Uncategorized – Page 21 – A Portrait of a Math Teacher as an Aging Man

Finding inspiration

Been a rough couple of weeks. Lost my dad to a too short battle with cancer and then found out a dear friend from my FLA days died just last week. Both were too young to go.

So, I’ve been trying to focus on the day to day and look for triumphs right now. There are a few to be savored. In Calc BC we are studying Differential Equations and I was proud of both of my classes this week. I posed the following challenge to them. Suppose I leave the dorm this morning with a cup of coffee (with a lid) in each hand. I place one of them on the sidewalk and take off the lid. I bring the other to my classroom and remove its lid. Now, sketch what the temp v time graph would look like for each. We noticed and wondered for awhile (I”m not good at using that language explicitly, but I am pretty good at generating some noticing through careful questions) and we decided that the slopes were in some ways related to the difference in temperature AND that there had to be a horizontal asymptote. We had a good conversation about the difference between the theoretical and the measurable temp differences between the room and the cup of coffee. We talked about the relative size of the surroundings versus the size of the object at hand. We got hung up on whether the initial temp of the object was all that important in the end. We realized that there was a proportionality constant to be accounted for (one student pointed out that the specific heat of the object mattered – I was impressed and I think he even used that lingo accurately) and we finally arrived at Newton’s Law of Cooling. I’m not naive enough to think that many of them will remember the exact conclusion, but I am pretty convinced that many of them will remember the process. The conversation that gives me hope about this is one I had in AP Stats today. We were introducing the idea of probability distributions and talking about finding means and standard deviations of random variables. We had to look at the ugly standard deviation formula and try to remember what it all meant. In each class kids were able to contribute meaningful memory of our earlier conversations and I even got a great challenge question from one of my students who doubles in BC and Stats. After we decided that we wanted all the differences between scores and the mean to be positive (so that they don’t all sum to zero) this student wanted to know why we bother squaring the difference between a score the mean score instead of just looking at absolute values. I was able to have a nice conversation about the differentiability of the square and square root functions and how they just behave more ‘nicely’ than absolute value functions do. I was just so pleased that there was such good memory about conversations we had weeks and weeks ago.

I’m also finding inspiration from blogs and tweets these days and it feels like something might be big brewing in the back of my head. Don’t have it together yet, but I’ve been so inspired lately by tweets from @gfrblxt, @JustinAion, @wwndtd and others by blog posts from Michael Pershan, Gary Johnston, Sam Shah and a slew of others, by the Nix The Tricks project that Tina has organized, the list could go on and on.

I’m so thankful for all of the inspirations I find in my daily contacts with family, friends, students, and colleagues for all the inspiration I find in my inbox and through my tweet deck, I just hope that I’m adding to that good karma in my own way…

The challenges of Technology in the Classroom

As is true of most of you, I wear quite a few hats at my school. They all pose interesting, and different, challenges. Tonight I want to think out loud about my role as the chair of a digital learning committee. I work with our lower school colleagues on this committee. Three years ago we decided to move toward 1 – 1 implementation in our middle school (grades 5 – 8 here) and we decided – after a great deal of deliberation – to go with a modified BYOB plan. Many of our middle school teachers are Mac proficient and use quite a few of the applications and programs native to the Mac environment. Our BYOD options are Macbook Pro, iPad, or another PC laptop. Parents were encouraged to consider the Apple products since our teachers had more hands-on experience with those. We introduced this program with a required device for 5th grade students during the 2012 – 13 school year. For this year, we require a device for 5th and 6th and we expect to continue to roll forward. As is to be expected, change produces some discomfort. Discomfort for our network as more and more machines are tapped in. Discomfort for our students as they try to balance the fun and distraction that technology introduces with the responsibilities of being a focused student. Discomfort for our faculty as they try to navigate technology glitches in a classroom packed with young students and packed with curricular expectations. We are doing a fine job of helping each other out and sharing our growing pains, but I know that we can improve our focus and do a better job. This, of course, is a perpetual feeling with any aspect of schooling, isn’t it? As I began preparing mentally for our next meeting I ran across the following blog post from Sean Nash . I urge you to flow that hyperlink. It’s an eloquent and thorough discussion of the patterns behind failed technology initiatives. I especially appreciate his telescope/microscope image. This is probably because I use this language to discuss problems students have in their study of calculus. Students struggle and the tighten up and focus in on little details (look through the microscope) rather than step back and really try to get a bigger picture (look through the telescope) of the binding themes of their study of the calculus.

This post has now been shared with my committee members and I am optimistic that it will generate some powerful conversation and help us to keep our focus.

The Spectre of Final Exams

So – yesterday I blogged musing on what I find interesting. Today I am blogging about something I DO NOT find interesting. I have had a troubled relationship with final exams in schools for some time. I believe – I mean, I really deeply believe – that learning should be a cumulative exercise. The ideas we work hard to understand, the skills we practice toward mastery, the meaningful conversations we have together in class are all experiences that we should be able to carry forward and use as building blocks to grow as learners. In this worldview a final exam should not be a cause of deep stress. Especially if the exam is structured in a way that places less of an emphasis on smaller facts and skills that we might ask in a quiz or a short unit test. You know, look for the big ideas and capture the broad strokes of what we have discussed during the term. However, I have been teaching math long enough to know that most of my students aren’t learning in this fashion. They feel pressured, they feel frantic at times, they feel overworked. In these conditions homework is often just something to get done. Studying turns into short, intense bursts of cramming material in short-term memory. Too often their teachers are complicit in concentrating on the day to day progress so that we are not explicit enough often enough to point out connections and remind ourselves and our students of what has happened in the past. Under this worldview final exams are a terrifying mess. In the span of four days this week my students will have up to five exams and those with fewer exams are trading off by having large papers turned in. What I see are tired, stressed kids who don’t seem to be growing as a result of this experience. Surely, there are better ways to use our time together. I am a team player and I administer exams in the fall and spring in my classes. We say as a school that we value these opportunities to show cumulative growth. If we say we believe in this process, then I want to be on board. We say that part of our role as a college preparatory school is to help prepare for the expectations of college and one of those standard expectations is a final exam for many courses. What troubles me is that there is an inverse relationship between the number of exams a student has and the grade level that they are in. Our freshman have the most exams and our seniors have the fewest.

I say as an individual that the ability to tie together ideas to move forward is a crucial sign of having internalized some skills and ideas. So I want to show my students I believe in this and I ask them twice a year to go through this process. I try to make sure that all my unit tests along the way include opportunities to make explicit the connection between current topics and past material. I hope that this helps some, but I still se a great deal of stress.

So, I ask for the wisdom of the internet community of teachers and administrators. Is this model of exam time just antiquated? Can it be modified in a meaningful way? What do you do at your schools?

What Do I find Interesting? – How Can I Help my Students Answer this Question?

One of the joys of my engagement in the interweb of math teacher bloggers (some of whom I stumbled across my self many of whom I have discovered through the MTBoS challenges) is that I feel my brain tickled and challenged. One of the most consistently challenging of the bloggers is Michael Pershan and he has recently been writing a series of posts about what he finds interesting. Kind of math-y in general, but also just musings. I used to think that success as a math teacher might be measured by running into a student after college and having him/her still be able to answer, say, a trig question about oblique triangles. Luckily, I grew out of that and have a different idea of what success might mean. I have a story from a former student (Chris S.) that I think is apropos here – and I apologize if it seems like I am patting myself on the back here, trust me when I say that there are many students who don’t see their experience with me the way that Chris did. For a few years, I was living in NJ a mere 35 minute express train ride into Penn Station. On days when I was off work but my wife was not, I would often head into Manhattan. Chris was working there at the time doing some high powered financial advising. He was one of the more brilliant kids I’ve ever taught and I have kept in touch with him since he graduate in 1994. So, one day we are having lunch and he is recalling a particularly thorny data analysis problem he had been wrestling with. Much of what he detailed was over my head, but it was great to sit and listen to him so passionately recalling a struggle. He said that his boss, let’s call him Ned (I don’t recall his actual name), helped him with a major breakthrough. He said that one morning – after wrestling with this problem for over a week on and off – he told Ned that he needed to take a long lunch and get out from under this problem. He came back a few hours later and Ned had made an important advance on the solving of this problem. Chris then said to me, “Jim, Ned kind of reminds me of you – he just asked some questions of the data that I did not think of asking and this allowed me to finally solve this problem.” I still get kind of chocked up thinking about this day. He did not say that he remembered a certain lesson or a success on his AP test. He did not say that he remembered having fun in my class, but I think he did. He did not say that he thought of me as a caring teacher, but I think our ongoing relationship says that he does think of me this way. No, what I took away from that conversation was that I challenged him by asking questions he did not think of. What I inferred (maybe this is just optimism on my part) is that he finds this to be a positive trait. He was speaking with admiration about his boss. Now, I know for sure that Chris is a smarter person than I ever have been and I know that many of my students fall under this category. But what I hope that I can convey is the value of questions. Many times in the classroom these are restricted to a mathematical context, but I want my students to develop an appreciation of a good question and develop the habit of asking good questions about the world around them. There is a quote I found in my reading years ago when I was a student and it is a quote I share with my students. I have not found the correct citation for it, so I apologize for not being able to give credit where it is due. Here is the quote:

Genuine enquiry is an important state for students to recognize and internalize as socially valid. Consequently it is an important state for teachers to enact. But it is difficult to enquire genuinely about the answer to problems or tasks which have well-known answers and have been used every year. However, it is possible to be genuinely interested in how students are thinking, in what they are attending to, in what they are stressing (and consequently ignoring). Thus it is almost always possible to ask genuine questions of students, to engage with them, and to display intelligent directed enquiry. For if students are never in the presence of genuine enquiry, but always in the presence of experts who know all the answers, then students are likely to form the impression that there is an enormous amount to know, and that experts already know it all, when what society wants (or claims to want) is that each individual learn to enquire, weigh up, to analyse, to conjecture, and to draw and justify conclusions.

QUICK UPDATE

One of the amazing librarians I work with found the citation for me. You find the whole text at http://www.math.jussieu.fr/~jarraud/colloque/mason.pdf

The author is John Mason

MTBoS Challenge #7 – A Day in the Life of mrdardy

I was happy to see the newest challenge in my email inbox this morning. Rather than work on my finals, I am going to tackle this challenge first thing today. For the purposes of this exercise, I will use Thursday which was my last ‘regular’ day here at school. Friday was 25 minute classes, a 45 minute chapel, and two and a half hours of conference time as we begin fall finals tomorrow. So, here we go on a trip back in time. Cue the harp music…

Thursday began at 6 AM. Most school days start a bit earlier, but I had dorm duty on Thursday night, so I slept in a bit. Normally, I have Monday duty and I did this past week. One of my colleagues was sick, so I agreed to take his dorm duty for the first two floors of our building. I live with my family (wife, 10 yr old boy, and 4 yr old girl) in a four story boys’ dorm with about 80 students.

We have an 8 period day at our school with each period meeting every day in the same order. We have a variety of schedules with classes ranging from 25 minutes on special assembly days (like Friday) to 50 minutes (like Thursday.) With exams around the corner and Thursday being our last regular class day, I had a day of reviewing and wrapping up the term. Not the most exciting stuff, to be honest.

At 6:40 we start waking up the kids to get the to the dining hall for breakfast before their bus. It’s always nutty getting four people out of the house and this morning was no different. On the way out, my boy decides he needs to bring a basketball to school. He is in his last day of full play practice and he also has basketball practice after. Not wanting a fight at 7:05, I just grab the ball on the way across the street. We have a pleasant breakfast catching up with friends, but my little girl is nervous because her bus buddy is not at breakfast. Luckily, she shows up at the bus stop – a mini crisis averted. Kids off on the bus, my wife heading to the car to head across the river to her job and I head upstairs. For seven years now, I have had the pleasure of walking to work. It’s a huge quality of life bonus.

I get to my room at 7:45 every morning and open up the computer lab first thing. I fire up some music (this morning it was mellow – I listened to some of Beethoven’s 3rd Symphony (the Eroica) and put up today’s schedule on the side board. We have no bell system at our school, so I always write the schedule to keep myself organized.

My first class is a quiet, small BC Calc class. They had two interesting AP FR questions for HW but this class is not big on conversations. I run through the solutions and look at one interesting question together. We get a nice conversation going but it’s clear I did not plan enough for today. I usually hope for some spark of conversation to eat up time. My backup in these cases is to share a TED talk to see if some interesting chat will ensue. Thursday I chose to share Dan Meyer’s TED talk since he touches on some issues that have frustrated my kids. I think that they sometimes feel I am less helpful than they want me to be. No one really says much and they wander off to the rest of their day. I have a second period planning slot but it often gets eaten up. Today I had a good chat with a new colleague who inherited my old non-AP Calc class. We looked at his term final together. Nice chat, but I wish i had some down time with a long day ahead.

My third period class is one of my AP Stats classes. We’ve been struggling with probability and had a great conversation Wednesday about the ELISA medical test accuracy problem. I’ve been pleased with the questions they’ve been asking. They had their final quiz for the term and we had a lively review before their twenty-minute quiz. While they were quizzing I was pushing through on reading their essays that they had submitted about the Spongebob TV study. I had dragged my feet on this work and was pretty mad at myself. We had just finished our unit on looking at experimental design and had asked them to make some smart commentary about the design and strength of this study. I got some good work from them.

My fourth period class is my Precalculus Honors class and we did some nice trig today. One of the problems we did was a conversion from revolutions per minute to miles per hour. I was pleased that the kids questioned the result so we went to google to verify our answer and discuss the implications for a typical car. We also had a few nice triangle problems and some graphing reminders. Honestly, by this point in the week we were all kind of reviewed out. Since my tests are not until Weds and Thurs next week, my kids are not exactly focused on my classes right now. Given that, I’m pleased with the engagement.

Lunch time! Lately, I’ve been grabbing lunch and coming back to my room, but today I enjoy the company of some of my colleagues. Two more classes to go – another AP Stat and then the other AP Calc BC.

The afternoon stat class is very similar to the morning with some good questions before the quiz. My afternoon Calc class is generally more engaged and outgoing and today is no different. We work together through the AP FR I had chosen and then I share Dan’s TED again. This time, a lively chat develops. One of my students feels that higher level math classes need more teacher driven practice and that Dan’s prescription works better for earlier classes and possibly for students who have seen less success. I counter that the students who have seen success are precisely those who can stand less support from their teacher. An interesting conversation about college pressures, etc. ensues. Normally this would be the end of my day. But the colleague who is sick also teaches an Algebra I class the last period of the day. I told him I’d cover for them, so it’s upstairs to his room to do some word problems with his class. I get a little resistance at first – ‘Just let us go, it’s the end of a long day’ – is the general sentiment at first. They settle in and we work our way through a couple of coin problems and have a nice conversation about some absolute value problems they did for review. It’s now 2:55 and I have another 9 hours to go before sleep. ugh.

After school I am in my room for about half an hour for our afternoon conference time but no one comes by for help.

My daughter and two of her friends – her bus buddy and her buddy’s older brother – have an afternoon date with a colleague to work on some Thanksgiving crafts. I head to a local bagel shop to get them some car treats (bagel and butter!) and head down to our lower school to pick them up. A fun ride back, happy kids with snacks, then an easy handoff to crafting. It’s 4:30 and I don’t have anything to do until 6:15 when our campus Thanksgiving dinner happens. We sit with our students two nights a week at ‘family-style’ dinners but exam week blows that schedule up. So, two weeks before thanksgiving we have our version of it. I head home for about a 45 minute nap and awake recharged.

Our dinner group has been delightful this time around (it usually is). We have a new girl from Ohio, a new boy from NY state, and a boy and girl from China both of whom are school vets. A day student joins us for dinner and my little girl arrives with some lovely crafts she designed. We have a yummy yummy dinner and some fun chatter. Having my little one at the dinner table makes conversations much easier.

We head back to the dorm after my son comes home from basketball. A colleague took him home for me since my wife is working late on her university’s fund raising phonathon. It’s 7:30 when we get home and my kids have each been out of the house since 7:05 this morning. I am on duty in 30 minutes and my wife won’t be hime until about 8:30. I start a tub and go looking for my RA who doesn’t know I am on duty. There has been an RA swap of duty as well as a swap of faculty so a little confusion ensues.

We have one night of study hall proctoring each week in the dorm. Study hall runs from 8 – 10 PM. For the first hour, the boys are supposed to be working in their room. For the second hour, they have the freedom of working with others. From 10 – 11 it’s a bit of a free-for-all until night time check in at 11 PM. Luckily for me, the combination of a tiring review week AND a heavy turkey dinner left most of the boys pretty sedate. It was one of the quietest nights of my time here. I got some more essay grading done (quizzes are put off until the morning) and I had a number of nice chats as I toured the floors every twenty minutes or so. An uneventful evening of dorm duty caps off a long day at the end of a long week.

Life is not always this full of activity – but it is usually more filled with planning thoughtful classes. My kids are getting active in their after school life, my wife is in a busy phase at her job and I keep agreeing to do things on campus. Whew… I apologize for the lengthy post here but I also wanted to actually walk myself and any brave readers through my most recent ‘real’ day of school.

Metablogging

So, Kate Nowak over at http://function-of-time.blogspot.com has asked folks to consider why they blog. I’ll take a swing at blogging about why I blog. I’ll stick to her questions and try to make sense of this in some way. I don’t know that I have much to say that moves the conversation forward, but I’ll try

1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation?

I’d be reluctant to call it desperation, but when I stopped being a student in 2007 and moved to a new school far from my previous home, I found myself really looking for stimulus. Much of it came from one of my administrators and some of it came from other colleagues. I still had student access to databases and was reading journal articles, but I also started poking around and finding some ideas on the net – I’d like to say it was around 2009 by then. I was home for awhile when my little girl was born and I remember starting to read some blogs I had run across. The first two writers I remember really feeling attached to – in a virtual way – were Dan Meyer and Sam Shah. I can’t swear to the timeline, but this is the past that I remember now.

2. What keeps you coming back? What’s the biggest thing you get out of reading and/or commenting?

I feel a bit restless intellectually and professionally at times. I enjoy the people I work with and I enjoy picking their brains. But, I think that when I was in my doc program I got spoiled by the level of discussion/debate and by the frequency with which new ideas/techniques were flying across my radar. I think that the tingle I get in the mornings when I start opening my email links to the blogs I subscribe to is a way to recapture some of that sensation. It’s rewarding to feel part of such a large community of people anxious to share. I’ve been in the classroom since 1987 as a teacher and I can’t even remember how isolated I must have felt all those years before I had the ability to reach out the way we do now. Again, I had some colleagues I loved, but the sheer amount of interaction that is possible now is just mind-boggling. A little intimidating, in fact.

3. If you write, why do you write? What’s the biggest thing you get out of it?

Is it a little too self serving to say that I get a sense of validation from my writing? That, I’d have to admit, is my first motivation. Organizing my thoughts and trying to make sense of them is the second motivation. The third would be my need to not simply feel like I am not just a parasite. I hope to, in some small measure, add something to the culture,knowledge, and experience that is being shared so freely on the blog world.

4. If you chose to enter a room where I was going to talk about blogging for an hour (or however long you could stand it), what would you hope to be hearing from me? MTBoS cheerleading and/or tourism? How-to’s? Stories?

Some stories of what you see as the arc of this community. Some tips about how to forge and maintain connections. Some vision statement of what you see as the near future of this community endeavor.

A New Challenge – MTBoS Mission #6

So – I finally figured out (with the help of Tina C on twitter) how to start a Virtual Filing Cabinet page on my own blog here. Currently there is a small clickable link right above my unwieldy blog title. I am in the process of gathering worthwhile links that have been languishing under my Safari bookmark tab. I hope that this will continue to be a work in progress and I hope to be able to figure out how to make the Virtual Filing Cabinet title much more prominent so that it can capture the attention of any eyes that wander through here.

Trolling for Ideas

We have started a STEM initiative at our school. I am hoping to gain some traction for a conversation centered on a joint Physics/Calculus curriculum. We have two courses in place at our school that are joint teacher operations. We have a course called Seminar that is co-taught by our history and english department chairs. We also have a course called Creative Spirit co taught by a studio art teacher and our music director. So, we have the vision in our school to create courses that break the mold a bit. I would love to try and launch a course combining physics and calculus ideas. I am certain that there are schools where such a program exists and I would love to have some curricular conversations along these lines. Anyone out there with ideas they’d love to share?

Magic in Stats Today

I’ve been feeling grumpy about my AP students lately and I was determined to try and have a serious talk with them about daily diligence and about taking advantage of resources. I also wanted to make sure that I had something positive to do today. So, I tried an experiment that I had read about in the past.

I had read in a couple of places about a stat professor who does an eye opening experiment with her students. I tried it out today and it worked pretty well. I have 20 students in one section and 17 in the other. In each class I formatted a sheet with 93 numbered blank spaces (just how many fit in three columns) and I had 10 pennies in my hand (9 for the smaller class.) I gave them the following instructions:

1) I am going to leave the room for a few minutes. Come and get me when you are done with the following task

2) Randomly distribute the pennies to half the class

3) Those with pennies – toss the penny and record the results until you fill the sheet

4) Those without pennies – imagine you have one and write down the results of your imaginary tosses

When I returned I browsed through the sheets turned in. I was looking for sheets with a few long runs of the same result. I know that in 93 tosses, you are bound to have a couple of runs of 5 or 6 repeats. With the kids that did not have a real penny, I anticipated only runs of three or four at most. In my first class I encountered a student who used his calculator and the result fooled me into thinking he had a penny. Another student who was penniless had a run of seven and fooled me. I did, however, correctly identify three of them. In my second class I was more explicit in my directions about pennies or none (no technology!) and I was five for five in predicting. The students were impressed and the activity resulted in a lively discussion about randomness and unlikely events.

Later tonight, at the dining hall there was an impromptu loud and rowdy round of Happy Birthday for one of our boarding students.

All in all, a pretty good day.