Monday, September 29, 2008
Friday’s are always good, but this Friday was even better, thanks to ending the day with a great lesson to the grade 8s. We are about to start a study of area and volume, so I was introducing a few definitions. I wrote the definitions and drew examples for a square and a rectangle before unleashing the chaos.
As part of an assignment during my teaching internship I had interviewed students (in America). I was shocked to find out that none of those I interviewed fully grasped power of the definitions of a square and rectangle, realizing that a square was in fact, also a rectangle. My first class on Friday was the other grade 8 classroom, so I already knew that learners in Namibia weren’t different from those Americans in this respect.
I asked the learners if they understood the definitions. (They always say yes regardless of if they do, think they do but really don’t, or don’t.) I pointed to the picture of a square and asked them if it was a square. YES! I asked them if the rectangle was a square. NO! I asked them if the rectangle was a rectangle. YES! So far, so good. Then I asked them if a square was a rectangle. NO!
(No doubt some of you as well don’t recognize the error. It’s okay, but I must clarify before proceeding. A rectangle is a four sided figure with four right angles. A square is a four sided figure with four right angles AND all four sides are the same length. Squares are a subset of rectangles. Namibian learners don’t understand the word “subset.”)
I shook my head with a smile on my face. I pointed to the definition of rectangle and pointed to the drawing of the square asking Does this have four sides? YES! Does this have four right angles? YES! Then, is it a rectangle? NO! Again I smiled and shook my head and repeated the whole process three or four more times.
After pretending to bang my head on the board in frustration – they just love when I do that – I stopped and pretended to start on something new. I asked those learners who are from the Kavango region to stand up. Okay, sit down, and those learners who are from Namibia stand up. Every learner stood up. I told Enock to sit down; he could not stand up for Namibia because I saw him stand up for Kavango. He reluctantly sat down, so I continued. I told Immanuel to sit down but he explained to me that it was true that he was from both Kavango and Namibia. Right as he said that several of the other learners had that “ah ha” moment and someone shouted out “like a square and rectangle!”
Then I drew an outline of Namibia on the chalkboard and shaded in the Kavango region. As I traced the outline of Namibia and then Kavango, I said “this is…rectangles” and “this is…squares.” Then I drew Windhoek and Nkurenkuru, saying Windhoek is a rectangle that is not a square, like the example over there, and this (Nkurenkuru) is a rectangle that is also a square. Most of the remaining learners then had their “ah ha” moment and the classroom got brighter as the figurative light bulbs lit up.
The next definition was for a parallelogram. I wrote the definition, drew and had them draw several examples of parallelograms and non-parallelograms, then drew the outline of Africa around the Namibian rectangle, and the room brightened once again.
As part of an assignment during my teaching internship I had interviewed students (in America). I was shocked to find out that none of those I interviewed fully grasped power of the definitions of a square and rectangle, realizing that a square was in fact, also a rectangle. My first class on Friday was the other grade 8 classroom, so I already knew that learners in Namibia weren’t different from those Americans in this respect.
I asked the learners if they understood the definitions. (They always say yes regardless of if they do, think they do but really don’t, or don’t.) I pointed to the picture of a square and asked them if it was a square. YES! I asked them if the rectangle was a square. NO! I asked them if the rectangle was a rectangle. YES! So far, so good. Then I asked them if a square was a rectangle. NO!
(No doubt some of you as well don’t recognize the error. It’s okay, but I must clarify before proceeding. A rectangle is a four sided figure with four right angles. A square is a four sided figure with four right angles AND all four sides are the same length. Squares are a subset of rectangles. Namibian learners don’t understand the word “subset.”)
I shook my head with a smile on my face. I pointed to the definition of rectangle and pointed to the drawing of the square asking Does this have four sides? YES! Does this have four right angles? YES! Then, is it a rectangle? NO! Again I smiled and shook my head and repeated the whole process three or four more times.
After pretending to bang my head on the board in frustration – they just love when I do that – I stopped and pretended to start on something new. I asked those learners who are from the Kavango region to stand up. Okay, sit down, and those learners who are from Namibia stand up. Every learner stood up. I told Enock to sit down; he could not stand up for Namibia because I saw him stand up for Kavango. He reluctantly sat down, so I continued. I told Immanuel to sit down but he explained to me that it was true that he was from both Kavango and Namibia. Right as he said that several of the other learners had that “ah ha” moment and someone shouted out “like a square and rectangle!”
Then I drew an outline of Namibia on the chalkboard and shaded in the Kavango region. As I traced the outline of Namibia and then Kavango, I said “this is…rectangles” and “this is…squares.” Then I drew Windhoek and Nkurenkuru, saying Windhoek is a rectangle that is not a square, like the example over there, and this (Nkurenkuru) is a rectangle that is also a square. Most of the remaining learners then had their “ah ha” moment and the classroom got brighter as the figurative light bulbs lit up.
The next definition was for a parallelogram. I wrote the definition, drew and had them draw several examples of parallelograms and non-parallelograms, then drew the outline of Africa around the Namibian rectangle, and the room brightened once again.
