As we know, there are many options to teach a lot of different subjects
in mathematics. Today, I will give some suggestions to teach some objectives. Firstly,
I want to say the objectives which I select and I will show and explain how we
teach this topic by using Sketchpad software. These objectives are:
9.1.1.1 Üçgende açı özellikleri ile ilgili işlemler yapar.
9.5.2.2.b) Kenarortayların kesiştiği noktanın, üçgenin ağırlık merkezi olduğuna ve üçgenin ağırlık merkeziyle ilgili özelliklerine yer verilir.
9.5.2.2.d) Pergel-cetvel kullanarak veya bilgi ve iletişim teknolojileri yardımıyla üçgen üzerinde değişiklikler yapılarak ve üçgen çeşitlerine bağlı olarak değişikliklerin kenarortaylar üzerindeki etkisi gözlemlenir.
9.5.2.1.c) Üçgenin dış teğet çemberleri çizdirilir.
According to these objectives, the teachers can use the applet which we
are prepared in Sketchpad. This applet include the mixture of these objectives in order to that students can connect many topics for deeply understanding. In order to use, teacher has to download The
Geometry’s Sketchpad. Unfortunately, this application is not free. If you download this application, we made a
video of how to construct the applet from scratch to the full version. We
uploaded the video in Youtube. Its link is: https://youtu.be/rMFGy3OhIjU
Now, I am going to mention user manual and pedagogical explanation of
this applet respectively.
After download of Sketchpad, the teacher can ask the question for
students’ thinking. This question is: “A power company wants to select most
efficient location to build a power station to supply 3 cities (A, B, C). They want
to build it at the spot where the sum of the distances to the 3 cities is a
minimum. Can you construct the optimal point based on A, B, C?” Firstly, the teacher selects 3 non-linear points
(A, B, C) on the Turkey map. (Turkey map can drag and drop on the page.) Then,
one more arbitrary point (D) is selected. The teacher should show the sum
distances of A-D, B-D, and C-D. S/he can ask like “In which point, the sum of
three distances in minimum?” Then, s/he can change the point until that the
students realize the minimum place. After that, s/he should get the students
about how this minimum point can be constructed. Students may discuss and give
some ideas.
In order to show how this point can be constructed, the teacher may open a new window then s/he try to construct this point with the students. After making triangle with the same 3 non-linear points, they should construct 3 equilateral triangles based on each side and they should find the centroid in order to draw circumscribed circles. Teacher should emphasize the center of circle is the centroid of equilateral triangles. Moreover, s/he should say that the intersection point of medians form the centroid. After that, s/he shows that the intersection of circumscribed circles is in the minimum distance to 3 vertices. Finally, she compares these two windows to show that the points are same. For elaboration, s/he can say that these steps are explained by Fermat Torricelli Theorem.
You can reach the construction parts in Geometry's Sketchbad with this link:
In addition, I want to explain pedagogical aspects. Beginning with real life problem enables the students to make a sense of the topic. Their attention for thinking may increase. By asking the questions which is not directly related the one topic of curriculum, brainstorming can be mostly enhaced among the students. On the other hand, using this application makes easier to show this theorem. It allows a deeper understanding of the concepts. Students can see the sum of the distance easily. Contrary to hand held construction, the error in calculation and measurement cannot be mentioned; so, the accurate results can be seen effortlessly. They probably are bored in Geometry lesson because using ruler and compasses are difficult and take much time. Using Geometry Sketchpad can motivate the students by constructing in less time. Also, hiding and showing of some constructions lead to visualize for the students.
In order to show how this point can be constructed, the teacher may open a new window then s/he try to construct this point with the students. After making triangle with the same 3 non-linear points, they should construct 3 equilateral triangles based on each side and they should find the centroid in order to draw circumscribed circles. Teacher should emphasize the center of circle is the centroid of equilateral triangles. Moreover, s/he should say that the intersection point of medians form the centroid. After that, s/he shows that the intersection of circumscribed circles is in the minimum distance to 3 vertices. Finally, she compares these two windows to show that the points are same. For elaboration, s/he can say that these steps are explained by Fermat Torricelli Theorem.
You can reach the construction parts in Geometry's Sketchbad with this link:
In addition, I want to explain pedagogical aspects. Beginning with real life problem enables the students to make a sense of the topic. Their attention for thinking may increase. By asking the questions which is not directly related the one topic of curriculum, brainstorming can be mostly enhaced among the students. On the other hand, using this application makes easier to show this theorem. It allows a deeper understanding of the concepts. Students can see the sum of the distance easily. Contrary to hand held construction, the error in calculation and measurement cannot be mentioned; so, the accurate results can be seen effortlessly. They probably are bored in Geometry lesson because using ruler and compasses are difficult and take much time. Using Geometry Sketchpad can motivate the students by constructing in less time. Also, hiding and showing of some constructions lead to visualize for the students.
That’s all for now. See you in the next applet J
Yorumlar
Yorum Gönder