties of the…

Visual representations and the process of visualisation have an important role in geometry learning. The optimal use of visual representations in complex multimedia environments has been an important research topic since the end of the last century. For the purpose of the study presented in this paper, we designed a model of learning geometry with…

This is an exploratory study considering instructional methods in mathematics education. The study examined misconceptions arising from selected assignments undertaken by sixty-five students. The students were attending a calculus mathematical course unit on limits of functions, in different academic areas offered at selected tertiary institutions…

The introduction of new standards of mathematical education requires to stop understanding of the learning process as the transfer of ready-made knowledge and experience. Educational activity built on the principle of self-construction of knowledge by schoolchildren is highly demanded in new environment. Tasks with parameters have high learning,…