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.

MTBoS #4 – Listen and Learn

So, thanks to Julie and the MTBoS crew, I remembered to login last night to the Global Math Department. Family took me away before it was over but not before I saw some great Geogebra tools that I did not know about. I knew – in theory – that GeoGebra had some built-in stats software but I had never seen if before. Thanks to the crew leading the convo last night ( Jennifer, John, and Audrey) I came away with some skills I did not have when I woke up yesterday. That’s a good thing. I intend to listen in on some Infinite Tangent podcasts to catch up – probably this weekend on my iPod while I am supervising some campus activities. This week’s challenge reminded me of some important lessons. If I let life just move along I can feel busy as hell, I can take care of what I NEED to take care of, and I can find time to be with family, friends, and students. However, if I commit to taking care of the teacher part of myself, I need to carve out time in a very conscious way. I need to remind myself of these learning and sharing opportunities because the recharge me. I need to consciously set aside time where I plug in in a quiet way to tap into my resources. What I think I am also discovering – and this is related to the whole MTBoS challenge series – is that twitter might not fit me very well. I got excited at first when I sent out a plea for help and was contacted by Keith Devlin within an hour offering me help. Pretty damned cool, I thought. However, since that first call for help I have sent out two others and received nothing in reply. I check in on my twitter at night and feel overwhelmed by trying to catch up to what has happened since I was last on. Perhaps I just need to adjust how I interact with it. Perhaps it is just not for me – not for the way I want to digest info, not for the schedule my life has now. I engaged for a little while in an Algebra II chat on Monday while I was on dorm duty. I felt swamped by the multiple threads and by my loaner iPad binging at me constantly. I had a few nice exchanges with Jennifer (who was one of last night’s co-hosts) but it was not a satisfying experience overall. I was sent to a blog post recently from a former teacher who pointed to his efforts to being plugged in as the source of his leaving the profession. I don’t know that he sold me on that with his story, but parts of it did resonate. Finding a balance these days is a serious challenge. 

Help with a Teaching Strategy

I’m still (relatively) new at the AP Stats game. When I was hired here in March of 2010 I was told that I needed to add AP Stats to my toolbox. I’ve loved the course and teaching it has really changed my point of view about teaching/learning. This year, I decided to try something new with this course. My enrollment exploded this year and I wanted to find a way to adjust to this. I had 12 students, then 12, then 19, and now I have 38 students in AP Stats. I wanted to find a way to get/give some feedback in low stress ways (low stress for me AND for them) and I went out to the local office store and bought some marble notebooks for my kids. I have been digging through my old files (assessments I’ve created and assessments from the publisher) and I have been making time for exit slips for my kids. I am trying to do this at least once each chapter – but I have not been as diligent as I should. I pass out the marble composition books that all have a question glued in them. I pick a question from an old assessment and give the students about 10 minutes to work. I explained to them at the beginning of the year that the goal of this exercise was two-fold. First, I could check in and see where their level of understanding is. Second, they would get some feedback from me to guide them to better understanding. No grades – but helpful (I hope) feedback. Seemed like a great plan. I am running out of enthusiasm fro this project as I have noticed that very few of my students seem to be taking this seriously. Students earning an A regularly on graded assignments are turning in work that is sloppy, incomplete, or even just completely blank. What this says to me is that many of my students don’t actually do work (study, read the text, finish their HW) until just before the actual assessment time. I had a direct conversation with one of my students about this. I talked about daily diligence and his response was that he felt that the course calendar – the document with nightly HW assignments and reading assignments – was simply a set of suggestions about what to do and when to do it. He genuinely did not see any problem with the fact that he was not doing his work on a daily basis. He asked why I was concerned with this since he got around to doing his HW before tests. I’m not surprised to hear that some (many?) of my students are only getting around to doing their work right before a test. I live with 80 students in a 4 story boys’ dorm and I see them at work. Many of them are working hard, but not working terribly efficiently. Lurching from assessment stress to assessment stress. I had genuinely thought that my exit slip strategy would help fight this. It’s pretty clear that this is not working this way. I want to have a conversation about this with my class but I don’t want to be a total cranky pants about this. I’ve got some thinking to do. Any clever advice out there?

MTBos Mission #3 – Daily Desmos

So, the challenge this week was to pick a collaborative site and … collaborate! So, I chose DailyDesmos for a number of reasons. Years ago, when I was a student again for a glorious time, I fell in love with GeoGebra. For the past few years I have been preaching to my students and colleagues about the wonders of GeoGebra. I reached out to a colleague from Lawrenceville and had him come out and do a workshop for my school teammates. Fun has been had with GeoGebra. Recently, I was introduced through the wonderful blogger world to Desmos and I am in the process of falling in love with it as well. Recently, with my precalc honors class we had a triumph using Desmos. I blogged about it on Sept 10 and included this link ( https://www.desmos.com/calculator/nvinc8pwdh ) when my kiddos wrestled with creating a trig function to match the daily average temps of my old, beloved hometown of Gainesville, FL. This morning I dove in and took on challenge 201a ( http://dailydesmos.com/2013/09/23/daily-desmos-201a-advanced/ ) which was presented by the awesome Michael Fenton. Here is my crack at a solution to that one ( https://www.desmos.com/calculator/zmuvzpmvti ) and it is probably not as dynamic as it could be. I still need to learn about leaving traces behind rather than simply having the slider generated graph be new at each stage. I am imagining a sort of spirograph and I am certain that Desmos can handle that. I still love my GeoGebra – especially for individually rescaling axes as I go – but I am finding room in my heart for Desmos as well. As my school inches toward greater tech integration, I am seeing a day where my students would be spending time in class (on their own or in their pods) where they are tackling these daily challenges now and again. I am also dreaming of a time when I feel that I have time and energy on a regular basis to tackle these challenges.

I have thoughts about these graphs that I need to organize and make coherent. Another post for another day.

New Challenge – Curriculum Development

Our school is ready to change two textbooks in our curriculum for the fall of 2014. We have been using an edition of the Larson Geometry book for 10 years now and we have been using Stewart’s Precalculus 5th edition. Neither of these texts are available anymore. I want to move to a precalculus curriculum that is a little more narrative and ‘big picture’ than Stewart’s approach. I am partial to Foerster but I have to get my whole team to agree. Where things get interesting is on the Geometry front. I was speaking with my division director – who is a part-time math guy as well – and he encouraged me to think about creating our own Geometry curriculum. We’ve been having conversations about electronic texts, about textbook costs, and about curricular flexibility. This morning he urged me to talk to my Geometry team about the idea of creating our own course supplies. Our Chem Honors teacher created his own course binders years ago that our kids use rather than a commercial text. With the explosion of online resources, I am imagining trying to create something that takes advantage of our own vision of what is important in Geometry, the technological resources available to our kids and teachers, and the wisdom of the world outside our walls. That’s where you come in dear readers. I imagine that others are wrestling with these ideas as well and are creating their own curriculum. I have seen the Exeter Problem Sets and the Park School math curriculum but each of these are probably a little farther outside the box than my school is looking for. I love the idea of tackling a big create our own curriculum project, but I admit that I am a bit overwhelmed about where to start. It also seems that a rich Geometry text – one that kids might actually read on a regular basis – will require some pretty time intensive work on graphics and layout. I am reaching out to the big, wide virtual world for advice here. I’d love to hear about successes and failures along these lines. If anyone has examples to share, I’d appreciate seeing them. I’m excited by this idea and want to run with it, I just want to make sure we do it the right way.

 

Wish us luck and lend a hand where you can!