I should have wrote this before my last post to better describe how my math class has been going. We are currently working on a basic geometry unit of area, perimeter, volume, and surface area. I was excited because this would be "easy" to teach with out a textbook.
I started off by explaining a problem I had of needing to know how much wood chips I needed to cover some landscaping that I did with a class last year. We discussed what we needed to know to figure this out and then went outside and measured the circle. They told me we needed to know the length and width of the circle so I had them measure where they told me those were. I did not try to correct their improper terms. We came up with 7 meters and 6.9 meters. One student noticed that they were approximately the same. We ran out of time for the day.
The next day we started in class and discussed the wrong use of terms. I had them search and find the area of a circle and we talked about what the formula means. Then I asked which of our measurements was right. They argued that 7 meters was correct because it was a whole number. We finally concluded that we did not know which one was right and that we had to go outside and take more measurements and then average them. We also talked about the fact that the circle was eye-balled when created and not perfect.
We ended up solving the problem and then solved two more wood chip problems for some rectangle gardens. Through out these lessons I asked lots of questions and guided their learning but did not give out any information. The students either came up with the answers themselves or surfed the web for them.
My evaluation of this teaching method was that I did not see the high engagement that I had hoped for by the class. My top students were with me and the bottom students seemed to be daydreaming or not really participating. I don't have a great story of the student who always fails getting excited and being successful.
Next I needed to cover parallelograms and triangles which are harder shapes to find in the real world. So we did some visual proofs together in Geometer's Sketchpad so they could play around and see why the area formulas work.
Again I have to give the district unit test so I gave them some practice problems with area and perimeter of parallelograms and triangles. They were totally lost. They could not remember the formulas or even use them when I gave the formulas to them. I ended up going around the room and individually teaching how to use the formulas.
We measured a bunch of food boxes and found their surface area and volume. I demonstrated how to use the formulas on the board and the majority of the class still needed me to re-teach individually.
So in response to the comment from Matt Townsley on last post about teaching at a deeper level. I have tried (I am not giving up!) but in the end I have to prepare the students for the district test. That is why I found ThatQuiz to be a useful tool for students to check their work on the basic problems that they need to know. I know it is not technology integration but doing the same old thing just on the computers. I do think the immediate feedback to students of whether or not they found the right answer is helpful. And unfortunately these are exactly the kinds of problems on the required tests.
All right push me back some more readers :)