Wednesday, November 26, 2008

Discovery

November 21st, 2008

Today, I began a new unit on geometry. To begin, I posed questions to find out what they knew about length, perimeter and area of rectangles by using a problem called Changing Gardens. This problem can be found in Navigating through Measurement in Grades 3-5. (see reference list for details.) This required students to recognize that when given a fixed perimeter, there are different possibilities for the dimensions of the rectangle, leading them to recognize that the areas can change. At the end of the activity, there were several open ended questions that helped to lead students to make the necessary connections about length, width, perimeter and area of rectangles. Student’s responses to these questions enable me to plan the next activity for this unit. From these questions, I saw that there were still a few students whose ideas about area and perimeter were sketchy. Their concept of area and perimeter were not concrete, not where I thought they should be at grade six, and as a result, I knew I could not proceed in the way I had intended. Instead, I would focus my next lesson(s) on doing activities that would reinforce the concept of area and perimeter.

If I to give students a page or two, asking them to look at a figure, maybe a square or rectangle, and tell me what the area and perimeter was, I am confident they would be able to do this. This would lead me to believe, and themselves, that they understood what these concepts were. Hey, there is no real thinking involved, once you know how to do it. It wasn’t until I asked them to describe how they knew the area they had calculated was correct, or why, when the length of the rectangle decrease, the width had to increase with a fixed perimeter, that their ‘real’ understanding of these concepts came to light.

What would have happened if I did not give them these types of questions, or had them complete this activity? I would have continued with the lessons as planned and assumed that because they got the right answer; they knew what was meant by these terms. They would still be playing the game, and I would not have known the difference.

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