In my last post, I described my frustrations with how my teaching is reverting to basic lecturing with worksheets this summer. I am so sick of talking. I see the glazed expressions and I know there is no transfer of knowledge happening. Then I have to talk more later because (a few) students have questions if the assignment differs from the notes even by a little.
So, today I tried something new. Nothing spectacular... just an attempt to get them thinking on their own. To introduce surface area, I posed a simple problem:
I have a rectangular box I need to wrap for a birthday present.
Given certain dimensions, how much wrapping paper do I need?
In small groups students worked together to determine an answer, but also explain what they were doing and why. Throwing numbers on a page and calculating does not demonstrate any understanding of the concept of surface area.
Group 1 - Absolute silence. I come back in 5 minutes and they still aren't talking. Although, one of them has written a potential answer on paper without consulting her teammates. Wrong answer.
Group 2 - This group includes the boy recently arrived from India who has already taken calculus. Correct answer but he is the only one who understands it.
Group 3 - A decent discussion emerges. Half the group has calculated volume. They saw a bunch of numbers on the diagram and started doing some math. Their explanation amounts to, "Isn't this what your supposed to do?" One girl in the group is suggesting the correct method. When I ask her to explain her thinking, she has some vague recollection of doing this before. So in effect she is fishing for a mathematical technique that some other teacher taught her last year. No conceptual understanding. Just matching the right method with the right problem.
Group 4 - Also volume calculation. Although one student has the correct answer on his own. He understands that the front face is the same as the back, etc. But still no real understanding of surface area as a concept.
Group 5 - One student has drawn a diagram of each face and calculated the perimeter for each. Then he erased it all when he saw me coming. I try to tell him, I like his method and he is on the right track but he interrupts me to say he was just messing around.
Conclusions? The activity was not stellar but then it was not meant to be. All I wanted to do was get them thinking. Unfortunately the extent of their thinking was to try to remember what another teacher taught them once long ago. Some randomly multiplied numbers. Others started on an interesting path only to fall victim to self-doubt.
These students in particular are not used to thinking for themselves. It will take a lot more than one simple problem to break the culture of learned helplessness. I am going to try to introduce each remaining topic in a similar way. And after each chapter test, we will work on a project that should get them thinking.