Physical phenomena for quadratic relations

I’m working on a quadratics unit for my MCF3M (online) and MBF3C (F2F) classes. The Ms need to be able to do a few more things, but both groups have to be able to model quadratic “stuff” using an equation.

I’ll be using desmos.com pretty heavily, and I got some great ideas from Heather Theijsmeijer (@HTheijsmeijer).

I’m trying to find some examples of physical phenomena that I can have students in either class play with to practise/demonstrate modelling. Here are my ideas so far:

Throwing or Bouncing a Ball

This is the first thing I thought of. A ball follows a nice parabolic path in the air if it’s moving horizontally.

My plan is to have students use a phone or camera to record a video or a rapid burst of images, overlay a set of axes, and fit a curve to the path. My iPhone can record at 120fps, which is great. I also found a handy post at Stack Overflow that explains how to extract images from a video, so that might be helpful too.

Pouring Water from a Hose

Set your hose at an angle, turn on the water, and snap a picture. Parabola. Beauty. Maybe put a piece of grid paper behind it, or just import it into Desmos.

Rolling a Ball Up An Incline

This one’s messy, but I think it might work.

Dip a marble in some ink or paint. Set a piece of grid chart paper on an incline (say, a piece of plywood) and roll the ball on an angle up the paper. When it crests and rolls back down, it should have left parabolic paint. On graph paper.

Other ideas?

I’m open to suggestions. I have stuff like photos of suspensions bridges, etc., but I really want something students can generate on their own.

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Key Learnings from our e-Learning Collaborative Inquiry

I learned a lot over the past couple of days. My board brought in Donna Fry (@fryed) and Tim Robinson (@timrobinsonj) to guide our group’s learning, and several folks from the board’s central program team were helping out as well. Check out #elADSB for a bunch of new Twitterers, too.

Here are some prompts that we were asked to respond to, and here are my (rather brief) thoughts.

1. ​​What questions, wonderings do you have ​with respect to our problem of practice?

How do we encourage collaboration that isn’t false collaboration? How do we ensure that the collaboration is meaningful and valuable? I don’t want to force collaboration among students when it doesn’t make sense.

What does a rich task look like in a course which has a lot of technical, procedural learning? Is it enough that there is inquiry in the task, or does it need to be “authentic” and relevant? I’m concerned about fauxthenticity: forcing an unrealistic application out of a concept just so that we can say it’s “real-world”.

2. What key learnings have you had over yesterday and today?

I need to provide more structure for self-monitoring and self-reflection for my students, and then ensure that they follow through on that self-assessment. They’re still kids, and they need a firmer hand with organization and checking on their learning, or they may neglect important stuff (or even delude themselves into thinking they understand concepts that they don’t).

I need to consider including more face time in my course – maybe having “Math Chat With Mr. G” or something on certain afternoons… Even if some students can’t get me live, I shouldn’t prevent it for those who can.

3. Moving forward, as a result of your learning, how do you envision your courses/practice changing?

I need to be more careful about connecting students with each other instead of encouraging them to rely on me.

I need to set up a fast, reliable, easy-for-me-to-check-in-on self-monitoring system for my students.

I will set up Adobe Connect or Google Hangout time periodically.

I’m going to work on figuring out when requiring collaboration makes sense, when students should be working independently, and when they just have a choice (most often?).

I’m going to make some plans and then ask someone else to give me suggestions about them before I implement them. :)

LaTeX Math for e-Learning in D2L

I am teaching MCF3M online this semester, so I need to be able to include math notation in my online content, quizzes, etc. I know how to write math notation using LaTeX from my days at the University of Waterloo, and I find it a lot faster than using a graphical equation editor. I’ve tried Microsoft Word’s editor, which accepts LaTeX-like input as well as graphical input, but I still find it frustrating to use.
I’m teaching in the Desire2Learn/BrightSpace learning environment, so I need to ensure my content works well in there. Last semester I taught Computer Science/Programming and used PDF files that I created in Word Online, and I considered doing the same thing again.

But D2L has an equation editor as part of its HTML editor for webpages, discussion posts, etc. Could it be all I need?

I’ve taken it for a spin before. Here’s the workflow:

Create a new page and type into the HTML editor.

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Expand the toolbar so that the Equation tools are available.

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Choose \∑ LaTeX equation.

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Type in the LaTeX expression, using \( and \) as delimiters for inline mode (otherwise it defaults to block mode).

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Looks good.

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But look at the source HTML code:

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Uh-oh… that’s MathML (Math Markup Language), not LaTeX. What if I want to change something in my original LaTeX?

Well, you can see at the bottom that my LaTeX code is still there, but it’s not being used. I could remove all the MathML, cut out my LaTeX, modify it, and re-insert it using the LaTeX equation editor.

Ugh.

I thought that MathJax, the rendering engine that D2L uses for math notation, could only handle MathML (since notation from both LaTeX and graphical editors are converted to MathML), but it turns out that’s not true. MathJax can do LaTeX.

So I tried putting LaTeX directly into the WYSIWYG editor:

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No dice.

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The trouble is that D2L has parameters on its JavaScript call to MathJax:

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That config=MML_HTMLorMML bit is saying that only MathML is acceptable input (and HTML or MathML can be output).

So I added another call directly to MathJax in my own source code:

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I set the parameter to be config=TeX-AMS_HTML, which will accept my LaTeX input and render in HTML/JavaScript.

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Magic.

But this is kind of a pain.

I can use D2L’s editor to insert math, but I get MathML (which I find hard to edit).

I can write in LaTeX and have it be preserved, but I need to add a script call to the start of the HTML source code (a hassle, but not too serious, I suppose).

Or I can write in some other (offline) development environment, include my script call all the time, and just upload my completed HTML files to my course. This has the advantages of being independent of D2L, available without internet access, and very shareable.

So that’s what I’ve decided to do, at least for now. So I’ve learned a little CSS to make my pages less vanilla/more functional, and I’ll try to improve the look and feel as the semester progresses.

Wish me luck.