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This study aimed to determine the effect of a computer-assisted instruction method using GeoGebra on achievement of prospective secondary mathematics teachers in the definite integral topic and to determine their opinions about this method. The study group consisted of 35 prospective secondary mathematics teachers studying in the mathematics education program at a state university in Turkey. The study was carried out using an embedded design, and the Definite Integral Knowledge Test and an opinion form were used for data collection. Upon analyzing the data, the computer-assisted instruction method using GeoGebra was found to positively contribute to the success of teaching the definite integral topic. Prospective teachers stated that this method should be used in math courses as it creates a fun and interesting environment with dynamic learning elements, provides visualization and opportunities to learn mathematics through practice and exercises, enables thorough understanding and explication of skills, and makes way for conceptual learning instead of memorizing. Furthermore, this study was found to facilitate conceptual learning of the relationship between the lower sum, upper sum and Riemann sum.

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... GeoGebra is embedded in the course content and previous teaching through practicals, tutorials, and simulations to achieve teaching goals [20]. Computerassisted teaching can reduce students' time to study and can contribute to mathematical reasoning and thinking [22]. GeoGebra's ability to build relationships between geometry and algebra can help students understand mathematics by activating problem-solving ideas and diagnosing their learning difficulties and misunderstandings [23]. ...

... Likewise, it can be deduced that the two lines intersected when m 1 × m 2 ≠ -1 as shown in Figure 3b. According to Tatar [22], GeoGebra's interesting visualization, such as moving and changing its shape and size, could accommodate exploration and observation activities carried out by students more easily. The software provides features that are suitable for linear equation material, including the creation of points and linear lines as well as the determination of the equation of any arbitrary line. ...

... For this reason, GeoGebra can be used in learning mathematics, especially calculus, to increase student achievement [33]. Furthermore, GeoGebra creates a fun and interesting environment and facilitates students' ability to concretize abstract concepts [22]. ...

The important role of visual representations in supporting students’ learning of geometry concepts and their reasoning is well established. GeoGebra is dynamic and interactive software that can assist students in exploring mathematical concepts effectively. This research aims to examine the effectiveness of GeoGebra in enhancing eighth-grade students’ mathematical reasoning on the topic of linear equations. The study used a quantitative approach with a non-equivalent control group design by applying GeoGebra. Data were obtained through interviews and a mathematical reasoning ability test. The interviews were analyzed descriptively, and the reasoning test was analyzed using dependent t-tests. The findings revealed that GeoGebra significantly helps students’ to have a better understanding of linear equation properties, such as the gradient of parallel, coincident, perpendicular, and intersecting lines. The mathematical reasoning test revealed that learning with GeoGebra can improve students’ mathematical reasoning skills, specifically in linear equations. Teachers are encouraged to incorporate GeoGebra, as its visualization function enables students to explore linear equation properties.

... Students do not try to understand the topic of calculus and the concept of differentiation meaningfully and conceptually. Aspinwall and Miller (1997), Mahir (2009) and Tatar and Zengin (2016) stated that one of the reasons why students have difficulty in learning calculus is the lack of conceptual knowledge. In addition, students see calculations performed in solving differentiation problems as a priority, and thus, they focus on procedural knowledge (Aspinwell & Miller, 1997). ...

... Given the use of differentiation in calculus, many researchers showed that GeoGebra-assisted instruction has a significant influence on students' conceptual achievement. Mathematics teaching with GeoGebra has a positive impact on students' conceptual achievement in various mathematical disciplines, according to experimental investigations from various grade levels (Dikovic, 2009;Praveen & Leong, 2013;Tatar, 2012;Tatar & Zengin, 2016) compared with those who received instructions or interventions based on texts or textbooks. ...

... In terms of conceptual understanding, students in the experimental group who got GeoGebra tuition outperformed those who received traditional teaching. Similarly, Tatar and Zengin (2016) discovered that the experimental group whose teaching was conducted using GeoGebra had a better conceptual comprehension of calculus than the control group. Finally, Hutkemri and Zakaria (2014) investigated the impact of GeoGebra on students' achievement relating to their conceptual and procedural knowledge of functions in calculus. ...

The Brain-Based Teaching Approach is a strategy that implements methods from a brain-based learning (BBL) model. This approach was designed to be compatible with the inclinations and optimal functions of the individual brain to ensure that students can learn effectively. The module uses the Brain-Based Teaching Approach integrated with GeoGebra Software (B-Geo Module) to help students conceptual understanding of the topic of differentiation. Therefore, this study aims to explore the possible effects of the Brain-Based Teaching Approach with the integration of GeoGebra Software on conceptual understanding of the topic of differentiation in rural secondary schools in Malaysia. This study used a quasi-design of pre-Test and post-Test experiments involving 118 form 4 students from rural secondary schools. The researchers used cluster sampling techniques for school selection and intact group for sample selection. The school selection was divided into two groups, namely, the control group using conventional information and communication technology (ICT) modules and the experimental group using the B-Geo Module. The instrument used was the Conceptual Understanding Test of Differentiation. The results of the data analysis show that the conceptual understanding of the topic of differentiation amongst rural secondary school students increased when using the Brain-Based Teaching Approach with the integration of GeoGebra Software.

... With regard to calculus, there are numerous claims about the benefits of using digital technologies to improve students' understanding of calculus concepts (Akcay, 2017;Chipangura & Aldridge, 2017;Leng, 2011;Nobre et al., 2016;Ocal, 2017;Ocal & Simsek, 2017;Tatar & Zengin, 2016;Vajravelu & Muhs, 2016;Verhoef, Coenders, Pieters, Van Smaalen, & Tall, 2015;Zulnaidi & Oktavika, 2018). The availability of technological tools in classrooms has offered new approaches for teaching calculus Chapter 2: Literature Review 46 and better opportunities for students' development of a conceptual understanding of calculus topics. ...

... It provides visual and effective teaching and learning environments for both teachers and students. GeoGebra software has been shown to not only be effective in increasing pre-service teachers' attitudes towards proof and proving in mathematics (Zengin, 2017), but it has helped to bridge concepts of geometry (Reis & Ozdemir, 2010;Saha, Ayub, & Tarmizi, 2010;Shadaan & Leong, 2013;Tarmizi, 2010), trigonometry (Zengin, Furkan, & Kutluca, 2012), algebra (Reisa, 2010), and calculus (Nobre et al., 2016;Paoletti et al., 2017;Tatar & Zengin, 2016;Verhoef et al., 2015;Yuniarti, Sari, & Khotimah, 2017). The following discusses studies specifically focused on teaching and learning calculus using GeoGebra in school and university settings. ...

... The study results revealed that the use of GeoGebra created interactive learning opportunities about the definite integral concept. Tatar and Zengin (2016) used an embedded design research study with thirtyfive mathematics teachers (secondary) undergoing a course in the mathematics education program. The research study found that the computer-assisted instruction approaches positively enhanced the teaching of the definite integral topic. ...

This research explored the beliefs, knowledge and skills of Bhutanese pre-service mathematics teachers and their preparedness to teach a reformed mathematics curriculum. Data were collected when the participants joined a series of inquiry-oriented, technology-enabled calculus workshops. These data analyses revealed many inconsistencies between the participants’ espoused and enacted beliefs and is alignments between their mathematical knowledge and skills when compared to the intentions of the newly reformed curriculum. From this, implications have been drawn about the preparedness of the soon-to-graduate pre-service mathematics teachers, and recommendations are made regarding ways future pre-service teachers mathematical beliefs, knowledge and skills may be enhanced.

... GeoGebra is preferred by primary school instructors owing to its free resources and pedagogical influence in meeting a learning aim [25]. Several studies related to GeoGebra have been carried out on prospective teachers [26], [27], but still few studies focus on prospective primary school teachers. In the context of Indonesia, Putra et al. [28] found that there is only a study on GeoGebra with the subject of prospective elementary teachers comparing to twelve studies with prospective mathematics teachers. ...

... Several previous studies [10], [11], [26], [27], [30]- [32] have focused on using GeoGebra in mathematics learning from elementary school to university. A study conducted by Khalil et al. [33] showed that the use of GeoGebra in learning analytical geometry in high schools had a significant positive effect on students' abilities compared to students who traditionally studied using paper and pencil. ...

... In initial teacher training, Tatar and Zengin [26] discovered that prospective teachers have optimistic attitudes toward incorporating GeoGebra into their courses. They mentioned that the computer-assisted instructional method using GeoGebra should be used in mathematics classes because it provides an enjoyable and engaging environment of diverse learning components, visualization and opportunities to learn mathematics through practice and experiments, thorough comprehension, and explication of abilities, and logical learning ratchet. ...

p class="0abstract">The integration of technology in learning is increasingly popular and inevitable, especially during the Covid-19 pandemic. In mathematics education, Geogebra has been used as a pedagogical tool in learning mathematics from elementary to university. The present study aims to explore first-year prospective elementary teachers’ experience constructing 3-D shapes using GeoGebra. This study uses a case study method with 40 first-year prospective elementary teachers from an elementary initial teacher training from a public university in Riau, Indonesia. The participants worked in small groups and discussed some 3-D shapes through an online platform, and in the end, each participant reflected their attitudes towards the integration of GeoGebra in learning 3-D shapes. The findings show that prospective elementary teachers discussed six types of 3-D shapes; cube, rectangular prism, rectangular pyramid, cylinder, cone, and spheres. They prefer to discuss curved surfaces rather than flat surfaces of 3-D shapes. In addition, prospective elementary teachers have positive attitudes towards integrating GeoGebra in elementary initial teacher training. They believe that GeoGebra supports them to understand better the concepts of volume and surface area of 3-D shapes, facilitate students to understand the properties of a geometry object, and compare the object one made using hand drawing to using GeoGebra. Meanwhile, difficulty in using the tools to construct 3-D shapes in GeoGebra becomes a hinder to understand mathematics concepts and properties. The implication of this study is that there is a potential to integrate GeoGebra in mathematics learning in elementary teacher training.</p

... However, many studies report that students have difficulty understanding Calculus [1], [3]- [5]. Derivatives and integrals are the most difficult concepts [6]. Most students do not have a deep understanding of calculus concept [7]. ...

... Using technology not only can contribute to mathematical problem solving but also develop creative thinking skills [12], [13]. It can foster mathematical reasoning and mathematical thinking [6]. Using technology (technology-supported environment) in calculus learning specifically the use of GeoGebra in Riemann sums [14]. ...

... GeoGebra provide an alternative method to overcome the difficulties about calculus [6]. GeoGebra has been designed for improved learning out comes. ...

The goal of this study is to develop a GeoGebra-assisted worksheet to enhance students' understanding of calculus. Many studies report that students have difficulty understanding calculus. GeoGebra provides an alternative method to overcome the difficulties associated with calculus. The Plomp development model consists of three phases: specifically, preliminary analysis, prototype development and an assessment was used in this study. The subjects of this study were 37 students. The results of this study are valid in terms of content, presentation, linguistics and graphics and practical in terms of implementation, time, ease of use and effective in terms of its potential impact on students' mathematical understanding. The GeoGebra-assisted worksheet can help students rediscover the given concept, while the use of visualization of the calculus concept can significantly enhance students’ mathematical understanding. Likewise, GeoGebra-assisted worksheets can be used to enhance students’ understanding of calculus. Teachers are suggested using GeoGebra in order to build students’ understanding on calculus subject.

... The use of GeoGebra in mathematics learning from elementary school to college has been the concern of several previous studies [5]- [7]. A study conducted by Tatar and Zengin [8] revealed that prospective teachers have positive attitudes toward implementing GeoGebra in their courses. They mentioned that the computer-assisted instructional method using GeoGebra should be included in mathematics classes because it offers an enjoyable and engaging atmosphere of diverse learning components, offers visualization and opportunities to learn mathematics through practice and experiments, allows for thorough comprehension and explication of abilities, and allows for logical learning rather than memorizing [8]. ...

... A study conducted by Tatar and Zengin [8] revealed that prospective teachers have positive attitudes toward implementing GeoGebra in their courses. They mentioned that the computer-assisted instructional method using GeoGebra should be included in mathematics classes because it offers an enjoyable and engaging atmosphere of diverse learning components, offers visualization and opportunities to learn mathematics through practice and experiments, allows for thorough comprehension and explication of abilities, and allows for logical learning rather than memorizing [8]. Therefore, we are interested in investigating prospective elementary teachers' experience with GeoGebra on a specific mathematics activity. ...

... The results show that prospective elementary teachers have different experiences. Some of them have shown a positive view toward the use of GeoGebra in learning mathematics, and it is in line with a previous study that found that prospective teachers support the use of GeoGebra in learning mathematics [8]. They expect the instructional learning using GeoGebra to offer visualization and opportunities to learn mathematics through practice and experiments, allow for thorough comprehension and explication of abilities, and allow for logical learning rather than memorizing [8]. ...

... In recent years, the use of computer technology and educational software has increased in mathematics education. It has been expressed in many studies that dynamic geometry software (DGS) provides students opportunities to establish connections between mathematical objects and graphical representations (Öçal, 2017;Shadaan & Leong, 2013;Taş, 2016) and supports the active construction of mathematics knowledge within a dynamic learning environment (Dayi, 2015;Hohenwarter & Fuchs, 2004;Hutkemri & Zakaria, 2014) and enables conceptual learning with the aid of animation and visual materials (Dikovi c, 2009;Tatar & Zengin, 2016). Moreover, it has shown in the results of some studies that using DGS has positively increases students' mathematics/geometry achievement (Chan & Leung, 2014;Erbaş & Yenmez, 2011;Günhan & Açan, 2016;Köklü & Topçu, 2012;Özmen, 2019;Pilli & Aksu, 2013;Topuz, 2017;Turk & Akyuz, 2016) and conceptual learning (Caglayan, 2014;Hutkemri & Zakaria, 2012Zengin, 2018). ...

... It has been expressed in some studies that GeoGebra provides students opportunities to explore connections between mathematical objects and graphical representations (Öçal, 2017;Shadaan & Leong, 2013;Taş, 2016), as well as supports collaborative learning and student motivation (Tatar & Zengin, 2016). It has also been shown in other studies that GeoGebra-supported instruction of mathematics subjects such as trigonometry increases students' academic achievement compared to instruction where educational software is not used (Zengin et al., 2012), circle and circle (Topuz, 2017), polygons (Erbaş & Yenmez, 2011), exponential and logarithmic functions (Birgin & Acar, 2020), limit and continuity (Kepçeo glu & Yavuz, 2017), derivative (Zengin, 2018) and integrals (Tatar & Zengin, 2016). ...

... It has been expressed in some studies that GeoGebra provides students opportunities to explore connections between mathematical objects and graphical representations (Öçal, 2017;Shadaan & Leong, 2013;Taş, 2016), as well as supports collaborative learning and student motivation (Tatar & Zengin, 2016). It has also been shown in other studies that GeoGebra-supported instruction of mathematics subjects such as trigonometry increases students' academic achievement compared to instruction where educational software is not used (Zengin et al., 2012), circle and circle (Topuz, 2017), polygons (Erbaş & Yenmez, 2011), exponential and logarithmic functions (Birgin & Acar, 2020), limit and continuity (Kepçeo glu & Yavuz, 2017), derivative (Zengin, 2018) and integrals (Tatar & Zengin, 2016). In addition, it is indicated in some studies that use of GeoGebra promotes retention in learning (Genç & Öksüz, 2016;Mercan, 2012;Taş, 2016;Topuz, 2017), conceptual learning (Dayi, 2015;Hutkemri & Zakaria, 2014;Öçal, 2017), develops to problem solving (Hutkemri et al., 2017) and geometry thinking skills (Öztürk, 2012). ...

Lay Description
What is already known about this topic?
The subject of functions and their graphs are the basis of many mathematical concepts and subjects such as logarithm, limit, derivative and integral.
It is indicated in many studies that middle‐grade students have some misconceptions and difficulties in learning the concept of a straight line and slope.
It was determined in previous studies conducted at different grade level that using dynamic geometry software (DGS) increases students' mathematics achievement according to traditional instruction.
There is a need for research investigating the effect of using GeoGebra software on eighth grade students' conceptual understanding and retention of learning regarding linear equations and slope.
What this paper adds?
A quasi‐experimental design with pre‐test, post‐test and delayed post‐test was conducted.
Using GeoGebra software had positive effects on eighth‐grade students' conceptual understanding regarding linear equations and slope.
The learning environment with GeoGebra software increased the retention of learning.
The implications of study findings for practitioners
This research provided evidence regarding the effects of using GeoGebra software on eighth‐grade students' conceptual understanding and retention of learning in mathematics.
In future studies, the long‐term effects of GeoGebra on other mathematics topics and other learning outcomes within similar settings should be examined.

... The study of geometry gives students a variety of fundamental skills, such as problem-solving skills, reasoning skills, logic skills, and critical thinking skills (Dimla, 2018;Tatar & Zengin, 2016). These skills are useful in life and in a variety of scientific fields. ...

... Geogebra is open-source and dynamic multi-platform geometry software that can be used as a medium for learning mathematical contents such as geometry, calculus, and algebra (Hohenwarter & Fuchs, 2004). According to Tatar and Zengin (2016), teaching with the support of Geogebra software produced a lively and dynamic learning environment, provided opportunities for students to practice and learn mathematics, and provided a setting for conceptual learning rather than memorization. Moreover, numerous empirical studies have shown that GeoGebra is used as a tool for geometry presentation, visualization, construction, and sketching in mathematics exploration, allowing students to expand their own understanding (Hohenwarter & Fuchs, 2004;Vasquez, 2015). ...

Learning geometry with conceptual understanding requires the implementation of appropriate methods that actively engage students and support them in becoming autonomous, critical thinkers, and self-directed learners. The purpose of the study was to investigate the effect of GeoGebra-supported learning on grade ten students’ conceptual understanding of geometry. The study adopted a non-equivalent pretest-posttest quasi-experimental research design. Three secondary schools that were purposely selected for the study, along with three classes and mathematics teachers (one from each school), were randomly assigned to treatment group 1, treatment group 2, and the control group. For a 10-week period, these groups were instructed with GeoGebra, using a collaborative approach; with GeoGebra, using a conventional approach; and with a conventional approach, respectively, and the instruction is supported by the 5E (engage, explore, explain, elaborate, and evaluate) instructional model lesson plan. All groups performed a pre-test and a post-test of their conceptual understanding of geometry. Paired sample t-tests, Scheffe’s posthoc test, and ANOVA were used to analyze the data. The study’s findings showed that GeoGebra technology supported by collaborative methods had a greatly stronger effect on students’ conceptual understanding of geometry topics than other forms of classroom instructional methods. These, then, provide information about potential approaches that secondary school teachers might use to enhance their students’ understanding of geometry topics.

... The time series of monthly data spans from 2017 to 2020 and also includes the first quarter (three months) of 2021 (the most recent available data), totaling 51 observations for each variable in the analysis. The software GeoGebra (Tatar and Zengin 2016) was employed for calculations, and Minitab 17 was used to perform normal (Aprausheva et al. 2015), logistic (Guia et al. 2013), Weibull (Krylov et al. 2009)), and Gamma (Bagui and Mehra 2017) probability distribution fitting tests. The economic importance of the Quintana Roo region and its contribution to the national tourism industry have been crucial to place Mexico among the top ten countries in terms of international tourist arrivals worldwide (World Tourism Organization 2019). ...

... The time series of monthly data spans from 2017 to 2020 and also includes the first quarter (three months) of 2021 (the most recent available data), totaling 51 observations for each variable in the analysis. The software GeoGebra (Tatar and Zengin 2016) was employed for calculations, and Minitab 17 was used to perform normal (Aprausheva et al. 2015), logistic (Guia et al. 2013), Weibull (Krylov et al. 2009), and Gamma (Bagui and Mehra 2017) probability distribution fitting tests. ...

Given the tourism industry’s risk and vulnerability to pandemics and the need to better understand the impacts on tourism destinations, this research assesses the effect of the COVID-19 outbreak on the variation of taxpayer units in the Mexican Caribbean region, which includes some of the major sun-and-sand beach destinations in Latin America. Using monthly data of registered taxpayer entities at the state and national levels as the analysis variable, probability distributions and definite integrals are employed to determine variations of the year following the lockdown, compared with previous years’ data. Results indicate that despite the government’s measures to restrict businesses’ operations and a reduction in tourism activities, registered taxpayers at the regional level did not decrease for most of 2020. Further, as business activities and tourism recovered, taxpayer units increased at the end of 2020 and beginning of 2021. Surprisingly, such a pattern was not observed at the national level, which yielded no statistically significant variations. A discussion of factors influencing the resilience of the tourism region in the study (e.g., outbound markets’ geographic proximity, absence of travel restrictions, closure of competing destinations) and implications for public finances are presented.

... Besides, only few students reported that they were struggling to manage the GeoGebra software (S6 & S4). The finding is in consonance with different research studies [31,42], which incorporated GeoGebra during mathematics learning. For instance, Nobre et al. [31] confirmed that the GeoGebra software has a positive contribution to students' motivation while learning calculus contents. ...

... For instance, Nobre et al. [31] confirmed that the GeoGebra software has a positive contribution to students' motivation while learning calculus contents. Tatar and Zengin [42] also disclosed that students have positive opinions about the use of GeoGebra for learning definite integrals. Furthermore, employing different teaching approaches, which involve effective technology that stimulate students' interest in mathematics, inevitably improve their understanding and achievement [9,10]. ...

The notion of limit is one of the fundamental concepts which underpins advanced calculus of one or more variables in the field of analysis. However, understanding the concept of limit has been an impenetrable problem for many students in Ethiopian Universities. Only very few literatures were documented focusing on overcoming the difficulty of learning the concept of limit. For this reason, the overarching aim of the present study is to enhance students' conceptual understanding of limit by empowering their visualization skills using GeoGebra integrated with multi-teaching approaches. The study employed mixed methods experimental (intervention) design within an APOS paradigm. Both qualitative and quantitative data were collected. Qualitative data was collected using students' reflections and interviews, whereas quantitative data was collected through pretest and posttest using diagnostic tests. The results of the qualitative data analysis revealed that the learning milieu created a positive impact on students' understanding of the concept of limit. Additionally, students provided coherent and viable reasons while making mental constructions and their coordination in the learning process based on the genetic decomposition grounded in APOS theory. Furthermore, the results of the quantitative (posttest) data analysis proved that students' mean scores on conceptual understanding of limit in the experimental group was significantly better than those in the control group. Thus, it could be possible to conclude that students’ conceptual understanding of limit is improved using GeoGebra integrated with multi-teaching approaches within an APOS paradigm. The findings open a great opportunity to suggest technology integrated mathematics curriculums for the teaching and learning of mathematics.

... In another sense, technology in schools will become "new" if the pedagogy using it is innovative, as emphasized by Bibeau [23] in a conference discussing the difficulties of integrating computers in schools. I this context, the results of the study support those of numerous studies that show that the use of GeoGebra contribute positively to the process of students' learning [24]. Based on these results, we can say that the GeoGebra software alone cannot promote effective learning, but its use in a cooperative pedagogical context where learners are engaged in the process of a creative use of dynamic digital resources related to the learning objectives allows them to construct their knowledge through its construction protocol, visualization functions, and concretization. ...

The study presented in this research aims to study the impact of the implementation of GeoGebra software and the cooperative pedagogy on the performances of 1st year of high school scientific students. Our sample for this study is conducted on thirty-six learners, divided into two groups. GeoGebra software and cooperative pedagogy were assigned to be adopted by the experimental group. Whereas, the second group followed a focused learning on the collective visualization of animated productions via PowerPoint. We have conducted a pre-experimentation diagnostic test which served to the repartition of learners and to verify their uptake. Thanks to the tests of control and evaluation, respectively organized within and after this experience, we have collected the quantitative data. the use of ANNOVA analysis and Tukey test displayed that the implementation of the GeoGebra software teaching and the integration of cooperative teaching promoted the 1st group's acquisition success in comparison to second group. The outcome showed that using GeoGebra software in a transmissive teaching environment is still limited in the competence's development and the students' knowledge.

... Subsequently, GeoGebra examined the impact on students' roles in terms of logical and procedural information. When the experimental students consider their logical and procedural skills, there are slightly better results than those in the control sample [22]. In his research [23], he agreed on GeoGebra's impact on students' logical and procedural skills: the case of the implementation of derivatives. ...

The use of ICT in teaching and studying mathematics helps students to develop mathematics. The practice's application, therefore, depends on different considerations, amongst which: teachers' expectations of their ICT teaching skills, instructor attitudes towards teachers in mathematics, teacher attitudes towards ICT contributions to student mathematics awareness. The research was undertaken to assess ICT integration readiness in the classroom in the Paracelis district for mathematics teachers at secondary schools. The thesis used a questionnaire with comments on any of the above variables. This questionnaire was forwarded to 15 mathematics teachers at Paracelis District secondary schools. It shows that ICT teachers' intervention in mathematics has an average limit of 4.06. It also ensures that mathematics teachers are confident and willing to use ICT in mathematics and mathematics instruction. The research results indicated that the controls and the sample groups were substantially different and verified. It shows that the research group was higher than the test group. The use of Microsoft Excel in integrating machine data in the resolution of statistics positively affects the student's performance. The integration of ICT into teaching, therefore, has an advantageous effect on the progress of students.

... Hasil pengabdian kepada masyarakat tentang penggunaan aplikasi geogebra sebagai media pembelajaran inovatif pada mata pelajaran matematika yang sifatnya abstrak dapat membantu siswa untuk memahami konsep matematika. Hal ini sejalan dengan hasil penelitian terdahulu bahwa penggunaan GeoGebra dalam pembelajaran matematika dapat meningkatkan pemahaman siswa terhadap konsep-konsep matematika yang abstrak (Saha et al., 2010;Tatar & Zengin, 2016). Selain itu aplikasi Geogebra ini memungkinkan siswa untuk memvisualisasikan dan memanipulasi objek matematika, seperti grafik, fungsi, dan geometri, sehingga membuat materi menjadi lebih mudah dipahami (Turmuzi et al., 2021;Birgin & Acar, 2020). ...

Innovative learning media is a form of developing learning media designed to provide a more interesting and interactive learning experience for students. Due to the importance of using innovative learning media, prospective elementary school teacher students must be equipped with various technology mastery skills to develop their abilities so that they can present a meaningful teaching and learning process. Meaningful learning certainly requires interactive media to support the implementation of classroom learning. One program that can be used is the GeoGebra program. The GeoGebra program is a computer or smartphone program that can visualize abstract mathematical material. The GeoGebra application shows that this program can be used as a bridge in delivering mathematics material so as to make it easier for educators in the teaching and learning process. The purpose of this training is to increase the knowledge and abilities of prospective elementary school teachers in designing and using GeoGebra in learning mathematics. In this service, an example of the material practised during the training is. The results of this service can be said to be successful, as seen from the enthusiasm of the participants in participating in the training. This is also marked from the results of the posttest questionnaire that 100% of participants are ready to use the GeoGebra application in developing learning media.

... The use of GeoGebra can help students to articulate their visual, analytic thinking, and understanding in the learning process (Takači et al., 2015). Different research study revealed that GeoGebra can help to make mathematics classroom interesting through mutual interaction of teachers and students (Hernández et al., 2020;Putra et al., 2021;Tatar & Zengin, 2016). ...

This present study aims to examine the effect of GeoGebra-assisted interactive learning on student mathematical achievement of coordinate system. The study applied a quasi-experimental method that included 41 fifth grade students from a private Islamic school in Pekanbaru, Riau. The students were randomized into an experimental group (n=21) that received GeoGebra-assisted interactive learning and a control group (n=20) that received traditional teaching approach. Student mathematical achievement was measured using items of coordinate system developed by the researchers, and the data gathering in this study was analyzed using nonparametric statistical analysis. The findings indicated that there was significant statistical difference in student mathematical achievement of coordinate system between the experimental and control group (Asymp. Sig. (2-tailed) = 0.000 < 0.05)). The study concluded that the instruction based on GeoGebra-assisted interactive learning had a statistically significant positive effect on improving student mathematical achievement of coordinate system.

... F. Yerizon et al., 2021). An alternative approach to reduce those challenges of abstractness of calculus is provided by using GeoGebra (Tatar & Zengin, 2016). But students still have difficulties on the using GeoGebra to learn calculus. ...

With the use of a variety of digital tools, services, and applications to enhance the learning environment, technology is now deeply interwoven within the educational process. Technological, pedagogical, and content knowledge (TPACK) model was used as a lens to evaluate GeoGebra’s potential and limitations in the teaching and learning of Limits and Continuity of Functions. Intact classes were assigned as experimental and control groups purposively. The study subjects were 252 students and 78 mathematics teachers. The Limits and Continuity of Functions Achievement Test and the Advanced Mathematics Teachers’ Survey were the two data collection instruments. The findings revealed significant differences in conceptual knowledge (t [df] = -11.46, p $\gt$> .05) and procedural knowledge (t [df] = -11.027, p $\gt$> .05) between control and experimental group. The output lacks detailed instructions, drawing out some functions requires other content knowledge which is not covered by packages of GeoGebra like the graph of discontinuous functions is not automatically represented in a correct manner are some limitations heighted in this study. Results show the necessity of including GeoGebra in the teaching of Limits and Continuity of Functions.

... 9 (17), 63 -77. https://doi.org/10.55560/arete.2023.17.9.3 Dentro de los trabajos que potencian el uso de tecnología y convergen en el estudio de la integral definida, se han identificado las siguientes problemáticas para el proceso de enseñanza-aprendizaje de dicha integral (Domínguez et al., 2019;Aranda y Callejo, 2017;Tatar y Zengin, 2016): 1) no es clara la dependencia entre la sucesión de sumas de Riemann y en valor n de la partición realizada; 2) no se emplea el concepto de sucesión de forma funcional, sino como un listado de elementos; y 3) no se relaciona el límite de las sumas de Riemann y la idea de área bajo la curva. ...

Este artículo explora el tratamiento y la conversión de los registros de representación semiótica que movilizan estudiantes de ingeniería en agronomía acerca del objeto matemático ‘integral definida’ cuando tratan de apropiarse de su significado, apoyándose con el uso de GeoGebra. Con el sustento de la Teoría de Registro de Representación Semiótica y un análisis de carácter cualitativo de un estudio de caso, se muestran los desarrollos generados por los estudiantes a la tarea de modelar la integral definida de una situación contextualizada. Dentro de los resultados se identifica que el uso del software apoyó, principalmente, a la mediación entre el tratamiento tabular y gráfico, y a su vez, la conversión de estos a un lenguaje algebraico fuera del computador.

... Se considera que las deficiencias presentes en el aprendizaje del proceso de integración como análisis matemático en el segundo ciclo de nivel secundario son atribuibles a situaciones de enfoques metodológicos. Diversos investigadores han alertado sobre las dificultades en los procesos de enseñanza y aprendizaje de la integral definida (Jones 2015;Tatar et al., 2016;Susac 2018;Domínguez et al., 2019). En primer lugar, esas deficiencias tienen mucho que ver con el arraigo de ciertas ambigüedades al momento de abordar los conceptos, así como también la aplicación de un enfoque geométrico, como lo manifiesta Monroy et al. (2020). ...

El objetivo del presente estudio fue analizar las actitudes y el grado de empoderamiento de las competencias básicas curriculares sobre la integral definida que presentan los estudiantes que aprobaron la prueba de orientación y medición académica del Instituto Superior de Formación Docente Salomé Ureña, Recinto Emilio Prud’Homme, cuatrimestre septiembre-diciembre 2020. La metodología se enmarcó en el enfoque cuantitativo, con alcance descriptivo-correlacional y diseño no experimental. La muestra censal estuvo conformada por 31 estudiantes a los cuales se les aplicó la técnica de la encuesta, la misma se hizo a través de 2 instrumentos tipo cuestionario. Dentro de los resultados obtenidos, un grupo de estudiantes no disfruta los ejercicios de integrales definidas. En cuanto al empoderamiento de las competencias básicas curriculares, un porcentaje de informantes clave, manifestó no haber visto el tema de las integrales definidas en el último año de la educación secundaria. Como conclusiones, el nivel cognitivo de las integrales definidas que presentan los estudiantes es deficiente. Sobre los educadores de matemática, deben impartir el tema de las integrales definidas en el segundo ciclo de la educación secundaria. Para ello, se debe desarrollar programas de capacitación y desarrollo permanentes, a fin de promover estrategias de enseñanza y aprendizaje que articulen lo concreto, pictórico y abstracto del cálculo integral.

... The use of technology has been shown to improve not just one's ability to solve mathematical problems, but also one's capacity for original thought (dos Reis, Miranda, & Pereira Filho, 2019;Xu, 2016). supports the development of logical and arithmetic reasoning (Tatar & Zengin, 2016). A technology-supported environment (TSE) for studying calculus with a focus on using GeoGebra for Riemann sums (Caglayan, 2014). ...

The objectives of these mixed methods were to 1) improve students’ performance in calculus by using GeoGebra software and 2) investigate students’ experiences with and perspectives on using GeoGebra software in calculus. The participants were 58 mathematics teacher students at a university in Thailand. The instruments in this study were a test; this was called the Calculus Achievement Test (CAT), which consists of limits and continuity; a derivative of function; and its application; and a questionnaire with an interview with a student. The statistics for qualitative data were gathered from instruction; we used percentages, mean scores, standard deviations, and a one-sample t-test; while quantitative data was gathered from students’ reflections and interviews. The results showed: 1) the results of the one-sample t-test show that using GeoGebra Software in Calculus is effective in students’ performance; 2) the data, the quantitative findings show that students were more interested and excited during the intervention. Students could better show their creativity and learn about themselves because of the intervention. Teaching calculus with GeoGebra embedded is a good and effective way to do things. The finding shows a good chance of developing technology-integrated math curricula for teaching and learning calculus.

... Dolayısıyla belirli integral konularının öğretiminde kavramsal öğrenmeye de odaklanılmasının gerektiği açıktır. Literatürdeki çalışmalarda belirli integral kavramlarının öğretimini desteklemek için teknoloji desteği ve çoklu gösterim kullanımından faydalanıldığı görülmektedir (Çağlayan, 2016;Çetin & Dev, 2021;Delice & Sevimli, 2010;Milovanovic vd., 2011;Tatar & Zengin, 2016). Bu çalışmada ise literatürdekilerden farklı olarak belirli integral öğretiminde kavramsal öğrenmeyi desteklemek amacıyla öğrencilerin düşüncelerine ilişkin açıklamalarını ve gerekçelendirmelerini sundukları argümantasyon süreçlerini oluşturmak hedeflenmiştir. ...

Çalışmada Analiz I dersinde dönel cisimlerin yüzey alanını hesaplamayı sağlayacak modelin oluşturulması sürecinde ilköğretim matematik öğretmenliği öğrencilerinin ortaklaşa argümanlarının incelenmesi amaçlanmaktadır. Durum çalışması olarak desenlenen çalışmanın katılımcıları Analiz I dersine kayıtlı ilköğretim matematik öğretmenliği öğrencileridir. Veriler dönel cisimlerin yüzey alanı modelinin oluşturulması esnasındaki argümantasyon sürecinin video kayıtları ile gözlem notlarından oluşmaktadır. Veriler analiz edilerek argümantasyon sürecinin bileşenlerini içeren Toulmin argümantasyon şemaları oluşturulmuştur. Çalışmanın bulguları öğrencilerin birbirlerinin iddialarına gerekçe sunarak ve bu iddiaları çürüterek argümantasyon sürecine aktif katılım sağladıklarını ortaya koymaktadır. Bu aktif katılımda dersi yürüten araştırmacının argümantasyon sürecini destekleyici eylemleri, öğrencilerin ön öğrenmeleri ve sınıf içindeki normlar etkili olmuştur. Argümantasyon sürecinin bileşenlerinden veri, iddia, gerekçe ve çürütücü bileşenleri ortaya çıkmıştır. Özellikle öğrencilerin birbirlerinin açıklamalarını dikkatle dinleyerek çürütücüler öne sürdükleri ve bu çürütücülerin kendinden sonraki gelen argümanların gerekçeleri olması dikkat çekici bir bulgu olmuştur. Çürütücülerin başka bir görevi de sadece iddiayı değil bazı durumlarda veri, iddia ve gerekçeyi içeren alt argümanların da geçerliğini yok etmek olmuştur. Ayrıca verilerden iddiaya geçişte araştırmacının sorgulatmasıyla birlikte öğrencilerin gerekçelerini ifade ettikleri anlaşılmaktadır. Tüm bunlarla birlikte katılımcıların argümantasyon sürecinde destekleyici ya da niteleyicileri ifade etmedikleri de görülmektedir. Araştırmacının ortaya atılan iddialar yanlış da olsa müdahale etmemesi ve öğrencileri şüpheye düşürecek bir şekilde yanlış iddiaya yönlendirmesi argümantasyon sürecinde önemli bir eylem olmuştur. Bu durum sayesinde öğrenciler iddianın yanlışlığını fark ettikleri derinlemesine bir sorgulama yapmışlar ve neden yanlış olabileceğine ilişkin ayrıntılı tartışmışlardır.

... For example, the Geogebra application, due to its powerful resources and access, has become a catalyst for mobile scenarios and a potential enhancer for practicums, class laboratories and collaborative work (Rueda, 2021). Likewise, Takači, Stankov and Milanovic (2015), Tatar and Zengin (2016) and Ponce Campuzano, Matthews, and Adams (2018), indicate that the use of GeoGebra can significantly improve learning outcomes in mathematics. Another case is that of Nygren, et al. (2012), who used the UFractions application to solve real life problems through interactive games. ...

In the last decade, the use of mobile devices has been intensified at all educational levels. They have recently been included in the design of strategies and methodologies that contribute to mathematics education, especially in the resolution of mathematical problems. In this research, a systematic review is carried out on the use of mobile devices in the teaching and learning of mathematics in higher education institutions, with the purpose of identifying advantages, limitations, effectiveness, trends, and characteristics that have been presented in the last 10 years. Thirty articles were selected between 2011 and 2021 in 15 indexed journals with three specialized on mobile learning. The insights found allow us to see the current state of the use of mobile learning in the teaching and learning of mathematics in higher education institutions and evolution in new research in mathematics educational scenarios.

... With rapid progress in technology, the use of teaching software has drastically changed the way mathematics is presented to students (Tatar & Zengin, 2016). Among the various types of software issued in recent years, GeoGebra has become most commonly used. ...

... This finding showed that students who had learned the definite integral using GeoGebra software was significantly better in their conceptual understanding of definite integral compared to students have who underwent the traditional learning. It's consistent with the results conducted by Kado and Dem(2020), Hodanbosi (2001), Sur (2020), Zulnaidi and Zakaria (2012) Tatar and Zengin (2016), and Tasman et al., (2019a). In particular, GeoGebra software keeps mathematics from becoming abstract by assisting students in visualizing and concretizing concepts, relationships between concepts, learning by doing, and providing a learning environment in which students can practice, all of which contribute to improved conceptual understanding of the definite integral. ...

The purpose of this study was to investigate the effectiveness of GeoGebra software on students’ achievements regarding their conceptual understanding of definite integral. This study used a quasi-experimental with a pretest-posttest non-equivalent group design. The participants were fifty-two students from two intact sections of postgraduate in the second semester at the University Campus, Kirtipur, with one section assigned as the experimental group and the other section as the control by a convenience sampling method. The experimental group of 24 students received instruction with the GeoGebra software module, while the control group received the traditional method. The independent sample t-test was used in the analysis of data gathered from CUDIT which was subjected to before and after treatment. The results of this study revealed that there were no significant differences in pre-test mean scores between the experimental and control groups at CUDIT, but there were significant differences in post-test mean scores. These results indicated that the conceptual understanding of definite integral of students in the experimental group outperformed those in the control group. This study recommends that mathematics teachers use the GeoGebra Software for the conceptual understanding of the mathematical content to help learners in their learning process.

... In the interviews, the preservice teachers generally stated that they understood the concept of asymptote better due to the visuality provided by GeoGebra and that it increased the permanency. In fact, the visual feature of GeoGebra is frequently emphasized in the literature (Hohenwarter, 2004;Hohenwarter, Preiner, & Yi, 2007;Guncaga & Majherova, 2012;Tatar & Zengin, 2016;Zengin, 2017). However, participants stated that teaching only with GeoGebra would be incorrect just as they did not think that teaching only with the blackboard was correct. ...

The aim of this study was to investigate the effectiveness of GeoGebra software in preservice mathematics teachers’ process of correcting and making sense of errors regarding the concept of the asymptote. Case study method, one of the qualitative approaches, was adopted in the study. The study group consisted of 11 preservice teachers studying in the mathematics teaching program. This study comprised of three parts: pre-GeoGebra application, during the GeoGebra application and after the GeoGebra application. Data were analyzed using descriptive analysis method. The participants’ written answers before and after the GeoGebra-assisted application revealed that their approaches to possible errors regarding the concept of asymptote changed positively. Moreover, interviews with three participants who showed “development” “a partial development” and “no development “ supported this result.

... Lately, the growing interest in use of computer technology and educational software in mathematics education has drawn attention. The related research studies has reported that dynamic geometry software (DGS) allows students to make relations between mathematical objects and graphical representations (Shadaan & Leong, 2013), promotes active construction of mathematics knowledge in a dynamic learning context (Hohenwarter & Fuchs, 2004;Hutkemri & Zakaria, 2014), facilitates conceptual learning through the use of animation and visual materials (Dikovic, 2009;Tatar & Zengin, 2016), positively affects students' mathematics achievement (Chan & Leung, 2014;Köklü & Topçu, 2012;Pilli & Aksu, 2013;Turk & Akyuz, 2016) and their attitudes towards mathematics (Barkatsas et al., 2009;Pilli & Aksu, 2013). It points out the importance of teaching with technology. ...

The purpose of this study was to investigate the trends of GeoGebra related studies. We focused on the articles published between 2009 and 2021 and existed in Web of Science database. The bibliometric analysis of the GeoGebra related articles exposed four-clustered structure according to the degree of relationships among terms that reflect the articles. The clusters were identified as learner anatomy (the use of GeoGebra to improve students' mathematics learning), teaching analytics (the role of GeoGebra in mathematics teaching), technological focus (the technological and procedural issues), and conceptual extension (the attempts considering the features of GeoGebra, mathematics topics and skills). This study offers evidence to show trends and practices in GeoGebra related studies, as well as to clarify their relationships with other concepts. The investigation into GeoGebra's dynamics would help researchers, teachers, students, and policymakers gain insight into areas that need further research, as well as plan for future studies.

... Through Geogebra, students could see the effect of changes in algebraic formulas on graphic representations. This gives students the opportunity to make the link between the two algebraic and graphical representations of the solution functions of differential equations (Botana & Valcarce, 2001;Hohenwarter & Fuchs, 2007;Tatar & Zengin, 2016). ...

In mathematics, a differential equation uses important mathematical concepts like function, derivative, integral, etc. Geogebra is a dynamic mathematical software uniting geometry, algebra and differential calculus. There are two objectives in this study. The first objective is to examine the impact of the use of Geogebra on the students’ understanding of differential equations. The second objective is to see how the students interact with a Geogebra environment according to their styles of mathematical thinking. The subjects of this research were 35 and 32 students for the experimental and control group, respectively of 12th grade at a government school, west of Morocco, in the academic year 2020-2021. These participants have different mathematical thinking styles (MTS): visual, analytic, and integrated. The results show that teaching differential equations with GeoGebra is more efficient in terms of conceptual knowledge than the conventional method. In procedural knowledge, students in both groups were in similar achievement levels. We can conclude that Geogebra was more beneficial for students with integrated thinking, especially for conceptual knowledge. Received: 19 July 2021 / Accepted: 3 October 2021 / Published: 5 November 2021

... The embedded mixed method design study showed that the computer assisted instructions method using GeoGebra had significant influence on teaching and learning outcome of definite integral. Additionally, this study found to facilitate conceptual learning of the definite integral [15]. [16] conducted a quasiexperimental study to investigate the efficacy of developing conceptual understanding and procedural knowledge of 124 high school students in Indonesia. ...

... Some researchers have warned against excessive emphasis on procedural knowledge at the expense of developing conceptual understanding (e.g., Aspinwell & Miller, 1997;Mahir, 2009;Tatar & Zengin, 2016). However, other researchers have also deliberated on the importance of substantial exposure to procedural knowledge, which is required to build up an individual's procedural fluency. ...

p style="text-align:justify">The purpose of this paper is to report a part of a calculus research project, about the performance of a group of pre-service mathematics teachers on two tasks on limit and differentiation of the trigonometric sine function in which the unit of angle measurement was in degrees. Most of the pre-service teachers were not cognizant of the unit of angle measurement in the typical differentiation formula, and a number of participants recognized the condition on the unit of angle measurement but did not translate this to the correct procedure for performing differentiation. The result also shows that most of the participants were not able to associate the derivative formula with the process of deriving it from the first principle. Consequently, they did not associate it with finding . In the process of evaluating this limit, the pre-service teachers exhibited further misconceptions about division of a number by zero.</p

... This discovery provides the reason that the application of geogebra can facilitate students in understanding the material quadratic functions. This application provides a dynamic and interactive environment and helps students make connections between algebraic representations and interpretations with graphs [13]. ...

The purpose of this study is to analyze the use of geogebra applications in mathematics learning on quadratic function material. In addition, it needs to be seen how respondents’ conceptual and procedural understanding of the quadratic function material. This research uses quasi-experimental by taking a sample of 80 respondents. Samples were given treatment with the use of geogebra applications in mathematics learning with quadratic function material. Data analysis was performed using SPSS. The results showed that the use of geogebraic applications was effective in developing respondents’ conceptual and procedural understanding of quadratic function material.

... Desde la década de año 1980 se han documentado estudios que muestran las causas de estas dificultades, así como sugerido propuestas para superarlas (Cornu, 1981;Robert, 1982;Orton, 1983;Dubinsky y Lewin, 1986;Sfard, 1988). La literatura más reciente muestra, por una parte, la dificultad de los estudiantes para comprender los conceptos abstractos del cálculo diferencial e integral y, por otra, para aplicarlos en la solución de distintos problemas cotidianos y de aplicación científica o técnica en los que sería adecuado su uso (por ejemplo, Tatar & Zengin, 2016;Bresoud, 2017;Wagner, 2018;Pino-Fan, et al., 2018;Fuentealba, et al., 2019). ...

... This platform allows its users to create, share, and use [11]. Referring to integral calculus, GeoGebra has been proposed in the past as a tool for facilitating the teaching of Riemann sums: through visualizing the rectangles that could approximate a given area under the curve, and giving its approximate value [12]; practices in which students were instructed into coding apps that could calculate the area under a curve for lineal and non-linear functions [13] and, similarly, by teaching students how to solve contextual problems, related to branches of physics like mechanics and thermodynamics, that required Riemann sums and asking them to validate their results by hand calculation [14]. ...

Abstract. Integral calculus is a fundamental subject that enables the teaching of branches
of physics like, mechanics, thermodynamics, and electromagnetism to engineering students. However, the incapacity of understanding either the concept of the area under a curve or to develop an efficient and simple way to calculate integrals continues to be a major cause of the high failure rate of students in these subjects. This work was developed parting from the proposal of using Information and communication technologies, in combination with flowcharts, for helping students to solve integrals trough Riemann sums. Even, a poll was used to recollect and do a qualitative evaluation on the degree of comprehension that students had on Riemann sums and their relation to integrals and to get feedback on their impression about the proposal of this work. The results are compared against traditional learning, based on memorizing the steps of the algorithm for each method and the representation of the convergence of successive
roots by numerical tables

The present study assesses the mediation of the GeoGebra software of problem optimization feedback with the application of the derivative by students of aquaculture agroforestry engineering at the Universidad Nacional Intercultural de la Amazonia (UNIA) from Peru. The methodology is applied based on understanding, figural representation, reflection and satisfaction, analytical-algebraic development, and graphic visualization mediated by GeoGebra, and has a mixed design with connectivism and semiotics approaches. The didactic strategies are: contextualized problems resolution, figural representation, analytical-algebraic development, graphic and algebraic visualization of the model function, and reflection linked to student satisfaction. The results show that input and output diagnosis have a significant improvement in the understanding of the problems by students with mean scores of 11.23 to 15.86, respectively. It is concluded that the mediation of GeoGebra allows improving student performance through mathematical synopsis variability and the mathematization of problem scenarios.

El objetivo del presente estudio fue analizar si existen descriptores asociados con un razonamiento covariacional en los procesos de resolución de problemas sobre la integral definida. En las investigaciones sobre este tema se identifica de forma implícita o explícita la presencia del razonamiento covariacional, lo que sugiere la necesidad de conocer sobre la relación entre este tipo de razonamiento y los procesos de resolución que involucran el concepto de integral definida. En este estudio se adoptó el constructo teórico de razonamiento covariacional y se llevó a cabo una investigación documental mediante una revisión sistemática de trabajos de investigación que abordaron el estudio de la integral definida y que fueron publicados durante los últimos ocho años, de acuerdo con cuatro índices de valoración en el área de Educación Matemática. Como resultado de la revisión sistemática, se identificaron cuatro trabajos que abordan este concepto mediante procesos de aproximación o acumulación; en ellos se reporta que los estudiantes hicieron referencia a: cambios en el valor de una cantidad como si ocurrieran simultáneamente con los cambios en el valor de otra; dos variables cambiando continuamente; y, un elemento que resulta de la coordinación de los valores de dos cantidades que varían juntas, todos descriptores de diferentes niveles de razonamiento covariacional. Se concluye que los estudiantes razonan covariacionalmente durante la resolución de problemas sobre la integral definida y parece que las características de su razonamiento están relacionadas con el éxito en el proceso de resolución, aspecto que requiere de mayor investigación.

Covariational Reasoning in an Approach to the Concept of Definite Integral Using GeoGebra Within an Economic Context
Mihály André Martínez-Miraval, Martha Leticia García-Rodríguez & Daysi Julissa García-Cuéllar
Conference paper
First Online: 20 August 2023
Part of the Lecture Notes in Networks and Systems book series (LNNS,volume 692)
Abstract
Definite integral is usually associated with area problems and it is approached through a process of approximation with Riemann sums; this process can be particularly complex for a considerable number of students enrolled in non-science careers, hence it is important to develop intuitive notions in these students, and one option is to do so through the use of digital technologies. This study aims to analyze the covariational reasoning of university students who go through the stages of partition, product, sum and limit, in an approach to the concept of definite integral through the use of GeoGebra in economic context tasks. The theoretical approach of covariational reasoning and a qualitative methodology were considered. Behaviors associated with mental actions of a covariational reasoning up to the level of coordination of values in the stages of partition and sum, and smooth continuous covariation, associated with the use of the notion of limit at infinity, were identified. The use of digital technologies and the fact that the problem considered an economic context related to spending, raised the interest of the students to learn a new mathematical concept.

italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Contribution:
This article presents a new look at teaching the Laplace transform for engineering students by emphasizing the obsolescence of the current method of finding the inverse Laplace transform when solving differential equations, and by recognizing the important role of a computer-assisted environment in helping the students understand the main idea behind the Laplace transform, instead of asking the students to repeat computational processes by hand.
Background:
The Laplace transform is a widely used integral transform that has important applications in many areas of engineering, and therefore, has a central place in the curricula for engineering education. However, according to several research articles, many students experience great difficulties understanding the Laplace transform.
Research Question:
Is the use of partial fractions and Laplace transform tables necessary for a proper
conceptual
understanding of the Laplace transform method?
Methodology:
Using the anthropological theory of the Didactic as an educational platform, the current teaching of the Laplace transform method, is analyzed. A parallel discussion of the teaching of logarithms at the upper secondary school level is drawn, where, previously, this also took place using the tables of logarithms, but now the reliance on calculators is overwhelming. The authors suggest a method of teaching the Laplace transform in a computer-assisted environment.
Findings:
In the light of the shift in computer hardware and software, the authors conclude by calling for innovation in and revision of engineering education through bridging the gap between procedures and understanding, by using computer software, where it is suitable.

The aim of this paper is to present the statistical model simmulation about the definite integral concept based on upersum and lowersum random partitions by using geogebra. The random partitions of the uppersum and lowersum in determine the value of definite integral is used to find out the statsitical distribution of its generated random variable. Based on Kolmogorov Smirnov Test, the random variable data of subinterval partitions on uppersum and lowersum by using goegebra followed the certain statistical distribution. The random partitions of uppersum and lowersums followed Burr 4 parameter, Log-Pearson 3, and Pearson 6 distributions.

This study aims to analyze changes in mental actions associated with the covariational reasoning of one pair of students when working on tasks to approach the concept of definite integral through Riemann sums. Mental actions are gathered from student interactions in GeoGebra, from their written reports, and from a semi-structured interview applied to one pair of students from an engineering school in Mexico. Data are analyzed with the theoretical construct of covariational reasoning. The results show an evolution in the way students coordinate simultaneous changes between the variables involved in tasks, from the no coordination level to the chunky continuous covariation level. It is concluded that questions to propose conjectures on the use of rectangles in approximation processes to the area of a region, including their justification, and the process of inferring behaviors from hypothetical situations, reveal behaviors associated with higher levels of covariational reasoning.

The purpose of this study was to examine how pre-service mathematics teachers (PMTs) integrated a dynamic geometry environment (DGE) into their reasoning process while solving geometric locus problems. Task-based interviews based on the locus problems were conducted with eight PMTs working in pairs. The PMTs could use a computer with access to GeoGebra in addition to plain papers, pencils, graph paper, a ruler, and a compass in the interview environment. They were free to use any of them. The PMTs’ reasoning was analyzed by focusing on their use of DGE as they were producing mathematical arguments during problem-solving. Toulmin’s argumentation model and Hollebrands’ strategies for using DGE were combined to analyze the data. The results revealed that the PMTs used DGE reactively to make claims and proactively to test or justify their claims. Their proactive use of DGE differed depending on whether they included their warrants for this use or not.

A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers’ collaborative work based on their interpretation of the school mathematics curriculum. Through a study of the instructional material, the teachers’ instructional goals and their alignment to the curriculum were examined. It was clear that the instructional material was more than a mere compilation of resources for the instruction; the teachers’ effort was also in building the close connection within and across the concepts and sub-topics. The discrete parts of the content were organized under a “big idea” in the lecture notes. Anchor questions were used in the tutorial practice worksheets to facilitate students to recognize the similarity of the underlying structures of seemingly different questions. In addition to the teachers’ articulated instructional goals such as covering all the key concepts, reducing students’ cognitive load, or developing their algorithmic mastery, the study revealed the unarticulated goal as to raise the students’ cognitive growth, which could be explained by the APOS cognitive growth model. In aligning to the school curriculum, it was observed that the teachers made judgement to tap on the advantage of the spiral curriculum to advance their students’ understanding of calculus from the secondary level using a higher perspective, and to better their students’ understanding of calculus concepts in addition to focusing on algorithmic mastery. The effort to engage their students in problem-solving and the use of technology to develop higher order thinking or enhance conceptual understanding remained implicit.

The objective of this research has been to determine the influence of GeoGebra software on the learning of geometry in fourth grade students of secondary education at the Señor de los Milagros educational institution. The research problem was the presence of the low level of student learning in mathematics courses, especially in geometry. The study is quasi-experimental and the sample was 67 students divided into two groups. Both groups were evaluated with a geometry learning assessment test that was applied after the inter-vention. The results were finally discussed. The use of GeoGebra software significantly improved the learning of geometry in fourth grade high school students. Where the students of the experimental and control group obtained an average score of 13.3611 and 8.9354 points respectively, giving the difference of 4.4257 points in favor of the experimental group.

GeoGebra Calssroom memberikan solusi bagi pembelajar matematika untuk mendesain pembelajaran matematika secara daring di masa pandemic covid-19. Tujuan Pengabdian Kepada Masyarakat (PKM) ini adalah untuk memberikan keterampilan kepada pembelajar matematika untuk menggunakan GeoGebra Classroom guna mengoptimalkan pembelajaran matematika secara daring. Kegiatan PKM ini menggunakan pendekatan edukatif, yaitu kegiatan ini memiliki unsur Pendidikan yang dapat mendinamisasikan masyarakat menuju tujuan pendidikan. Metode yang digunakan berupa pelatihan secara daring penggunaan GeoGebra Classroom dalam mendesain kelar virtual. Hasil pelatihan menunjukkan adanya manfaat positif atas pelatihan ini, motivasi guru untuk mendesain kelas virtual, dan keaktifan guru dalam menyelesaikan latihan mandiri setelah sesi pelatihan 1. Kendala utama yang dialami peserta selama pelatihan online adalah kualitas sinyal yang buruk sehingga mengurangi kualitas suara dan video selama pelatihan. Hasil pelatihan ini memberikan keterampilan dalam mendesain pembelajaran matematika secara daring menggunakan GeoGebra Classroom.

Pre-service education and in-service teacher professional development (collectively termed teacher professional development or TPD here) can play a pivotal role in raising teaching quality and, therefore, learning outcomes for children and young people in low- and middle-income countries (LMICs). However, TPD opportunities in LMICs are limited, unsustained, and often not informed by recent research evidence, and outcomes are mixed. Educational technologies offer potential to enhance formally provided programmes and informal peer-learning forms of TPD. We present the first systematic review of the literature pertaining to technology-mediated TPD for educators of school-aged learners in LMICs, aiming to characterise appropriate and effective uses of technology along with specific constraints operating in those contexts.
An in-depth synthesis of 170 studies was undertaken, considering macro-, meso- and micro-level factors during TPD design and implementation in the 40 LMICs represented. Volume of publications increased dramatically over the review period (2008–2020), indicating that the field is rapidly developing. Results largely showed benefits for teachers, but evidence for sustainability, cost-effectiveness or tangible impacts on classroom practice and student outcomes was thin. Promising, locally-contextualised forms of technology-mediated TPD included virtual coaching, social messaging, blended learning, video-stimulated reflection, and use of subject-specific software/applications. We report on the variable effectiveness of programmes and limited attention to marginalised groups. To maximise effectiveness of technology-enhanced TPD, the role of facilitators or expert peers is paramount – yet often glossed over – and the interpersonal dimension of teacher learning must be maintained. Recommendations are made for researchers, policymakers, teachers and teacher educators.

The purpose of this study was to investigate university students’ conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem about calculating the volume of a solid of revolution. Representational fluency was used as a lens to analyze the conceptions of the students. Results indicated that the students imagined certain aspects of one main summation conception of the definite integral at different times in calculating the volume of the solid. They also used the conceptions of function matching and perimeter and area/boundary and volume. The students were comfortable explaining what they were doing in the solution if their conceptions of the definite integral allowed them to understand integral notation and build representational fluency. Implications based on the different conceptions that the students used and the representational fluency that they developed were discussed.

In this paper some representative examples of a project proposed to second year environment and civil engineering students are presented. The project aim was to deepen the understanding of multivariable functions, stimulating students' creativity and connecting concepts to the content of other disciplines and to the real-world situations through examples that the students themselves have found as applications to engineering. To visualize the problems, students had often utilized GeoGebra, tool widely used during lectures to visualize theoretical aspects and to better explain the exercises. The appreciation of students involved in this activity and their relationship with GeoGebra is also presented. Students appreciated very much this approach as highlighted analyzing their written reports about the activity and GeoGebra use.

The main purpose of this study was to determine how and to what extent in-service secondary mathematics teachers’ technology practices and technological pedagogical content knowledge (TPACK) improved when they were collaboratively and iteratively involved in preparing, implementing, and assessing GeoGebra mathematics modules. A second purpose was to determine the factors that influenced teachers’ integration of GeoGebra in their classrooms. A third purpose was to determine the impact of the GeoGebra intervention on teachers’ Valsiner’s zones relating to technology integration, namely: the zone of free movement (ZFM), the zone of promoted action (ZPA), and the zone of proximal development (ZPD). A qualitative multiple case study design was conducted with four in-service secondary mathematics teachers (three females and one male) with different backgrounds and GeoGebra practice levels. A design-based research (DBR) methodology was used which involved two phases: a pre-intervention phase (one iteration) and an intervention phase (two iterations). Before the intervention, teachers went through an introductory workshop and were asked to complete questionnaires about their practices, TPACK, and the barriers they faced. Then, they conducted GeoGebra lessons in collaboration with the researcher over two iterations. After each iteration, teachers answered semi-structured interviews to measure the effect of the intervention on these dependent variables. Analysis of the data consisted of determining means, medians and modes for the purpose of categorizing teachers by their TPACK, practice and zone levels. In addition, responses to the questionnaire and interview items were analyzed qualitatively. Overall, the results indicated an improvement for the four participants in their extent of use of GeoGebra in their practices as well as in their TPACK integration level. The change in practices over the iterations was slow at first (static) and then dynamic, but for TPACK it was dynamic and then static. In addition, teachers’ zones changed with collaboration and iterations. Specifically, the effect of the hindering factors of the ZFM and ZPA decreased as the intervention progressed and some assisting factors like ZPD improved. Implications for theory and practice as well as recommendations for future research are also discussed.

Dynamic geometry software (DGS), especially GeoGebra, have been used in mathematics lessons around the world since it enables a dynamic learning environment. To date, there exist so many published researches about DGS, which leads to the need for meaningful organisation. This study aims to give a broad picture about researches related to DGS. For this reason, 210 articles accessed from the Web of Science database were analysed in terms of their purpose, research design, sample level, sample size, data collection tools and data analysing methods by using the content analysis method. According to the findings, for each section the most frequently used ones were as follows: ‘the effect of DGS on something’ as a purpose, qualitative method as a research design, high school students as a sample level, 101–300 intervals as a sample size, documents and achievement tests as instruments and descriptive analysis for quantitative and qualitative studies. These results can help researchers to see the past trends in DGS and conduct new studies. Keywords: Dynamic geometry software, DGS, GeoGebra, content analysis, mathematics education

In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques; and (3) an emphasis on procedural over conceptual knowledge. Following that analysis, a review of the performance of a group of pre-university students on selected calculus tasks in a calculus survey prior to and after their learning of pre-university calculus is discussed. The students’ performance in the survey shows that many students did not visually identify calculus concepts that were studied procedurally. They demonstrated a lack of conceptual understanding of the calculus procedures. This study suggests that the partial calculus knowledge acquired in the early upper secondary levels might not necessarily facilitate the acquisition of a more complete concept at the pre-university level. Furthermore, the students’ procedural knowledge of calculus did not seem to develop their procedural fluency or flexibility.

This chapter presents a model-centered theoretical framework for integrating GeoGebra in mathematics teaching and learning to enhance mathematical understanding. In spite of its prominence in the ongoing mathematics education reform, understanding has been an ill-defined construct in the literature. After reviewing multiple perspectives from learning theories and mathematics education, we propose an operational definition of understanding a mathematical idea as having a dynamic mental model that can be used by an individual to mentally simulate the structural relations of the mathematical idea in multiple representations for making inferences and predictions.

This paper describes how prospective secondary mathematics teachers’ Technological Pedagogical Content Knowledge (TPCK) and perspectives about teaching and learning mathematics were enriched as they worked individually and in small groups to develop and present lessons with GeoGebra. We also note how Geogebra can be used as a vehicle for building links between a research-focussed university and secondary school teachers.

Bu araştırmanın amacı, dinamik bir yazılımın matematik öğretmeni adaylarının türev uygulamaları konusundaki başarılarına etkisini tespit etmek ve bilgisayar destekli öğretim yöntemi hakkındaki görüşlerini belirlemektir. Çalışma grubunu Türkiye'de bir devlet üniversitesinin Matematik Öğretmenliği Programında öğrenim görmekte olan 35 öğretmen adayı oluşturmaktadır. Karma araştırma yaklaşımı içerisinde yer alan gömülü desen (embedded design) ile yürütülen bu çalışmada veri toplama aracı olarak türev uygulamaları bilgi testi ve görüş formu kullanılmıştır. Elde edilen verilerin analizi sonucunda, dinamik bir matematik yazılımının kullanıldığı bilgisayar destekli öğretim yönteminin, türev uygulamaları konusunda öğretmen adaylarının başarılarına olumlu yönde katkı sağladığı görülmüştür. Ayrıca öğretmen adaylarının, görselleştirme, somutlaştırma, uygulama yaparak anlama ve yorumlama, kalıcılığı arttırma gibi özelliklerden dolayı bu yöntemin matematik derslerinde kullanılması gerektiğini düşündükleri belirlenmiştir. Özellikle bu yöntemin maksimum-minimum problemleri, ortalama değer, Fermat ve Rolle Teoremlerinin görselleştirilmesine ve somutlaştırılmasına da katkı sağladığı tespit edilmiştir.
Anahtar kelimeler: Dinamik matematik yazılımı, türev uygulamaları öğretimi, GeoGebra, bilgisayar destekli öğretim, öğretmen adayı

The study documents representations, resources and strategies that first-year engineering students demonstrate as a result of using Derive software to comprehend and solve problems that involve the concept of defi-nite integral. Three student profiles appear to emerge from analysis of their problem-solving approaches: (a) students who relied on the use of the soft-ware as a means to validate their paper and pencil work, (b) those who used the software to represent graphically and calculate approximated areas and (c) a group of students who combined both paper and pencil and software ap-proaches to solve problems but often did not connect concepts that appeared in the study of the definite integral with basic ideas (and procedures) previously studied (e.g., area of simple figures). There is evidence that the use of Derive software helped students elicit ideas that needed to be discussed in order to refine their initial approaches to problems.

The aim of this study was to determine the effect of dynamic software on prospective mathematics teachers' perception levels regarding information and communication technology (ICT). The study was conducted to senior prospective teachers studying in a department of secondary mathematics education. The data of the study used both quantitative and qualitative research approaches have been obtained using two different tests, namely "Technology Perception Scale" and "Computer Assisted Mathematics Instruction Perception Scale". Consequently, it has been observed in the study that learning how to use dynamic software positively affects prospective mathematics teachers' perception levels in a statistically significant way regarding the use of technology in education. In addition, at the end of the study, almost all prospective mathematics teachers were of the opinion that mathematical software will contribute to teaching activities, and they have added that such a contribution will manifest itself in visualization, concretization and result in more effective teaching.

Calculus reform and using technology to teach calculus are two longtime endeavors that appear to have failed to make the differences in student understanding predicted by proponents. We argue that one reason for the lack of effect is that the fundamental structure of the underlying curriculum remains unchanged. It does not seriously consider students’ development of connected meanings for rate-of-change functions and accumulation functions. We report an approach to introductory calculus that takes coherence of meanings as the central criterion by which it is developed, and we demonstrate that this radical reconstruction of the ideas of calculus is made possible by its uses of computing technology.

In this paper we present the research results showing the main features of the students' answers to a set of laboratory practices (LP) when they use the CAS (Computer Algebra System) Derive. From the research results analysis we obtain elements to allow us conjecture that students do not have difficulties when calculating definite integrals of continuous functions and at the same time they interpret this as the area under a curve. However, when the functions are only piecewise continuous, or the integrals come from other contexts, the students show difficulties, related to the use of a software, that need to be analysed from a cognitive point of view.

The purpose of this study is to determine the effects of dynamic mathematics software GeoGebra on student achievement in teaching of trigonometry. The sample of the study consists of 51 students. The experimental group was subjected to the lessons arranged with the GeoGebra software in computer assisted teaching method, while the control group was subjected to the lessons shaped with constructivist instruction. The data collected after 5 weeks of application show that there is a meaningful difference between experimental and control groups’ achievement in trigonometry. This difference is in favor of the experimental group which had lessons with GeoGebra.

Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students’ learning requires carefully designed lessons. This paper reports on design research conducted with nine teachers in nine classes across two schools. The lesson came at the end of their study of quadratic functions (Year 10). Technology offered the ability to link representations and the teaching challenge was to use this ability effectively. Four issues emerged: variable naming; reducing cognitive load; maintaining motivation; and retaining a clear learning focus.

The use of information technology has been used to improve capability and success in teaching and learning environments. This case study has been carried out with a view to replying the question of how we can make the subject of integers, which students in the 6th grades find too difficult to learn, easier and more permanent. The subject of Integers is one of the most difficult subjects that students have difficulty in grasping because they have only learnt natural numbers in Math. In general, when students come across a new number system, they have difficulty in learning it. Also, as they haven’t conceptualized the subject, they do not like the subject and cannot correlate the mathematical links. However, as teachers and mathematics educators, our duty is to make our students enjoy the subject of integers and ensure its retention. For this purpose, so as to eliminate the problems faced during the learning process, we have tried to conceptualize the subject by employing new software, Geogebra, by which we aim to provide a permanent learning for our students. The subject of integers has been taught with different methods to two homogeneous classes. One of the classes was taught with traditional teaching techniques, whereas the other was taught by Geogebra. In order to evaluate how much they understood the subject, a test has been applied immediately after the lesson. Two weeks later, a new test was applied to see how much of the subject they remembered. Thereafter, by comparing the results of both exams, the contributions and benefits of Geogebra in teaching Math have been analyzed.

The purpose of this study is to determine what special learning difficulties may be about the practices of definite integral. Wit h this purpose, a test prepared by the researchers and consisting of 8 open- ended questions has been applied to 64 students from the Science Teaching department of Ataturk University Agri Educational Faculty during the general mathematics lesson. The data obtained from this study has been classified with their frequencies. In the direction of this obtained data, what kind of difficulties the students may h ave about the practices of determined integral have been pointed out. 2000 Mathematical Subject Classification: 97D50

This discussion group focuses on visual explorative approaches to learning mathematics. We address several issues in the discussion such as technology use in mathematics education and its evolution from static to dynamic in conjunction with the visual characteristics of new learning form of mathematics. Among various representations used in mathematics and mathematics education, visual representations of mathematical concepts, the effects of the implementation of visual techniques, and more importantly the importance of visual exploration of mathematics and its effects to mathematics education will be discussed. Background The focus of this discussion group will be situated at the intersection of the technology use in mathematics education, representation systems in mathematics education, and developing a conceptual understanding in mathematics. An enormous corpus of literature has been accumulated on these topics, and many researchers discussed the topics in the various national and international meetings such as PME, PMENA, and ICMI (Arcavi, 1999; Duval, 1999; Hitt,

This paper discusses ways of enhancing the teaching of mathematics through enabling learners to gain stronger links between geometry and algebra. The vehicle for this is consideration of the affordances of GeoGebra, a form of freely-available open-source software that provides a versatile tool for visualising mathematical ideas from elementary through to university level. Following exemplification of teaching ideas using GeoGebra for secondary school mathematics, the paper considers current emphases on geometry and algebra in the school curriculum and the current (and potential) impact of technology (such as GeoGebra). The paper concludes by raising the implications of technological developments such as GeoGebra for the pre-service education and inservice professional development of teachers of mathematics.

This paper describes a study aimed to identify most common impediments related to the introduction of an open-source mathematical software package GeoGebra. We report on the analysis of data collected during a three-week professional development programme organised for middle and high school teachers in Florida. The study identified challenges participants face during workshops and evaluated the difficulty levels of GeoGebra tools. Findings of the study, complexity criteria of software tools and commonly occurring difficulties, provided the basis for the development of several new materials assisting workshop activities and contributed to the improvement of introductory GeoGebra workshops. (Contains 1 table, 2 figures, 3 online resources and 1 note.)

Many research indicated that ICT has been proven useful as a tool in supporting and transforming teaching and learning. In mathematics classroom, ICT can help students and teachers to perform calculation, analyse data, explore mathematical concepts thus increasing the understanding in mathematics. This quasi-experimental study with non-equivalent control group post-test only design was conducted to examine the effects of using a free-software called GeoGebra in the learning of Coordinate Geometry among students classified as high visual-spatial ability students (HV) and low visual-spatial ability students (LV). The Spatial Visualization Ability Test Instrument (SVATI) had been used to categorize the students in different spatial ability level. A total of 53 secondary school students in Wilayah Persekutuan Kuala Lumpur participated in the study. They were assigned into two different groups. One group was taught Coordinate Geometry using GeoGebra while the other underwent learning the traditional way. Students’ mathematics achievement was measured using post test at the end of the intervention. The test format was based on Additional Mathematics KBSM syllabus. Independent samples t-test results showed that there was a significant difference in mean mathematical achievement between the GeoGebra group (M = 65.23, SD = 19.202) and the traditional teaching strategy group (M = 54.7, SD = 15.660); [t (51) = 2.259, p = .028 < .05]. This study also found that the HV students performed better than the LV students in both group. Findings showed that there were no significant different among HV students between GeoGebra group and traditional group. Meanwhile the LV students in GeoGebra group (M = 64.07, SD = 21.569) significantly outperformed the LV students in traditional group (M = 48.79, SD = 15.106); [t (51) = 2.222, p = .036 < .05]. These findings showed that the use of GeoGebra enhanced the students’ performance in learning Coordinate Geometry.

This paper presents new trends in technology and learning through Geogebra, which could be especially important for the future development of e-learning for College mathematics. Also, contribution of this paper is presentation of methodological frames on several specifics examples for teaching mathematics at the college level on interactive and creative way. Discussed in this paper are the findings of a didactic experiment where some number of undergraduate students were exposed to an innovative (to the departments) method of teaching and learning a part of calculus supported by GeoGebra. Statistical analysis confirmed the fact that the use of the applets created with the help of GeoGebra and used in differential calculus teaching had a positive effect on the understanding and knowledge of the students.

This chapter argues for a future-oriented approach to mathematical problem solving, one that draws on the investigation of real world modeling activities with the aid of GeoGebra, a conceptual tool that integrates dynamic geometry, algebra, and spreadsheet features. We give consideration to the?odels and?odeling Perspective (MMP) as a means for introducing modeling activities, and we address how GeoGebra enriches students’ exploration and understanding when solving such problems.

The aim of this study was to determine the efficiency of the computer-assisted instruction method in which dynamic mathematics software is used in the teaching of trigonometry. The sample of the study comprised 58 freshmen of two different classes in the department of elementary education in the faculty of education. One of the classes was selected as the experimental group in which computerassisted instruction was used; and the other class was selected as the control group in which the traditional teaching was given. The selection was performed randomly. The data of the study were obtained by using two different tests. One of these was the trigonometry knowledge test, and the other was the test where the opinions of the students, who were in the experimental group, on the computerassisted instruction method were questioned. As a result of the study, it was determined that the computer-assisted instruction method provided a positive contribution to the success compared with the traditional teaching method in teaching of trigonometry.

The purpose of this study was to determine the effects of dynamic mathematics software on the achievement of pre-service mathematics teachers in the topic of polar coordinates and to solicit their opinions about computer-assisted instruction. The study was conducted for 11 weeks with 33 pre-service teachers in the Department of Mathematics Education Program of a state university in Turkey. Data collection tools comprised a knowledge test of polar coordinates and administration of a semi-structured interview form developed by the researchers who conducted the study using an embedded design as part of a mixed-method research. The results of data analysis showed that the computer-assisted instruction method in which dynamic mathematics software was used positively contributed to the success of pre-service teachers in understanding the subject of polar coordinates. Furthermore, it was found that pre-service teachers supported the use of this method in lessons as it provides visualization, increases retention, concretization of abstract mathematical structures, better understanding and learning, and creates an interesting and interactive learning environment.

The clear and practical writing of Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Researchhas made this book a favorite. In precise step-by-step language the book helps you learn how to conduct, read, and evaluate research studies. Key changes include: expanded coverage of ethics and new research articles.

This study investigates prospective secondary mathematics teachers’ visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a framework of productive disposition and visual representations in pre-calculus. The main result was that the role of GeoGebra as a cognitive tool fostered the research participants’ productive disposition, despite recurrent mismatches between the algebraic and visualized formalisms. Moreover, participants exhibiting dynamic productive disposition seemed to understand and make better sense of the conceptual underpinnings of the mathematical content they explored in contrast to those embracing static productive disposition.

This mixed-method study investigated the impact of graphing calculator use on high school calculus students' reasoning skills through calculus problems when applying to concepts of the definite integral and its applications. The study provides an investigation of the effects on reasoning when graphing calculators are used, since it is proposed that, through reasoning, conceptual understanding can be achieved. Three research questions were used to guide the study: (1) Does the use of the graphing calculator improve high school calculus students' reasoning ability in calculus problems applying the definite integral? (2) In what specific areas of reasoning does use of the graphing calculator seem to be most and least effective? and (3) To what extent can students who have used the graphing calculator demonstrate ability to solve problems using pencil and paper methods? The study included a quantitative, quasi-experimental component and a qualitative component. Results of the quantitative and qualitative analysis indicate that (1) graphing calculators had a positive impact upon students' reasoning skills (2) graphing calculators were most effective in the areas of initiating a strategy and monitoring progress (3) students' reasoning skills were most improved when graphing calculators were used together with the analytic approach during both instruction and testing and (4) students who used the graphing calculator performed equally as well in all elements of reasoning as those who used pencil and paper to solve problems.

A survey was administered to calculus students who had previously been exposed to a course on integral calculus. The purpose of the survey was to explore students' understanding of the definition of a definite integral, their abilities to evaluate definite integrals, and their graphical interpretations of definite integrals. The analysis of participants' survey responses develop ed insight into their conceptions of integration. Survey results suggest that understanding the definition of a definite integral did not imply procedural fluency and that these students did not make connections between definitions and procedures in integral calculus.

A clinical interviewing method was used to investigate students' understanding of elementary calculus. The analysis of responses to tasks concerned with integration and limits led to detailed data concerning the degree of understanding attained and the common errors and misconceptions. Some conclusions were drawn concerning the teaching of integration and limits.

Sosyal bilimler için veri analizi el kitabı [Data analysis handbook for social sciences

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The effect of emphasizing multiple representations on calculus students' understanding of the derivative concept (Unpublished doctoral dissertation)

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Türev kavramına ilişkin ögrenme zorlukları ve kavramsal anlama için öneriler [The learning difficulty in derivative and suggestions for conceptual learning

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Research in education: Evidence-based inquiry

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˙ Integral kavramına ili¸skinili¸skin ö˘ grenme zorlukları ve integral ö˘ gretimi [The learning difficulty about integral and teaching integral

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Mathematics teacher candidates' multiple representation and conceptual-procedural knowledge level in definite integral

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The potential and challenges of the use of dynamic software in upper secondary mathematics: Students' and teachers' work with ıntegrals in GeoGebra based environments

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Views of primary school mathematics teachers on the applicability of GeoGebra software in courses

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˙ Integral kavramına ili¸skinili¸skin ö˘ grenme zorlukları ve integral ö˘ gretimi

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Limit ve süreklilik konularında kavram yanılgıları ve çözüm arayışları

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Özmantar, M. F., & Yeşildere, S. (2010). Limit ve süreklilik konularında kavram yanılgıları ve
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