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Quick Update

I’ve been VERY pleased this week with my classes and with carrying out my new year’s resolution about shifting my classes. In my AP Stats class we worked on a fun project from the Mathalicious crew examining Simpson’s Paradox. The kids were in small groups working pretty well together. They did not need me to talk much (remember – it’s important for teachers to be able to become invisible!) and I was able to listen in on some pretty great conversations. We looked at three years of batting information about Derek Jeter and David Justice and saw that Justice had a higher batting average each of the three years but a lower cumulative percentage for those three years. The activity starts off with a fun parlor game. I had six groups in my room. Three of them received year-by-year data and the other three received cumulative data. I asked them to conclude who was the better batter and the predictable vote of 3 to 3 happened in one class, the other class went 4 – 2 for reasons I could not decode. Then we worked our way in to a conversation about school admissions and looked for evidence of discrimination. It’s a great activity that they designed. We also watched a pretty interesting TED talk by Dan Ariely. It’s been a good couple of days and we close out the week with another Mathalicious activity.

I am typing this while my quiet morning Calculus BC class works on the second of my in-class problem sets. Again, they are silently working and I have decided not to fight against this as long as they are willing to share when we look back at the work. 

Next week it is back to the text for my AP Stats class, but I feel that this week has been an important breather for them AND an important reminder that they don’t need to hear my voice all the time. they’ve been doing fine listening and talking to each other.

My School

This weekend is one of my favorite weekends of the year. Our school, a co-ed day and boarding PK – PG independent school, hosts an annual international dinner. This year there will be 21 tables set up in one of our gymnasiums with students serving food from their home country. The list is impressive – France, Russia, Czech, Hungary, China, Vietnam, Thailand, Spain, Puerto Rico, Taiwan, Japan, Korea, Afghanistan, Pakistan, Italy, Holland, India, Greece, USA, Venezuela & Germany. Many of these meals are prepared on campus in the kitchens of dorm parents and campus faculty members who live in homes that the school owns. This year, we will host China in our kitchen. Last year we had a contingent of Taiwanese kids and we have also hosted a Saudi boy and Thai scholars in our kitchen over the years. It’s a major event and I often see people at the dinner who are alumni (especially our international alum) and people who have retired from our school coming back to share in the lovely food and companionship. It’s hard to get my little ones to try too much in the way of adventurous food, but I tend to stuff myself silly. The students preparing the food take such joy and pride in their work on this day. The students eating have so much fun and the conversations are lively at the tables. Overall, it’s just a wonderful day.

I’m now in my 4th year here and I made some adjustments in my life coming here. We live in one of the boys’ dorms and I had not lived in a dorm since I was 20 years old. My wife had never lived in a dorm. I was asked to teach AP Stats – a course I had never taught before, so I went to a summer workshop and worked hard to learn the material. I have been asked to teach Calculus BC which I had not taught since the 200-2001 school year. I am learning (still) to teach in classrooms with speakers of many different native languages. I’m a wordy math teacher, so this has been a challenge for them and for me. I love it here and I’m excited about the future of our school and of my department. We have a new STEM curriculum initiative. We launched it this year with a trimester sequence of science courses that ALL of our freshmen take. Next year we are looking to expand to create some upper level STEM electives. We are looking to expand our robotics program and infuse programming into more areas of our school instead of simply in our AP Computer Science class. We are hiring a new teacher under the STEM umbrella and we envision that this new teacher will teach two math classes and two science classes. I have a departmental colleague who came out of retirement from our local public school system five years ago when we were in need of a replacement teacher in the spring. He’s done a great job anchoring our Precalculus courses, but he has decided that it is time to retire again. So, we’ll be looking for a new teacher there as well. New faculty members are always cause for excitement as we infuse new ideas and new energy into our school. 

If any of this sounds appealing to you, you should check out our school at http://bit.ly/1dMbDQl

 

Curious

Today was an assessment day for Mr Dardy

Two sections of BC Calculus taking quizzes. Two sections of AP Stats taking tests. One big question for me in each situation. I’m interested in hearing your opinions.

My first class is a Calculus section. We’ve been working with parametric equations and dipping our toes into the relationship between polar and cartesian equations. We spent a day with Desmos and we spent a day on regular old lecture. They had a five-question quiz and four of the questions were very standard. On one of the questions, I asked them to convert an ellipse in rectangular form (factored already so they could see the center and lengths of the axes) into a parametric equation. Now, they had already had homework converting parametric equations into non-parametric forms. We had also looked at polar forms and I reminded them of the polar equations that would result in a unit circle. My hope was that they would piece those two skills together. It is an AP class and I feel that I owe it to them to ask them to react on the fly to situations that are at least slightly novel. Much grumbling ensued. I haven’t graded them yet to see how they responded, but I did not walk away with a positive feeling. 

My next class was an AP Stats class and we were (finally) taking a test on probability distributions. Between the Christmas break and our snow day this week, this unit has felt very choppy to me. I had two girls finish the test in about twenty minutes and they are two of my stronger students, so I don’t think it was due to just folding up their tents. Some students stayed the whole 45 minutes, but I am sort of convinced that some students will stay sitting and pondering any test as long as they are allowed to. 

 

So – my two questions are 

  1. What is your feeling about questions on assessments that don’t match up with a practiced skill?
  2. Should I feel any sense of concern that some students finished a 45 minute test in less than half the time I allotted? It somehow feels like I must have aimed too low with them. Again, I haven’t graded yet, so my opinion may change by the end of the night.

Dorm duty calls and I am bound to stay in my apt near my desk all night – so I suspect I’ll get a good amount of work accomplished.

 

Changes for the New Year

So, I had recently blogged about some ideas to change the pace of my Calc BC class and I want to report on how it is going so far. We are one (partial) week into the new year. We lost Tuesday to extreme cold and I am losing the second of my two BC classes today because I’ll be visiting another classroom. As department chair, it is one of my obligations (and one of my real pleasures) to visit my colleagues to watch them at work.

I have two very different sections of BC this year. My morning class has seven students and they are somewhat reluctant to work together. They get along fine, they are just much more independent workers by nature. My afternoon class has seventeen students and they are much more social and collaborative.

 

I want to summarize the past two days by section, rather than by day.

Yesterday we were in our computer lab for both sections working on the Desmos activity I slightly modified from Sam Shah’s Virtual Filing Cabinet. By the way, if you haven’t seen this resource, click on the link. You’ll be glad you did. My 1st period class was typically quiet and worked individually with only a little bit of collaboration. I started class with a quick exploration of the polar functions of the form r = 1/(1 – kcos(theta)) and r = 1/(1-ksin(theta)). After five minutes, I left them alone for the next half an hour. I wrapped up class with a verification that, when k = -2, the graph is a hyperbola. A Desmos graph shows this quickly and some recall from precalc days allowed us to convert this to a rectangular equation. It was not a pretty one and the process required recalling the standard form of a hyperbola as well as remembering how to complete the square. I was pretty much the lone voice (unfortunately) but it sure seemed like they were all fine. Today, they worked on the problem set that I also linked to in my last post. I sat and worked myself and had all 7 of them sit at one of my two big tables together. Normally they split themselves with five at one table and two at the other. I thought that this would encourage more collaboration. Instead, I sat working quietly for 30 minutes while they all worked quietly as well. No talking, no looking over each other’s shoulders, no recognition of each other at all that I could see. I must admit that I was getting kind of frustrated. At one point, I catch the eye of one of them and his attention seems to be wandering. I ask him why he’s not talking to anyone and he says he answered them all except for the first question. This is very surprising to me on a number of levels. I think that the first question is the most straightforward (and most related to Calculus) and I thought that this was the one that would seem the least intimidating. The next fifteen minutes were spent sharing solution ideas to that problem as well as the other problems (we only made it through the first five together) and I have to admit I was knocked out by their creativity. Especially on the question involving counting digits. Three of my students actively shared their solution ideas and they just knocked it out of the park. Frustration turned to a combination of delight and confusion. I’ll ask some of my questions later.

 

Yesterday, my afternoon class also met in the computer lab to work with Desmos. Again, I spent about three to five minutes looking at an animated drawing of the polar curves I mentioned above. For the next thirty minutes the class had a consistent hum of chatter, people arguing with each other about conclusions, kids looking at each other’s work. When I reconvened the class to focus on the same k = -2 case, they were engaged. telling me what the hyperbola equation was, catching a mistake I made in factoring, just a lively discussion. When class ended, I checked in with two students who were just packing up. One of them said something to the effect that my class made his head hurt a bit. He said it cheerfully and his neighbor said that my class was ‘interesting’ which is the word I use to describe difficult or challenging questions. He, too, said this rather cheerfully. I won’t be around to see them work on the problem sheet but I have asked the colleague who is subbing for me to collect their work so I can see what they can accomplish and how they approached these problems.

Now, I am left with these questions as I move forward.

  1. How do I create a situation so that my first period class actually talks to each other?
  2. Is it important enough to make that happen, given that they are productive workers? I have a pretty strong belief that talking about ideas is important, but I don’t know how to win this class over to that point of view. Is my personal bias important enough to try to change the nature of my learners in my 1st period class?
  3. Can I build momentum for these problem solving days if they only happen once per week?

I’ll keep reporting on progress and I’ll keep an eye on any wisdom that you can share int he comments section.

 

 

Brrr…

So, today we saw school cancelled due to the cold weather here. Woke up to an air temp below zero and wind chill about 20 below. Took the morning to finish the first of my weekly problem day assignments. I’m sticking to my guns and using this Thursday as our first class work day despite losing today to the weather. I sent out a parametric/polar practice sheet to my kids and asked them to spend some time with Desmos. Tomorrow we’ll be in the computer lab working with Desmos (gotta get started on that doc next) and then we’ll have our problem day. I’ll report back on how it goes. The doc I created that is linked above is a collection of stuff I’ve scoured from the web.

Parametrics / Conics

As I have written before, we teach AP Calculus BC here as a second year Calculus course in our school. This gives me loads of time to play and explore with these students. On Monday we start up again – weather permitting – and we start with our study of parametric and polar equations. Our precalculus class does not cover either topic in great depth (a situation I hope that I can remedy starting next year) and a number of our BC kids are ones who start off in AB Calculus when they come to our school. With so many of our students coming from different parts of the world at different times in their career, we have a wide variety of experiences in the BC group. I guess this is a long-winded way of saying that I have to treat this material as if they have not encountered these ideas at all, really. I intend to spend two days in our computer lab working with building up some fluency with Desmos. I have my room set up in a sort of Harkness-style where the kids are facing each other. Being in the computer lab gives me the flexibility of having the students work with Desmos in a hands-on fashion rather than just watching me. That’s the plus. The downside is that they are working in isolation in this room. I’ll have to deal with that downside for a few days. So, I was digging through my memory bank and I remembered that the great Sam Shah had written a lovely post about introducing conics through Desmos. I downloaded his Scribd file and modified it a bit (you can see my version here) but I still need to go back and play with it a bit more. The way the file looks to me now is way too close to plagiarism – though I do give his website a nod of thanks there. I want the language and the feel to reflect my language and the way my students react.

I am making a real commitment to myself to get out of the way more in 2014. There was a lovely piece that was tweeted out by an old colleague named Gayle Allen. It was called ‘Becoming Invisible in My Classroom‘ and it has given me a renewed sense of mission here. I am also thinking of my visit to SLA last year for EduCon. I walked into a physics class and could not figure out who/where the teacher was for a few minutes. I was amazed and humbled. Need to hold on to that feeling…

So, I’ll start on Monday with a bit of leading/lecturing to set the stage. I’ll give them an assignment to play a bit with Desmos Monday night, then we hit the lab. I’ll be giving an update on how it goes. Wish me luck!

PS – I have a fun Desmos file to look at for them as well. You can see it here. It’s fun to animate the slide and see what happens.

Time to Reflect and Regather

With the beginning of my Christmas vacation only 24 hours away now (one class and then a long committee meeting today followed by a committee meeting tomorrow morning) this feels like a natural time to think about what has gone right this academic year and what can be better in the next calendar year.

I was hired at my school four years ago to teach four sections a day and to serve as department chair. For a variety of reasons, during the first three years I taught five classes per day during 8 of the 9 trimesters. This year I started off with five classes again and now I am finally down to four per day. I have had as many as four different preps in the past, but now have two. The difference in energy level required during the day is stunning. I like to think that I was doing alright in the past. I am optimistic that I am a better teacher (day by day) now. I am able to spend more time and energy planning at night and in the morning. I have found some fun activities and problems to explore. I feel sharper and fresher when we have discussions in class. However, there are some big issues I want to address.

Before the year began I purchased a marble notebook for each of my stats students. I wanted them to have more regular feedback from me and I envisioned taking time about once a week to give them the last ten minutes of class to work on a problem attached in their notebook as a formative, non-graded assessment. My hope was that we’d look at it the next day and by the time graded assessments rolled around, they would have a clearer understanding of what they understand. I’d have a clearer sense of what I needed to explain in better detail, or at least have a sense of what points needed reinforcement. What I discovered was that ungraded meant unimportant to most of my students. Even those who were earning A’s by the time of a graded quiz or tests were turning in blanks or sheer nonsense. Frustrated by the time and energy I was spending with little obvious return, I stopped doing this after four or five rounds. I need to grow up, deal with the disappointment, explain myself better, and do what I believe is the right thing to do.

We teach AP Calculus BC as a follow-up to AP Calculus AB. Consequently, we have nowhere near the calendar pressure of other AP courses. I need to take greater advantage of that freedom. In 2014 I want to devote one day per week to some combination of games, puzzles, and cooperative problem sets. These are the sharpest math minds at our school and they deserve to be challenged regularly. We instituted this curricular decision so that we would have more time for reflection for our students. I know that many of them would have been successful by and measurable metric if they raced their way through this curriculum in one year. However, I am convinced that they benefit from the time we allow them to revisit ideas and explore them more deeply. They benefit from some space to breathe and reflect. I do not want to restrict that time and energy only to problems from the AP curriculum. There is a larger world of ideas to play with. the game of Set, the game of Ultimate tic-tac-toe, visual patterns. These are all things I talk about, I visit these sites, I advocate for these activities. However, I too often fall into the trap of just turning the page in our text and worrying about the next test or quiz. They deserve better.

 

So, even though it’s early these are my New Year’s Resolutions. I have always believed that I am more likely to carry through with them if them if they are public so I am putting myself on notice.

The Beauty of Community

It’s not math that is on my mind tonight – at least not here, been tweeting a bit looking for help!

My wife just recently started a new job. Rather than working at the same school where I work and where we live, she is now working at a Catholic college about a mile away or so. Yesterday morning we took the kids with us to a breakfast with Santa. I was so charmed by the co-workers I met, by the good cheer in the room, by the warmth of the people who interacted with my kids – especially my 4 year old little girl. It was a great way to start our day. It was snowing when we went, a gentle snowfall that ended up lasting all day and into the night. Being a Florida boy, I don’t have much inherent appreciation for the whole white Christmas thing, but I was taken by it yesterday.

Tonight we had our community Christmas dinner at my school. We eat twice a week with students at a sit down mean we call family style. The students rotate through and receive new assignments every three weeks. Our res life director tries to switch it up so there are boys and girls at each table, kids from different dorms, friends and strangers. I really appreciate these dinners for a variety of reasons. Tonight we dressed up, had a lovely meal prepared by our hard working dining staff, had kids sing holiday songs and had a student play Santa for all of the faculty kids (there are about 20 of them on campus!) One of the dining hall staff buys individual gifts for all the campus kids, the students sit and watch the Santa festivities and coo over the youngest ones. It’s a pretty magical night really. We have four more days left – if the weather allows us to! – and this is just one of the terrific traditions of our boarding community. I’m going to go to sleep feeling happy and peaceful tonight.

 

Looking Ahead

Excited about news at my school. We’re working on a job description for a fall 2014 hire. Looking to bridge between the math and science departments. We are hoping to find someone to teach some upper level math and work with our freshman in our STEM foundations class. Our school has made commitments to cross curricular work in a couple of important courses. We have a two period class that is co-taught by our history dept chair and our English dept chair called Seminar in American Studies. We have a course called Creative Spirit that is taught by our Performing Arts dept chair and one of our studio art teachers. So, we know how to make this work. Our next challenge is to define a job for a teacher who will work with both our math curriculum and our science curriculum. We are in our first year of an exciting 9th grade course called STEM Foundations and as math chair, I am excited to see and hear what they are up to. I know we are going to continue moving forward in this direction and this hire will be an important one. Who out there is interested in being part of this project?