Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics

GeoGebra is an interactive geometry, algebra, statistics, and calculus application designed for teaching and learning math, science, and engineering. Its dynamic interface allows its users to accurately and interactively visualize their work, models, and results. GeoGebra employs the synthesis of three key features: modeling, visualization, and programming (MVP). Many studies have shown the positive effects of GeoGebra on the efficiency and effectiveness of learning and teaching topics related to science, technology, engineering, and mathematics. In this study, we discuss how GeoGebra provides an environment for learning that is very interactive and collaborative between the learner and the instructor. We also show how integrating GeoGebra into the learning scheme can help improve the skills and knowledge of school and university students in numerous advanced mathematical courses, such as calculus, mathematical statistics, linear algebra, linear programming, computer-aided design, computer-aided geometric design, analytic and projective geometry, and graphical representation. Therefore, this study shows the effectiveness of GeoGebra and its MVP key features in science and engineering, particularly in topics related to mathematics. Each key feature of GeoGebra is thoroughly analyzed, and further analyses, along with how GeoGebra can be helpful in different topics, are discussed.

According to Hohenwarter et al. [1], GeoGebra is an educational mathematics software program that conceptualizes and utilizes dynamic mathematics and is frequently used as a learning and teaching tool from middle school until the tertiary (postsecondary) level. GeoGebra was first presented in the school curriculum, but it was then expanded to include disciplines such as geometry, algebra, and calculus at the university level. GeoGebra is a software program designed for both teaching and learning, whose first and foremost goal is to make mathematical concepts clearer and easier for students to grasp. It is designed to enable proactive teaching and can, thus, be used to focus on problem-solving and assist with the development of mathematical experiments and concept introduction both in face-to-face and in remote class settings. With this program, learners can create sample problems of their own and then solve such problems using mathematical schemes and vital investigations. In this way, what would usually seem like taxing and daunting coursework and topics is given an appropriate avenue for proper, flexible, and supported exploration. This results in student learning that is based not on spoon-fed information, but rather on the learner’s independence when they are making use of and honing their mathematical skills.

Besides this student-led exploration, dynamic worksheets are easily utilized in GeoGebra [1]. This makes it useful not only for middle- and high-school students, but also for college and university students, who can use it in more advanced mathematics classes, such as analytic and differential geometry and numerical methods. Overall, the dynamic preface of GeoGebra makes it very suitable and helpful for students at different educational levels. In some sense, GeoGebra can be regarded as a helpful tool for each and every learner in different mathematical areas. It allows for HTML exportation, which in turn allows for creative teaching kits for artistic visuals and mentoring aids, and this helps garner more class participation, which is widely attributed to dynamic worksheets [2].

In the current digital era, handheld devices such as mobile phones and tablets have become vital to the daily lives of individuals, students, and people in academia. Such transformation is widely due to the societal adaptability and mass acceptance of the continued digitalization of the current world. Mobile devices provide a reliable alternative for desktop computers in many ways, including in the conceptualization and understanding of mathematical discourse [3]. In comparison to computers, they are regarded as useful tools for cultivating proactive study places, hence proving their capability in bridging the gaps in learning mathematics at the university level, as opposed to relying on textbooks. They also help increase the focus and attention of learners through the visuals that they provide, along with the ease with which the students can send responses when they encounter a learning problem. One of such problems faced by younger generations is the increasingly short attention span. As an educational application, GeoGebra is highly recommended and can be downloaded from Google Play or Apple’s App Store. It only requires the users to simply log in and allows them to publish and share their work with other users, thus making learning highly interactive and collaborative [3]. It also allows for the integration of technology into the academic curriculum, and it offers a collaboration of blended learning, both traditional and digital. Moreover, it helps university learners develop a deeper and more comprehensive understanding of mathematics, and its user-friendly interface allows learners to draw and simultaneously have algebraic functions that can all be entered directly with a keyboard, suiting the different learning needs of each learner.

GeoGebra is useful not only for students in middle and high school, but also for college students and educational instructors. In a study in 2019, Machromah et al. [4] tested the advantages of GeoGebra for university students studying and practicing calculus and found that it provides a substantial discourse. In another study, Haciomeroglu et al. [5] showed that GeoGebra helped the teachers familiarize themselves with the concepts of geometry, algebra, and calculus, which are commonly taught to university students. Particularly, it was found that the importance of representations, visualizations, and dynamic worksheets was imparted to the teachers [5]. Moreover, the courses that the teachers enrolled in helped them improve their skills to provide better and more up-to-date teaching aids and methods.

Overall, GeoGebra helps decrease the level of anxiety that many instructors might feel toward technology-integrated learning. To be able to effectively serve 21st-century learners, teachers need to modernize their pedagogical approaches, preferably with the current technological trends. In their research on GeoGebra’s contributions to the professional development of mathematics instructors, Escuder and Furner [6] found that the teachers obtained experience particularly by navigating through the software and that this helped them improve their skills in order to productively pass on their knowledge to their students. Overall, a positive influence was linked to the mathematics teachers’ perception of learning that is integrated with technology. Hence, GeoGebra helped increase their self-confidence in using technology in teaching.

Besides decreasing the level of anxiety and difficulty that teachers feel toward their digital literacy skills, GeoGebra provides a promising course of action in which instructors can practice and explore mathematics and subjects related to science, technology, engineering, and mathematics (STEM). It allows them to hone their digital literacy skills. Digital literacy refers to a person’s capacity to find, assess, and clearly transmit information on a variety of digital platforms using typing and other media. According to the UNESCO, digital skills are defined as a set of abilities to access and manage information through digital devices, communication applications, and networks. Digital competence is one of the competences that educators need to instill in learners [7].

In general, GeoGebra can allow achieving two goals at once. That is, not only can it allow instructors to explore what technology has to offer and improve their own skills, but also it can allow them to hone their mathematical and STEM-oriented teaching skills. Ultimately, this can help instructors improve their self-efficacy and their relationship with their profession and with their students. Exploring GeoGebra allows teachers to improve their pedagogical knowledge and skills, thus providing them with an opportunity for an enhanced, more engaging, and more interactive learning atmosphere in the classroom.

In a study by Verhoef et al. [8], the authors showed the positive effects of GeoGebra on the professional development of instructors. This study focused on a four-year lesson study project conducted by teachers who were determined to elaborate and study derivatives with the help of GeoGebra. The study results showed how teachers coming from different Dutch schools explored and delved into calculus with the help of GeoGebra. They also showed how GeoGebra allowed these teachers to realize that conceptual embodiment and operational symbolism work hand in hand. Through a synthesis of GeoGebra and derivative consolidation, the teachers were able to zoom in on a graph of a derivative to infer and observe its local behavior [8]. In that study, the instructors tackled how they can acquire knowledge related to the importance of visualization and its significance to their students. Overall, the study findings revealed how teachers realized the advantages of GeoGebra in learning mathematics, particularly how GeoGebra helped them perceive the general learning process of their students.

The aim of this study is to assess the significance of GeoGebra to university-level learners. More importantly, our goal is to provide a synthesis of modeling, visualization, and programming (MVP), which are all achievable with GeoGebra’s tools. In particular, in this study, we examine GeoGebra’s success in teaching topics that are related to mathematics, such as science and engineering. Moreover, we provide a discussion of MVP along with a discussion of the problems that learners face pertaining to solving problems related to science and engineering.

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