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?
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.
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.
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?
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.
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!
So, in my BC classes we are wrapping up our tour of integration techniques. It’s pretty easy when you are convinced that integration by parts is the strategy to use, or when you know you are supposed to use a trig substitution, etc. Little parcels are easy enough to deal with. Throw them all in a bag at once and choose? Much much more challenging. Yesterday, in our 40 minute classes, each of my two sections of BC Calc made it through two problems and I could not be more proud of them. They fought, they tossed out ideas, they stuck through some thorny algebra. They critiqued each other’s ideas. They questioned mine. I tried – I really did – to give them space and let it unfold. Other than one idea that I knew would lead to pain, I did my best to let them run the conversation. It was the kind of day that justifies – at least in my mind – our decision to have BC as the second year calc class. In a one year track these kids would not have days like this where they could just play with ideas without regard for the clock. The problem that was the real winner is below (if my cut and paste graphic works right)
Edit – Image pasting is not my strength right now. Sigh. The challenge at hand was to integrate the fraction dx/(x^(2/3) + 3x^(1/3) + 2)
One student in each class suggested completing the square and that was pretty thrilling. The first one even pushed a step or two through on a trig substitution involving secant. That’s where I intervened because I was pretty sure that this path would lead to pain. We looked at GeoGebra and tried to work backwards from its answer after we went down the partial fractions path. Man, what a good day and I was fortunate enough that one of my colleagues came to visit yesterday morning. She was their AB teacher last year so it’s possible that they stepped up their game for her. If that’s true, I’ll have to enlist her for future challenge days.
Our school had a day off on Friday (and a day off today as well) for a long fall weekend. We were asked by the powers that be to use Friday for professional development. I chose to drive a couple of hours in the morning to go visit another school. When I did my last job search in the early months of 2010 there were a number of schools that caught my eye and the school I visited on Friday was one of them. The chair there was remarkably kind and helpful in setting up a too short visit that morning. Since I had kid pick up duty that day AND we had agreed to house sit for some friends to look after their dog AND my boy had an ice skating birthday party to go to (there is a theme here about how life unfolds in the dardy household) I did not have quite the leisure I had hoped for. I arrived at 8:30 ish for a warm, quick chat with my host, I saw a Geometry class, then I saw a Precalculus class, then I saw an AP Stats class. A nice follow up chat and lunch with the chair, then I was off to home.
I always enjoy seeing classes – it is a part of my job as a chair that unfortunately gets buried under other tasks. It is fun to pick up tricks from other teachers. In this case, the geometry teacher had a lovely way to highlight parts of the parallel line with transversals problems that they were working with that morning. She had spools of different color tape that looked like athletic trainer tape. She pulled off two of one color to highlight which lines in the diagram were parallel to each other and a different color for the transversal. It was SO COOL to see this way of making the relevant information in the diagram just pop out to the kids. It was also fun to see her improvise. The kids were checking their work from the night before and were having disagreements about measures they had taken. Out the window went the lesson plan for the day and out came a class set of protractors so that they could practice with their measuring skills. The teacher confided in me that some of her attitude about this was strongly influenced by her husband who is a woodworker. In the AP Stats class I was privileged to watch someone who was a real, honest to goodness statistician before entering the classroom. As a stats novice myself, it was great to chat with her beforehand and to watch her in action. I think that she convinced me to try an activity that has been previously pretty intimidating to me. The precalc class was fun to watch as well as the kids were hanging in there working through some complex polynomial graphing ideas.
I know that I have a tendency to look at my world and see the potential for excellence in the people around me. I know that I focus at times on what is not quite right instead of celebrating what is right. A visit like this worked wonders for me on a number of fronts.
1. It’s always great to reach out to more people to bounce ideas off of
2. It’s fun to watch kids at work – especially when I have no preconceived notions of who they are or what they SHOULD be doing
3. It’s rewarding to talk to others who are working through some of the very same struggles. How do we accurately place test kids who are new to a school? How do we balance ambitions for kids with their abilities and previous track record of achievement? How do we find TIME in the school day/week/year for meaningful problem-solving while still serving an ever expanding curriculum? The chair I met with is thoughtful, experienced, and intelligent. The fact that she is struggling with these questions as well makes me feel better.
I’m proud of my school, our students, and my colleagues. I believe that we can all be better than we are but I want to try and focus on what we’re doing right and I think that this experience on Friday can help me with that.
A number of years ago I was fortunate enough to be able to attend the Ajna S Greer summer conference at the Phillips Exeter Academy. In addition to great mini courses, terrific connections, lovely food and drink, and just general all around wonderfulness there I was exposed to their Harkness table teaching. I had long struggled with the traditional rows and desks layout of my classroom and I remembered how I would utilize it as a way to hide as a student. Being relatively small in stature I was able to disappear into the classroom seating arrangement when I did not want to be engaged in class. As a teacher I want to avoid that. At my last school our desks were very moveable and I played around with a ‘pod’ system in my classes. The girls took to this system (it was a single gender school) and they took a certain amount of ‘pod pride’ in their group work. I played with group quizzes and I was feeling like I was moving forward as a teacher. I still found myself a bit frustrated by the lack of whole group interactions. I came to my current school in the fall of 2010 and inherited older desks that were not so flexible in their use. So, I prowled around campus looking for solutions and I found some old library tables that were sitting in a storage room on campus. My boss got our maintenance drew to help and over christmas break I removed all individual desks from my room replacing them with six rectangular tables. When my students returned they were taken aback by this new set up and by the new classroom behavior expectations I put before them. I simply asked them. I told them that it was understandable if I was the person who talked the most in class – not always desirable, but understandable – but my challenge to them was to make sure that my voice was not heard more than 50% of the time. I wanted them to talk to each other. I wanted them to toss out ideas and questions. I want them to interrupt me and to share their ideas. I want them NOT to interrupt each other when ideas are being voiced. In general, I wanted them to be active participants in the classroom not passive vessels waiting to be filled. I am the only math teacher in my school who has a room set up this way so when they get to me there is a learning curve. I encounter a number of different situations as they learn how to be a student in my class. There are social conversations occurring. More of them than there used to be. I wish that there were fewer of them, but it’s a price I’m willing to pay. There are students who are not sure enough of their ideas to share them with the class. So they try them out on their neighbors instead. I try hard to listen and pull those ideas out and toss them to the crowd. There are students who are distracted by their neighbors and want to just focus on me. I try to move people around so that this effect is minimized. The physical layout of my room means that some students have to turn around to see certain boards. I don’t know how to fix that and I am not sure it is a critical problem. Some students monopolize the class conversation. This used to happen anyway. I think that now I at least have the benefit of students making eye contact with each other. It is easier to listen to your classmate if you are not staring at the back of her head. Some students are quiet and more shy. I get that. I watched the TED Talk from Susan Cain about introverts. In fact, I shared it with my class and talked about the impact of the classroom set up. We had a great conversation about it. I know it’s not a perfect setup for everyone but I also hear back from my students that this setup has helped them put their own voice to their mathematical ideas. I have had students tell me that before my class they thought that their job as a math student was to know how to use certain formulas and know when to use them. After my class, I hope that they have a larger view of their job in the classroom. There is a learning curve at the beginning of each year and I hope that we are beyond it now as we head to week 7. I feel that I am more aware of my students and that I have a better sense of their level of understanding. I think that my students get better everyday at listening to a variety of voices in the classroom. I still spend too many days doing more than 50% of the talking in class but I think that I am still on that learning curve myself. I would not be so bold as to say that I am implementing Exeter’s Harkness style the way it is intended, but I think that I have found a way that makes sense inside my school.
So, we are almost done with our deep and quick tour of AB topics in my BC class. We use the Stewart text which has an interesting section at the end of each chapter. The section is called Problems Plus and I have been browsing through these sections for class examples. On Friday I picked a problem that looked pretty challenging. The set up is this – Imagine a square region with sides measuring two units. In the square a region is shaded. This region is the set of all points that are closer to the center of the square than to the nearest side. What is the area of this region? I did not try this problem first, I had confidence that we could work our way through it. In each of my two sections this was the second problem of the day. Each group dispensed with the first problem in about 5 minutes. Each class spent almost 40 minutes discussing/debating/arguing over this square problem. What thrilled me was that both classes (the small morning class of 8 and the large afternoon class of 18) stayed engaged offering ideas, questioning each other, thinking about circles, etc. We looked at GeoGebra to try and sketch some regions. We thought about the distance formula and circles since the kids were convinced that the region where the distance to the center and the side was equal would be somehow circular in nature. None of our ideas came to find a final solution. To me, this fact is SO tiny in comparison to the fact that they fought, they were engaged, and some of the afternoon kids stayed after to share new insights. I am so proud of this group for being willing to engage and not being at all angry or visibly annoyed when we did not come to a solution. I can’t wait until Monday to see what ideas they bring to the table.