# Getting Graphs to Instructure Canvas Discussions

May 21, 2012 by

It’s not too hard to get graphs (or any kind of image that you can grab off your screen) into Instructure Canvas. From the instructor side, you can upload an image, which is easy enough, but what about from the student side?

An example of a student post that includes a graph (copied from Wolfram Alpha using Jing)

The trick seems to be copying and pasting from a stable URL. For example, in our first attempt, we tried to just copy and paste an image from WolframAlpha. Initially it looked like it worked. The image appeared on the discussion board as expected, and it seemed to save when the post went live. However, as soon as I visited the post from a different computer, the images copied directly from WolframAlpha were gone.

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# Logarithm Graphs in Wolfram Alpha

Mar 16, 2010 by

At the Wolfram Alpha Workshop at ICTCM, there was universal disappointment about the fact that you cannot get a graph of a logarithm that is only over the real numbers.  We tried everything we could think of to remove the complex part of the graph.

Personally, I have tried and tried and tried and tried to explain the problem with this in the feedback window for Wolfram Alpha, but been universally unsuccessful.   Every time I suggest a change, I am told that the “After review, our internal development group believes the plots for input “log(x)” are correct.” … yes, I know that … that doesn’t mean it’s the answer that most people will be looking for.

I find it ironic that “inverse of e^x” produces the graph we’d like to see, and even gives log(x) as an equivalent.

But then ask for a graph of  log(x) or ln(x) and the graph will always include the solution over the complex numbers.

What’s worse is that W|A inconsistently decides when to use reals only and when to use both complex and real numbers.  For example, the output for y=ln(x), y=x includes the complex numbered plot, while the output for y=ln(x), y=2x-3 includes only the Reals.  What!?!  Actually, I have some idea why this is … it seems that in some cases, if the extra graph intersects the real part of the log graph, then you get reals only.  If the graphs do not intersect, then you get real+complex.  For example compare the output for y=ln(x), y=2x-3 to the output for y=ln(x), y=2x+5.  On the other hand, when I tried to show a graph transformation, like y=ln(x) with y=ln(x)+4 (including the extra graph y=4x-3), I was back to getting the graphs with complex numbers again. Maddening.

We spend a LOT of time in the algebra and precalculus levels working with  transformations of graphs, understanding inverse functions, and specifics like the domain of a graph.  We can’t use Wolfram Alpha for any of these topics with regards to logarithms because of the way the graphs look.  I can live with the fact that W|A uses log(x) instead of ln(x) … it’s not great, and is confusing to students, but I can explain it and live with it.  But as long as the Wolfram Alpha graph includes the complex number system with no way to see the graphs on only the reals, we’ll have to pull out that old-fashioned graphing calculator to teach this section, and that’s a shame.

I’ve also heard the argument that we should just include the domain we want to see in the W|A input.  For example, y=ln(x), x>0.  But how is a student, learning logs for the first time, supposed to recognize that this is required?  After all, the graph they see when they first try W|A with y=ln(x) leads them to believe that y=ln(x) has a domain that includes all real numbers but zero.  This argument also means that to show graph transformations, we need to use much more complicated graphing commands, restricting each domain separately (to tell you the truth, I have not yet figured out a way to do it … although I suspect it’s possible).

It seems to me that there are two obvious solutions to this math teaching nightmare, and I can’t imagine why either one wouldn’t serve all parties using Wolfram Alpha (both high-level mathematicians, and the rest of us):

Solution #1: Use a toggle-able option to see the graph with only reals or both complex and reals  (I would prefer a default to the Real numbers graph, since my guess would be that the majority of the world’s population would be looking for that one).

Solution #2: Display TWO graphs.  Show a graph of the logarithm that is only on the real number system.  Then, below it, show a graph that includes both the complex and real number systems.

That’s all – end of rant.  This is the one thing I absolutely hate about Wolfram Alpha.  And I’m guessing that I’m not alone here.  Please can’t we just find a solution without hearing “After review, our internal development group believes the plots for input “log(x)” are correct.” again?

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# Wolfram Alpha Discovery

Mar 15, 2010 by

Okay, technically it was a workshop at ICTCM, but with 30 math faculty in one room, all armed with computers, I couldn’t help but make it a discovery and brainstorming session too.  I’m a firm believer in harnessing the power of a room of people instead of talking to them (provided that we have some technology to facilitate that).

This post is Part I … the discovery portion of the workshop.

One of the things that made this workshop a bit out-of-the-ordinary for math workshops was that I set up a “backchannel” for participants to use to share their thoughts, discoveries, and ideas.   To do this, I used a Chatzy Virtual Room – anyone can “join the room” as long as they know the URL – just state your name, and you’re in the chat room.  This made the discovery process collaborative, as well as fast and furious as everyone in the room got a chance to contribute to the conversation in real time.

The first question I was asked (which I am asked in almost every workshop I do), is how on earth I was magnifying just a small portion of the screen (like where the input box was).  I use a free tool called the Virtual Magnifier.

The group “play” with Wolfram Alpha lasted for about an hour, during which we (they, mostly) discovered quite a few interesting things, all of which I am sharing with you here in a clickable format.

Did we forget to mention that you can copy images (or save them) directly from W|A output? [right click or command-click (mac) on the image to get copy and save options] You can actually do this for any output of W|A, including tables, equations, and images.

• When you use ln(x) the output shows log(x), which has traditionally been Mathematica notation for natural log.  To get a log with base b, use log(b,x).  Yes, the graphs suck.  That’s something I’ll post about later this week.

With Wolfram Alpha, you can compare any list of items that have some kind of data associated with them.  Just separate the items with a comma:

Participants also stumbled upon Alpha’s sense of humor …

That was approximately one hour of our Wolfram Alpha Workshop with about 95% of the content and discovery being done by participants.  It took me three hours to write that up, which just goes to show you how powerful a backchannel chat window can be!  I will save the brainstorming session “How can we restructure classroom learning and assignments to use Wolfram Alpha?” in another post.

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# Best of the Ed Tech Freebies!

Jan 26, 2010 by

In a “pilot” program, we used Camtasia to record several sessions at the 2009 AMATYC Conference in Las Vegas.  Several of these recordings are now available on the AMATYC 2009 Conference Proceedings Website.

In particular, you might want to check out my live presentation “Best of the Educational Technology Freebies” … at least, you can check out the first 24 minutes of it (before my spectacular graphics-overload-induced red-screen-of-death computer crash).  The live presentation starts approximately 1 minute into the video.

There is a Part II (audio with a few PowerPoint slides – all my computer was capable after burning up the graphics capability temporarily), but I guess they haven’t put it up yet.  Update: Part II is now also available here.  Incidentally, this incident sealed the deal on my getting a new tablet PC (I was running with the memory capacity and hard drive maxed on the old one).

Word to the wise: You should not attempt to simultaneously record new audio narrative for a Camtasia video project running in the background, while running that video in a player on the notebook and projecting to a screen.  Sure, it works for 5 minutes, but will it work for 60? [no, unless you have a really powerful computer and graphics card]

The easy way to find all the recorded videos from the 2009 AMATYC Conference is to search the Conference Proceedings website (Ctrl-F for find) for the word “flash” (as in Flash video).

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# Teaching Math with Technology (Discussion Panel)

Dec 3, 2009 by

While I was at Wolfram Alpha Homework Day, I participated in a Panel Discussion about the Myths about Teaching with Technology. The panel ran 30 minutes and was mediated by Elizabeth Corcoran. There were three of us (all women, weirdly enough), Debra Woods, a mathematics professor at the University of Illinois at Urbana-Champaign; Abby Brown, a math teacher at Torrey Pines High School; and myself.

I no longer remembered anything that I said in this panel, so it was fun to watch the discussion from an outside point-of-view. I am glad to see that I talked about the value of play during the discussion, because I am finding more and more that introducing play (and exploration) back into learning makes a big difference in engagement and in retention of the subject.

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# What we’re doing with WolframAlpha

Oct 20, 2009 by

Originally, I started this post with the title “What I’m doing with Wolfram|Alpha” and then I revised it, because it’s not just me using Wolfram|Alpha. My students are using it too. Here are some of the things we’re doing:

Discussion Boards: Wolfram|Alpha + Jing = Awesome

Before Wolfram|Alpha, it could take several steps to get a graph or the solution to solving an equation to the discussion board in an online class. You had to use some program to generate the graph or the equations, then make a screenshot of the work, then get that hyperlink, image, or embed code to the discussion board.

With Wolfram|Alpha, sometimes a simple link suffices. Suppose, for example, I needed to explain the last step in a calculus problem where the students have to find where there is a horizontal tangent line. After finding the derivative, they have to set it equal to zero and solve the equation (and calculus students notoriously struggle with their algebra skills). Rather than writing out all the steps to help a student on the discussion board, I could just provide the link to the solution and tell them to click on “Show Steps.”

Sometimes, a bit more explanation may be required, and in these circumstances, Jing + Wolfram|Alpha really comes in handy. For instance, I needed to show how to reflect a function over the line y=1.

Here’s what the reflection over y=1 looks like. If you graph y=sqrt(x) and y=-sqrt(x)+1 you will see that they are not reflected over y=1.

Here’s another example of Wolfram|Alpha + Jing:

Classroom Demonstrations

We’re also finding that Wolfram|Alpha can be a good program to use for exploratory learning. One of the subjects we cover in Math for Elementary Teachers (MathET) is ancient numeration systems. Rather than just tell students how the Babylonian number system worked, students can use Wolfram|Alpha to explore the number systems until they’ve worked out the pattern.

1. Start by exploring numbers under 50 (42, 37, 15, 29).
2. Now ask students to figure out where the pattern changes (hint: it’s between 50 and 100).
3. Explore numbers in the next tier and see if they can figure out at what number the next place digit gets added.
4. Discuss how a zero is written (and why this is problematic).

Supplement to Online Course Shell

Another topic in Math for Elementary Teachers is learning to perform operations in alternate-base systems (like Base 5 and Base 12). You can easily supplement your online course shell by providing additional practice problems and then linking to the answers with Wolfram|Alpha.

1. Find the sum of 234 and 313 in base 5. (answer)
2. Subtract 234 from 412 in base 5. (answer)
3. Multiply 234 by 3 in base 5. (answer)

Student Projects

Wolfram|Alpha has also started making its way into student projects because of the ease of just linking to the mathematics instead of writing out or drawing the math. Here are a few examples.

For one of the calculus learning projects, the group built a mindmap that demonstrates the graphs and translations of exponential and logarithmic functions.

Another group recorded some help tutorials on using Wolfram|Alpha for evaluating limits. Here are two of their videos (one with sound and one without).

Several of the MathET students have used Wolfram|Alpha and Wolfram Demonstration links as they mapped out the concepts in our units.

Checking Solutions and Writing Tests

Personally, I’m finding that I use Wolfram|Alpha from a simple calculator to a CAS for checking answers as I write a test. I’ve also been snagging images of graphs from Wolfram|Alpha to use on tests (use Jing for simple screenshots). Here’s a short 1-minute tutorial on how to change the plot windows to get the image you desire.

Homework Day

Oh, I almost forgot to tell you. I’ll be down in Champaign, IL for the rest of the week at Wolfram Research. Tomorrow I’ll be one of the “experts” participating in Wolfram|Alpha Homework Day (a live, interactive web event). The events begin at noon (CST) and end around 2am. I’ll be interviewed somewhere around 3 pm and participate in a panel discussion about technology and math education at 8pm.

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