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.

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.

latex01

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.

latex12

But look at the source HTML code:

latex07

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.

latex12

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.

Neat-o stats from my blog for 2014

I wrote 106 blog posts in 2014, or about two per week. The actual number is higher, but I wrote a bunch of drafts that are either living in the trash folder or shivering in the drafty darkness, and I removed one post from public view.

I like writing on my blog. I write here to think, to share, to socialize, to converse, to have fun, and to avoid getting down to work.

It’s interesting to look back on the last year’s posts and see what I did, and how it was received.

For instance, the blog received about 11,000 views this year, up from about 3000 in 2013.

My Favourites

When I flipped through the list of post titles, these are the ones that I remember liking more than others, or that I thought were important. They’re mostly about education, but not all. Not stats, exactly, but still neat-o.

That’s nine posts; not one of those arbitrary numbers we call “round”, but still a nice number.

All-Time Greatest Hits

I find the most-accessed-posts list interesting. I always wonder whether the readers were “satisfied”: whether they got what they were expecting or wanting.

You can read my entire blog just by scrolling on the homepage, but these are links that were clicked directly:

Because three of these were written in the last 14 months (interesting, eh?), those are also the top three posts of 2014.

Other Neat-o Stats

I wrote the most posts in April (31), mostly because of NaPoWriMo.

I had the most views during November (1476).

Views-per-visitor is fairly consistent, usually around 1.4 posts per day (including the homepage).

Canadian and US visitors accounted for the vast majority of the views, with nearly equal numbers of each. This is an increase in the proportion of US visitors. The next three countries are the UK, India, and Australia.

Apparently Akismet has protected my site from 18,147 spam comments already. Neat-o. This means about 1.9% of comments are legitimate, and 1.3% of comments are legitimate and not written by me.

Search Engine Terms Used

When people use search engines and find my blog, the terms used are sometimes logged. The most frequently-occurring term is brandon grasley (surprise!). Many times it’s spelled incorrectly (grasely is common), and happily there are few capitals used (Grasley is the same as grasley according to Google, after all). Some of the more interesting searches that landed people here were:

  • how to build an igloo out of legos
  • importance of laptop to rural school pupils when teaching
  • “i didn’t publish it because i thought
  • technial skill the least inportant, why
  • tired of being the go-to-guy
  • how long can a 500 g brick of cheese last
  • email id of people who create a cover for novel
  • can i read kindle comics on chunky

and my personal favourite:

  • a lot of brandons who are on facebook or twitter

Neat-o, eh?

Any cool stats from your blog?

My Unresponsive Course

You have me thinking again, Mr. Peterson. Today it’s with your post, “You Need to Be Responsive“.

My own blogs are responsive and so they display well on multiple device types.

My blog on a computer browser.

My blog on a computer browser.

My blog on a phone browser.

My blog on a phone browser.

Students tell me they like the theme (The Suits Theme) on my class blog; they say it looks professional.

The class blog in a computer browser.

The class blog in a computer browser.

The class blog on a phone browser.

The class blog on a phone browser.

However my e-learning course is less responsive. There is a mobile interface which becomes active when you use mobile device, but there are a couple of components on my course homepage which only appear using the desktop interface (custom widgets with links to the Padlet and the YouTube playlist for the course). Some course tools aren’t available in this view (e.g. the Checklist Tool).

My course homepage on a computer browser.

My course homepage on a computer browser.

Course homepage in the mobile view.

Course homepage in the mobile view.

Tools in the mobile view.

Tools in the mobile view.

What’s more, I have created quite a few PDF files for the programming concepts in the course. These files, because they are paginated, are not responsive.

PDF in a mobile browser

PDF in a mobile browser – portrait

PDF in a mobile browser - landscape

PDF in a mobile browser – landscape

Honestly, I don’t remember considering that issue when finally deciding to use PDFs. Since students are coding on computers anyway perhaps it doesn’t matter that much. And other stuff, like news and discussions, are mobile-friendly.

But I’ve unintentionally made it difficult for them to use small, mobile devices to keep up with the “text” part of the course (i.e. when they’re not actively programming). I do have a lot of video on there, which is (I think) fairly accessible.

I’ll have to think about whether it’s worth fixing the responsiveness of those PDFs.

Assessment and Evaluation: sacrificing complexity for granularity

I teach Math in Ontario. We have an “Achievement Chart” (see pages 28-29) which lists four categories of knowledge and skills. When we assess and evaluate student work, we separate student performance into the “TACK” categories: Thinking, Application, Communication, and Knowledge. The Chart includes criteria for each category and descriptors for different Levels of performance.

The curriculum itself is divided into Strands for each course, and these strands describe Overall Expectations and Specific Expectations (essentially the details of the Overalls).

So when evaluating student work, we evaluate Overall Expectations in the context of the four Categories of Knowledge and Skills, and we should have a “balance” between the categories (not equality, necessarily).

The truth is that I’m having some trouble with it. I posted a little while ago that I was struggling with the Thinking category, and that’s still true. But there is another issue that’s more pervasive and possibly more problematic.

Isolating skills

When trying to separate out the different components of student performance, we would often ask questions that “highlight” a particular area. Essentially we would write questions that would isolate a student’s understanding of that area.

That’s a fairly mathematical, scientific-sounding thing to do, after all. Control for the other variables, and then effect you see is a result of the variable you’re hoping to measure.

For example, we wouldn’t ask a student to solve a bunch of systems of equations which only had “nasty” numbers like fractions in them (or other unfairly-maligned number types) because we fear that a student who is terrible with the fractions will stumble over them and be unable to demonstrate their ability to solve the system of equations. So we remove the “barrier” of numerical nastiness in order to let the skill we’re interested in, solving the system, be the problematic skill.

This isn’t a great idea

But we do that over and over again, isolating skill after skill in an effort to pinpoint student learning in each area, make a plan for improvement, and report the results. And in the end, students seem to be learning tiny little skills, procedures, and algorithms, which will help them to be successful on our tests without developing the connections between concepts or long-term understanding.

We want to have “authentic, real-world problems” in our teaching so that students can make connections to the real world and (fingers crossed) want to be engaged in the learning. But authentic problems are complex problems, and by julienning our concepts into matchstick-size steps we are sacrificing meaningful learning opportunities.

What if we didn’t have to evaluate?

We’re slicing these concepts so finely because we’re aiming for that granularity. We want to be fair to our students and not penalize their system-solving because of their fraction-failings.

But if there were no marks to attach, would we do the same thing? Would we work so hard at isolating skills, or would we take a broader approach?

My MDM4U class

I’m teaching Data Management right now, and the strand dealing with statistical analysis has a lot of procedure skills listed followed by a bunch of analysis skills. If I evaluate the students’ abilities in summarizing data with a scatter plot and line-of-best-fit, do I then ask them to analyze and interpret the data based on their own plot and line? What if they mess up the plot; don’t I then have to accept their analysis based on their initial errors? Oh wait, I could make them summarize the data, then I can give them a summary for a different data set and ask them to draw conclusions from that summary! Then they’ll have the same starting point for analysis, and they can’t accidentally make the question too easy or hard!

But I’ve just messed up one of my goals, then: I’ve removed the authenticity and retained the ownership of the task. I haven’t empowered my students if I do it this way, and I’ve possibly sacrificed meaningful complexity. Worse, I’m only doing this because I need to evaluate them. I’d much rather require them to gather, summarize, and analyze data that interest them and then discuss it with them, helping them to learn and grow in that richer context.

As always…

…I don’t have answers. Sorry. I’m trying hard to make the work meaningful and the learning deep while still exposing as much detail about student thinking as I can. I’m sure in the end it’ll be a trade-off.

Why I’m happy with the design of my first e-Learning course

I’m teaching ICS3C/3U (Computer Programming/Computer Science) online this semester. I was the e-Learning Contact for my board for several years, but this is my first time teaching online in “real life” (i.e. not a professional learning session).

Overall I’m fairly happy with how I approached the design of my course, and I’ve also learned a few things that I’ll improve upon.

I work in Ontario using the Desire2Learn/Brightspace platform. The Ministry of Education here has provided a “starter course” for each of my classes. I’ve discussed the problems with the format of that course before (see here), and thoughts I had about improving on it. I mostly followed my own advice.

In the end, there were significant differences between the provided course materials and the approach I wanted to take with the course, so I ventured out on my own.

News

I use the News area to share interesting links, reminders, and extra details. Notice I don’t post a news item every day; I’ve decided that’s too much without a real payoff.

A screen capture of a news feed.

 

YouTube

I post a lot of “instructional videos” in the course. The videos show me coding applications live, so students can hear my thinking while I work, see the errors I make and how I correct them, and see how the development environment works visually.

A screen capture of a link to a YouTube playlist.

Of course, playing videos successfully in the online learning environment is a bit device-dependent, so I also post every video to YouTube. I maintain them in a playlist (here) and I post a link in a widget on the course homepage. The YouTube videos also have the advantage of sometimes being faster to download, and users can change the resolution on the fly (not very helpful for code, I suppose).

And most importantly, those videos are available for anyone on the Internet to use. That makes me feel good in my heart.

Other Resources

In an out-of-the-way place on the course homepage I maintain a Padlet. I use this to post related-but-not-necessary links.

A screen capture of a Padlet.

Calendar

I don’t use the Calendar directly, but I do use due dates for Content items so they show up in the Upcoming Events list. More on that later.

 

A screen capture of a calendar and upcoming events list.

 

Units, Activities, Modules

I divide up a Unit into Activities, and I number everything:

 

A screen capture showing the activities of a unit.

 

Within each Activity I also “letter” my items sequentially (3.1A, 3.1B, etc.):

 

A screen capture showing activities organized into modules.

Due Dates

I used to only put due dates on the items that needed to be submitted/completed, like Dropboxes and Discussions. After helping an e-Learning student in the library here with her English class, I realized that students were using the Upcoming Events list in the Content area. I had never explored it before, but it was a sparse list in my course.

Now I add due dates to Content items which I want students to consume as well; for example, I put a due date on 3.2E, which is a video I want them to watch by the end of today. They don’t have to submit anything, but I’m hoping the due date helps to keep them on track.

(Note: This is not an “end date”, which would make the item unavailable after the date has passed.)

A screen capture showing upcoming events.

 Content in PDF

I have tried to use HTML, Word documents, and PDF files to post CS content, but I’m happiest posting a PDF that I generate in Word. I get excellent control over the look and feel of the text/images, but the links I put in there still work. It’s also universally-readable.

HTML takes too long to format correctly/beautifully, and Word documents are rendered as images by D2L (disabling any links).

In the end I think the videos are more valuable for the students, especially later in the course. I have several students now requesting videos explaining a certain aspect of the course, but not a lot of PDF requests.

A screenshot showing a PDF file from the course

Still Thinking

I have a lot more to learn, but I’m pretty happy with the workflow I’ve developed now. Suggestions are very welcome!