The lesson will be executed without words. The goal with this lesson is to make the students realize that there always is a relationship between the circumference and the diameter of a circle and therefor find an approximate value of this relationship that is pi. The students will be measuring the diameter and the circumference of different circular objects with the use of red and blue string. Hopefully the students will realize this relationship and the value of pi.
The lesson begins with us hanging three drawings on the blackboard that describe the working process and then we draw a big pi followed by a question mark. There are different circular objects on the table that by the help of drawing one shows that the students have to choose some of the objects. Hereafter we will demonstrate how to measure the objects by the help of the blue string to measure the circumference and the red string to measure the diameter. This is shown on drawing too. Then we will hang the cut out strings on the blackboard and then point to drawing three where there is shown the relationship between the blue and red string. If the students have a hard time figuring this out, we can show them drawing three B that shows that the relationship between the strings are approximately 3:1. If they still have a hard time figuring out the relationship, we will show them drawing four where it is clear that they have to measure the circumference and the diameter of the different circular objects to find the relationship between the two.
Planning a lesson without words
Working with math without words presents numerous advantages. Since the project took place in the Netherland, a very obvious advantage was the ability to communicate regardless of the different languages. This however is not only an advantage outside Denmark. It can also be helpful to students with linguistic difficulties whom can now get the best possible out of the lesson. With the use of body language and mimics, we can step into a random classroom in a random grade; execute a lesson, without modifying our language. As well as linguistic difficulties, problems with reading and writing will not become a problem since we do not use words trough out the lesson.
Another advantage is that the wordless lessons force the teacher to become more visual in teaching. In the Netherlands we discovered that explanations of area and volume became more understandable to the students because of the visual explanation.
Often, teachers think on behalf of the students not letting them reach their own conclusions. This habit is easy to avoid with use of no words at all. When the students have to interpret mimics they get the opportunity to work out their own explanations and solutions. They are forced to think individually as well, as they cannot communicate with words amongst each other.
That being said, we have to admit, that we did not make the most out of the “math without words”-project. A great number of advantages fade when the lessons are not planned with the wordless as the main purpose. In this case, working without words becomes a hurdle more than strength. When a lesson is to be planned without words, the wordless aspect has to make the lesson better and for this to happen we have to think “outside the box”. Unfortunately we joined the project at a late stage and the Dutch students had already planned most of it. It was clear that the lesson, in many ways, had been planned to be executed with words, followed by the words being taken away...