teaching philosophy

How Good is Your Model (Angry Birds) Part 2 – Refining my process

A year ago, I wrote about my attempt to integrate Angry Birds as part of my quadratic modeling unit. I was certainly not the first, and there have been many others that have taken this idea and run with it. This is definitely a great way of using the concept of fitting parabolas to a realistic task that the students can have fun completing.

As I said a year ago, however, the bigger picture skill that is really powerful with modeling is making do with less information. I incentivized my students last year to come up with a model that predicts the final location of the collision of a bird earlier than everyone else. In other words, if Thomas is able to predict the correct final location with ten seconds of data, while Nick is able to do so with only seven, Nick has done the better job of modeling. I did this by asking the students to try to do this with the earliest possible frame in the video.

This time, I have found a better way to do this. Five videos, all of them cut short.
I’m asking the students to complete this table:

The impact ratio is defined as the ratio of the orange line to the yellow line, as shown in this image:

Each group of students will calculate the ratio for each video using Geogebra. Some videos reveal more about the path than others. I’ll sum the errors, rank the student groups based on cumulative error, and then we’ll have a great discussion about what made this difficult.

The sensitivity of a quadratic (or any fit) fit to data points that are close together is what I’m targeting here. I’ve tried other techniques to flesh this out in students before – I still get students ‘fitting’ a table of data by choosing the first two or three points. I’m hoping this will be a bit more interesting and successful than my previous attempts.

Trimmed Angry Bird Videos:

[wpvideo Em5oyDGw]
[wpvideo oJJml7i5]
[wpvideo gf2zXikv]
[wpvideo EY77wnKI]
[wpvideo DENYt0RX]

Telling students not to procrastinate solves the wrong problem.

In seeing my students working to prepare for semester exams over the last week, I have spent some time thinking about the advice I give students about how to manage the stress associated with this time of year. The reality for them (and for me, for that matter) is that there is a lot going on right now. A quick rundown of my obligations: exams have to be written, assessments marked, comments graded, recommendations written, assignments double-checked for accuracy in the grade-book…this doesn’t even mention the non-school related tasks on my plate. Some tasks I spread out over a few days usually in order to avoid the non-linear way that unpleasantness increases as a deadline approaches. Some tasks have to be done last minute, and there’s no way around them.

When I see students cramming and working feverishly to get things done, part of me wants to channel the oft repeated (and nonsense) advice that ‘if you had started earlier, you wouldn’t have this problem.’ And then I stop. Grand scheme of things, this is not really helpful. You don’t tell someone that just cut off his finger that doing so was a dumb idea. The important part is managing the situation in a way that balances all of the relevant costs and benefits to maximize the overall outcome. The biggest problems my students have is not (only) that they put things off. It’s that they think they can effectively manage the stress that comes with it by following some common, but misdirected principles. Here are my categories of guiding principles:

Ways students foolhardily trick themselves into doing what they do:

Principle of Work-Equivalence: As long as I am working on something I need to be working on, I am using my time effectively. After all, it all needs to get done, so why not just pick something and work on it?
Principle of Longevity: I’ve been doing this school thing for long enough – I know this has worked for me in the past, so I’m going to keep doing it. This comes from a major trend that I see with my students at the moment. Even more frightening is that the older they are, the better they think they are at managing things during stressful times. The way I see it, the opposite is true.
Principle of Education through Suffering: If I am not suffering as I get things done, I am not working hard enough. Carrying around stacks of papers, losing sleep, having unproductive (but fun) study parties seems to be par for the course. It certainly isn’t something that disappears after high school graduation.
Principle of Poor Prioritization: I know what I really should be spending my time doing, but this other mindless task seems like a much better use of my time. This is not about online distractions, though that is a big factor for all of us. This is when a student decides to white out all of the mistakes in his/her notebook from throughout the semester because he or she thinks this will make studying easier. Rewriting notes can be a useful exercise if it involves some sort of processing/summarizing/grouping of ideas. Simply copying them over is a passive activity that feels like it should help, but probably is less productive than other tasks.
Principle of Confidence: I’m going to work on the things I am already good at doing to boost my confidence. This will better make me able to tackle the things I don’t understand. I’ve had conversations with students that do know what they need to work on, but avoid those things like the plague because learning new things is difficult. Revisiting strengths is occasionally a good idea, but again, it is not truly productive.

Figuring out how to shake students of following these guidelines is really what we need to work on. We need to not just just lecture them about getting organized, planning out stressful times, taking effective breaks, and being deliberate about all of these processes, but model how to do these things. My question is one of practicality though – what are the best ways to do this? Is the best way integrated as part of existing courses? (My gut says yes.) Is it about going back to pencil and paper planners? Is it about using technology to help with reminders, calendars, etc?

The thing that I find most difficult about discussing this is that it always turns into a conversation about avoiding procrastination. I agree that this would help…if our students weren’t already told this hundreds of times per year. The design problem that needs to be solved is: given that our students are stressed, how do we help them work through it? Furthermore, how do we make the most of our own experience as adults working through stress, but deliver that experience in a way that doesn’t start by telling students what they believe is wrong?

Crowdsourcing a learning-to-teach framework

After a good conversation with a friend that is getting started with teaching, I was thinking a bit about the process of learning to teach. Things that I obsessed about as a first year teacher come much more naturally now, but if you asked me what I needed to learn in the beginning, I would have babbled on like an idiot. Knowing what to focus on when everything is so new, not to mention feeling you aren’t good at any of it, you understand why it is so easy for students to shut down when we ask them to ‘be responsible’ without helping them understand what we mean. Our job as teachers is to provide students with a framework that will help them be successful in learning what we teach them.

You would hope that guidance in this would be an essential component of teacher preparation programs, but it often doesn’t, particularly in cases where observation is a box to be checked, not a pathway to improvement. There are many frameworks for observation, but I haven’t seen one that specifically gives guidance (or even a curriculum?) for what new teachers should be looking for when in a mentor teacher’s classroom. Most of the observation forms I’ve seen are in evaluating teachers for teacher quality. When I go to watch a colleague, I’m thinking about how I’m going to use what I see to improve what I do, not how to make them a better teacher. I know what I am looking for because I’ve had the keys to my classroom for a little while.

C’mon internet, let’s work together to create this and help our newbies. We were all new to this once, and there’s a lot that we may not realize we are thinking about after pulling out our hair and having teaching nightmares for so long. (Do they ever stop?)

To be clear, the goal is to start conversations between new teachers and their mentors, not put new teachers in a position to evaluate those who are being observed. We want to make the most of this time that is probably the most valuable teacher preparation tool outside of standing in front of a class yourself.

I’ve put a document designed to compile these ideas here:

So you’re a new teacher. What should you focus on this week?

Please add to the list and snarky-up the title. There may even be a better way to organize this so that it isn’t a big list that again serves only to intimidate. Maybe along the lines of Emergency Compliments?

Who’s gone overboard modeling w/ Python? Part II – Gravitation

I was working on orbits and gravitation with my AP Physics B students, and as has always been the case (including with me in high school), they were having trouble visualizing exactly what it meant for something to be in orbit. They did well calculating orbital speeds and periods as I asked them to do for solving problems, but they weren’t able to understand exactly what it meant for something to be in orbit. What happens when it speeds up from the speed they calculated? Slowed down? How would it actually get into orbit in the first place?

Last year I made a Geogebra simulation that used Euler’s method to generate the trajectory of a projectile using Newton’s Law of Gravitation. While they were working on these problems, I was having trouble opening the simulation, and I realized it would be a simple task to write the simulation again using the Python knowledge I had developed since. I also used this to-scale diagram of the Earth-Moon system in Geogebra to help visualize the trajectory.

I quickly showed them what the trajectory looked like close to the surface of the Earth and then increased the launch velocity to show what would happen. I also showed them the line in the program that represented Newton’s 2nd law – no big deal from their reaction, though my use of the directional cosines did take a bit of explanation as to why they needed to be there.

I offered to let students show their proficiency on my orbital characteristics standard by using the program to generate an orbit with a period or altitude of my choice. I insist that they derive the formulae for orbital velocity or period from Newton’s 2nd law every time, but I really like how adding the simulation as an option turns this into an exercise requiring a much higher level of understanding. That said, no students gave it a shot until this afternoon. A student had correctly calculated the orbital speed for a circular orbit, but was having trouble configuring the initial components of velocity and position to make this happen. The student realized that the speed he calculated through Newton’s 2nd had to be vertical if the initial position was to the right of Earth, or horizontal if it was above it. Otherwise, the projectile would go in a straight line, reach a maximum position, and then crash right back into Earth.

The other part of why this numerical model served an interesting purpose in my class was as inspired by Shawn Cornally’s post about misconceptions surrounding gravitational potential and our friend mgh. I had also just watched an NBC Time Capsule episode about the moon landing and was wondering about the specifics of launching a rocket to the moon. I asked students how they thought it was done, and they really had no idea. They were working on another assignment during class, but while floating around looking at their work, I was also adjusting the initial conditions of my program to try to get an object that starts close to Earth to arrive in a lunar orbit.

Thinking about Shawn’s post, I knew that getting an object out of Earth’s orbit would require the object reaching escape velocity, and that this would certainly be too fast to work for a circular orbit around the moon. Getting the students to see this theoretically was not going to happen, particularly since we hadn’t discussed gravitational potential energy among the regular physics students, not to mention they had no intuition about things moving in orbit anyway.

I showed them the closest I could get without crashing:

One student immediately noticed that this did seem to be a case of moving too quickly. So we reduced the initial velocity in the x-direction by a bit. This resulted in this:

We talked about what this showed – the object was now moving too slowly and was falling back to Earth. After getting the object to dance just between the point of making it all the way to the moon (and then falling right past it) and slowing down before it ever got there, a student asked a key question:

Could you get it really close to the moon and then slow it down?

Bingo. I didn’t get to adjust the model during the class period to do this, but by the next class, I had implemented a simple orbital insertion burn opposite to the object’s velocity. You can see and try the code here at Github. The result? My first Earth – lunar orbit design. My mom was so proud.

The real power here is how quickly students developed intuition for some orbital mechanics concepts by seeing me play with this. Even better, they could play with the simulation themselves. They also saw that I was experimenting myself with this model and enjoying what I was figuring out along the way.

I think the idea that a program I design myself could result in surprising or unexpected output is a bit of a foreign concept to those that do not program. I think this helps establish for students that computation is a tool for modeling. It is a means to reaching a better understanding of our observations or ideas. It still requires a great amount of thought to interpret the results and to construct the model, and does not eliminate the need for theoretical work. I could guess and check my way to a circular orbit around Earth. With some insight on how gravity and circular motion function though, I can get the orbit right on the first try. Computation does not take away the opportunity for deep thinking. It is not about doing all the work for you. It instead broadens the possibilities for what we can do and explore in the comfort of our homes and classrooms.

Simulations, Models, and the 2012 US Election

After the elections last night, I found I was looking back at Nate Silver’s blog at the New York Times, Five Thirty Eight.

Here was his predicted electoral college map:

…and here was what ended up happening (from CNN.com):

I’ve spent some time reading through Nate Silver’s methodology throughout the election season. It’s detailed enough to get a good idea of how far he and his team have gone to construct a good model for simulating the election results. There is plenty of description of how he has used available information to construct the models used to predict election results, and last night was an incredible validation of his model. His popular vote percentage for Romney was predicted to be 48.4%, with the actual at 48.3 %. Considering all of the variables associated with human emotion, the complex factors involved in individuals making their decisions on how to vote, the fact that the Five Thirty Eight model worked so well is a testament to what a really good model can do with large amounts of data.

My fear is that the post-election analysis of such a tool over emphasizes the hand-waving and black box nature of what simulation can do. I see this as a real opportunity for us to pick up real world analyses like these, share them with students, and use it as an opportunity to get them involved in understanding what goes into a good model. How is it constructed? How does it accommodate new information? There is a lot of really smart thinking that went into this, but it isn’t necessarily beyond our students to at a minimum understand aspects of it. At its best, this is a chance to model something that is truly complex and see how good such a model can be.

I see this as another piece of evidence that computational thinking is a necessary skill for students to learn today. Seeing how to create a computational model of something in the real world, or minimally seeing it as an comprehensible process, gives them the power to understand how to ask and answer their own questions about the world. This is really interesting mathematics, and is just about the least contrived real world problem out there. It screams out to us to use it to get our students excited about what is possible with the tools we give them.

Automating conference scheduling using Python

I’ve always been interested in the process of matching large sets of data to a set of constraints – apparently the Nobel committee agreed this past week in awarding the economics prize. The person in charge of programming at my school in the Bronx managed to create an algorithm that generated a potential schedule for over four thousand students given student requests and needs. There was always some tweaking that needed to be done at the end to make it work, but the fact that the computer was able to start the process always amazed me. How do you teach a computer to do this sort of matching in an efficient way?

This has application within my classroom as well – generating groups based on ability, conflicting personalities, location – all complex situations that required time and attention to do correctly. In the end though, this is the same problem as arranging the schedules. It’s easy to start with a random arrangement and then make adjustments based on experience. There has to be a way to do this in an automated way that teaches the computer which placements work or do not. Andy Rundquist does this using genetic algorithms – I must know more about how he does it, as this is another approach to this type of problem.

This became a more tangible challenge for me to attempt to solve last year when I saw that the head of school was doing the two days of parent-teacher conference scheduling by hand. This is a complex process given the following constraints he was working to fulfill:

Parent preferences for morning/afternoon conference times.
Consecutive conference times for parents that had siblings so that the amount of time parents had to wait around was minimized.
Balanced schedules between the two days for all teachers.
Teachers with children had breaks in their schedule to attend conferences of their children.

This was apparently a process of 4 – 5 hours that sometimes required starting over because he discovered that the schedule he had started putting together was over constrained and could not meet all requirements. During this process, however, he had figured out an algorithm for what was most likely to work. Schedule the families with the largest number of children first, and work down the list in order of decreasing size. Based on the distribution of younger vs. older children in the school, start by scheduling the youngest children in a family first, and move to the older ones. Save all families with single children for last.

Hearing him talk about this process was interesting and heartbreaking at the same time – he works incredibly hard on all aspects of his job, and I wanted to provide some way to reduce the requirements of at least this task on his schedule. I was also looking for a reason to really learn Python, so this challenge became my personal exercise in problem based learning.

It took a while to figure out all of the details, but I broke it down into stages. How do you input the family data based on how it is already stored by the front office? (I didn’t want to ask the hard-working office staff to reformat the data to make it easier for me – this was supposed to make things easier on everyone.) How do you create a structure for storing this data in Python? How do you implement the algorithm that the head of school used and balance it with the idea of fairness and balance to all families and teachers?

Over the following few months, I was able to piece it together. It was, needless to say, a really interesting exercise. I learned how to ask the right questions that focused on the big picture needs of the administration, so that I could wrestle with the details of how to make it happen. The students learned that I was doing this (“Mr. Weinberg is using his robots to schedule conferences!”) and a few wanted to know how it worked. I have posted the code here as a gist.

I put in more than the 4-5 hours required to do this by hand. It was a learning experience for me. It also paid serious dividends when we needed to schedule conferences again for this year. We wanted to change the schedule slightly to be one full day rather than two half days, and it was a simple task adjusting the program to do this. We wanted to change the times of conferences so that the lower and upper schools had different amounts of time for each, rather than being a uniform twenty minutes each. (This I was not able to figure out before we needed conferences to go out, but I see a simple way to do it now.)

The big question that administration was about the upper school conferences. Last year we had seven different rooms for simultaneous conferences, and the question was whether we could reduce the number to five. I ran the program with five rooms a number of different times, and it was unable to find a working schedule, even with different arrangements and constraints. It was able to find one that worked with six rooms though, which frees administrators from needing to be in individual conference rooms so that they can address issues that come up during the day. Answering that question would not have been possible if scheduling was done by hand.

The question of using computers to automate processes that are repetitive has been in my head all this year. I’ve come to recognize when I am doing something along these lines, and try to immediately switch into creating a tool in Python to do this automatically. On the plane during a class trip last week, we needed to arrange students into hotel rooms, so I wrote a program to do this. I used it this week to also arrange my Algebra 2 students in groups for class. Generating practice questions for students to use as reassessment? I always find myself scrambling to make questions and write them out by hand, but my quiz generator has been working really well for doing this. Yesterday I had my first day of generating quizzes based on individual student needs.

The students get a kick out of hearing me say that I wrote a Python program to do XXX or YYY, and their reactions certainly are worth the effort. I think it just makes sense to use programming solutions when they allow me to focus on more important things. I have even had some success with getting individual students to want to learn to do this themselves, but I’ll write more about that later.

Mislabeling inquiry – a brief rant

I’m a big believer in the power of inquiry based learning. This is both of my roles teaching math and physics. As often as possible, I have my students make observations, ask questions, make a hypothesis or mental model to describe what is being observed, and then test that model against new situations to see how well the model describes them. It goes along with why kids like science in the early years – you get to play with stuff, cool stuff, and try to figure out how it works.

I was looking at an online resource for teaching science that says it uses a step by step inquiry approach, and was naturally excited to see what was involved. This is the outline of what it includes for its lesson on heat transfer.

It shows an interesting set of rock formations and explain how they were formed through the transfer of energy.
It asks what happens when a glass of ice water is submerged in a tub of warmer water. Students can submit their open ended responses using a text box for (presumably) the teacher to read.
It shows four clear explanations for what is going on, and asks students to choose one. The teacher can see which ones students pick overall.
Students can explain their reasoning for picking an explanation, or perhaps explain why the others are not correct. It isn’t clear whether these explanations go back to the teacher or not.
Students then are given a set of some specific resources, mostly text, but including one video and an image to ‘collect data’ on their hypothesis.
Students then take a quiz to assess their understanding based on reading the short explanations in the previous step.
Students talk about what their hypotheses were, and how the information they found either supported or refuted each of the four statements.
Students describe their new understanding of heat to a text box. Sadly, it does not talk back.
In case it wasn’t clear, the web page then tells the students what conclusion they should have made in the preceding activity. This is accessed through a convenient button that says ‘Display Conclusion’.
Students are asked one more multiple choice question, and are then told they can explore other things. It makes suggestions, and then gives the slightly hopeful statement that they can also choose something they want to explore.

I apologize for getting slightly sarcastic at the end, but this really got under my skin. I have a real problem with educational solutions that help students learn science by looking at a screen with right answers on it. It perpetuates the idea that that is what science is: right answers, a whole slew of them, and you have to collect them all, or you are bad at science.

I get that this is better than students sitting and listening to teachers telling them all the answers. I see that the students are made to be slightly more active and have to find the answers in the reference materials on the website. Of course, that is notably better than chalk and talk.

I just found myself shuddering the whole time because at no point in the online lesson is the suggestion made to actually perform an experiment.

The real power of inquiry is not just getting students to go out and find the answers themselves and then take a multiple choice exam to see what they learned. It is about getting to struggle with open-ended questions. Deciding what to measure, or minimally, making A measurement. I get that the goal of this is to create something that can scale to a classroom of thirty students and give them something better than lecture. I just have a problem with justifying it by saying it’s better than the alternative.

Why SBG is blowing my mind right now.

I am buzzing right now about my decision to move to Standards Based Grading for this year. The first unit of Calculus was spent doing a quick review of linear functions and characteristics of other functions, and then explored the ideas of limits, instantaneous rate of change, and the area under curves – some of the big ideas in Calculus. One of my standards reads “I can find the limit of a function in indeterminate form at a point using graphical or numerical methods.”

A student had been marked proficient on BlueHarvest on four out of the five, but the limit one held her back. After some conversations in class and a couple assessments on the idea, she still hadn’t really shown that she understood the process of figuring out a limit this way. She had shown that she understood that the function was undefined on the quiz, but wasn’t sure how to go about finding the value.

We have since moved on in class to evaluating limits algebraically using limit rules, and something must have clicked. This is what she sent me this morning:
[wpvideo 5FSp5JDn]

Getting things like this that have a clear explanation of ideas (on top of production value) is amazing – it’s the students choosing a way to demonstrate that they understand something! I love it – I have given students opportunities to show me that they understand things in the past through quiz retakes and one-on-one interviews about concepts, but it never quite took off until this year when their grade is actually assessed through standards, not Quiz 1, Exam 1.

I also asked a student about their proficiency on this standard:

I can determine the perimeter and area of complex figures made up of rectangles/ triangles/ circles/ and sections of circles.

I received this:
…followed by an explanation of how to find the area of the figure. Where did she get this problem? She made it up.

I am in the process right now of grading unit exams that students took earlier in the week, and found that the philosophy of these exams under SBG has changed substantially. I no longer have to worry about putting on a problem that is difficult and penalizing students for not making progress on it – as long as the problem assesses the standards in some way, any other work or insight I get into their understanding in what they try is a bonus. I don’t have to worry about partial credit – I can give students feedback in words and comments, not points.

One last anecdote – a student had pretty much shown me she was proficient on all of the Algebra 2 standards, and we had a pretty extensive conversation through BlueHarvest discussing the details and her demonstrating her algebraic skills. I was waiting until the exam to mark her proficient since I wanted to see how student performance on the exam was different from performance beforehand. I called time on the exam, and she started tearing up.

I told her this exam wasn’t worth the tears – she wanted to do well, and was worried that she hadn’t shown what she was capable of doing. I told her this was just another opportunity to show me that she was proficient – a longer opportunity than others – but another one nonetheless. If she messed up a concept on the test from stress, she could demonstrate it again later. She calmed down and left with a smile on her face.

Oh, and I should add that her test is looking fantastic.

I still have students that are struggling. I still have students that haven’t gone above and beyond to demonstrate proficiency, and that I have to bug in order to figure out what they know. The fact that SBG has allowed some students to really shine and use their talents, relaxed others in the face of assessment anxiety, and has kept other things constant, convinces me that this is a really good thing, well worth the investment of time. I know I’m just preaching to the SBG crowd as I say this, but it feels good to see the payback coming so quickly after the beginning of the year.

Flipping, Week 1: Stop the Blabbing.

One of my major goals this year is to stop talking so much. Even in my tenth year, I still spend far too much time explaining, questioning, and presenting in front of the class.

The nature of this talking has changed a lot though. When I first started teaching, it was almost all explaining. That’s what I thought good teaching was all about – if you could just explain it the right way, then everyone would get the concept you are teaching, right? A perfect lesson consisting of a perfect development, a perfect explanation of all concepts, perfect example problems, and perfect students. This is how I looked at it during my summer training, and before I got into my classroom.

That changed pretty quickly once I actually got started. Explanations were important, but more important was getting students to be somehow involved. My coaching from administration was focused on good questioning over talking and explaining as a way to do this, so I put a lot of energy into this during my first couple years, and it has since stuck.

The problem is that I am often addicted to asking questions when it’s really time for students to get working and thinking on their own. I can ask questions like crazy, which might have really impressed administrators in my room at one time, but it probably infuriated (and still infuriates) my students to no end. As good of a question I could have asked, they were still just sitting there thinking and not doing any active learning on their own. Furthermore, when the one or two students do answer a question I ask, it isn’t necessarily a real indication of what thinking is going on in the heads of the other students in the room. Students who self select to participate make for a bad sample for the level of understanding in the rest of the room.

The technique to address poor participation (as pushed by my administration in my first couple years) was to cold call students. This is a bad sample in the other direction – pushing a student to go from full listening mode to full participation mode with the rest of students is not an effective way to make dialogue an important part of what goes on in your classroom every day. This is especially the case for students that have poor self esteem about math in the first place. Good conversation is rarely one or two to many. When was the last time you saw twenty people actively involved in a discussion? Why would you really try to get that going in a classroom when it doesn’t work for a room full of adults at a faculty meeting?

In reality, real learning doesn’t look like a kid staring into space pondering a good question. It involves experimenting, testing a theory, writing down an idea and trying it out. It involves taking what you have produced out of your own thinking and getting active and reliable feedback.

Back to my main point – I am attempting this year to put any direct instruction for a particular day’s lesson in two minute video chunks, and limiting the number of these to no more than four per day. A few really nice things have happened since doing this:

I’m putting a lot of thought into exactly which ideas are best left to video or direct instruction, and which ideas will come out through conversation and the activities. Some things are better taught in a big group, I’m not going to deny this to be the case. Some things are better learned one-on-one, and thinking about the difference has really changed the way I organize the activities for the day.
My students are spending a lot less time listening to me, and more time engaged in the videos and what I ask them to do. The videos sometimes include straight example problems, but I try to include a couple things for students to actually do, write down, or talk about with the person next to them as they watch. The conversations that students have during the videos are really rich (and remarkably on-topic), and are so much more useful than having me tell them things while they stare at me.
I can do other things while they are working on the activities I give them. I can see how they are watching the video and make suggestions on things they should be writing down. I can test their knowledge by asking one-on-one questions and get a really good sense for the level of understanding for each student. I can look at quizzes I gave at the beginning of the period, make comments on them, and have a conversation with the students about their work before the end of the period! The quality of my interaction with students has been much higher than before, which has resulted in larger amounts of quality feedback. That is really the goal here.
My ESOL students are loving it. They can take time with vocabulary, which is the hard part for them, and make note of the mathematics concepts at the same time. Some students are using the videos to create their own glossaries in other languages. I’ve always suggested that students do this, but until now, I haven’t seen them do it so well, let alone of their own volition.
The learning in my room is messier than ever before – everyone is at different points and is having different conversations. There are papers all over the place. Students are crowded around tables working and are facing all different directions. Seeing this sort of thing happen my first year would have meant that this was a spent lesson, that I had lost them. Here, it just looks like (and is so far proving to me) good learning experiences for students.

This post is partly in response to one of the new blogger prompts about what I want my students to remember ten years down the road. I really don’t care if they remember how to factor quadratics. Moving to a more student-centered learning model though has made the students in charge of making sure they understand what they are learning. I would love if students tell me in ten years that they learned how to learn something new in my class. Real learning is messy, and actually doing math (not watching), making mistakes and growing from feedback is part of the game. There’s not as much room for that in the more traditional math structure of “I-Do,We-do,You-do” model because the last part is where the real learning happens. Maximizing that part (and simultaneously providing ways for that feedback to happen) is the real meat of teaching, and it’s where I am focusing my energy this year.

Here’s to keeping it going as long as possible!

Standards Based Grading – All in, for the new year

I’ve written previously about wanting to be part of the Standards Based Grading crowd. My quiz policy was based in the idea – my quizzes cover skills only and in isolation, the idea being that if students could show proficiency on the quizzes, then I would know for sure that they had really developed those skills. If they had demonstrated proficiency, but then failed on tests to perform, it was an indication that the problem was seeing all the skills in one place. This is the “I get it in class, but on tests I mess it up” mantra that I’ve heard ever since I first started teaching. My belief has always been that the first clause of that sentence is never as true as the student thinks it is. The quiz grades have typically shown that to be the case.

The thing I haven’t been able to get at is why I can’t get my students to retake quizzes as I thought it compelled them to do. I told them they can get 100%. I reminded them that they just needed to look at each quiz, recognize what they got wrong, and work with me on those specific skills to improve. Then, when they were ready, they could retake and get a better score. Sometimes they do it, but they are always missing either one of those three things. They would retake without looking at the quiz. They would take it knowing what they got wrong, but never asked me to go over the things they didn’t get. There were exceptions, but curiously not enough to impress me.

After really committing to reshaping the quiz grade as a real SBG grade for a unit last year, I saw the differences pretty clearly in how the students went about this aspect of their grade. The standards I expected students to demonstrate were clearly listed in the grade book (fine, Powerschool). The students knew what they needed to work on, and were directly linked to examples and short videos I had created to help them with those specific skills. Class time was spent working around developing those skills, along with some bigger picture ideas to explore separately from the routine skills the standards were centered around for the unit, which was on exponential and logarithmic functions. I was impressed in this short time with how changing this small (15%) portion of the grade changed the overall attitude my students had while they were working with me. It was one step closer to the Montessori style classroom I have always wanted to have while working within the structure of a more traditional program – students walk in knowing what they need to work on, and they get to work. My role becomes more to push them in the way I think they can and need to be pushed. Some need to work on skills, others need to attack context problems and the challenging ‘why is this so’ threads that are usually all teacher driven, but don’t need to be in many cases.

I did some thinking over the last couple of weeks on how I wanted to do things differently, so I wrote up a new grading policy and posted it online. I had renamed my quiz grade to be ‘Learning Standards’, bumped up the percentage by 10% (to 25%), and reduced the homework and classwork components to 5% each, with a portfolio at 10%, and tests to 55%. In sharing my new grading policy with people through Twitter, there were some key comments that really guided my thinking.

Kelly O’Shea pointed out the fact that even with the change, the standards were not a huge part of the grade. Even by cutting classwork and homework into the standards, it still wasn’t good enough:

@emwdx 30% isn’t anything. Standards 90%. Portfolio 10%. Go all in!

— kellyoshea (@kellyoshea) August 12, 2012

A few other people made similar suggestions. John Burk probably put the final nail in the SBG-lite version I thought was safe with this comment:

One problem for getting buy in on SBG is that if it isn’t a big part of the grade, and there are still so many non-sbg things, they might not really understand the rationale for SBG.

If I really believe in the power for Standards Based Grading to transform how learning happens in my classroom, I need to demonstrate its importance and commit to it.

The final result? My grades for Algebra 2/Advanced Algebra, Geometry, Calculus 12, and Physics are going to be 90% Learning Standards, 10% portfolio. I am going to give unit tests, but they are opportunities to demonstrate proficiency on the learning standards. In the case of my AP Calculus students, the grades are still 60% unit tests, 30% standards, and 10% portfolio, primarily because I still will be giving tests that are similar to the AP exam with multiple choice, and free response sections. I also had my first class last year with 100% fives, and am admittedly a bit nervous tweaking what worked last year. That said, I am accepting that this, too, could become a thing of the past.

I am a bit nervous, but that’s mostly because change isn’t always easy. From a teaching perspective, the idea feels right, but it’s not what I’m used to doing. The students sounded pretty cool with it on the first days of class when I introduced the idea though, and that is a major positive. I’ll keep writing as things proceed and my implementation develops – it feels great to know I’m not alone.

I really appreciate all of the kind words and honest feedback from the people that challenged me to think this through and go all in. If I can do nothing else, I’ll pay that advice forward. Cool?

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