Monthly Archives: November 2013

How the MTBoS has Changed my View on Lesson Planning

When I first started teaching, I used to lesson plan with the thought of “I can’t wait until I’ve got plans for all my classes, so that I won’t have to spend so much time preparing for class!”.  Now, after interacting with the #MTBoS (Math Twitter Blog-o-Sphere), I think to myself “I can’t wait until I’ve got plans for all my classes so that I’ll have more time to improve these lessons and find better ones!”

I only recently realized this change of mindset, but I attribute a large part of it to something I read on Fawn’s blog.  Once again, I can’t find exactly which post it is [1], but it went something like “Each year I re-do fewer and fewer lessons.  After about 10 (?) years, I’m now only re-doing about 70% of my lesson plans”.  Wow.

[1] Looking for that quote did get me to go back and read ton’s of Fawn’s previous blog posts.  It’s better than a gold mine over there!


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[Productive Struggle] Precalculus Logarithms

I’m trying to keep a positive spin on my Precal lesson from Wednesday (a few weeks ago, now), but it really, really flopped.  To be fair, it wasn’t entirely my fault: I had lesson plans using the internet, and the internet was totally out.  So it was only mostly my fault because I didn’t have backup plans

So I decided to try a 3-acts on the spot.  Note to self: do not try this unless you’ve done the specific 3-acts before and you’re very, very experienced at 3-acts.  I have been doing about a 3-act lesson every week or every other week or so, but this little amount of “experience” does not make up for the lack of planning and preparation.

I saw this chart shooting around the Twitterverse:

TECHNOLOGY Price of 1gb of storage over time:
1981 $300000
1987 $50000
1990 $10000
1994 $1000
1997 $100
2000 $10
2004 $1
2012 $0.10

After asking “What questions do you have?”, and discussing “how much a GB is”, they got to work plotting this on a whiteboard.

My first goal for students was to graph this and quickly realize that a “normal” scale wouldn’t work here because over half the points just sit on the x-axis, not really telling you anything.  A few creative students decided to make the “squiggles” and represent a significant change on the scale of the y-axis, but these students did not realize that (a) you really shouldn’t do that between data points and (b) you really, really shouldn’t do that multiple times on the same scale.  So they saw the need for a logarithmic scale, but even after they graphed the points on Desmos, they had no way of making the data scale that way.  Mistake #1.

The next mistake that I made was thinking that “because the data merits a logarithmic scale, then the best-fitting function must be logarithmic”.  I didn’t tell students to choose a specific function, but I hinted that since we had been working with “logarithmic functions recently, it’s probably a good place to look”.  I need to get better at Dan Meyer’s slogan of “be less helpful”.  I might as well have required them to use logarithmic functions with that kind of hint.  Even 2 minutes of playing around with the data before class and I would have realized that it is definitely not a logarithmic function.  Instead the students struggled for a good 10-15 minutes before I realized what was going on.  Mistake #2 (at least).

So I decided to give students a “break” while I regrouped and gathered together my thoughts.  Since my school has regular classes on Monday, Tuesday, and Friday, and block periods on Wednesday and Thursday, most teachers give students a break partway through the long periods for students to use the bathroom, get water, and just regroup mentally.  Until this class, I hadn’t given my Precal students a break because they’d been busy with the 3 Acts lesson we were doing.  However, my own fumbles demanded a break.

When the students got back, I explained to them my mistake and pointed out what kind of function they should have been looking for.  They jumped back into groups and started working on Desmos to find an exponential function that fits the data.  Once groups started getting an appropriate equation, I asked them more probing questions about the domain, range, and other specific questions (“How much will a GB cost in 2020?”).  However, I didn’t have one specific goal for all the groups to come back together and discuss, so I lost their focus unless I was standing over their group shooting questions at them.  Mistake # too-many-I-lost-count.

There are tons of other mistakes with this lesson that I’d like to point out:

  • I didn’t have a good “hook”, or even a good idea where to take the students after they got their graph.  If I had spent some planning time before to come up with that, then it would have vastly improved their experience.
  • I didn’t have any good ideas for how to view the data-that-should-be-on-a-logarithmic-scale.  I’ve never learned how to put data onto a logarithmic scale accurately, so I wouldn’t feel comfortable showing students how to do it.
  • A “hook” isn’t just a bunch of questions, but you do need questions before you get a good hook, and I had neither.  I didn’t record the students’ questions beforehand, like I almost always do, and therefore I certainly didn’t come back to them at the end of the lessons, which I also almost always try to do.  In short, I just killed some of my students’ trust in asking me questions in the future.
  • I didn’t have any sequels ready for students.
  • The information, by itself, wasn’t particularly compelling.  I can imagine making a slide-show of the cost and amount of data on a slide with a picture of an object with that storage capacity.  To actually see it go from several buildings down to the size of less than a thumbnail would leave an impression and provide some other sequel questions.  Missed opportunities.

There were a few positives: students felt the need to create and use a logarithmic scale (however fleeting that feeling was), students practiced fitting an exponential curve to data (they’re getting quite good at fitting all kinds of functions lately), and they learned what a GB is (super-important in today’s world, in my opinion).  However, it felt worse than a wasted class period–it felt like a wasted block period.  Even though this is my 4th year teaching, I’ve got to have back-up plans for technology failures and I’ve got to get better at putting time into these kinds of tricky lessons.

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Take a Look… In my Grade-book

I just wanted to show what my SBG Google-spreadsheets grade-book looks like 3/4 the way through a semester.  Thanks to Julie’s (@jreulbach) trick, the spreadsheet colors itself in when I enter a grade.  A big thank-you to Jim Pai (@paimath) for making brainstorming sessions and helping me to get this worked out over the summer.

Gradebook Look 0

Before today, if I had a quiz which covered several standards that were spread in very different parts of my spreadsheet, then I’d spend most my time, while plugging in grades, just scrolling left and right along the spreadsheet.  Today I had the bright idea to shrink all the columns between the two points so that I can type in everyone’s grades without any scrolling (see below).  Yay Google & spreadsheets.

Gradebook Look

For this last image, I’ve re-sized all the columns to show as many grades as possible in a single view for a single class.  Wow, that’s a lot more grades than I wrote down last year, but I think that’s a good thing.

Gradebook Look 2EDIT

Thanks to Jasmine for reminding me to show you all this: Students have their own spreadsheet they can check which automatically pulls from my spreadsheet.  Here’s what their spreadsheet looks like.

StudentSnapshotIf you want to make the cells change automatically, go to Format –> Conditional Formatting … –> and then check the box for “Background”.




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[MTBoS] Mission #4: Infinite Tangents Podcasts

Having attended many Global Math meetings, I became super-excited about the “Autumn Special”, which is packed with rock-stars great teachers & presenters and generally awesome people.  Unfortunately, my school’s internet has been awful lately [1], so I was unable to hear the presenters.

However, I am fortunate that this happened because it turned my attention to Ashli Black’s (@mythagon) podcast: Infinite Tangents.  I had listened to her first podcast several months ago and had every intention of continuing to use them, but the problem is that I don’t regularly listen to podcasts, so I don’t have a program or a method to “catch up” with podcasts like I do with blogs [2].  I also don’t really commute to work [3], so I don’t often have that time where I can just listen and work on what I’m doing.

So I was very excited to find that my iPad has been faithful in keeping the Infinite Tangents podcast up to date, so I didn’t need internet in order to listen to some of the older podcasts. The one I chose to listen to was episode 103 interviewing Tina Cardone (@crstn85) of Drawing on Math.

Her first topic was about this program in Boston called PROMYS, which is where advanced students and teachers work through problem sets and learn advanced math through discovery.  I loved math/science camp when I was a kid, but never imagined there was something like that for teachers.  Unfortunately Tina pointed out that most teachers who attend the program are Boston locals or commuters because there’s no boarding available, and living in New Mexico makes it kinda a long commute.  That’s probably for the best because I already have a lot I want to do this summer between TMC, going to a Modeling workshop, and just visiting friends and family in MD and NC.

She went on to talk about Productive Struggle, which I subscribe to, but have only submitted one or two times.  I could definitely blog about that more and help my own teaching out by explaining all the times I’ve given lessons that have been total flops.

One of the great things that Ashli does is she has a handful of neat questions that really help you get to know these people whose blogs you read & follow but, unless you are fortunate enough to attend TMC, never really get to know as people.  I certainly plan to make time to listen to Infinite Tangents in the future!


[1] I live in housing provided by my school, and we live close enough that we don’t have to pay for internet: we can steal our school’s internet.  Which is great except for when the internet is awful at school, so it becomes frustrating at work and at home.

[2] I use Feedly and there’s always too much backed up on there for me to finish it all in one sitting.

[3] I walk to school and it takes me about 50 seconds. See footnote #1.


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