First of all, today is my daughter’s TWENTY FIFTH birthday. Don’t blink, guys – that’s how fast it goes. Happy Birthday, my very dearest Marilyn. You are one of the two best things I have ever done.
Up at 5:34, which is actually OVERSLEEPING, but made my bus (the later one which still gets me to school on time). There is a beautiful pink sunrise peeking through the buildings on Coney Island Avenue, which will only be visible at this hour for a few more weeks. I’ve got bookroom duty during 1st period, which begins at 7:15, so I don’t have a lot of time for my 2nd period prep. I learned early on, however, that leaving school the night before not ready for the next day meant for sure that the copier would be broken, or that you would be assigned a coverage, or that some other impediment to preparation would occur. So I am ready to continue with practicing linear systems in three variables with my Algebra 2 classes. I just need to find a good Desmos activity for those [few] students for whom one day was enough; I’m thinking Function Carnival will appropriately engage and challenge.
I see many students I know on the bus, but most are plugged in and sort of sleepwalking. I don’t disturb their last few minutes of rest; I get it. Usually, I would be grabbing a few minutes of pleasure reading on the bus (I’m currently reading How It Went Down by Kekla Magoon), but I’m drafting this post!
I arrived at school at 6:55. This may sound ridiculously early to some of you, but I love the school when it’s so quiet. I remember that not only will I be distributing books, but that my students will be receiving them as well, so I go down to the math office to get some book receipts, only to discover that my school keys are not where they should be. Mentally retracing my steps before I left school yesterday, I realize that I probably left them inside the office I am attempting to enter; I stopped by to make photocopies on my way out yesterday. I find another early bird math teacher to let me in, and thankfully, the keys are exactly where I thought they would be. Crisis averted.
When the first bell rings, I get ready to go to the book room. I hope the 1st period teacher remembers to send his students…..
My book room duty is over at 7:27. I make a quick stop at the Dean’s Office to drop off some work for a student on in-house suspension. I’m saddened that this young man will be out of my class for 4 days so early in the term; I hope that he attends in-house, and that the teacher there helps him complete his work so that he maintains some kind of feeling for the class. This fall I will be participating in a Restorative Justice training workshop, and am feeling somewhat more sensitive to the deleterious effect of removing a student from class. I hope this student returns, and attends regularly after this disruption.
30 minutes to showtime. I head down to my classroom with my trusty cart (a traveling office supply store) and start thinking about the date. When I was a grad student with the NYC Teaching Fellows, one of my Math Methods professors, Erica Litke, always made a math problem out of the date. I adopted this practice the day I began teaching, and have continued it every day (really, every single day) since. I love it when I make a mistake and a student points it out in the middle of class; one year, there were two boys who weren’t in my class who would stop by every day and compete with each other to figure out the math problem. I make a second trip between my office and the classroom with the iPad cart, and then run down to the mailroom to get my attendance folders. It’s not even 8 am, and I’ve already walked more than a mile and climbed four flights of stairs three times. But I’m ready to go. Hopefully, the kiddies are too.
10:04 AM My teaching day is 40% complete already. The two morning Algebra 2 classes were spent with students wrestling (struggling productively, I hope) with the three variable systems. The vast majority of the kids understand what they need to do, but little mistakes, such as flipped or dropped negatives, or not multiplying on both sides of an equation when eliminating a variable, abound. I brought the iPads for those students who were sure (yesterday, at least) that they didn’t need more practice, and I set up Function Carnival for those students to work on after they had tried this lovely system which arrived in my inbox yesterday, courtesy of a piece by James Tanton in the MAA Math Messenger.
As it turned out, no one asked for an iPad. Several students worked away at this system, although I did not see a correct solution (which means I can use it as extra credit on tomorrow’s quiz!). I repeatedly stressed to the students to keep their work neat and to leave themselves lots of room in order to avoid the aforementioned common errors, but that is a lesson that is usually learned the hard way, through trial and much error.
I’ve got a triple coming up – two sections of Discrete Math sandwiching another Algebra 2 class. We are working on Matrix Logic problems and I’m hoping the kids will enjoy working on them independently – I think I am talking way too much at the board. We will start, however, with a number talk. Yesterday we moved from dot cards to addition (67 + 28) and I’m thinking today we’ll take the leap to multiplication. The students seem to like these number talks, although I would like the conversation to be a bit livelier. I am contemplating asking specific students what they think about someone else’s strategy, but I am concerned that this could either backfire or create resistance. I am looking forward to the day that I am more comfortable with this! But with most things in teaching, I find, you’ve got to go through the inevitable awkward learning period before you get to the flow.
On an exciting note, a pair of hawks has built a nest in the fire escape across the street from my classroom! I haven’t gotten a good picture yet (the birds are well camouflaged by the brick building), but every time they appear, I get excited and call the students’ attention to it. And when the birds take off, it’s breathtaking. Got to turn this into some kind of math…hmmm.
It’s 1:45 P.M., and my official day is done – the upside to being up at a ridiculously early hour. The Discrete Math classes went pretty well. I am doing Number Talks every day as a warm-up; in the first class, I used 18 x 5, which was, I think, too simple for my students. One student described decomposing the numbers, but the rest of the class steadfastly claimed that they mentally used the long multiplication algorithm. In the second class, I reverted to dot cards, using this representation:which provoked a much richer discussion, and a greater diversity of response. One student came up to the board three times to share his perspectives.
We are working on our first unit, Matrix Logic (taken in part from the book Crossing the River with Dogs), and today we began tackling problems in which each statement is a falsehood. The students take to these problems as the logic behind them becomes clear, and engagement, in both sections was high. I distributed problem sets for them to work on at their tables (finally getting away from the board), gave some guidance regarding how to get started, and many of the kids dug right in. Those that needed help asked for it, which is great – my Algebra 2 classes aren’t always so forthcoming when they don’t know what to do. Problematically, however, many students stopped working after they finished the first logic question, and needed a lot of encouragement to continue. The problems are quite wordy, and although absolutely capable of reading through the material, I think some of the kids assume they ‘can’t do word problems’. I scribed while they described the set-up of each problem to me, listened to their reasoning about what each clue allowed them to assume, and pushed them along their way without really giving specific input. My expectation (read: hope) is that tomorrow each student will complete the first problem set in their notebook; I will begin each class by showing them an example of a former student’s notebook to provide a model.
Today was the big ‘equalization’ day – the day by which all classes must have 34 (or fewer) students on their roster per the UFT contract with New York City. I knew there would be some shifting in my Algebra 2 classes since they were all oversized. But I also received several new students in Discrete Math, students who had been removed from Algebra 2 and programmed for my elective instead. The disappointment that they feel by this re-assignment is 99 times out of 100 unmistakable, and I empathize with them – they are being bumped off the higher math track, and for no other reason than scheduling exigency, and perhaps a lower grade in a previous math course. I tell these children that they are welcome in my classroom, and will definitely learn math, but, if they truly want to take Algebra 2 instead, they need to make some noise, and have their parents make it as well.
My Algebra 2 class was more of what I did this morning – systems with three variables. I found myself getting caught in a trap of checking work on the spot – a student would claim they did everything correctly and were still getting the wrong answer (so there must be two solutions to the system! they said). After reviewing some work to find the aforementioned careless errors, I realized I wasn’t supporting cooperative work at the tables, and began referring all errors back to the students. Looking for arithmetic mistakes prevented me from helping children with bigger conceptual problems. I’m glad I caught myself doing this so early in the year. Hopefully this extra day of practice will boost their performance on tomorrow’s quiz.
Speaking of which, my monitor came up for her 8th period shift only to tell me that my quizzes had not yet been copied, and therein lies tomorrow’s disaster that requires averting. I didn’t have any work for her, so I helped her revise some PreCalculus homework. Yesterday, we had worked on problems involving the changing of logarithm bases, and her teacher (one of my office mates, actually) told her she couldn’t use the method I taught her, which is described and proven here by Dr. Math at the Math Forum. I’m not sure whether I want to engage with this other teacher about the validity of this method, but I am saddened by this instance of a teacher insisting on one correct way to do a problem, especially at this level – and unhappy that my lovely monitor is caught in the middle; she clearly understands why the method we used works, and in my view, should be able to use it.
Other than my quizzes not being ready for tomorrow, I have nothing to prep right now, so I can head home! I have two tutoring students later today – one, a girl I have been working with for 3 years (she’s now in 8th grade) on enrichment, and the other, the daughter of a dear friend who needs a little geometric guidance. Both of these girls are terrific kids with good senses of humor and an appreciation of math, so it won’t even feel like work. And hopefully tonight, I can get to bed on time to make that 6:10 AM bus.
1) Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?
I am proud of how I engaged the Discrete Math students in the Matrix Logic puzzles. This is foreign content, and many of them are suspicious (but not hostile) of the course. But I guided them towards finding their own solutions, and heard a lot of positive comments. Not so ideal: I mentioned that I caught myself combing student work for errors, not realizing that I should have redirected that effort. I hope I can correct this in the coming weeks.
2) Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately?
I am looking forward to the results of the first quiz in Algebra 2; I still don’t have a sense of who my students are, and I will gain some perspective on (a) how well I’m doing at teaching them, and (b) what their strengths and weaknesses are. I’m also looking forward to hearing some friendly debate as the Discrete Math classes work more independently on the logic puzzles.
One challenge for me is work/life balance. I desperately want to stay well-rested this year, and even maintain some attendance at the gym. I’m working on it, always.
3) We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.
I’m enjoying working with my monitor, Rachel, this year. She was my monitor all of last year, and had just transferred into the school. She’s more mature this year, and better adjusted, and we talk more honestly and productively about her workload and priorities in school. When we discuss the logarithm/PreCalculus situation, we went over the proof of the method we had used, and she took the proof – I hope – to show to her teacher.
4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year.
I continue to keep getting to know my Discrete Math students as a priority, and to keep reiterating to them – in words and in deed – that they can do math, that their voices are important in my classroom, and that there is something valuable that we can learn together.
I am struggling with keeping up the Contemplate then Calculate routine (but it’s still on my radar, and I will try again), but I have kept up the number talks every day for the last week. I’m proud of that.
5) What else happened this month that you would like to share?
I’ve signed up for a Google Apps for Education training to earn Level 1 Certification – I am SUPER excited about that!