Monthly Archives: August 2013

The Day the Scaffolding Fell Apart (and Got Put Back Together)

The Setting

Being in only my 3rd year teaching at this school, my principal still wants to do semester observations on us “newbie teachers”, and so I decide I’m going to show him another 3 Acts lesson since the first one went so well. (Side note: this is not a nervous or bad experience for me, not because I think I’m an awesome teacher or anything like that, but because our principal is so approachable and dedicated to helping us teachers grow. He’s “on our side”.)

The Lesson

In Precalculus, we’re still getting used to (read: remembering) different functions and their various representations. After much debate with myself, I decided to use Dan Meyer’s “Will It Go In The Hoop”, where he shoots a basketball, freezes it halfway and asks the students to predict.

I’m learning how to better “hook” students, and this time I did it by record a simple “yes” or “no” next to each student’s name after asking them “Do you think the basketball will go in the hoop?”  Takes 30 seconds, engages them for the rest of the lesson–at least the first leg of the lesson.

I then put Dan’s Geogebra applet, complete with the picture of the ball, sliders, and parabola (he did all this), onto my website for students to access. Geogebratube wasn’t working the night before for me, so I didn’t want to take chances and actually had them download the .ggb file.  The downside is that it’s a few small steps to use that on the Chromebooks. Fortunately, Geogebra has a Chrome applet, so (1) the had to install Geogebra on their Google account, (2) download the .ggb file from my website, (3) open Geogebra (not just click on the file like they’re so used to), and then (4) go to “file–>open–>open”.  Not very many steps for any competent computer user, but as we all know, most teenagers are woefully incapable when using the computer doesn’t involve Facebook or Youtube.

Crash & Burn

So they open the file, and of course they’re all moving at different speeds: some figured out what the sliders do right away.  If you’re wondering, the variables in this particular applet are a, h, and k in the equation y=a(x-h)^2+k.  I decided I would remind them of parabolas & equations at the same time as teaching them to use Geogebra.

That was my first mistake.

The first two .ggb files had sliders already built, but I actually deleted Dan’s work so they only had the picture because I wanted them to want (and then create) the sliders and not just take them for granted. They need to understand what they do and why they’re so nice and helpful.  However, we ran into a few “speed-bumps”. (Hitting speed-bumps when travelling 60 mph isn’t smart, btw.)

  • Creating and using sliders is much tougher in the Chrome applet than with the desktop version. For one thing, I never figured out how to edit the max and min on the slider unless you create a new one.
  • Having to click the “mouse” button on Geogebra always throws students for a loop (although these were doing better than in the past).
  • Students’ understanding of variables is tentative at best, so connecting the slider to the equation via a variable almost always had to be explained explicitly (“Type in exactly what I tell you…”)
  • Even I find using a mouse much easier than a track-pad, especially if there’s no clear button to click outside of the touch-pad. Clicking and dragging items are trickier.
  • The screens on the Chromebooks are just a tad smaller than it seems the applet was created for, so they had to shift and zoom the sheet to see the equation, the picture, and all the lines.
  • One girl at the front became very flustered and frustrated with herself and her computer, which can quickly change the dynamic of the whole class.

I felt the class slipping away from where I had them when I recorded their guesses. We managed to get through two of the shooting videos fine, but when I took away the slider, they became “disengaged”.  I guess I should have known it was their first time using Geogebra as I’m the only teacher in the school to use it.  I just need to give them a better intro than one where they crash & burn so they come to appreciate how easy it can make things.

It really felt like I had pulled too much out from under them and they were collapsing under all that they were required to do. This is one of those cases where the technology was becoming a hindrance rather than supporting more dialogue and investigation.  On the one hand, giving them sliders felt like making it too easy for them. Yet taking away that simple tool made it much more difficult.  I’ll need to try to tread the line between challenging/engaging and frustratingly, pointlessly complex.

The Putting Back Together

I should have pulled these out sooner as a “recap” to help the students bring together their thoughts, but in the excitement, I honestly forgot about them at first.  (Fortunately in my 2nd precal class of the day, I corrected my error and they got this as a summary immediately). I attended a conference where I learned about these “Link” sheets.  This is excellent because it brings together four representations of a function: in this case (1) equation, (2) verbal description, (3) table, and (4) graph.  Sometimes I fill in some parts and they fill in others, but for this I wanted them to take their Geogebra & the video and put it onto the sheet. Here’s a word version (LINK-Blank Linear v 2)  if you’d like to edit it.

After all that technology, I think some students were honestly relieved to have a piece of paper in front of them that they could write on. This helped them to see what the goal of this activity was in the first place.  We’re still not to the point where they understand how to translate any given function, but we’re more used to seeing functions and connecting equations, graphs, tables, and verbal descriptions, which is not a bad block period. The afternoon went better, mostly because I never took the sliders away from that group.

My Analysis

I think I need to do a better job of deciding what I want the students to get out of my 3 Act lessons. I’m trying to remain flexible and “go where the students want to go” in case they mention some great ideas, but I also need to have a plan and something in mind that I want them to learn, rather than just generic “understand & play with functions”. That’s on me.  More planning than I am sometimes motivated to do, if I’m being honest.

And of course there’s also the technology aspect.  I am fairly comfortable with new technology (I find installing operating systems and customizing them fun, for example), so it is very difficult for me to understand how little technology some of my students understand. (One unfortunate girl started at me questioningly when I asked her to “reload” the current web page. My mind was blown, and not in a good way.)  Somehow I became good at being patient with them when they don’t understand math, but I get much more frustrated and tired when they are so slow with technology. Perhaps it’s because I’m not expecting it: they grow up with technology all around them, but they can’t transfer it, mostly (I suspect) because they don’t want to as badly. Figuring out how to find the most popular Youtube video is more essential to their lives than figuring out how to open a file through a program other than the browser you just used to downloaded the file. Ugh. Well maybe next time I’ll be more mentally prepared.

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[SBG] Grading Chemistry Labs

I haven’t liked how I’ve been grading Chemistry labs for the past 2 years. I used to break labs down into categories with different weights of points adding up to 30.  The categories looked something like this.

And since I didn’t overwhelm my students enough in the first two years, I decided to give them wall of text to never read through & (never) understand how they were supposed to write labs.

All of this I made from scratch because I had never been trained as a science teacher (my teaching license is still only in mathematics), but enough of the cheap excuses.  As my 10 grade chemistry teacher used to tell us

Excuses are tools of incompetence,

they build monuments of nothingness,

and those that engage in their usages

are seldom capable of anything but excuses!

Yup, I still remember this, even down to her use of the word “usages” instead of “uses”. Unfortunately we did very few labs that year, so most of what I learned about writing down labs came from my college professors, who always had a particular pet peeve, such as “everything must be written in pen instead of pencil” and would count off disproportionately for doing their pet peeve.  So what I learned was a bunch of random rules that had little do with helping students actually become better writers or scientists.

Fortunately, with my switch over to SBG this year, I can revamp my grading accordingly and use SBG on labs, so I can start looking for the right things in lab books.  Plus, I’ve got a little better idea of what I’m looking for, having taught Chemistry for two years now.

So I’ve got the following rubric, where each of these 5 standards are graded separately.

Students tape this to the inside of their lab book so they can easily reference it.  This is much cleaner and more to-the-point than my previous attempt at explanation.  Hopefully this will help students to become better at writing these labs.

I just finished grading the first round, and I felt like I was looking more comprehensively at the lab as a whole by doing this.  When grading, I use the following document.

I cut these up and one of them to the student’s lab.  The nice thing is that if any other standards from the course were included in the lab, I can just write that down on the lab book right under where I staple this, so they can see it.  I still have to explain SBG to the poor students, so I’m still debating when to do that: now as they receive their first grades in the class, or in a week when they’ve got their first repeat of a standard?

It took me a while to grade these (about 2 hours for 45 or so students), but then again, if I’m being honest with myself and my students, it should always take me a long time to grade lab books because they took a long time to write them up.  I think that breaking down the lab book into standards helps me to focus on one standard at a time and focus on each part of the lab appropriately.

I’ve already hit a dilemma where Significant Figures is its own stand-alone standard, and part of a standard within lab books.  Perhaps in the future I’ll combine those somehow, though I’m not sure how at the moment.

In addition to writing a number for each standard, I’ll still continue to leave comments throughout the lab, though these are also made easier by the little sheet.  Instead of asking “where’s your Error Analysis?”, the student actually sees their score on that element, and realize that they forgot it.

Here’s an example of a graded lab book page.


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Improved Lesson: Review of Function Families

In Precalculus, it’s important to learn the shapes, equations, names, and domain & range of all those graphs that teachers spend weeks upon weeks on in Algebra I and II. See below for the specific names.

Here’s how the lesson used to go. I would hand them the worksheet and they I would write on the board the name and shape of the first one.  As I started to get “creative”, I’d ask them if they remembered the shape.


So this year I had a spur-of-the-moment-night-before-idea to spice it up.  The idea probably came from the 3 Acts lesson that just went so successfully not a few days before, but it’s equally likely that it came from being immersed in the MTBoS over the past year (well, “immersed” is a strong word for someone who mostly just reads others’ blogs and steals way more ideas than he gives).

Instead, I decided I would give the students a situation and have them come up with a graph of the situation.  Working in groups of 3 on individual large (2′ x 3′) whiteboards, they would sketch a graph and decide on the domain and the range.  I’d walk around and give suggestions or ask specific questions.  Then after 5-10 min of this (depending on the difficulty of the graph), we’d come together as a class, briefly share the graphs, and I would sketch a class graph which they’d have time to copy down into their notes.

After sketching the graph specific to the situation, we’d then talk as a class and decide on the generic fuction and its respective equation, name, and domain & range (domain & range are almost always different for situations than they are for generic function).

Example of situations we’d graph and talk about are: Coffee temperature over time; Distance from the start points over time of x-country runner running at a constant speed; Runner runs out to a point and then turns around and runs back: distance from that point over time, again at a constant speed; Basketball shot: height over horizontal distance traveled.  Yes, I do need more (& better) ideas for the rest of the equations, and I would welcome better ones for the equations I’ve already done so I can show the students other situations where these equations might arise.

We only got through 3 types of graphs in about 30-40 minutes, but I think it was much better spent time and the students have a better understanding of D & R, not to mention a specific situation where each graph applies.  Now, when I ask them to create a function out of thin air, I think they’ll do better this year than the unfortunate students last year.  Here’s a picture of our class’s work (my writing) on the board.


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[3 Acts] Coffee followup

I just showed the video from my first ever 3 Acts lesson, and the results were awesome! The students were really into it, throughout the entire hour and a half class (the only day that is that long for the class), and they even commented throughout how interesting it was!

I was a little worried at the start when their first 10 questions had very little to do with the point of the video lesson that I had planned.  It verified my initial concern that the video was too long. It also had a bunch of irrelevant stuff, which prompted even more irrelevant question (“Mr. Newman, have you ever thought of a career as an actor?” jokingly mentioned). But with just a little nudging, we got onto the questions I wanted them to discuss, which in turn led to a wide variety of solutions that I had to “run” with.

Here are some of the questions they actually asked (in the format of a Think-Pair-Share):

Why is the lion king music there?

Why did you use the mug that had OUR class’s Popsicle sticks?

Did you wash the mug out before you drank from it?

Was that water you were heating up?

Was the mug hot when you touched it?

Did you record that this morning?

As you can see, none of these questions are ones I was prepared to turn into a math lesson, though I was willing to branch out a bit.  I had to ask them “What do you think I was wondering as I sat there waiting for my coffee?”  A little artificial, but not so artificial that they shut down the lesson.

One of them finally asked “How long before you can drink it?”  I made sure to listen to a few more questions as if that wasn’t the one I wanted before deciding with them to settle on that question.

From there we made guesses, and after the guesses we clarified the question (“How long from the time you put the thermometer in to when you could drink it?”), so of course we had to make new guesses so that everyone was on the same page.

Then we did a Think-Pair-Share on “What do we need to know for this problem?” and after writing them down, we eliminated a few as a class.  I gave them the first 5 data points that I measured and, finally, we jumped into group work–groups of 3 around a big (2′ x 3′) whiteboard.  This is where the lesson took off and my kids shined (shown?).

I had in mind that they would ask for the equation and I would give it to them and we’d talk about functions, variables, domain, range, graphs, etc.  But they had something else in mind.

Some groups tried an arithmetic sequence (and knew to call it that!).  Some tried that and then tried a geometric sequence (and knew it by name, too!).  Others tried graphing it.  Two of the five groups found the geometric sequence and turned it into an exponential equation right before my very eyes!  I was astonished! (I hadn’t taught them this and I, probably like most math teachers, don’t expect students to come to me with any math knowledge.)  What’s great is I think they just figured that out–they weren’t using “formulas” or anything (although a few asked “What’s the formula?” to which I gave a quizzical look).

By the time we came back together and had our “board meeting” (haha), I had 5 groups that started the problem 5 different ways.  I told them that they were NOT sharing “how they did the problem”.  Instead, each group has a story, a story that they just created, and they are to share their story with their friends and classmates.  I think they jumped on that idea a little better than “show how you got the answer”.  For one thing, I emphasized that I wanted to hear what mistakes they made because that is one of the things that sets their story apart from the other groups.

Students shared and they learned, and I think that even though we hardly talked about functions, THEY figured out the purpose of functions without my help, even though they wouldn’t call it that and don’t know that they did.  Infinitely more valuable.

Only at the very end did I show my function and we briefly compared what two of the groups found with my function.

Things I can fix for next time

Better summary.  We ended quickly because we ran out of time (yes, 1.5 hr class period…), and the students were working 100% of the time (except for one time when I looked over and saw a student on Facebook on her iPad). I need to return to students’ guesses and their other questions.  We’ll definitely do that Friday, but we have sequels to answer, and other questions cropping up… I think I could teach on this video and topic for a week straight and not run out of steam.  How do you guys teach these lessons and close them?

Better video. The video needs a few things.  For one thing, you can’t see the temperature (thermometer is too small), and the stopwatch is in the background, so it doesn’t lend itself very quickly to the natural question I wanted the students to examine.  Part of the problem is that I like using Linux, so I’m restricted to open-source video editing software. I’ve yet to find one where I can put text or something like a timer on the video.

Better discussion.  Perhaps this comes through practice (on the students’ part) of sharing what they did, and being engaged in each other’s work.  Many of the students didn’t seem interested, and I had to call on a few of them to (a) pay attention and (b) ask questions that I could see on their faces but didn’t want to ask for whatever reason. They all presented well, however, for a first time, and nobody showed signs of being intimidated to share their work, which was great.

Oooh, and I didn’t even show “the answer” (I totally forgot about it). I’ll need to remember to do that Friday. What’s great is I’m blogging about this during my planning period, and I teach this lesson to the next Precalculus class, so I’m excited to see where they take it and what they do with it.

Much thanks to Dan Meyer and others who have developed the 3 Acts lesson idea to the point that I can take them and use this format in my class.  If I have time, I’ll post pictures of the whiteboards with students’ work.

Edit: here are two of the whiteboards that weren’t erased to give you an idea of the variety of approaches they took.

photo 1

This group guessed the closest even though they approximated very, very roughly.

This group guessed the closest even though they approximated very, very roughly.

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[3 Acts] My First 3 Acts

I really like what Dan Meyer & others have developed in the 3 Acts lessons.  I created my first video this past weekend, and it involves me heating up a cup of something (coffee?) in the microwave, sipping it, burning my mouth, and then sticking a thermometer in it next to a timer.  My main concern is that the video is too long right now.  I think it will capture their attention (we’ll see), and I’m actually expecting a wide range of questions, which will be great for sequel(s) and further exploration.

The question I’m hoping to answer is “How long before Mr. Newman can drink the coffee?” but I am definitely willing to take it in any number of directions, so long as we’ll be graphing temperature vs time and can talk about functions & graphs.

Here’s the info I’ll give them if they request it. (I’ll give them one slide at a time, and only as they demand it!)

And if they keep digging/begging, I’ll show them how to find the exponential function of best fit.  We’ll see if we can get into why it should be exponential… it is only the first week of school after all.

Of course, the third act should show rather than tell the students that their answer was right or wrong.  Here’s all the data I took.

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Start of Year Difficulties

I haven’t posted all summer because I was away in NC, MD, MI, and France (wohoo!).  But I completely plan on continuing to reflect this upcoming year and I hope that my teaching practices improve significantly.

Ask I started to plan for the first few days (which happened last Wednesday–4 school days ago), I realized that there was a TON of different things that students had to know how to do in order to succeed in my class.  So much so that it was nearly eclipsing the material and content (perhaps it is?).  An experienced teacher once told me that he always wanted to do some math on the first day so that students recognize what is important in the class: doing math. This man is also my father-in-law, and so I honestly believe he was an incredible teacher and want to emulate everything I can that he did.

However, I feel like I have the following things to do before I can “get down to learning”:

  1. Talk about the Syllabus.
  2. Put names on Popsicle sticks (students doing this saves tons of time)
  3. Website scavenger hunt.  My teacher website has become huge due to all the online opportunities I want to give my students. So big that I decided to do a scavenger hunt (see below) for them to find things on my website.
  4. Participation Points.
  5. Have students create Google Accounts. Our school has decided to do away with school e-mail accounts because when they leave school, the school doesn’t have the money to continue giving them e-mail accounts, but that means that we can’t contact our alumni (mostly for Advancement).
  6. Student Survey.  Many of the questions are stolen from other excellent bloggers.
  7. Quiz.  I want to do this before explaining SBG so that they have some point of reference.
  8. Explain SBG.
  9. Explain SAS.  This is my student-initiated assessment form for students to fill out, if they want to improve one of their grades on their own time.
  10. Have students create a blog (using Kidblog).
  11. Setup Remind101 for students.

At this point I’ve done almost everything in all of my classes except setup Remind101.  I have so many options for participation points right now, however, I think I need to introduce them only a few at a time so students can swallow them and try them out. One thing I like is that I purchased a Facebook-like Stamp and I can use this on warm-ups or HW to entice them to work even though HW is 0% of their grade. Forget the 5 points that the stamp is worth, the students really just want to get stamped on their paper! Unfortunately, I think that fascination will wear off soon, which is why I decided to make them worth PPs.

One thing I did that I think worked out well was not trekking through the whole syllabus on the first day.  Instead, I did a scavenger hunt on my website.  That way students are navigating through it and getting comfortable with it, and it’s not just one more class where the teacher talks about procedures (even though I definitely could talk for 3 days straight about procedures!).  Here’s my scavenger hunt below if you’re interested. (Yes, both pages are the same–I saved it that was so I could print them side-by-side on our printer and save paper).


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