While school has not quite ended yet, (we end on the 25th due to several snow days), I wanted to give a recognition to two excellent resources for teaching mathematics, Estimation 180 created by Andrew Stadel and Visual Patterns created by Fawn Nguyen and a shout out to Andrew and Fawn.
The lack of a well developed number sense that many of my students possessed this year was bothersome and with the pressure of standardized testing gone, during the last month and a half of school I experimented with these resources.
During this time period, I started most lessons with an estimation task from Estimation 180 as a warm-up. I made a screen capture of the days estimate in a Smart Notebook file as a way to present it. To record their estimates, the students completed a Google Form that was modified from the Make an Estimate form that Andrew has on the side of each estimation. After each class, I parsed each classes results into a class specific spreadsheet. The following day, we would look at the answer to the most recent estimate, discuss the estimates that the class had made, and then do the next estimation. (In particular, the children seemed to enjoy watching the video answers). We started with some of the counting estimations, then moved to ones that involved length, ones that involved volume, and ended with ones that involved coins and their values.
The process worked pretty well and while anecdotal, the children definitely seemed to develop a much better way of explaining their reasoning and using previous clues and information to help with their new estimations. In particular, by the time we ended with the coin tasks, more than half of each class was nailing their estimations. They of course asked all the usual questions about Mr. Stadel - what is his job?, (he is a math teacher) - does he have a life?, (yes, obviously), does he eat the candy/drink the soda presented in his estimations?, (I do not know), can he come to visit?, (he has offered to come if we pay his expenses).
While I did not use the Visual Patterns web site on a daily basis, I did use it on more than a dozen occasions during the last month and a half. To get the children to record their thoughts and slow their thinking process down a bit so they would not miss some of the subtle changes in the different patterns, I used the form that Fawn provided on the site. I do think that next school year I will attempt to develop a Google form for this because when their results are displayed, it will help all students see the thinking process of their classmates. It will also help them to slow down their thinking process even more as the desire to rush to an answer was still quite prevalent, (even with the use of the form).
We were not able to get to some of the more complicated patterns but in particular some of the beginning patterns with the circles, (pattern 5 and pattern 15), the penguins, (pattern 8), and the surface area with the cubes, (pattern 2) brought out some spirited discussion regarding their predictions. The work in figuring out the patterns offered from this site will significantly help improve my students ability to recognize mathematical patterns.
I will be using both of these resources on a routine basis during the next school year. They will provide a significant enhancement to my teaching as evidenced by my positive experiences for the last month and a half. I would like to thank both Andrew and Fawn for their tremendous effort and willingness to share. Actually I am in awe of their ability to provide these resources while teaching! Their contributions to teaching middle school mathematics cannot be overstated.