It has been, as usual, a busy year. It seems that this is absolutely the norm in our professions, isn’t it? I am teaching three classes this year – AP Calculus BC, AP Statistics, and Geometry. In the next few days I want to comment on all of these classes as time allows. Unfortunately, this is the week we are working on midterm grade comments for every one of my 68 students AND my mom arrives tomorrow night for a visit as this is grandparents’ weekend here at our school. The two things I want to share today are reflections on the progress of my Geometry class and a class visit I made last week. I’ll tackle last week first.

We have a number of students who finish the Calculus curriculum before they graduate here. Those students – who have has two years of AP Calculus (we teach BC as a second-year course) move on to an Applied Differential Equations class taught by our school’s President. He is a retired Army engineer and he teaches a lovely Problem-Based curriculum using Mathematica. He ran into me in the hall last week and mentioned that his students were presenting the results of their first research problem and he invited me to join them on Friday. I was able to watch as two of my former students presented fantastic work that they had done on their own on a research topic of their choice. One was presenting a supply and demand curve. She explained her choice of parameters and shared the results. Her classmates made note of the similarities to a predator-prey problem that they had worked on together. She eloquently addressed the similarities and differences between the problems, but what most impressed me was her response after one of her first graphs. She remarked that the graph did not fit what she suspected should happen and her slide suddenly displayed the phrase “Question Results” and then she moved on to discuss her modification. I loved the directness and the simplicity of this message. Just because a fancy machine, and Mathematica is a VERY fancy machine, tells you something, it is not necessarily true. I have to incorporate such a simple response into my repertoire when looking at surprising or counterintuitive results. The second presentation was analyzing the forces involved in walking on high heels. It was a fun discussion and I was impressed by the depth that the student found in examining this situation. Unfortunately, our school President is retiring and I suspect that our new administrator might not have an engineering background. It’ll be up to me as department chair to find someone capable of carrying on this kind of high level work with our best math students.

I start each day with my Geometry class. We have had a blast so far playing with GeoGebra in the lab, discussing reflections, rotations, and vector transformations, talking about distance and Pythagoras. I have been pleased with the level of engagement I have seen from the students. They are reading the text (and finding typos!) and they are engaged in class discussions. Now we are getting ready to begin discussing proof. So I want to sloooow their brains down a bit. I borrowed (okay, maybe it is just stealing) an idea from Max Ray in his book *Powerful Problem Solving*. I asked my Geometry students to write directions for making a peanut butter and jelly sandwich. I wanted to show them just how hard it can be to carefully describe something. I did not have people act out the descriptions, though. I was a little worried about embarrassment. So, I dealt out cards at random to sift the kids and I had plates, paper napkins, knives (plastic ones – just to be safe!), peanut butter ( one table had sunflower butter due to allergies) , and some jelly. I bought both grape and strawberry. I shuffled the instructions and handed them out and we had a terrific conversation about the assumptions made and about being careful with details. We had some laughs talking about how peanut butter might magically appear on knives to be spread and what side of the bread gets put together. Then we came to the description made by a student I’ll simply refer to as E. She typed her description ( which can be found here ) and she did such a lovely job. Her list is detailed and she took great care to break down the actions involved. All of the class agreed that hers should have been the first one read since we decided to go ahead and eat as soon as we dissected hers. She seemed really proud when I asked her for her copy to share out.

i’ve been thinking about this all day. Remember, this is my 8 AM class. I have resisted some activities like this in the past thinking it just was not my bag. However, I am working closely with two terrific colleagues in Geometry this year and they sort of encouraged me to try. I stepped out of my comfort zone and the result – at least this time – was a relaxed and fun class. Kids were engaged, they supported E and gave her some real praise and after class one of my students who has been struggling so far came up to me to tell me how much fun she had. I think I may have earned some important personal capital in working with her and this may be a gateway to building a relationship with a student who does not seem to have much inherent love for my subject. I also think that some valuable points were made about the challenge of explaining what you know to someone who does not know it. I am optimistic that this will help build a bridge toward understanding some important principles of proof in the next week or so. So, thanks to my colleagues for encouraging me to try something that seemed a bit silly to me. Thanks to E for being a model of thoughtfulness and detail. The rest of her work this year has been uniformly outstanding, so I was not exactly surprised by this. Thanks to my students for trying an assignment that probably seemed a bit weird. Finally, thanks to Max Ray for this thoughtful book that got me going on this path.