In this presentation, we visualize vector fields and their divergence and curl through the GeoGebra tool. GeoGebra is a powerful tool which can be used to demonstrate many concepts of multivariable calculus. This presentation aims to enhance the geometric intuition of vector calculus students and make them enable to visualize the concepts of vector fields, divergence and curl rather than to have abstract intuition. It is very difficult to draw 3D vector fields on the chalkboard clearly, GeoGebra tool make it convenient for students to understand the clear picture of vector fields and physical meaning of divergence and curl of vector fields.

Applet link: https://www.geogebra.org/m/atp5c66r

Science and engineering undergraduate students learn about curvature of a plane curve in their very first semester. Purpose of this short presentation is to illustrate the meaning of curvature of a plane curve at a point by fitting an appropriate circle to the curve at that point (osculating circle). Radius of circle is defined as radius of curvature of the curve at that point. Its reciprocal is defined to be the curvature. Centre of this circle is called the centre of curvature of the curve. Locus of centres of curvature of a curve is defined to be the evolute. Presentation will show evolutes of various conic sections by animating movement of point on the given curve.

Applet link: https://www.geogebra.org/m/aytwenzc, https://www.geogebra.org/m/cvb8mpzm

The aim of this presentation is to demonstrate that interactive applications created with GeoGebra can contribute to students' computational thinking and prepare them for programming. The application was made within the scope of computer aided mathematics teaching course with mathematics teacher candidates. In the presentation, "Number Guessing Game" task given for students to create with GeoGebra and this game will be examined in terms of programming. In the review, "Number Guessing Game" flowchart, Scratch and Python codes will be presented and compared with the created GeoGebra application. In addition, examples will be diversified with the application of Collatz Conjecture and Pi's steps, which can be described as preparation for programming.

Applet link: https://www.geogebra.org/m/r2wzgz9y

A geometric method is presented to model those convex polyhedra with GeoGebra that have regular polygonal faces and they can not be created by Euclidean constructions (that is, by ruler and compass constructions and their straightforward 3D generalizations). Those polyhedra are the snub cube, the snub dodecahedron, and Johnson solids J84-J90.This method was successfully used during the course "Space Geometry with Computers"at Ybl Faculty of Architecture and Civil Engineering of Óbuda University, Budapest.

Applet link: https://talata.istvan.ymmf.hu/igci2021

This presentation include the brief about the various applications of GeoGebra, I have used while teaching college students of B Tech (Engineering) first year and second year students. I would like to show that how the software GeoGebra has helped me in making the students understand about the various topics like Asymptotes, Curve Tracing, Integral Calculus, Differential equations, LPP and many others, using the visuals.

Applet link: https://www.geogebra.org/m/npkfecta

The introduction of rational numbers as terminating decimals and non-terminating but recurring (repeating) decimals and irrational numbers as non terminating and non recurring (non repeating) decimals to young students can be enhanced by the use of digital tools. Allowing them to ""see"" more digits than the typical ten or twelve digits afforded by calculators, and also letting them explore more examples on their own with the tool can give them a more convincing learning experience.

Applet link: https://www.geogebra.org/m/hudgdmqu

Conventionally constructing the triangle's centres allow limited opportunities. School Students rarely have the chance to observe and comment on peers' work which gives a wide range of examples. Considering the pitfalls of the centre of the triangle, we have developed a workshop to enhance the experience of learning mathematics by doing. 40 students, who have passed 9th std from central government school has participated in this workshop. The sessions allowed students to explore the basic mathematical processes, like finding examples, making conjectures, proving theorems, etc. In this particular session on GeoGebra, students explore basic geometric constructions which they encounter in their geometry textbooks. Students were asked to find the centroid, circumcenter, or orthocenter of a triangle they have constructed on GeoGebra. The question then posed to the students that how are these centres related? Is there a ratio that is obtained as a distance between orthocenter and centroid and centroid and circumcenter? If yes, what is that ratio? Such Aha! Moment encourages students to learn mathematics. It also helps students to verify their geometric constructions, which is a limitation of human error in construction. GeoGebra also allows students to explore examples which lead them to come up with more informed conjectures from observation.

This is a collaborative work jointly with Deepa Chari, HBCSE, TIFR.

Use of GeoGebra in upper secondary school physics - main focus on simulations the author has created using GeoGebra . I held the same presentation in Nordic & Baltic GeoGebra conference in 2019.

GeoGebra is often underestimated as an ICT that can be used to demonstrate only the curriculum topics and most workshops/courses focus on getting familiar with the tool commands. The course content, designed at Center for Creative Learning, Indian Institute of Technology Gandhinagar is focused on problems/challenges/stories that excite students/teachers to experiment with mathematics using the tool. The course - ""From Zero to Enigma"", starts with a WWII story - Enigma machine, followed by a demonstration of the machine - physical model and visualization model. The course modules start from very basics application - making sliding ladder animation (how to draw point, line, segments, slider) and iteratively progress on interesting examples and problems to build the Enigma machine at the end of the course. The content is designed with keeping the following three dimensions in mind:

(i) Breaking Subject Boundaries (Writing name with only straight lines patterns- integrating Art, Math, and Science),

(ii) Sense of Wonder (Buffon's needle),

(iii) Relating it with daily life experience (circle on a maousambi and disappearance of π in cucumber).

Till now, we have conducted a series of sessions/demonstrations for 500+ teachers of Kendriya Vidyalaya and Jawahar Navodaya Schools of various disciplines across the country as a part of the In-service course.

Applet link: https://www.geogebra.org/u/ccl_models

Abstract 1: During the pandemic situation, as I started exploring GeoGebra again, I realised it is a great opportunity to introduce it to students as all of them have a computer now! The first applet was made to introduce various features of GeoGebra, which they had explored by themselves. Before I was starting to teach constructions, I made this simple applet.

Applet link: https://www.geogebra.org/m/mguw3quc

I would also like to share the responses of the students:

Task 1: https://www.geogebra.org/classroom/t9jjfp7m#tasks/mguw3quc/27217924

Task 2: https://www.geogebra.org/classroom/t9jjfp7m#tasks/mguw3quc/27217925

Task 3: https://www.geogebra.org/classroom/t9jjfp7m#tasks/mguw3quc/27217926

Abstract 2: This activity is usually done in groups in the classroom. This problem is a low floor high ceiling problem. As I did not have a chance to do it in the classroom, I made this applet. Here along with learning and exploring the GeoGebra features, the children were challenged to think about the last few questions.

Applet link: https://www.geogebra.org/m/crjurj6f

Some responses. The live responses provided an opportunity to observe their thinking closely and question them if required.

Task 1: https://www.geogebra.org/classroom/z7mwubu9#tasks/crjurj6f/27084341

Task 2: https://www.geogebra.org/classroom/z7mwubu9#tasks/crjurj6f/27084345

GeoGebra is a software package which has all of the standard Geometry functions. This app can be installed in the system and utilise in the classroom teaching in order to bring the concept to the students effectively. The tools are self-explanatory. Once installed the app, we can explore the endless possibilities through those tools. The topics can be prepared and save in the files for teaching purpose, partial work can be done and bring the remaining work with the participation of the students or the entire work can be done with the students participation. For example, the following concepts are some of the Geometry topics which are found helpful teaching using GeoGebra in class.

Circles - angle properties:

• The angle that an arc of a circle subtends at the centre is double that which it subtended at any point on the remaining part of the circumference.

• Angles in the same segment of a circle are equal.

The theorem statement can be demonstrated by drawing the circle and the required angles using the tools. The move button from the tool can be used to demonstrate the generalisation of the statement of the theorem. The explanation is effective as this demonstration is a visual experience for the learners.

Applet link: https://www.geogebra.org/m/ys7bqyu4

In this presentation, the classroom teaching process of the relationship between the angles and sides of the triangle will be presented through GeoGebra digital material supported with a worksheet. First, we prepare our digital material with the help of circles, sliders, segments and angles from GeoGebra toolbars. Then, we distribute the worksheets prepared to be used simultaneously with the material to the student groups we have determined before. We apply each instruction on the worksheet in turn with all groups. The goals we want to achieve at the end of the application are as follows:

1. In a triangle, as the length of any side increases, the size of the opposite angle increases (or vice versa);

2. Triangles with equal lengths on three sides have equal interior angles (60 degrees);

3. It is aimed to see that the triangle whose two sides are equal in length is also equal in two interior angle measurements opposite the equal sides.

In this activity, there is an opportunity to draw more with the students in a short time. However, the fact that the activity was supported with a worksheet offers the student the opportunity to explore the targeted concept.

Applet link: https://www.geogebra.org/m/zys9eajp