Getting Back to Business

So, our school works on a trimester system with Thanksgiving Break (a full week) marking the end of the fall term. We also have fall term finals, so my last full day of classes was November 12. I set myself some lofty goals for the break and met about 80% of those goals. My number one goal, by far, was to do what I could to plan out our next fourteen days for all three of my preps. We have fourteen days of class until the long winter break begins.

I found out late in the summer that I was teaching a new course (around August 10) and I also have two brand new colleagues in my  department. I have not been able to spend as much time mentoring them as I had planned to. The combination of this disappointment, along with perpetually being only a few days ahead of my Discrete class made the fall term a pretty stressful one. I have three preps, five sections, and my chair responsibilities. Luckily, I have a pretty light student load this year.

So, I have my calendar mapped out for Geometry and AP Calculus BC and I have about ten of the fourteen days of Discrete taken care of. Overall I am pretty pleased. Add in the naps and the time with my wife and kiddos and it has been a good break with just enough productivity thrown in.

I am starting off my Geometry kiddos with a three day workshop on Reasoning and Proof. I found this somewhere on the inter webs recently but I cannot recall where. You can find the link here and if you recognize it, please let me know. I am pretty excited about this. I think that it will be a lively way to restart my classes and I am optimistic that the students may make some inroads into understanding the logical structure of proofs. We had a great activity with making peanut butter and jelly instructions for each other earlier in the year. I think that this serves as a nice follow up and I am happy that there is such time between them. My optimistic hope is that the students will make that connection on their own without me pointing it out. This unit has a similar idea with sentence strips outlining the process of making spaghetti. I do know that when I do the PBJ activity again in the future I will scaffold it a little more carefully in advance so that more of the students will have a solid idea how to approach that. If you want to read about our PBJ adventures you can look at this post or this one.

I am also already committed to a project for my winter break. Right before Thanksgiving I engaged in a lengthy and lively twitter discussion with Henry Picciotto (@hpicciotto), Elizabeth (@cheesemonkeysf), Peg Cagle (@pegcagle), Julie Reulbach (@jreulbach), Mattie B (@stoodle), and Chris Baldus (@Chrisbaldus04) We were discussing HW strategies. When to preview ideas, when to lag and let ideas catch up, how to possibly blend those strategies. It was an amazing conversation with people from all around and at least two of whom I am certain that I have never met. One of those great examples of why engaging with twitter has improved my practice. So, I am too weary to rewrite my HW sets that I wrote last year when we rolled out the Geometry text I wrote. But, I realize that the time before January will allow me to write a few more sets that I can use as buffers near the beginning of the year while I let ideas settle in and percolate for my students. The assignments that they would have been working on the night they were introduced to an idea will now come three or four days later. In the interim we will concentrate on in class discussion and practice and I will write some homework sets that concentrate more on helping to cement definitions and some new mechanical skills along the way – along with reminding them of highlights from 2015. I am excited to do this and I would not have had the motivation to do so without the urging of those virtual colleagues who took the time and care to share with me their ideas and experiences. I am a little anxious because change = bad for too many of my students, but I am convinced that the time off will allow me to think deeply about how to be as intentional and clear as possible with my students. The other fear I had and came to grips with is this – I am one of four Geometry teachers at our school. I am also the chair of the department and the author of the text. My ego keeps creeping in and wanting everyone to follow my lead because of both of my roles here. I came to peace (thanks Julie and Elizabeth!) with the idea that I do not have to have everyone on the same page AND with the idea that I can be a better leader in this process next year if I go through it myself this year. I will still share out my old (and new!) pacing guides and homework assignments. I will simply make it as clear as possible that not everyone needs to agree with this HW strategy and with the timing of assessments that this will entail. If the students are not doing homework concentrating on, say, section 6.4 until three days after we introduce that section in class, they cannot be held responsible for that material on an assessment until they have had time to practice. Consequently, assessments will lag behind where we are in class as well. I need to rethink my ideas about what review days mean and look like, but this kind of rethinking is one of the things that makes this job such a joy.


Exam Review Week

Our school operates on a trimester schedule. The fall term ends as the Thanksgiving vacation begins and the winter term ends when our spring break begins. Before our fall finals I have been taking some time to review and reorganize some ideas with my students. I have to say that the past two days with my Geometry students have been filled with a combination of two strong feelings.

The positive feeling is that I am really proud of how my students have been working together. My class is set up in three ‘pods’ of six desks each. I am spoiled and my largest class has 16 students. At the beginning of the week I uploaded five review problem sets for my Geometry students. My plan for this week is to have one problem set each day and to circulate through class during the week, putting some burden on my students to be actively reviewing ideas rather than sitting and listening to me. The students have really been going at it and I have enjoyed listening to them. A couple of good hearted heated debates have popped up and I get called in to moderate these debates. There was one particular problem that I asked that I am proud of.

The points M(3, -1), N (4,3), and P (0, 5) are the midpoints of the sides of a triangle. Find the coordinates of the vertices of this triangle.

I am not certain that I can remember the origins of this question. It is likely that I found this somewhere and if anyone recognizes where it came from, please remind me. What really pleased me about this problem was the response of one of my students. I overheard a number of students discussing this problem, so I took the opportunity to gather up the class and lead a conversation here. I drew a triangle on the board, not on a coordinate plane, and joined the midpoints of that triangle (rough sketches here) then I asked them to make some guesses about the relationships between this ‘midpoint triangle’ and the ‘parent triangle’. It was very quickly apparent that the students expect that the midpoint segments are parallel to sides of the original triangle and the guess that lengths are related came out as well. No questions were raised during this part of the conversation. This group chat convinced me that the question I asked is much more interesting than if I had asked the question in the opposite direction where I gave the parent triangle and asked for the midpoint one.

Even with an agreement in class about the relationships here, the work to translate this to the coordinate plane is a tough leap. Early in the year I gave a few questions where I would give a segments endpoint and a midpoint and ask for the other endpoint. Not a creative problem, but one that the students remember. Since I knew that I wanted to introduce vector notation early in the year, I would frame these midpoint questions by talking about this problem in terms of taking half of the journey here. So the movement from one endpoint to the midpoint is half of the journey and we want to repeat this path. This way, I try to get the students thinking in terms of component movement and not simply in terms of distance. So, I took this approach with the class on this midpoint problem. Time did not allow a conversation that was as deep as I wanted it to be and I plan on starting class today by revisiting this problem. I am unsure whether I will use the same coordinates or not, I am inclined to think I will not. I also know that I will start class today by simply trying to get a few students to explain the thought process we outlined, not to focus directly on the necessary calculations. I have been working hard at getting my Geometry students to frame a process of problem solving for complex problems. We recently worked on finding the distance between two parallel lines and I asked my students to outline their approach to the problem rather than calculating the distance, so framing a question like this in the terms of describing their problem-solving approach will make sense to many of my students. After we discussed this problem at the end of class yesterday, one of my students remarked out loud that this problem was really hard but really interesting. I was pretty pleased to hear her think out loud like that.

i started off by mentioning that I had two strong feelings so far this week and I started with the positive feeling. The not so positive feeling is a deep sense of frustration about the overwhelming lack of recall of some simple facts. At least five of my students were stymied by a simple question of finding the midpoint of a segment. They consistently wanted to apply a simple formula and they could not (would not?) stop and think about what kind of formula might even make sense. For any teacher who has taught this idea, it will be no surprise to you that the debate centered on whether to add endpoint coordinates or to subtract them. I reply by asking what midpoint means and every student quickly says middle. Then I ask what number is in the middle of 2 and 10. I try to convince them that they do not need a formula if they are willing to stop and think. I wish that I had gone to the coordinate plane quickly to try and tie together some physical sense of these points. Instead, I was visibly frustrated and asked a few students what their average would be if they earned a 90 on one test and a 100 on a second. Would their average be 5 or 95? However, thinking back on this exchange I realize that I was not effectively making a point here, I was simply showing my frustration. This phase of the year where students are trying to tie ideas together should be a time when I am happy to see the growth in my students understanding. More often, this ends up being a time of frustration with finding myself repeating ideas that I thought we had successfully conquered early in the year. I understand the pressure that students feel when they are faced with a week of long exams and stress related to trying to show mastery of twelve weeks of knowledge all at once. I have been at this for a long time now so I feel that I ought to have a better idea about how to navigate this challenging time of year. I have worked at four schools now and they all believe in final exams, so I have tried to work within that context. I also believe in the principal behind cumulative displays of knowledge. I just know that the way we do it creates such stress for most of our students that they do not feel like this is a show of knowledge, they feel it is simply more of a test of their endurance.

I would love to hear how any of you navigate this challenge.