Teaching Mathematics with Desmos

I found a creative application related graphics in math. Actually, I really liked an activity in this application. So I want to share it with you. Also, I would like to briefly introduce this practice to you. Firstly, I will mention about this activity called Marbleslides: Lines.

 (Desmos, no date)

Students need to change given equation so that they can collect stars. They can learn what variables of x and y in the equation affect and how they affect the equation by playing this game. Also, students who do not understand this topic do this activity and they can easily learn what the equation represents. I want to show an example from the activity:

(Desmos, no date)

Students can change the equation in this app. They try to fix this equation by considering location of the stars. You can see many examples in this apps. I share the web site with you for the activity . Link of the activity is https://teacher.desmos.com/marbleslides-lines#preview/d0490916-ebd5-422a-8001-bf6d0ef63136 .

Finally, Desmos presents the teachers various opportunities to teach graphics, equations and so on. It makes these topics funny.  I will show some example below from this apps.

(Desmos, no date)

   

   I advice you visit this site for learning more informations about this app.

References

Desmos. (no date). teacher.desmos.com: https://teacher.desmos.com/marbleslides-lines adresinden alındı

Teaching Mathematics with Games

In mathematics classroom, giving lessons with games is much effective method for students  in new generation to adapt on the lesson. The students are interested in technology and good at using it. If teachers become math lessons funny with games related math content, the students engage in math lessons. I will give an example about this situation. In my practicum school, teacher I observed sometimes plays online games with 5th grade students in the classroom. In a such lesson, the teacher has opened games from the internet about the topic that she had previously worked on. Then, the teacher wanted the students to enter the site that she opened and choose one of the games she said. There was a game played with the group among these games. The teacher was also playing a game with pupils attending a group. The game was about ranking in fractions. It was appealing to all of the students because it had an average difficulty. Both amusing and consolidating the previous work has been successfully accomplished. Using technology in this way will increase the interest of students in mathematics.

I want to share usefull sites about math games with you. First, I will show the game site mentioned above. The game is about comparing fractions and it has the property of group play. The images related this game is below.

 I think this game is easy for students but they really engage in it. This game also teaches them to be a team. The link of web site including this game is https://www.mathplayground.com . Another game site I like is Math Games. The site is designed in 5 categories. They are grades, skills, games, standards, and features. You can find worksheets or games related mathematics in these categories. Link of the web site is https://www.mathgames.com .

Construction of a Game on Geogebra

We constructed a game related fraction of shaded areas on Geogebra with my friend. All of things about the game are in the link below.

https://www.geogebra.org/m/WcSEVACg 

Cabri 3D Project

I shared development of hexegonal truncated pyramid that I constructed on Cabri 3D with you. The drive link including video recording about how to construct such pyramid and Cabri 3D file are below.

https://drive.google.com/file/d/1aW4IcYO3_JQ7dBqx6-8n8t44IW8dtMlI/view?usp=drivesdk (first part)

https://drive.google.com/file/d/1K6K3I5ZnUa-6mzr02YXxHjELc3a0Nm-0/view?usp=drivesdk (second part)

https://drive.google.com/file/d/1Zg3g_RGEaCxIG3XaNHaWa-SlSVFLGiN3/view?usp=drivesdk (Cabri 3D file)

Wittgenstein's Rod on Geometer's Sketchpad

Project 57

I will share an idea of math lesson with below a construction that is done on Geometer’s Sketchpad.

M.6.3.3.1. Çember çizerek merkezini, yarıçapını ve çapını tanır.

The above objective is that I aim to teach in math  lesson in which I will use the construction of Wittgenstein’s rod on Geometer’s Sketchpad. In this lesson, I expect students to do the construction for learning construction of a circle and radious and diameter of the circle . Students have to draw some circles to do the construction. For example, to be able to construct the road on the video, students need to draw a circle based on a paremeter on Sketchpad. This rod is radious of the circle and thus students see easily what a radious of a circle. Also, another circle at the end point of the rod is constructed with the circle tool but firstly the circle is drawn.I prefered this construction for these reasons.

Math teachers can easily use this construction by following the stages :

1.       Teacher briefly mentions what Wittgenstein’s rod is and what it tell us with animations.

2.       The teacher shows the construction of Wittgenstein’s rod on Sketchpad and want students to construct it.

3.       The teacher gives time for them to understand it and try to construct.

4.       The teacher should give some hints especially about the part of parameter while constructing the second circle.

5.       The teacher shows how the construction does and students try to construct all part themselves or with pairs.

6.       Finally, the teacher tell them circle and its properties by showing examples from Sketchpad.

The construction video of the project we prepeared is below link.

https://drive.google.com/file/d/1HbjrQqy6-QrBV-zgiHyd_3Qsb1Gm4_W_/view?usp=drivesdk

GSP Folder link of the project :

https://drive.google.com/open?id=1sc6P_agnyXTC7-u32zhAjUZQ220a1xvZ

Using Google Form in Mathematics

Assessment for learning is essential part of teaching mathematics. Technological tools for assessing math lessons is much practical and optional. One of the tools is Google Form. I think math teachers may prepare effective and appropriate formative assessments included a kind of questions such as multiple choices, short answer with the help of Google Form. Google form is a tool with a very simple infrastructure for preparing tests at the level that the teacher targets and applying them to the students in the desired class.

I will try to tell you advantages of using Google Form in math and share my own test about Angles prepared on the form. In this form teachers have informations about student’s name, surname, age, grade level, email address etc. Also, if the teacher wants to become some questions necessary for students to answer, s/he can do easily from options on the form. Furthermore, teachers have many options in type of questions that are multiple-choice, short answer, paragraph, checkboxes, dropdown, linear scale, multiple-choice grid, tick box grid while forming a question on the form. Also, they add a file or an image appropriate for prepared question. In the part of scoring the test, it is up to the teacher to decide whether to see the scores of the students and likewise it is up to him/her to show the answers of the questions. If the teacher wants students to see mistakes and trues about the questions, s/he can select the option created by the form. I think it is easy and useful to form a test by the form for teachers.

I prepared a multiple-choice test about the topic of angles. The link is below. If you want, you can see it.

https://drive.google.com/open?id=1_Kq0GLU133AyeoNIRxp8sWU-Q5kqttPUHesolL0cCU4

Technology Integration in Mathematics Education

Technology makes life easy and provides people to find new altenative ways and apply these ways to almost every fields of life in this century. I can use technological machine easily and like using it so that I got to know the technology early. In high school, my math teachers, especially in geometry lessons, have been very successful at using time effectively by taking advantage of technology. Our geometry teacher have reflected the questions using the overhead projector in the question-solving part of the lessons, helping their students see and solve more questions, that is, he have prefered using the technology in the exercise part. Likewise, I think that it can be used more while reinforcing topics and because there are so many abstract knowledge in mathematics, technology can be used in their concretization. For example , while showing development of 3D shapes , a teacher can reflect math applications related to the topic on projection. At this point , actually technology is like just for students with visual intelligence. I think paper and pencil would be more effective for the realization and persistence of learning. In this example, even if technology helps use time effectively, I think information will not be permanent so technology is not appropriate for every topics or technology integration in mathematics should be arranged to be effective.

In this age, our generation is inclined to use technology so as a teacher candidate the generation can integrate technology with mathematics easily than teachers from previous generation. Since current students is more interested in technological tools in every field of life, math teachers can try to motivate students with using technological tools, applications and programs. Thus, the students will be curiosity about topics taught. Finally, as a teacher candidate I think a math teacher should plan the lesson according to the possibilities by using the technology very well and also he or she should have the ability to teach mathematics without advanced technology by consider poor opportunities in schools. So teachers try to continuously improve yourself in their field.