Monthly Archives: December 2012

Mistakes

I was just reading a fascinating article about the fear of making mistakes and came across this quote in the article:

“’We translated some textbook pages from a Japanese math textbook,’ Stigler told me, sitting in his office in the rabbit warren that is the UCLA psychology department. ‘There was a really interesting note in the teacher’s edition, and it said: ‘The most common mistake students will make in adding fractions is that they will add the denominators.’ Then it said: ‘Do not correct this mistake. If you correct it, they will immediately stop doing it. But what you really want is for them to take several weeks to understand the consequences of adding the denominators and why that doesn’t work.’” (p. 193)

Wow.  The rest of the article is really great, too.  I suppose in my better moments, I try to lead students to show them why something doesn’t work, but so few of my students have an intuitive understanding of why adding the denominators like that doesn’t work.  And unfortunately at this point I could give them all the time in the world and they will never understand on their own why \frac{\cos(x)}{\sin(x)}+\frac{\cos(x)}{\sin(x)} is not equal to \frac{\cos(x)+\cos(x)}{\sin(x)+\sin(x)} unless they first understand why \frac{1}{1} + \frac{1}{1} is not equal to \frac{2}{2} .  Many of my students, when I show them \frac{1}{1} + \frac{1}{1} will go “oh, I know about that”, but I really get the feeling that they don’t understand why that’s the “rule”.  Perhaps one of these days I should investigate that more closely.  If they had a teacher who taught like the Japanese math textbook suggested above, they would be far less likely to make the mistake pictured above.

Of course, I don’t blame the elementary and middle school teachers.  I was these once, I know.  I would never have the patience to teach using that method.  Heck, I don’t even have the patience to teach those age groups with any method, so please, if you don’t do that, I’m not blaming you.  I just wish I had the patience and foresight to understand when I should employ a tactic like that.  But I feel like it would require an overhauling of the US system of teaching.  Hmm, it’s late and I’ve rambled too much.

Side note: I am in the middle of grading some tests and one student, in all seriousness, has \frac{1}{1} + \frac{1}{1} = \frac{2}{2} .  Seniors in Precalculus.  Sigh.

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Augmented Reality Lesson: Results, Pictures, and a Video!

There were some hitches in my augmented reality Around the World review activity.  First, I found out the morning of the activity that the QR Codes which are scanned by the Augment app expire after a certain amount of time.  So I created new QR Codes hoping they would last just an hour, that is, until my first class started the activity.  However, at the beginning of class it was not working either, so fortunately I was able to tell them to search for a specific compound, such as “NF3”.  This worked because there are not tons of models on their site yet, and so searching for “NF3” in their app only found the model I had created for them.  However, this had the drawback of showing students the description I wrote, where I put the correct name of the VSEPR shape of the molecule for my own use.  Oops.  I fixed it quickly by editing it online, but not after a handful of students saw the answer without thinking about the shape.

**EDIT Update: A representative from Augment contacted me sending just a normal “hey, how’s the app going?” e-mail, and I decided to reply with my above question about the QR Codes not working.  He explained why they were non-permanent, but he also said that he could make me permanent QR Codes if I needed them!  Awesome!!  Unfortunately this activity is over, so I don’t need them now, but I will definitely keep that in mind in the future.  He also explained that they were moving in the direction of creating a “For Educators” section, which would include permanent QR Codes.  What an awesome company!**

However, overall it was a great success.  I’ll leave a handful of pictures, and a video, for you to show the student’s enthusiasm.

2012-12-10 09.31.56

2012-12-10 10.59.15

2012-12-10 11.04.23

2012-12-10 11.04.50

Here are the QR Code Sheets which I cut up and posted around the room, if you would like to use them or see how it is done.  Notice that the Augment app QR Codes no longer work for the models I created.

Oh, and here are the wrong answers, most of which have some kind of helpful statement to get them on the right track.

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Augmented Reality: Whoa, This is COOL!

Augmented Reality is really, really, really cool.  No, seriously, if you have an iDevice, stop reading this and go check out one or more of these apps: Spacecraft 3D, AR Basketball, Augment, or String.

I was going to write a post about these really awesome iPad apps I discovered by reading Richard Byrne’s blog (here’s the specific blog post).  I was planning on asking (and trying to answer) an question like: How can we move this kind of technology from the “wow, that’s cool” stage, where we capture students’ attention simply because the medium happens to be different or interesting, to actually using this technology in ways that we couldn’t use previous technology?  Furthermore, how can we do this and avoid the time-consuming technology problem?

However, that question will have to wait, because I made at least one cool lesson using the program and I wanted to share that really badly.  The third app in the above list (Augment) allows you to upload your on 3D models on their website.  This is really awesome because you can use a program like Google Sketchup (now owned by another company, I know) or Blender to create 3D models and allow students to view these models.  There are already a handful of models in Augment’s gallery, but none that pertained exactly to the subjects I was teaching, so I decided to create a few of my own (very simple) models.

We are just now getting into VSEPR Theory and looking at 3D molecules in Chemistry, so the timing couldn’t have been more perfect.  I created a few simple molecules (Water, CH4, CO2, BF3, and NF3) and now students will be able to check out the molecules in 3D very quickly because there’s a QR code reader in the app to send them directly to the model I created for them.  This is particularly important because otherwise it would take me 10 minutes to teach them how to get to the correct model and another 10 minutes for them to figure out how to get there after they’ve ignored me for 10 minutes.

I’m actually making the models as stopping-points in my QR Code Around the World Review Activity (similar to the last QR Code Around the World I created for the last test), so it won’t just be “hey, come over and look at this” but instead I’ll be asking them a question based on what they see.

Just as a side note: while Sketchup isn’t too difficult to learn how to use, it doesn’t export very well to .dae, which is what you have to use to upload it to the Augment website.  I found Blender to be a much better program for creating things and being able to specify properties.  However,  is a complex and difficult program, and I only was able to complete this project in a weekend because I had played around with Blender and learned some of the intricacies of the program earlier this year.  If any teachers out there would like for me to create any shapes for their class (I’m thinking particularly of Geometry teachers who are actually working in 3D sometimes), then just e-mail (jnewman85 ‘at’ gmail ‘dot’ com) me and I’d be happy to create something simple.

And yes, I know that I could have physical ball-and-stick models sitting on the table in place of these, but I think these things will capture their attention just that little bit more and give the activity that “Wow” factor.  I’m still looking for a lesson that uses this Augmented Reality to teach in ways that were not possible before, so let me know if you have ideas.

I’ll try to remember to post pictures of my students doing this activity soon!

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Stop-Motion Parametrics

The title says it all.  We just started Parametric equations today (it’s our block today, so I get my Precal students for an hour and a half), and I was fretting last night about how to make Parametrics more fun, when I saw a video on Colossal (awesome website) which used a stop-motion and thought “Hey, we have iPads–we can totally do this!”.

So after teaching the students what a parametric equation is (and giving them some cool examples), I showed them a cool stop-motion video (I couldn’t find the same video on Colossal, so I found another one on Colossal…), and asked them to make their own video based on their own parametric equation.  The results were awesome!! (See below)

For this project they just had to find an interesting parametric equation, write down the equation, a table, and a graph, and then submit their video using Google Drive. I recalled from previous experience that there is almost no other way to share pictures and videos from a class-set of iPads (non-personalized). Fortunately, last time, I was able to create a Google Drive account for the class, and they were each able to upload, rename, and reogranize their videos so that next class we’ll be able to watch each other’s videos and go “ooh” and “ahh”.  Below is a photo of a group’s work to match their video:

equationAndGraph

table

The app they used was iMotion HD (yes, it’s free!) and it is so intuitive that all my students were able to use it very easily (the stumbling block was the math, not the technology, as it should be).  The best part was how quickly students figured out how to make the video (and it looked cool!) after they created the graph.  In the app, there are a few options, such as changing the frame-rate once you’ve recorded the video, or triggering the photo button through use of sound, timer, or remote (requires another iDevice).  This is one lesson that I will definitely be doing next year!

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Mistakes Game: Gallery Mode

On a recent blog where I talked about error correction, Steve Grossberg reminded me about the Math Mistakes game.  I had used this once before in Physics, but it was less of a success than I had hoped for (I was really excited about it, but the “game” just flopped in class).  However, I hadn’t tried it with my advanced Precalculus class, and I must say that it went over pretty well!

It’s great for the setting of proofs in trig identities, however I had my students create the math mistakes on your standard 2′ x 3′ whiteboard.  Then, the next day, as they finished the quiz, they went one by one over to the “Math Mistakes Gallery” and looked for mistakes.  When they discovered a hidden mistake, they would write it down on their paper.  Once everyone got a chance to look through the gallery, we came back together and discussed what people found.  I even tallied up how many people found each mistake, and the “winner” was the person whose mistake was hidden the best.  Here’s the winner:

A Tricky Mistake!

A Tricky Mistake!  Also hard to read…

We even had a discussion about how good the mistakes were and what made them good!  We decided that the winner won because he put the mistake during multiplying the binomials, and students don’t like to multiply binomials (at least they admit it).

This variation–“Gallery Mode”–is good because it allows students to work at their own pace, AND it allows students to work and think the entire time.  Nobody discovered all of the mistakes, and almost everyone got to at least read all of the proofs.

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