## Choosing to Engage

I have Franco* in a course I’m teaching for the first time this year, Foundations of Physics. FoP was designed to help students who really struggle with math and reading, identified by test scores, to earn their required Minnesota physics or chemistry credit. It’s a below grade level class filled with students who largely have been unsuccessful in school in the past, and is certainly has an overrepresentation of students of color**. Franco has to some extent been a thorn in my side. He’s boisterous, distracts other students, and won’t stay in one place. He’s also demonstrated that he’s very bright, and he has a great sense of humor.

Earlier in the year I mentioned that we were going to perform a lab over again, and Tahvo* stood up and said “Another one!” Franco was among the students laughing; clearly this was a thing. I ignored it and moved on. A few days later it happened again, then again a few days after that. Finally I asked about it. “Just Google ‘DJ Kahled'” they told me, snickering. Turns out it’s a short clip that’s fairly mild (I expected way worse) that has become a meme. So here’s the thing; I could have assumed they were laughing at me. I could have reacted. By engaging in conversation instead, we’ve now gotten to the point where ‘another one’ is a class meme. It’s helped build culture in my classroom.

Another time Franco put an ear bud in my ear; it was NWA, which I recognized (I grew up listening to NWA, Easy-E, and Dre, coming back now with Straight Outta Compton). I’m not immersed in hip-hop culture now, but I can certainly have a conversation with kids and show a bit of interest. When they put in their earbuds, I can engage with them rather than react against them.

Today after class Franco was one of the last ones out the door so I stopped him.

“Hey, what’s your plans after school?”

“I don’t know…I gotta figure that out I guess.”

“Yeah, well, you got a lot of potential. You could do something really great. You just gotta figure out what that thing is.”

“Dang, you don’t hear that from many people.”

You don’t hear that from many people. Meaning, most people have written Franco off and he knows it. He’s been unsuccessful for undoubtably a variety of reasons. But he’s still a kid, and he still deserves to be believed in. I can engage in his positives, rather than react to the negatives. I can choose to engage.

*None of the student names in this story are their real names.

**I’m happy that our school district is working hard to correct this, both by ending below-grade level courses except for those required for students to graduate off their IEP (including this being the last year of FoP), and by implementing an Excellence in Equity team to find solutions for our students we have traditionally failed to help.

## The Seeds of Climate Change Denial (or Newton’s 3rd Law)

Today in class we were working on practice 3 from my Momentum Transfer Model (MTM) packet (which is a combination of standard modeling questions, Kelly’s questions, and a couple I wrote maybe). In first period we did problems 2 and 3, below, in a row. After problem 3 I gave students one of my standard speeches about how some students decide physics is about choosing an answer and then switching it because they know they’ll be wrong. I try to emphasize a number of times throughout the course that a good scientist isn’t one who’s initial intuition is correct; she is one who is willing to take a step back, consider the science of the situation, and then make sense of it. Anyway, in 1st period, almost every student choose that the VW experienced a greater force in 3a, despite the fact that we did quite a bit of work with Newton’s 3rd law, work I still think is pretty effective, back in November. The problem is, students haven’t made it second nature yet to start with science and end with conclusions. They start with their gut and go from there.

During 2nd hour I inadvertently gave my speech between questions 2 and 3. Every kid said that the forces were equal in 3a. Every kid.

This helped me to realize that even when students understand a concept at some point, they still tend to revert back to gut-first thinking over time. In this case, the students were attempting to make sense of the situation, but without considering the physics involved they tend to confuse acceleration (the affect of the collision) with the force of the collision itself. Instead, if they start by applying Newton’s 3rd law, such that the forces are equal, then apply Newton’s 2nd to show that the effect of that same force depends on the mass of the object, it makes sense that the forces are equal but that the effect, the acceleration, is different.

So it’s not really that big a deal in the scheme of things when students’ don’t correctly analyze a collision, but it’s a much bigger deal when we have policymakers denying climate change. The problem is summed up in a picture from a tweet that came across my feed the other day;

Teaching science should mean giving students the tools to analyze situations and make logical conclusions while at the same time emphasizing how to do so in a variety of situations. If we fail to give students the tools of science, or show them how they apply, or challenge them with different situations, or reiterate their prior understandings, we leave room for them to revert to gut-oriented thinking. I hope that my preaching about starting with science rather than intuition can help in some small way to move our society from one where people try to ‘prove’ their own biases to one where we use data on a real quest for truth.

## Starting Circular Motion

I’ve been looking for a better way to start circular motion for quite some time. Though many people use the spinning stopper lab, I found it difficult to get quality data or even a decent trend, even when I did the experiment. I tried using a pendulum setup, but I wasn’t happy with the hand-waving about non-uniform circular motion. I really like this particular treatment because it first focuses on the conceptual aspect of centripetal acceleration as toward the center, and then follows that up with lab quantifying the acceleration. It also gives some really nice opportunities to review and refine some lab techniques like uncertainty propagation and linearizing (both could be dropped or modified for your purposes) that my students will need as we progress through the year.

Day 1

We spend the first day investigating the accelerometers in Labquest 2s so that we understand the direction of the acceleration based on the graphs of x, y, and z acceleration versus time. (Note: certain this could fairly easily be adopted to use Arduinos or student phones; but note that asking students to risk their phones on a spinning apparatus in day 2 is tough). First the students turn on the built-in 3 axis accelerometer and observe that it reads approximately 9.8 m/s/s in the vertical direction, no matter the orientation. Then we watch the video below up to the two minute mark to explain why that is, and to help understand how the accelerometer is collecting data.

Next we do a series of short trials to confirm directions of positive and negative for each axis. We then turn off the z axis accelerometer as we will be working only with x and y.

Students are told they will be spinning in one place with arms outstretched, with very smooth, fast steps, as quickly as possible. They will be starting the data collection while spinning to eliminate the spin up process from data collection. I ask them to graph what they will see; most think it will be sinusoidal. Then students actually do the trial, and sketch what they see. It takes a lot of individual conversations here for them to see that the primary acceleration is in the negative y direction (based on how we hold the Labquests). Spinning faster and smoother helps this, and I have to point it out for a lot of groups, who then confirm with more trials (and more falling over from dizziness). It’s a good time.

Next we have a quick conversation about how the acceleration is negative y, so that means it’s….wait, what? Toward the center? “Hey everyone, go grab a bowling ball and a hammer.” I instruct them to make the ball go in a circle using small taps with the hammer. No, not spin…actually travel in a circle. Then I ask what direction they have to tap it in order for it to go in a circle. “Toward the center.” I go through a quick note about how applying linear taps speeds the ball up or slows it down, and that the net force from the taps is in the same direction as the acceleration. Thus for our circle, we apply a net force inward, and as a result the acceleration is inward. They don’t like this, not one bit.

Now is the right time to talk about turning in cars. I ask them to get in a car with me, and I slam on the gas. What way did the car accelerate? “Forward.” What way did you *feel* like you were moving? “Backward.” We do the same treatment of slamming on breaks, and talk about how really our bodies are just trying to keep on doing whatever they were doing, so we feel like we move the opposite direction as the actual acceleration. Ok, so now we are going to turn left. What direction does it *feel* like you are moving? “Right.” So what direction are you accelerating? “Huh. Left. Towards the center of the circle.”

And that’s enough for today.

Day 2

Now that we have the basic idea about centripetal acceleration it’s time to quantify it. We brainstorm; what factors affect how strongly you feel pushed to the outside of the car? (but are you really being pushed to the outside? No? Good) They come up with speed and radius pretty quickly. This part does have to go pretty fast, as data collection is tough to get done in our 48 minute periods. If there’s time we have a conversation about how investigating the radius and it’s affect on acceleration is tough because speed also depends on the radius. So we settle on changing the speed of rotation and measuring the resulting acceleration. On what you ask? Only the best equipment for my physics students.

To measure v; How far does an object go around this circle? “The circumference, $2 \pi r$.” Ok, so we’ll call the time it takes to go around once the period T, so the speed is $v=\frac{2 \pi r}{T}$.

Thus we measure the period to calculate the velocity (which we’ll do later). We use the statistics function on the Labquest to measure the mean of the acceleration, only while the acceleration is moderately constant, and use the standard deviation for the uncertainty. We collect data for 20 seconds since we now can’t avoid the spin up. Some very important student instructions;

• Only use the linear section of the y acceleration graph
• Each trial involves hitting play, starting to spin, maintaining that constant rate of rotation, then starting to count revolutions to measure the period. $T=\frac{total time}{number of revolutions}$
• It’s hard to actually spin the chair at a constant rate. I’ve seen a variety of techniques, but most groups either reach from above on the back, keeping their hand on the back the whole time (as discrete pushes show up as very obvious waves on the acceleration graph) or spin from below with quick, regular pushes.

This year I had some timing issues so we really only had time to collect data this day; in future years I think we’ll have time to go over the calculations of speed and uncertainty using Google Sheets here as well. I walk them through how to use the period data to automatically calculate speed using Sheets. We also have a conversation about uncertainty in the speed; it’s a propagation of the uncertainty in the radius and the period. So we estimate those uncertainties, then use sheets to calculate the maximum possible speed using the maximum radius and minimum period for any particular trial. It’s really nice to do this now, as we do an experiment later using photogates where we have to similarly propagate the uncertainty.

Day 3

Start today by graphing acceleration vs speed in linreg. In most cases their are two pieces of evidence that the trend isn’t linear; it looks a bit curved (though this depends a lot on the group), and the intercept is usually significantly negative.

As much as possible I have the conversation about these factors with each group, but as there gets to be more of them I toss it on the overhead and we hash it out there. We talk through why the intercept should be zero, and use the combined evidence to try linearizing. Below is a student spreadsheet with a wonderfully linearized graph.

Once the graphs all have linearized graphs, they whiteboard them. There will be a number of groups with data that makes no sense; I think they generally missed one or more of the “Important student instructions” bullets above. We talk about it, and I have them take a look at other groups’ data. The following discussion centers first on the quadratic nature of the data. Either someone does a unit analysis of the slope or I point out how nasty it is ($\frac{m/s/s}{m^2/s^2}$), so we simplify it to 1/m. Eventually someone notices that the smallest radius has the largest slope and vice versa. I ask them to combine the evidence of the units of the slope with the radius–>slope information into a claim about the slope, and we end up with $a_c=\frac{v^2}{r}$ (note that facilitating this discussion is significant, but material for a different post).

I then emphasize the evidence that we’ve used to get to that point; the curve in the acceleration vs speed data and the negative intercept leading us to a quadratic relationship, and the units and radius comparisons leading us to an inverse relationship between acceleration and radius. We finally test it against our original musings; as we go faster around a curve, does it feel stronger? As we decrease the radius, does it feel stronger? It’s good that our equation matches our experiences.

In addition to the reasons stated at the beginning of this post, I love that the kids have a blast doing the lab. Playing with spinning chairs is fun for people of all ages.

## On Personalized Learning

The term “Personalized Learning” has rubbed me the wrong way for quite some time. Admittedly this likely stemmed from stories like how Carpe Diem school ‘personalized’ learning by putting students in cubicles;

Raise your hand if you have a job where you work in a cubicle all day and feel energized, appreciated, and passionate about your work.

I can’t imagine much worse for my children. I want them exploring, interacting, discovering, and, most importantly, interested in learning. I don’t want them moving onto the next algorithm after earning a badge.

Recently it appears the Edtech community has strayed from the cubical, Khan Academy model of Personalized Learning in favor of something more nebulous; the basic idea that students can work at their own pace with the teacher guiding and tutoring on the side. This often comes with mantras such as ‘student choice’ and ‘individualized learning plan.’ These aren’t bad things, but I submit that students working primarily on their own, at their own pace, is.

Which brings me to my recent revelation about why personalized learning as a primary structure for learning bugs me; it’s still passive. It appears that most of the ‘content delivery’ is still about students absorbing information from a source passively, then working exercises or doing practice of some sort to work towards mastery. When I think of an ideal math lesson, on the other hand, I think of rich tasks that take collaboration and significant critical thinking, such as Fawn’s Barbie Bungie Jump (listen to the kids cheer in the video!), Dan’s 3 act lessons, or Desmos’s Central Park. Shooting for productive struggle, I want to walk into a math class and see kids pointing at each others work, arguing, and even cheering.  Summarized, I want math class to be engaging in the sense that students actually want to be there.

If I want students to be learning through collaboration and dialogue, then, generally speaking, I want them moving along at about the same pace. I do have times, particularly towards the ends of units, where students are working on problems independently for solidifying problem solving or receiving remediation as needed. This, however, is usually a few days to a week, as compared to the other three to five weeks in a unit where students learn primarily through collaboration. To be sure, my beliefs here are rooted in the decades of research on STEM education which has demonstrated consistently that a variety of methods centered around active learning are the best ways for students to learn. Additionally, in talking to my wife about this, she gave an incredible insight; “What skills can you gain from class time that you can’t gain from studying?” Precisely. Studying on one’s own helps to learn content, but collaboration, argumentation, sense-making through inquiry, and many other skills are emphasized when rich activities are the focus during class time.

There are some other things that bother me about personalized learning. It appears to be rooted in the theory of Learning Styles, which isn’t really a thing, as it turns out. (see also here and here). Students, generally speaking, learn from some types of teaching and don’t from others. Identified preferences in how that learning takes place hasn’t been shown to make any real difference in the actual learning that happens.

Then there is this post which makes the claim that the ‘factory model’ of education that many personalized learning proponents want to upheave is really the first experiment in personalized learning.

Finally, I agree with Dan Meyer who states that personalized learning is fun like choosing your own ad experience is fun. (Spoiler alert: It’s not).

I do believe that proponents of personalized learning mean well, and I believe that aspects of the model woven into a class at the right time can be useful. In the end, however, I choose rich, engaging, interactive tasks over learning at one’s own pace.

## Questioning Homework

Search twitter for “math homework” and you’ll find a lot of this;

Honestly, you’ll see a lot worse as well. Kids hate their math homework, and largely for good reason. Many math teachers assign 20-30 problems for students to complete every night; I was one of them. As a new teacher I came in with the assumption that this practice was essential for students to learn math. Ten years later I’m more convinced then ever that this kind of traditional, drill and kill math homework does more harm than good.

If you’re on Facebook you have likely seen the explosion of parents complaining about their kids’ “Common Core” math homework. I’ll leave the CC part to Christopher and focus on the homework aspect. My 1st grade daughter has homework to complete once a week. Most of the time they are puzzles and simple practice, and sometimes they are even games we get to play. It’s wonderful. We get a chance to interact, talk a bit about math (aside; check out talkingmathwithkids.com), and she learns that math is fun. One time she had homework that was challenging for her. It was frustrating; we had to continually push her to try, and things escalated. It turned out fine, but I can see how parents would get frustrated and vent on social media.

So maybe the problem isn’t Common Core; maybe it’s that the only time students should be doing homework is when they are actually ready for it. I’m not saying don’t challenge kids; I’m saying challenge them when there is an expert in the room ready to help them out. Homework in elementary can be simple, fun, and encourage interaction between parents and kids, if it’s there at all.

I have been thinking about this in context of my Physics classes. A few years ago in my college-at-the-high-school physics class I stopped grading homework. It was counter-productive. I had students who hardly did any homework and aced exams, and students who completed it perfectly that earned Cs. I did have a student one time who didn’t do homework all year, earned C’s and D’s on exams, then did all the homework for the final unit and aced the exam. I still believe practice can help students learn, but I’m questioning how I have students practice. There’s even research in physics that homework actually hurts some students’ learning. The research in general is mixed on homework’s effectiveness, which is exactly why we have to be very careful when and why we assign it.

The problem with not grading homework is that less kids do it, particularly if they were motivated only by the grade (not many of them) or if a different priority overshadowed their non-graded homework (like graded calc homework, for example). I tried a lot of methods to get them to do homework on a regular basis, and all failed. I was frustrated. Much of that homework was problems I wanted students to complete ahead of time so we could whiteboard them more efficiently. However, only half the students attempted the problems, so then I had frustrated students who had done what they ‘should’ explaining things to students who didn’t. It was not efficient, nor did it seem effective.

Kelly O’Shea moved to a no-homework policy a number of years ago, and her students perform as good as anybody’s. Instead of having students do the problems ahead of time, they simply do them in class, then whiteboard them. I decided to give it a try.

The first thing I noticed was the richness of the discussions as students worked on the problems the first time around in class. They ask great questions and help each other out. The second thing I noticed is that it took them waaaaaay longer to complete a worksheet than I expected, as well as struggling more than expected. ‘Honors’ kids! This made me feel awful about previous years; I was assigning a ton of homework they really didn’t know what to do with, and I had no idea. The in-class interaction has been huge to help students start a problem that they would have been stuck on. This experience reminded me of a teacher who once told me that the first time he taught a pre-calc class, he sat down to complete the first assignment that had been traditionally assigned. It took him two hours. That’s crazy. And I suspect it happens more often than we know.

Now the awesome part; the whiteboarding process, where we get to have discussions as a class about the problems, is way better and faster than before. It’s now a time to flesh out nuance and important generalizations rather than figure out how to do the work, and this happens quickly. I have been able to move at exactly the same pace as previous years. Not a day lost, and the kids are happier.

Not only are they happier, but they’re doing better work. the first two exams of the year (Kinematics and Forces) saw significant increases over last year, with probably 1/3 of the homework assigned. I want to emphasize that. Students are doing better with less homework. Though I can’t really tease out the variables, I think the combination of more working in class and more emphasis on actually doing the homework that is assigned makes the difference. I’m still assigning ‘Independent practice’ after the point where I think students have had enough in-class practice to be ready to try it on their own. Often there are 2-3 weeks between these assignments.

Some recommendations to get you started thinking about the homework you assign.

• Try it yourself. Take the time it takes you to complete and multiply by 3-4 for an estimate of how long it will take a kid.
• Ask yourself if they are going to learn to hate your class because of  doing your homework, and be honest with yourself.
• What is the quality of the homework? If you are picking 1-31 odd like I used to, it’s not quality. Choose 4 focused problems instead.
• If you spend a lot of time going through homework after the fact, would it be more worthwhile for students to work on it with you there? Same amount of time, but that way they are actually doing the work.
• Try doing something different with homework, and be prepared to be surprised. I didn’t expect that cutting students’ homework load by more than half would raise their achievement, but it did.
• Finally, listen. Listen to kids in your class. Listen to them rant on Twitter. And do something about it.

## Don’t Keep it Simple, Stupid

Teaching is hard.

I don’t mean that there’s a ton of work that can never get fully done (even though there is) or that parents/admin/the general public are hard to deal with (even though they are). I mean that crafting a quality lesson, set of lessons, unit, or entire course is really, really hard.

Every once in a while I run into a former student from long ago who tells me how much they enjoyed my class, and all I can think about was how horrible a teacher I was then compared to now. But I wasn’t a horrible teacher; I just wasn’t as good at it as I have become. I can only hope this will continue to be true 10, 20, 30 years into the future.

Over 10 years of teaching I’ve learned a lot of skills to incorporate into my teaching. I started out teaching Physics and Geometry via overhead projectors (you know, the kind with wet erase markers?), because if I was going to give scripted notes it seemed like a waste of time to write them on the board each hour (turns out scripted notes in general were the waste of time). Over the course of the first 5 years I learned a lot about teaching through inquiry in my physics classes; I went from stating emphatically in a grad class that it was too difficult to guide students through inquiry to being a leader in my 6-12 department on the subject. But that took a solid 5 years and lots of failure; I honestly only succeeded because of lots of support from a mentor through my grad program. Good inquiry learning requires a very structured release of responsibility to the students and a general culture of inquiry throughout the entire course. It took all of 5 years to work out all the aspects of this to implement successfully.

Then I started incorporating a home spun, mediocre version of problem based learning in my geometry classes, though at least it upped engagement and increased learning based on final assessment scores. That took a solid 3 years, and in reality required my inquiry background to accomplish. I only stopped because by this point my physics classes had grown to the point where I became full time in physics and had to drop teaching geometry; honestly, I still had a long way to go and hope to incorporate what I know now about ProbBL back into math classes at some point.

About this time I discovered Modeling Instruction, which taught me, among other things,  how student dialogue can significantly increase the depth of student understanding. I’m three years in and have a long way to go before I’ll consider myself an expert.

So here’s the rub; I’m 10 years in and I know I still have a ton to learn. I’m not that great at facilitating student dialogue yet. I have a long way to go in helping students solve real problems in math class. I struggle with helping students who give up when challenged. I’m sure there’s many other aspects of teaching out there I have yet to learn.

For this reason I think we cheapen teaching by trying to simplify it. Silver bullets in many forms are always popping up in the education world, but quality teaching requires a blend of many talents, and it shows up in many different forms. I think this is why teachers get upset at things like administrators forcing the posting of objectives; emphasizing that over all other important aspects of good lesson design says ‘here, you’d be getting better results if all you did was this.’ It’s patronizing. I think this is also why I’ve never been satisfied with the SAMR model for integrating technology. ‘Oh, you’re only on augmentation? Your students will really be learning when you get to redefinition!’ There are so many ways to go analogue for quality lessons or to use tons of tech for shitty ones. Good teaching is far too complex to be boiled down into an acronym.

The false notion that creating a quality lesson is simple is also why we haven’t had successful education reform.We have a culture in the US built on instant gratification; no one is willing to wait the 15-20 years it would take to make progress. And no one is willing to take on the really hard work of making sure all teachers are trained and continuously supported in the many techniques that have been shown through research and practice to work to improve student learning. Instead we throw technology into the room and ask teachers to redefine education on their own using their 45 minute prep period, because we can do that in the span of a couple of years.

I hear teachers complain that their pre-service training didn’t prepare them for teaching. The problem is, it can’t. One can’t be fully prepared to find the right potion of techniques for a classroom without experience, trial, and error. Maybe this means that longer apprenticeship-like experiences with more built in support for new teachers would be helpful. I don’t know. I do know that there’s always room for improvement, and creating a national culture to actually support and encourage that would be a great first step.

This post was inspired by this tweet by Ilana and the conversation that followed.

## What would you do with $x? Dan Meyer posted earlier this week about how, given$1000 for a classroom, he would spend it on whiteboards for the walls, a doc cam, and some miscellaneous hardware. I tweeted the article, and got the following response;

Challenge Accepted.

Some assumptions; A class of 30 is easy to do math with (adding up costs type math, not classroom type math). I assume solid wifi since I don’t have $1mil laying around for an upgrade. The classroom comes stocked with an overhead projector, a standard issue computer, and one 4′ x 16′ front whiteboard. I’m going to assume (based loosely on my memory) that a classroom is 30′ x 30′. Lets say one wall is windows from 4′ to 8′, because it depresses me to think of a classroom without windows. Generally speaking I took the first price I found on any particular item, and I reserve the right to round anything to the closest order of magnitude, for reasons of estimation (or laziness). Also, I currently teach only physics, but have taught math, particularly Geometry, for a number of years. I’m writing this post about a math classroom because it’s more universal and more in line with what Dan and Jeremy are positing. A physics classroom adds significant cost, as full computers are desired because of software and hardware demands for digital data collection, as well as the data collection hardware purchases themselves. That said, most of the stuff I list below I would like in my physics classroom, I just would have to do more cost/benefit analysis to compare data collection devices (likely from Vernier) with the more general items below. Spoiler alert; most of my purchases stem from a desire to encourage students doing rather than getting. Watch for that. Unlimited Funds: My first purchase is going to be on the assumption that some donor will fund whatever I ask for, and that money unspent is money lost. That is, I don’t affect anyone else’s classroom or materials by skimping, so I don’t have to be all that ethical. First of all, I agree with all the folks in Dan’s post and get a bunch of whiteboards; • 36 Medium sized (24×32 in) student whiteboards ($100)
• 36 Small (16 x 16 in) student whiteboards ($30) • Cover all the non-windowed walls in whiteboards ($5000, turns out quality classroom whiteboards aren’t cheap)
• 2 rollable whiteboard dividers ($1000) Frank Noschese wrote a great post about student whiteboards. Seriously, go read it, I certainly can’t improve on it as far as reasons to have students use whiteboards. Since I have unlimited funds in this scenario, I could purchase nice manufactured whiteboards at$120 a pop. But that’s so ridiculous that I can’t stand it. I can go to Home Depot and purchase a $15 sheet of 4′ x 8′ that makes 6 medium whiteboards or 16 small whiteboards. Why anyone would pay$12o for one of these aristocratic whiteboards is beyond me, let alone a class set for $3600. Next, covering the walls and adding dividers is to reduce barriers for students to talk about what they are doing. All they have to do is pick up a marker (I should probably have a$1000 marker budget….) and start collaborating. Clearly that takes some pedagogical skill (that I don’t know that I have yet), but we’ll save that for another post. I feel like 2 rollable dividers would be nice to be able to use in the middle of the room as well, but I think more of them would make it too cluttered. Honestly, what I really would want (but is even beyond reasonable for this unlimited funds exercise) is some system where students can easily drop whiteboards (or glass, that’d be cool too) from the ceiling, then raise it up again as a space saver. Plus then we’d have math on the ceiling, and that’d be pretty neat.

Noticeably missing: A SMART board. I don’t have one now, and don’t really want one. I want stuff that helps students collaborate and dialogue; a SMART board would be for ME. Seriously, even with unlimited funds, I wouldn’t get it simply because I want to do everything I can to encourage students to do the work. Whiteboard total: $6130. Next let’s look at the classroom setting itself. • 15 Tables on Casters ($7500)
• 30 Chairs on Casters (If you want to get crazy this could be up to $7500, but a simple internet search indicates I can do more like$3000)

Desks make it harder for kids to collaborate. I would love tables on casters for a number of reasons. I like that kids can easily group up on them. I like that we can move them into a whole class rectangle, put a couple together for larger group work, or get them all out of the way to do something more kinesthetic. Chairs on wheels would be nice too, but again I have trouble justifying the crazy expensive version. Class setting total: $10500. Now we hit the technology setting. I’m going to start with room-scale technology. • 70″+ TV on casters ($2000)
• Five 36″ TVs mounted on the walls. above the precious whiteboards, of course ($2500) • Apple TV for each TV to wirelessly project Apple products ($500)
• I’m going to assume we can install some magic circuitry such that each TV can be accessed individually or they can all show the same thing, but I don’t feel strongly enough to actually research this. (umm…$1000?) • A teacher Macbook Air ($1000)
• A teacher iPad mini ($300) • iPad doc cam setup ($130)

Actually, before I explain those, I want to add in the student technology;

• 17 Chromebooks ($5100) • 2 iPad Minis ($600)
• Chromecast for each TV to wirelessly project the Chromebooks ($200) I saw the TV on casters once at a presentation on room design, and I fell in love with it for physics purposes. I would love to be able to roll it to the ‘front’ of the room as standard use, but then move it to the lab space to demo lab procedures, and have the flexibility to move the ‘front’ to wherever feels right. I have a harder time envisioning its use for math, but hey, dreaming big here. The TVs on the sides are more for students. I think it would be really neat while students work if “Hey Jasmine, that’s a neat graph, can you bring it up on screen 3 to show everyone?” became a reality. I like multiple TVs so students can regularly show each other, in small groups, what they are working on, hence the Apple TV and circuitry. Note that Apple TV, Airserver, and I’m pretty sure Chromecast, all use Bonjour, which can mess with network stuff that is beyond my expertise. So definitely check with someone on the IT side of things before investing there. The Macbook is so I can be anywhere in the room and still bring up something on a screen (as opposed to a desktop computer). I really like the iPad mini for classroom use because it fits in my hand easily, so I can take lots of pictures and use it as a doc cam as I walk around. The doc cam setup allows me to use it like a ‘real’ doc cam as well. I hear doc cams can do some pretty neat things, and we may be missing out on that with the iPad, but I feel like the flexibility of the iPad makes up for that. Both the iPad and the Macbook will have to be replaced 2-3 times over 10 years, so let’s add$3000 for replacement costs. Room-scale tech; $7500,$10,500 including replacement costs.

For student tech, I would go with Chromebooks because of their ease of use in a cart setting. That is, students don’t have their own, but logging into and out of a Chromebook is really easy to do. I only want 17 because I want a 2:1 ratio plus a couple extra, since batteries die and hardware stops working randomly (just when you want it the most). I want a 2:1 ratio for two reasons; first, I have heard from a number of people in 1:1 situations (we’re not there yet, though I have 10 laptops in my room) that even though each kid has a device, they often have half  go screen downs anyway. This is to encourage collaboration and to discourage multi-tasking. Kids are much less likely to check Facebook if their partner is watching over their shoulder. My second reason for 2:1 is that managing a cart is really annoying, and I think it becomes much more manageable with half the devices. I would deal with that if I had a solid pedagogical reason for 1:1, but I personally want more collaboration rather than individualization in my classroom anyway. Both Chromebooks and iPads run Desmos and Geogebra well, which accounts for probably 75% of my tech use in a math class. I like iPads a bit better for the ability to use the camera and draw on the surface, but the annoyance of lack of profiles for sharing the device easily negates that. We’ll figure out a workflow to use student devices to capture pictures and video and get it to the Chromebooks as needed. I include a couple iPads since it will inevitably be nice for some kids to just use them instead of personal devices (which they may not actually have).

We can only assume Chromebooks and iPads last about 3 years, so we should add in about $15,000 in replacement costs over 10 years. This leaves us with a student technology cost of$6000, pushing $20,000 with replacement costs. So far in our unlimited funds scenario we are spending about$30,000 plus asking for $20,000 in replacement costs to sustain it for a bit. I don’t think money for replacement costs is common though. Self-limit. Now I’m going to take a few things out because I have a conscience and I can’t picture an acceptable cost/benefit ratio for a couple of the items. The TVs on the walls have to go first, then the rollable large TV, and probably even the rollable whiteboard dividers. I would keep one Chromecast and Apple TV to retain the ability for both student and teacher devices to wirelessly connect to the overhead projector that we assumed started in the room (though it needs an HDMI input, and if it’s older, that would be a problem). No more need for$1000 magic circuitry though. This trims about $6000, and if we assume no replacement costs, we’re down to$24,000 now.

$20,000 limit. I would start by skimping on chairs, so getting rid of chairs with casters saves about$2000 from the self-limit amount. Then I would cut the other $2000 in wall whiteboards. It still leaves a lot of whiteboard space (I figure I can still put standard 4′ tall whiteboard around most of the room with the leftover$3000 whiteboard budget), it just wouldn’t be floor to ceiling.

The $10,000 question. This is the number I think starts to get into the realm of ‘I could potentially convince someone to actually fund this.’ It’s also where my decisions get more difficult. In particular, I really want to keep the tables on casters. I really like (at least in theory) their flexibility. So I cheated a bit, did some more research, and founds some cheaper tables. Thus what I would keep, when nailed down; • 36 Medium sized (24×32 in) student whiteboards ($100)
• 36 Small (16 x 16 in) student whiteboards ($30) • Only add two 15′ x 4′ wall whiteboards ($1500)
• Cheaper tables on casters, chairs with no casters ($4000) • 15 student Chromebooks and one Chromecast ($4500)

This puts me over budget by $130. Pin me down and I’d cheat by finding even cheaper tables and/or chairs. I’m not getting rid of the whiteboards. In the end I basically agree with Dan and other twitter folks, but with extra cash I would add tables and Chromebooks. I think I’d add the Chromebooks first, as I really like what you can do even with just Desmos and Geogebra. But tables are really close. I honestly didn’t expect, when I started this process, that in the end I’d keep the tables. I think I need to get moving on asking for some for my actual classroom. Note that what’s left is a bunch of things for students to use. I didn’t even try to do that (really). Here’s hoping my practices reflect my apparent beliefs. On a personal note, this was a really interesting exercise for me to examine why I hold particular items dear in my classroom. I hope it’s insightful for you as well, and I would love for you to share your thoughts, additions, subtractions, or anything else in the comments. Here’s the spreadsheet I used to collect items and costs, in case you want to look at it more closely. UPDATE: Megan Hayes-Golding suggested something I really just had to add back in; a multi layered whiteboard. This definitely goes in the unlimited category. I would definitely consider finding room for it in the$20,000 limit.