Category Archives: Math

Questioning Homework

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

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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.

Other great reads on homework

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.