Room to Grow

I like this profession because it gives me room to fiddle. There are always new projects to try, or tools to use, or ways to approach a topic. Each crop of students is fundamental in this pursuit of fiddling. Ideas that sound great in my head can look wildly different in practice and I want them to feel like they have a bit of a say in what class structure looks like. Most school districts would agree with this and if you poke around on your district/campus website I'm sure there's a report you can read that has survey results about the things parents/faculty might want to know. The last two years, our district surveys have been composed of parent interviews, online faculty surveys, online students surveys, and paper student surveys. The paper surveys are administered during normal class time to a random class period. There are over 100 questions on it and the students are supposed to answer them relevant to whatever teacher handed it to them. So some students are evaluating their math teachers while others might be sitting in English at the time.

A month or two later we get to see our results compiled into seven categories, about a dozen specific items called out in each category. I find it pretty fascinating, here's what caught my eye:

The Good

Caveat City: This represents answers from only 26 students. School/District numbers were printed for comparison but I have hidden them. Questions were answered on a 1-5 agree/disagree scale.

This is a small sample of the entire result table:

Scouring the internet for lessons is paying off. I don't feel that all my lesson intros generate the kind of inquiry I want, but the number is apparently less than zero. It's something I will continue to iterate. As I scanned the results, all the talk about learning from mistakes, correcting mistakes, getting feedback, etc all scream SBG validation to me. Assessments are your main vector for offering comments on student work. They have be valuable. If you aren't offering a chance to see what they absorb from the comments, why bother leaving them? Second, how do you think I did so well knowing what they understand and don't? Testing roughly once a week is so ridiculously valuable. I have no idea how you can wait two weeks to see if a lesson worked. This year I easily did five or six course corrections because an initial assessment told me that something went horribly wrong.

The Hmmm

I was pleased to see that my methods are having an impact. Reading the results was great to see during that slump we all get at the end of the year when exhaustion rules. But, there were a couple head scratchers:

I have no idea if I'm supposed to be worried about the first one. While school/district numbers are hidden here, I wasn't far off from those averages. I mean, there are some opportunities for them to help me. But designing the activities? Is that something they should do? I always operate under the notion that exploration and presentation methods need to be modeled. Teenagers don't necessarily have an ingrained ability to motivate the study of conic sections. Ironically, this survey was given to a Pre-Cal class about a month before they created their class video, a project done entirely from student input. I don't know, that questions itches for some reason. I have a rant about open-ended projects that this question would complement.

Now the second one, that was scary to see. A huge percentage of the class answered this question neutrally. This tells me that apparently I'm happy without a lot of depth in their answers, or I never stressed explanations enough to skew the results to one side or the other. I really have to spend some time thinking about this one. Do I not have the class time for it or something? Are my assessments too skill based? Are the kids expecting that I am the only provider of absolute truth? Do they think explanation is reserved only for lab reports?

These results are just as valuable to me as my annual appraisal. If you don't value the opinion of the thirty people staring back at you, you're doing it wrong.

The Chaos Game

Towards the end of every school year comes testing week. It can be tough to juggle sometimes. In my school you could be administering the test, holding class as normal, or covering students not taking the test their teacher may be administering that day. Testing blocks also consume a good portion of the day and can leave you with planning difficulties. For instance, I saw my afternoon class periods somewhere around 10 times more than the others due to testing.

No matter how long you've been in the business, it never hurts to have ideas kicking around for days such as this. One I had been holding onto for a while is The Chaos Game. If you look around hard enough, there are some sites with embedded applets that will allow you to simulate thousands of dice rolls. These can be useful as a debrief. I first stumbled on this via Frank's180 Photos website.

Rules are simple. Create an equilateral triangle, assign values 1-2, 3-4, 5-6 to the corners and create a random starting point. Each roll of the die moves your point halfway to the given corner. Do this enough and you get a Sierpinski triangle.

It takes a bit of explaining to get the mechanics down, but after that it's smooth sailing. I dusted off some transparencies, borrowed some dice, and let them roll for about 10 minutes. I gathered up all the transparencies and found the ones where it was clear the student was detailed in their proceedings. When you overlay about 10 of them, you get a nice first order Sierpinski triangle. The kids are baffled as to how this happened.

I should mention I give them this activity with zero hints as to what we're trying to do. If anything, regardless of the lesson, that has been my most successful strategy. Can I cleverly hide the real objective? Can I get them to see the result without having to hand it to them?

So once I reveal the traingle out come the questions. How the heck did this happen? It was totally random. We all had diferent starting points. It's a great discussion about a branch of mathematics that doesn't get much love at the high school level. A few struggle with the idea that there could be order amid such chaos. Then if you get lucky, you can wander down a fractal rabbit hole.

A couple tips: a well-drawn triangle is key, ruler accuracy is key, and small dots are key. Otherwise it will just be a mish mash of points (with some falling in the center which shouldn't happen). I conducted this activity with two Algebra II classes (~60 students), so there were enough good results to succeed.

More on The $1 Textbook

Just about a year ago, I gathered my thoughts and samples into The $1 Textbook, an outline of notebooks and their importance in my classroom. During the 2011-12 school year, I began the year with notebooks and by the second semester had found a way to adapt my planning to incoporate them. For 2012-13, I set out to make every assignment notebook compatible, seek out more group projects, and incorporate the notebook better into the way I present material. Last year was heavy on philosophy, this year I'm back to focus on implementation, impact, and iteration.

What I hope you take away from this is that a simple idea completely changed everything about how I conduct class, from student expectations to my own lesson planning expectations.

Some hours after this was posted on June 11, I teamed up with James Cleveland and Megan Hayes-Golding to present multiple ways of using notebooks for math class. Interactive Notebook Ideas is available as a replay from Global Math Department.

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Implementation

My interest in notebooks began in 2010, and was amplified by Standards Based Grading. SBG necessitates a way for students to track their grades to have the proper impact. A cheap and efficient way for them to do this is in the front of a notebook. It's large enough they won't lose it, and creates a bit of ownership because I'm not having them fill something out I made. As long as they're doing that, there have to be creative ways to exploit all that extra paper they've now got with them.

My specifications for notebooks:

• composition notebooks work great, they consistently last an entire school year, but are not explicitly required
• the first two pages of the notebook are for tracking assessments, all students are required to do this
• all handouts go in the notebook via staples, tape, or glue
• all class work is to be completed in the notebook
• all data tables for group work are to be in the notebook
• students may change notebooks at semester or in the event they lose it
• students may store the notebook in the room at all times if they choose
• assessments can be kept in the notebook, but was not required

 How I support my specifications:

• two notebooks per class period are raffled off at the start of the school year
• three staplers, two tape dispensers, 30 safety scissors, and 30 glue sticks are always at the front of the room
• buckets are provided for storage and labeled by class period
• SBG charts are worth 10%, group work 10%, and class work 20%
• explicit class time is used to begin SBG charts at the start of each semester, this lasts through Test 3
• SBG charts are checked every 3 weeks
• all handouts are small enough to fit in a composition notebook, 1/2 sheets or 1/3 sheets
• all handouts are titled with the matching SBG topic name as best as possible
• class work is graded by quick inspection and marking grades on a clipboard       
  • class work is just that, work done in class, doing work at home is not required, though my methods are not incompatible with homework
  • typical class work grades are 0, 50, 70, 80, 90, 100; not much nitpicking is done
  • class work is checked for completion, not accuracy
  • class work is reviewed as a group to check for understanding, students are responsible for giving themselves feedback on it
  • class work is sometimes checked in batches "show me work from today and yesterday please"
  • class work is not necessarily graded 
• random "notebook health inspections" are conducted to catch students who are being lazy about taping/gluing/stapling
• work presented as a poster has been done previously or simultaneously in the notebook

 Other than some students being critical of my ability to cut 1/2 sheets and 1/3 sheets, this structure works pretty well. I don't grade every bit of class work because I don't want grades to be their sole motivation for getting it done. I check often enough to keep them thinking about it but not necessarily be fearful. From time to time in Algebra II I will do a bit of a crackdown if a class is being bad about completing their work. It varies every grading period but if I give out 8 assignments I might check 4.

From time to time a student will claim their notebook was stolen. It's almost always at the bottom of the wrong classes bucket. Maybe 2 out of 150 will legitimately disappear during a school year.

Impact

I conducted quickie exit interviews of all my Algebra II students to gauge their opinions on some things. Algebra II is a great group to ask because the age and skill rnages are huge. First, I had them rate their ability to keep up with the notebook on a scale of 1 to 10. Students typically grade themselves harshly, and 7/10 was the most common. Only a couple said 10 (and I agreed) with a sprinkle of 8s and 9s. The followup related to being required to keep the notebook. Would they have kept their class work organized if not given a structure to do so? Easily half (~30) said no. Others said they would, but it wouldn't be quite as organized, they'd have a folder with all their papers in it or something. All students rated the notebook as a reliable resource, but I'm not sure I asked that question well enough (it was a bit leading). Any volunteers to help me create a double blind survey?

There are two big takeaways from interviewing these students. One, organizational structure is not intuitive. As teachers, our experience is often a trap. We've been organized indiviuals for decades, so the solutions are obvious. We forget what it's like to be 15/16/17. You learned important lessons in organization from SOMEONE. Hey, now you're that someone. Teach before you expect. Second, 60 students rated their ability to adhere to a dictated structure at 6/10 or higher. All 60 of them are not A students. Many of them were C/D students. But were it not for this organizational intervention, how many of them are your D/F students who never write anything down and lose everything they're given? A simple little notebook can create a dramatic difference in the performance you get from students. The top will always be the top, the middle raises their game, and the bottom isn't so bottom anymore.

Professionally, I am forced to consider the notebook as a resource when planning my lessons. Assignments got shorter and more focused to fit the size constraints. I wasted a lot less copier paper. Matching activities are easier to implement because they could be relevant portions of notes, not lost in a folder or in the trash can. Group activities are no brainers. I'm not creating elaborate data tables and running off 100 copies, I'm sketching out important things to write down and THEY make the data table. I can incoporate reference tables (such as how to identify a hyperbola vs. an ellipse) into my presentations and feel like it will get used. I quit wasting time on test reviews because my assignments ARE the review.

Iteration

There is always room for improvement. Some considerations for next year:

• increase the size of the notebook buckets, it got a tad cluttered
• a lot of students admitted they did not reflect much on the SBG sheets
• a backup of SBG scores need to be kept by me somewhere
• tests need to be kept in a makeshift pocket in the notebook
• be a little more critical of class work completion
• keep a stockpile of spares, a few students lingered for months under the pretense of buying new notebooks

Overall, I love the effect of notebooks. It sets a tone that work is expected from students every day, they are accountable for that work, and that work is there to help them in the future. And there's no way they can argue we never do anything, there are 30 kids keeping records of what we do.

Wrap Up

The soccer games are all over. The bells are done ringing. The papers are all graded. The seniors are all graduated.

2012-13 is over and it was one of the most demanding from start to finish, but I never felt more comfortable from start to finish. Highlights:

• Mentored a student teacher, helped him get a job
• Taught a personal record 211 students (147 math, 64 athletics)
• Learned to drive a school bus
• Went 10-4-4 in 9th grade soccer, 2-3-1 in 8th grade soccer (37-21-17 lifetime)
• Taught 4 staff development sessions, presented to people who paid money to be there
• Documented almost every day
• Helped SBG gain traction in AP Calculus, AP Chemistry, Chemistry, Algebra II, Pre-Calculus, Geometry, and Math Models
• Built a small army of 15 iPads
• Produced 3 class movies
• Co-hosted Global Math with Kate Nowak to a record crowd
• Handed out over a thousand stickers
• Used hundreds of glue sticks and straws
• Produced a sidewalk chalk masterpiece

Last but certainly not least, the old projector was retired. Through administrative support, the large interactive whiteboard at the front of my room has been replaced with a 60" HDTV. Brighter picture, higher resolution, no fan noise, and the last piece in a slowly built puzzle. Many a student has asked "you don't use the ActivBoard anymore?" (ignoring the fact that I never used it as intended with the projector) before getting a look from me and realizing "yeah, this is better."

It showed up a little after Spring Break, and was accompanied by a cable upgrade. Previously I had a 8-port VGA splitter and miles of VGA cable snaking in the room. Everything has gone digital. Widescreen monitors at my desk and podium, and HDMI cables all routed to this little beast (which is ice cold to the touch despite all the work it does):

You say I'm crazy. I love being crazy. Happy Summer.

180 Photos

The premise is simple. Document something about your classroom every day. For the entire school year. I heard about the idea from Frank Noschese, who ran through it for the 2011-12 school year. It can be as simple as just taking a picture or as a way to build some writing chops by taking a picture and describing the classroom activity that went along with it. I set a goal this of completing the task myself to see what it would be like.

By February, it was pretty clear this was the best thing I could've done and one of the best aspects of the school year. There are a lot of little things that kick in once you get going with this kind of project. At first I had some issues remembering to take photos and I missed some days here and there. I also did not recenter my website around the idea, but added it as a complementary feature. Even without writing about each individual day, the photos are a fantastic reference for remembering the lessons I do want to write up in detail. Having to take a photo everyday also makes sure that the lessons/ideas I want to write about have plenty of visuals. In the day of Dropbox apps on smartphones, photos can be on your computer waiting before class ends.

The absolute biggest aspect of the project though, is that it inspires ideas worth documenting. If your classroom is full of repetitive notetaking and worksheets, this sort of thing is going to make that clear pretty quickly. After a while, half the fun of planning some of my projects this year is the excitement of knowing I get to document it and put it in my gallery. And now as I head into the summer, I remember so much more about what we did this year. I had a goal of taking advantage of each classes' weekly block day as much as possible, and now I have a ton of pictures to refer back to when analyzing the success of an activity.

Secondary bonus, if you have a structured staff appraisal system, a 180 Photo Gallery is the perfect resource to raid when it comes time to show off how you implemented target strategies, technology, or prove to people that your room is as fun as everyone has heard.

The 180 Photo movement got some traction this year. I was so happy to participate, if anything for my own ability to learn some more about what my room might look like to others. Though Posterous, the blog mechanism that made this easy, was shut down earlier this year, there are still a lot of teachers sharing the daily life of their rooms.

I encourage you to think about trying some version of the idea next school year.

Iterating - A 3D Graph Failure

I have been experimenting a lot this year. I have felt strong enough with the content this year to start to get exotic with our approaches to different subjects. Those of you who are new teachers and are finally coming up for air will get there soon, I promise. Pre Cal especially has become a bit of a playground for me just because of the flexibility offered by the structure of the course. I cut out a lot of topics, approached others more thoroughly, and tried to take advantage of the block days in our schedule for as many involved tasks as possible. One activity I had seen floating around forever was building 3D graphs out of index cards from the fabulous @mythagon.

The Potential

I found myself with some days to kill between the end of production of our class films and the start of senior activities so I thought it would be a perfect experiment. I gave two classes a crack at it while the third had a go with the planets. After a little fiddling I picked a function that would show a lot of change over a very small z-interval. 

I grabbed a couple index cards and developed an idea for a finished product. The function has a range of 0

Reality though, can be harsh. Organization is such a HUGE part of this process. Your average teenager who has no idea what you have in mind for the finished project is not going to know how to organize themselves for something like this. Especially if they are having a hard time visualizing what's going on in the first place. Knowing this in advance, I tried to be as explicit about organization as possible. We built the blocks first. Then we made 4 piles of 9 for the 4 component x-sections of each slice. Then we looked at the equation. We itemized the list of z-values needed and how that equated to a difference slice. I tried to set a lot of milestones along the way so that no particular group would get behind.

After some extremely lengthy explanations about what exactly was going on, we hit a good production groove. Kids understood what to produce, how many slices needed to be made, and how to prepare them for mounting. They dutifully set about the business of crafting what slowly became a massive effort. Bonus fact: use of desmos had become so routine, that I spent 0 seconds troubleshooting iPad problems.

The Problems

Right around Day 4 (we've invested about 3.5 hours with this thing so far), the problems became all too apparent. Some groups didn't label the tops of the curves and thus cut the wrong section of the cards. Most groups were not very diligent in recreating the curves, ruining any structure to the function. Markers make index cards curl up and flop over. Some groups didn't label the z value for a particular slice and had no idea what was what after a while. After cutting all the material out of the cards, there was hardly any substance left to allow it to stand up, even if the flopping problem wasn't there. Some groups managed to waste a lot of time even getting the simplest infrastructure bits going.

After absorbing all of this, I stopped them. Any group that was close to finished was told to lay their curves out and let me see what they had. The problems I outlined are pretty apparent. Try to tell if these slices have anything to do with one another.

And yet, amid the flaming wreckage of this project, there was one group who not only spent the time to accurately represent the curves, but knew which one was which and was able to produce the desired effect. The cards were still too limp to be mounted vertically, but the pattern was there. The pattern was there!

The Prescription

A lot of teachers are scared of unknown, expensive (timewise) endeavors because potential failure means the concept flops and you now have several days less than you did before. But if you want to improve, failure is something you should embrace. There are a ton of misconceptions and issues hidden in this project that I would've known nothing about if I didn't have 60 kids pilot the idea for me. I could have ironed out the construction issues if I spent the time to build an example, but I lack the visual miconceptions and organizational problems that slammed into them. For instance, I discovered that a 10 minute discussion about 3D printers cleared the whole thing up for a lot of them, and yet I didn't bring it up until we were done.

So what would you do? Throw this idea in the trash? Use it as confirmation that time-expensive projects are risky? No way. This project will be in the regular rotation next year and I found a least a dozen little items that will improve it and get closer to the intended results. Most importantly, I made a point of gathering all the students around and discussing the issues we had and why it didn't work out. You are allowed to tell them you're conducting an experiment and you have no idea what will happen. If anything it serves as an example to them that trying the unknown is the only way to learn.

We closed with some videos about 3D printing, to many oooohs and aaaaahs, and went about our business preparing for the final.

Same Song, Different Verse

Google had a keynote of epic length earlier in the week where they outlined plans for their platforms over the next 6-12 months. Tons of bullet points, lots of promise, though if last year is any indication, most of their hopes and dreams won't play out like they wanted. Deep within the 3h 25min feature film was 6 minutes about captial E Education. If you cue up the full keynote, the education part runs from 1:14:00-1:20:00.

In the brief section they outline a problem they encountered: teachers find there is a gap between what technology is capable of and what is practical for school environments. Google sees this as an opportunity to help them out. Their solution has two main ideas: fast deployment, and curated content.

The Promise

From Google Play for Education:

After finding apps they want to use, educators can push them instantly to student devices over the air. They can send the apps to individuals or groups of any size, across classrooms, schools, or even districts.

In the keynote video, there is a short sequence where an app is located via desktop browser, a Google account group is specified, funds are deducted as necessary from a district account, and the app is marked for deployment to the specified account group. Details are fuzzy on how this will look in practice. The implication is that student devices signed in to a privledged account will be pushed new content all at once. Should this work out, it would definitely beat the current way to get an iPad up and running. Apple has tools for mass deployment, but it's really intended for corporations, you have to have a business level iTunes account. It is not friendly to a situation where the teacher is seen as the primary maintenance person.

Second, they hint at a special section of the Google Play store with curated education content:

With Google Play for Education, teachers and administrators will be able to browse content by curriculum, grade, and standard — discovering the right content at the right time for their students. If your app offers an exciting new way to learn sixth grade algebra, we'll make it easy for math educators to find, purchase, and distribute your app to their classes.

I'm not sure if this is going to have the desired effect. Curated lists of "great education apps" are numerous. A search for "education iPad apps" yields a ton of "Top 12 Must Have..." or "20 Apps Teachers Can't Live Without" articles. Plus, Apple even carved out a chunk of their store for iTunes U to give us...hundreds of videos of lectures?

The Practicality

Google's first issue is one I hope they solve and Apple notices. Distribution and deployment should not be as difficult as it is currently. iPads are not what I would consider difficult to get up and running, but I'm a guy with an engineering degree who has played with computers since I was 8. Half the problem is absolute techno-phobia/indifference in your average classroom teacher. It's no different than a problem math student. A solution with more than one step is an instant "no way, that's too much mister." Should Google succeed in making it easier for an individual teacher to get something up and running, good for them.

The huge huge elephant in the room here is that at no point during the 6 minute presentation was there word one about monitoring the quality of technology based instruction. If you look under the Get Started section of their Educator Program, there are no guidelines about what teachers will be reviewing these things, how quality is determined, or provide a single sample use case for an aspiring developer. There seemed to be no focus on use cases in the Education Store screenshots either, just showing it as a nicely designed app directory.

The Problem

This scenario seems to be continued lip service to education without providing a single example of what they think a good education scenario looks like. Unfortunately, educators/administrators will buy what they're selling because a) technology stuff is hard b) Google and Apple are smart, they must know what they're doing.

But they don't!

Google's scenario will continue the idea that magical, wonderful education technology can be found with a magic bullet app. In their keynote, the presenter mentioned 550 different apps were used in their two pilot schools. 550! How do you build lasting routines like that? How do you expect a strapped school staff to manage that? What in the world is significant about 550 apps other than being a really big number that you can impress people with during a keynote?

Apple's official party line isn't any better. iBooks Author supports the notion that digital textbooks with embedded video are the answer. iTunes U supports the notion that there's nothing wrong with the current structure of college lectures, and that the world will be better served by getting to sit in a boring class for free. In March of this year, Apple published a very well made video about a high school in Boston that went 1:1 iPad. Take the time to watch it and see if you can find what is revolutionary about any of the activites done by those students. They are able to create some movies, ok. But...they take notes...digitally. They read a textbook...digitally. In one scene, a teacher projects something from a 90s era overhead and a student takes a picture of it.

Google set out on this mission because "when I go visit my kids' classroom it looks pretty much like it did when I went to school." But what are they really doing about it that isn't just a new coat of paint?

What Would Points Do?

A continuing series on the things I encouter while grading. I'm not sure what's been so special about it this year. I've had a harder time making myself do it, for one. But everytime I sit down to grade something, I have to make a decision "what am I looking for?" and "what proves there was a knowledge transfer?" Take this example:

It's a two-step polynomial multiplication problem. The first step is executed perfectly. In the next step the student made a typo. The result from part 1 should have been multiplied by (x + 10) but for some reason (x - 9) appeared. A little careless or they made a minor visual error when looking for the next item to use, possibly pulling the -9 at the end of the third binomial there. I suspect it results from not multiplying the binomials from left to right in the first place. There are people that would see this, mark a little "-2" or in the hardcore mindset mark the whole thing wrong because technically the student did not answer the given question, they answered an incorrect version of the question. But look at the work. Despite having the wrong term, the operation continues flawlessly even with the misplaced (x - 9) being used.

In a points world, this student does not receive full (or possibly any) credit. And yet it's very clear they understand the concept. One would argue they are fluent in the concept since they essentially made up a problem that demonstrates the mechanics of polynomial multiplication.

I gave the student full credit. What would you do?

Heads Up

Not that I'm crazy popular, but my Twitter account got suspended. Not sure what rule I violated. They may not like the way I was publishing new entries there? My feed seems to have switched off shortly after a notification about my latest entry. I sent an appeal to the great black hole of support. We shall see. I doubt anyone is around to listen over there so late on a Friday.

If it appears you're being ignored, that's what happened.

Any of you kids with private accounts that get a follow request from @rawrdimus, that's me.

The Unexpected

I recently closed out the academic portion of Pre-Cal. We're in the middle of producing a short film and then tackling some small projects that summarize everything we've done this year. The final act of their tested curriculum involved a little bit of calculus. We went through finding limits by direct substitution, determing the value of limits that seem to be undefined, limits at infinity, and derivatives.

Every year I play a dirty trick on them in the section on limits at infinity:

It's an exercise that draws inspiration from this test question by Sam Shah which was in turn inspired by a post from Bowman Dickson. Basically, what happens when you present a student with the unexpected? In the 90 or so papers I have, there are dozens of students that made the same mistake on this question. There were no in class examples like it. Though I did mention that the largest exponent has control of behavior throughout the course of the material. This is the kind of thing that makes it clear who processed the full concept and who was pattern matching to examples.

I would fall prey to these oversights in school all the time. A particularly nasty Thermodynamics exam I took was full of things like this.

Now the conundrum: is this a good test question because it showcases who internalized the concept completely? Or a bad test question because the answer is so obvious to me, the seasoned veteran, and hahaha can you believe these inexperienced teenagers are no match for me?