So, a post over at Mrs. Reilly’s blog (http://mrsreillyblog.wordpress.com/2013/07/30/first-days/) this morning has me thinking about the locker problem again. I am trying to imagine a semi-elegant solution to this follow up question. “So, after all 1000 students have gone through and done their thing, how many total times was a locker door touched?”
I am curious as to whether my students will try to keep track from the point of view of adding how many times each door gets touched or by adding up the number of times that each student touches a door. I’m thinking tables and thinking that the greatest integer function will need to be invoked. Don’t have a clear idea myself yet, and I am certainly open to any suggestions.
Just rolled in after a two hour drive and my brain is still buzzing a bit. A couple of quick impressions with more thoughtful reflection to come:
- The STEM phrase (and related ones) means different things to different people/schools. I know that this is essentially true of most words, but it seems especially true here. I think it is vital for each school to clearly define for its constituencies what they mean when they are talking about STEM.
- It is clear to me that there are MANY educators who thirst for time to talk with each other about their practice and their ideas. We need to work at each of our institutions to make this more possible.
- The notion of collaboration (between students, between teachers, between departments) was at the heart of all of the talks I attended.
Oh yeah, I won two raffle items! Sweet.
For as long as I can remember – even back when I was a student – the beginning of August signaled the beginning of dwelling on school. This year I get a two day headstart. Tomorrow I am off to visit an old friend in NJ on the way to EdCamp Steam. He has not only offered his home for Tuesday night (so I don’t have to leave home around 5 AM Weds) but he has offered to let me sit in on a PD session at his school. He’s the Upper School Head at his school so he has the right to do that…
I am excited about the EdCamp but really have no idea what to expect. I am just hoping to walk away jazzed about the new year. We are starting a STEM initiative at our school and I hope to come back with good ideas to share.
Speaking of sharing good ideas – I am scouring my brain to find ways to expand two of my favorite beginning of the year problems. I have been using the 1000 locker problem for years and I always find ti to be a great conversation starter. However, I have not found any particularly interesting extensions. I’ll poke around for some and I’ll certainly share if I find any. Another favorite is the question of how many squares are on a checkerboard. I have extended that to asking how many rectangles are on a checkerboard. I’ve always been pleased with that one.
So, this post is inspired by my most recent trip, my daughter, and by Christopher Danielson. We just returned from a trip to Pittsburgh to see my beloved Mets defeat the hometown Pirates. While on the road my impatient daughter is often asking how much farther we have to travel. Since I don’t imagine that she understands answers such as “28 more miles honey” (she will turn 4 on Thursday) I often answer by saying things like “only 20 more minutes, about the sam time as an episode of PowerPuff Girls”. So, when we were at the pool at a hotel on our trip we were playing a jumping game where she stood on the steps of the pool and jumped to my arms. One time I was too close for her tastes so she told me to back up. When I asked her how far away I should be, she said “Five minutes away.” I asked her, “Don’t you mean five feet away?” But she stood firm in her answer, she wanted me five minutes away from her. Christopher routinely writes about his children’s developing understandings of mathematics and, while I teach in the high school, it has made me more conscious of trying to get at what my students think that they understand about developing situations in the classroom. As a dad, these thoughts intrude as well. I am now debating my use of time as a marker for her, although I am certain that it is a more tangible way to answer her questions about how far away we are from our destination.
We math teachers love to talk about problem solving as a desirable curricular goal. However, I find that many of us don’t really agree as to what constitutes a problem. Not an original thought here, but in my mind I make distinctions between exercises and problems. I see it this way – an exercise is any challenge in front of you where the path to a solution is clear. It might be a technique you’ve been practicing, a new skill that has just been introduced, a specific formula to be applied. You might not get the answer correct, but it’s not because you don’t know WHAT to do. A problem is a challenge where the path to a solution is unclear. It might involve tying together multiple strands, creating (discovering?) a new technique that has yet to be presented, it may involve reaching across curricular boundaries to call on skills from other courses. So, if I am interested in teaching problem-solving, I need to have my cherubs on board and agree with me about what a problem is. I was happy to see the following link (http://fcit.usf.edu/math/resource/fcat/strat.htm) in Fawn Nguyen’s most recent post. Proud to see my old home state has a fairly cogent presentation of problem-solving. Of course, the father of talking about teaching problem-solving is still Georg Polya (http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm) A MAJOR goal of mine next year is to reach consensus with my students about this job of ours.
I’ve been reluctant to dip my toes into the math teacher blogging world for fear that I have little or nothing of note to add. However, I am going to overcome that fear even if my postings end up being read by few (and being of advantage to even fewer) as I try to discipline myself to organize my thoughts and the important thoughts and links I regularly read. Wish me luck!