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Reflection on the Machinima Project "Pythagoras"

Introduction

As a mathematics teacher I quite often encounter students who have problems with visualizing three dimensional objects. To help these students I used to have to bring shapes into the classroom to help them realize what happens when a figure like a cube is turned.

Nowadays I can use modern technology to help these students. Using interactive websites I can rotate, move and draw into all kinds of 3-D shapes, allowing for a better understanding with these students.

This particular topic of mathematics is not discussed a lot in the curriculum of the lower secondary grades. After the initial instruction on the names and properties of these figures in year 1 chapter 1, the figures are only used as an example sporadically throughout the curriculum. The next time students encounter these shapes and have to start working with them is at the topic "Pythagoras", when students have to draw and calculate the length of space diagonals.

I know from experience this topic is the hardest of the entire chapter, so this is the topic a machinima was constructed for.

Purpose of the machinima

This machinima explains the calculation of a space diagonal. Because I can hardly unfold a blackboard in real life when I draw a cube on it, the machinima allows for these modifications and animations so students are made aware of the changes when perspective is changed. This is vital for their understanding and very hard to explain without real 3-D objects.

The machinima first shows a 3-D object, after which is becomes transparent and shows the space diagonal that needs to be calculated. The cuboid unfolds and the different rectangles that make up the cube are taken out of the figure to show the diagonals in rectangular shapes. These shapes are easier for students to comprehend and with this animation the students clearly see how their prior knowledge fits into the current context.

The calculations are shown in the machinima, after which the shape is re assembled to show what was calculated. This is important for students as some of them might still not realize what they are calculating. This final animation makes sure all students see how their calculations fit into the bigger picture.

Activities in class

To make use of the machinima I created a worksheet that students would have to use to take notes.

This scaffolding is used to help them structure their thinking as well as training them in note taking. 

The students first had to read the worksheet for a minute to make sure they understood all of the words. Because the worksheet is in English, this is a second language to them.

Next I gave the students two minutes to write down some words related to the topic, as a warmer to the movie.  We discussed this shortly to make sure they would understand the machinima, after which I used the machinima to explain how to calculate a space diagonal. The students had to do a follow-up exercise after the machinima was finished to check their understanding.

Comparison

This topic was discussed in two classes of which only one was taught using the machinima. The other class was explained the 'regular' way.

In the lesson after the explanation, I asked both classes to make a small test. The results are shown below:

Results class with machinima

 

 

Results class without machinima

 

 

Mark

 

 

Mark

Student 1

4.3

 

Student 1

5.1

Student 2

5.1

 

Student 2

5.1

Student 3

4.3

 

Student 3

5.9

Student 4

6.7

 

Student 4

5.9

Student 5

10.0

 

Student 5

 

Student 6

5.9

 

Student 6

5.1

Student 7

10.0

 

Student 7

5.9

Student 8

9.2

 

Student 8

5.1

Student 9

8.4

 

Student 9

7.5

Student 10

9.2

 

Student 10

5.1

Student 11

10.0

 

Student 11

4.3

Student 12

10.0

 

Student 12

 

Student 13

6.7

 

Student 13

6.7

Student 14

10.0

 

Student 14

6.7

Student 15

2.6

 

Student 15

8.4

Student 16

10.0

 

Student 16

10.0

 

 

 

Student 17

8.4

Mean mark

7.6

 

Student 18

1.0

 

 

 

Student 19

5.9

 

 

 

Student 20

6.7

 

 

 

Student 21

6.7

 

 

 

Student 22

1.8

 

 

 

Student 23

7.5

 

 

 

Student 24

 

 

 

 

Student 25

7.5

 

 

 

Student 26

8.4

 

 

 

Student 27

8.4

 

 

 

Student 28

5.1

 

 

 

Student 29

5.1

 

 

 

Student 30

1.8

 

 

 

Student 31

5.1

 

 

 

 

 

 

 

 

Mean Mark

5.9

 

Conclusion

The understanding of this particular topic has clearly been more successful with the group of students that have used the machinima to improve their understanding. The results are even more special because the second group is supposed to be of a higher level, scoring better at most other tests most of the time.

The test of this chapter, which was done a couple of weeks after this machinima lesson, was also done particularly well by the group that had received the explanation with the machinima.

I would therefore conclude that the machinima (in combination with the worksheet) helped the students to improve their understanding of the topic and the visualization of the necessary objects. I will use this machinima again in the future for all of my explanations regarding this topic.