Archive for the ‘Math on the Internet’ Category

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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After several months alone to think about why education has become so transactional, I decided that I’d have to “walk the walk” and not just “talk the talk” and so I set about revamping my own classes.  For several weeks, my brain processors whirled while I tried to figure out how to make courses that have a highly structured and full curricula into courses that are transformational and revolve around learning.  Eventually, I hit upon the solution: Learning Projects.  Each student in Math for Elementary Teachers (MathET, as I like to call it) has to do five learning projects during the semester:

1. Writing a Learning Blog
2. Building a Mindmap
3. Giving an Inquiry-Based Learning Presentation in class
4. Creating a Video for the Internet
5. Creating a Digital Portfolio to house their projects (this will be done by everyone last)

We cover four “units” in MathET, and each student completes the first four learning projects in a random pre-assigned order (I made a chart of all project assignments at the beginning of the semester).  This means that at any time, 25% of the students are blogging, 25% are building mindmaps, 25% are working on a 10-minute presentation for class, and 25% are building a video on a specific topic.  Projects are due two days before the unit exam so that everyone can learn from reading and clicking through each others’ projects.

No lies.  This required a large amount of time to get a new syllabus in place, verbage about privacy and appropriate computer use, tutorials on the LMS, and grading rubrics (and I already knew how to use all the technology).  I had to move one hour of class (4 hours each week) into a computer lab (and lab time is as precious as gold on our campus).   I set up an RSS feed (via a class netvibes page) to put news about math and teaching at the fingertips of the students.   I have to create a page to hold all the RSS feeds from student blogs, videos, and mindmaps (see the Unit 1 Tab of the class netvibes page).  This project also required a pep talk on the first day of class to explain why I was requiring that students use technology as they learned (because it will help them find jobs and provide them with valuable ways to teach and learn).  It was a bit of a shock, especially to those students who had barely touched a computer before.

However, the work was 100% worth it (maybe even 200% worth it).  We have never (and I mean never) had so much fun with a class before.  Every day of class I automatically get fresh learning assessments from the students who are blogging or mapping out the concepts we’ve learned.  The students really enjoy participating in each others’ active presentations and gain lots of fresh ideas about how to incorporate different teaching strategies into their own classes.  It’s also fun to watch the students get more brave (technology-wise) as the semester progresses – I really can’t wait to see what these projects look like by the end of the semester!  As I walk through the lab or peek at laptop screens before class,  I see students getting sucked in to reading blog posts and news articles that they might not otherwise even see (e.g. Math in the News).  I see them playing with interactive manipulatives from NLVM, and getting hooked on logic puzzles.

Because every single project is organized around learning, they all enhance the students’ understanding of the material.   How do I know?   There were no failing grades on the first test.  Students write and talk about how learning Venn Diagrams is “awesome” and how learning base-5 arithmetic is “tricky but cool” … it’s like math has gotten turned upside-down. What was once scary and difficult is now fun and interesting (maybe still difficult, but more tolerable now).  I think it may even be possible that students are now more likely to study for the exams because they actually enjoy learning the material (this is just conjecture on my part).

There are lots more details to share about how, exactly, I’ve pulled this off (release forms, privacy issues, etc), but for now I’d like to share a few of the best projects from Round 1 of the Student Learning Projects.  I hope that by the end of the semester, every one of my students will have found a project where they had a chance to shine the best and brightest!

Best Student Web-based Projects: Round 1

• Blog: Hez B’s Math Adventures
• Blog: RoseMath
• Mindmap: Ashley’s Map
• Video: Deductive Reasoning

Honestly, I wish I had recorded more of the student IBL presentations, because many of them have been clever and well-designed.

In addition to the projects, we’ve found ourselves doing some other fun things:

• Venn Diagram Contest (Indexed-style)
• A short clip from Scott’s IBL Battleship Presentation (on coordinate systems)
• Video recordings of hands-on demonstrations during class (here is one on Base-5 Subtraction and another on the Closure Property)
• Using Wolfram|Alpha to look up numbers written in Egyptian and Babylonian or to complete number patterns

One more thing I’ve changed in all my classes this semester, I try to begin every class by asking students what they’ve learned in their other classes (an acknowledgment that these things are important too).  The only way to refocus education on learning is to make sure it actually is the focus.

Learning Projects Round 2 are already well underway!  Students can see each others’ blogs and mindmaps in progress from day one of the unit.  This (hopefully) encourages them to explore and read more about each topic as they follow links to resources and read about how math has been applied.  Stay tuned for more in our little learning experiment.

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For anyone who has ever had trouble convincing your administration to give you the proper tools to teach online, I give you this little gift: eLearning Tools for STEM, published today in eLearning Magazine.

The tools for STEM eLearning

1. Tablets
2. Recording & editing software
3. Jing
4. Equation software and training
5. Synchronous communication system
6. Online homework system

Other head-turning resources for STEM

• Wolfram Demonstrations
• Digital libraries (a lengthy list)
• Video collections (another list)
• TI-SmartView

Other tips (about accessibility, computer labs, etc) can be found at the end of the article.

You can read about all the tools, and why I recommend them, by going to the article, eLearning Tools for STEM.

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Very rarely do learning management systems (Blackboard, Angel, D2L, etc.) do math well.  However this is definitely the exception.

Personally, I use Moodle as an LMS on TeachingCollegeMath to host discussion groups and workshop materials.  It’s free, it’s relatively painless to get it up and running, and frankly, it tends to get features that incorporate new technologies faster than the other guys.

One thing that Moodle does particularly well is math.  Just turn on the LaTeX editor and you’re good to go.  When I was getting started, I asked Bob to make us a tutorial on how to get your math editing up and running in Moodle.  Kindly, he obliged (click here) and I was surprised how easy it is.   I swear, this one is painless.  First, you turn on TeX notation in Moodle:

Then you can use TeX or use MathType to paste the TeX into Moodle!  Since I am notoriously bad at using TeX, Bob was nice enough to make me a second video showing us exactly how to go from MathType to Moodle.  The surprising part?  You can go in reverse too!  Just drag the equations from Moodle back to MathType!  Watch the video to see how.

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Just in case you’re getting back into the swing of things this fall and finding yourself as forgetful as me, I thought I’d give a little Jing refresher here and remind you of some resources.

First, a little reminder of how Jing works!

Myth #1: I use Camtasia so I don’t need Jing

What about your students? Teach them to Jing and they can share screen captures and short videos with you!  Not enough motivation?  It’s much faster to whip out Jing and record a response to a student’s question than it is to create, edit, and produce a Camtasia video.

Myth #2: The 5-minute time limit is a problem.

No, the 5-minute time limit is a blessing.  Who really wants to watch more than 5 minutes of Internet video.  There’s great value in learning to get your message across in a concise little package.  When you ask students to submit videos to you for grading, you’ll quickly appreciate the 5-minute limit.  Plus, there’s nothing to stop you from recording a 3-part series if you really must get 15 minutes of information out there.

Myth #3: The EMBED button is gone!

The embed button is gone from the standard Jing installation, but you can get it back with about 2 minutes of time invested.   Use one minute to watch how to do it.  Use the second minute to do it yourself.

Myth #4: I’ve tried to use Jing, but I never get the image or video when it says my upload is complete.

The link (or embed code) for your captures is stored on the clipboard.  What’s the clipboard?  It’s that invisible place where content goes to wait between Copy and Paste.  What Jing does is create the copy of the URL or embed code on the clipboard.  All you need to do is paste (use Ctrl-V on a PC or Command-V on a Mac) and your code will appear!

Myth #5: Video EMBED doesn’t seem to work.

Many programs restrict the functionality of video embedding.  If your video takes up a large amount of screen real estate, or if video-sharing is disabled in the web-application you’re using, then you won’t be able to embed video.  You can, however, share the video with a live link.  It’s always good practice to include a live link even when you get the embed code for a video to work.  Many blog readers will cut out the embedded videos, and without a link, your reader will not be able to access the video.

Myth #6: Students will never figure it out.

Give them the links to videos on how to use Jing, a place to PRACTICE their newfound skills, and an incentive (2 points per skill seems to do it), and they will learn how to use Jing just fine.  One of my first assignments of the semester is a “Learning Project” that involves, among other things, practicing a bunch of different ways to use Jing (get handwriting to the discussion board, record a video and get it to the discussion board, get an image of some math equations you’ve written to the discussion board).

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Lately I’ve been getting some emails expressing bafflement at understanding the plethora of social networks and why on earth they are being used (many of these questions come from academics).  So, here’s a short introduction to social networking for academics (specifically geared towards the mathematics variety).  Watch the 8-minute video here or below.

In the meantime, I can assure you that the only way to “get” social networking is to dive in and try something.  There’s a reason our students enjoy it so!  I resisted for years (and only dove into Facebook in December).  I have made the choice not to “friend” students until they graduate, but that is a personal decision and can be made only by you.

If you are just getting started, I’d recommend FB.  I have not regretted the decision to join at all. If you let FB look at your email addresses (not stored, no worries) you will be able to see who you already know that is on FB (if a picture shows up for them, they are on FB already).

Very important if you decide on FB to try: Go immediately to Settings and turn off all email notifications (or it will swamp your email inbox).

If you decide to try twitter, look me up @busynessgirl.

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They say a picture is worth 1000 words.  Then here are about 15,000.

I’ve taken screenshots of several examples of the algebra through calculus that WolframAlpha will do.

You can see the album of screenshots here: http://tinyurl.com/q49xy8

I’ll let you see the implications for yourself.

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What if you could go to a free and readily available website and enter an equation, an expression, a question about math, a request to analyze data, or anything else, and the site would answer your question, elaborate on it, give you all the steps for the mathematical work, etc.?

Did that make you uneasy or excited?

Well, ready or not, it’s going online at 7pm CST today, and I think we ought to pay some attention to this.
http://www.wolframalpha.com/index.html

You can watch a screencast about Wolfram Alpha here.

It does have the potential to seriously wreak havoc on the way we teach math today if students can simply copy all their work from an A.I. website.  Whether you think that it’s time that somebody forced a change, or whether you think it’s just hype and not really a threat, I think we should all be aware that after today, it exists.

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I am planning to ask my fall online calculus students to create twitter accounts in order to tweet their studying in hourly increments. As you are probably aware, this is the way I’ve been holding myself accountable to working on my dissertation (227 hours and counting).

Since time management is an issue for online students, I want them to be accountable to themselves that they are honestly putting the time in. In particular, learning in math needs to be spread out over time for long-term retention, but it often gets crammed in at the last minute before a test.  Also, I want to know how they are progressing and what their frustration level is with the material.

Logistics: The students do not have to put any identifying information on the accounts as long as I have the “handle” they have chosen on twitter. They will be required to put a hashtag and the hour number on each study tweet (see example below) so that we can easily see the studying habits of the whole class on one page.  There will be a minimum tweet requirement of 8-12 hours of studying a week (4-credit course) for a total of 150 hours by the end of the semester.  I suspect that it will become a bit of a contest to see who can study the most in the semester (but I may live in a world of rainbows and unicorns).

Why not just ask students to make a written log of their study time? Twitter provides a time stamp, which makes it a little harder to “throw together” a study log during the 10 minutes before it is due.

Why twitter and not something like a discussion board? The ease of posting from either a cell phone or any computer with Internet with minimal log-in (since you can have your twitter login “remembered” on your home computer or use a twitter application, this makes it much easier that logging in to our LMS).  Also, the brevity of the tweets are nice.  While I encourage writing about math, I do not need to read 150 paragraphs x 20 students worth of study habits.  150 sentences x 20 students will be plenty (and using twitter will ensure that it will be kept to a manageable level).

What if they want to share a math problem they are having trouble with? Have you heard of Jing? (no? see the Jing for Math tutorials)

How will I keep track of them all? Students will have to add a chosen hashtag (#m161f09 comes to mind) to each tweet so that we can all see all the study tweets on one page.  They will be free to follow each other, but they don’t have to.  Our LMS does not have a feature where you can see who else is online with you, so this will provide a little bit of feedback about who is studying when.

Good tweets / Bad tweets:

Good: #m161f09 (hr 103): Worked on the first two parts of the chain rule homework set, but I’m just not seeing how I choose the u-substitution, or really why I do it.

Bad: #m161f09 (hr 103): Studied for one hour.

Training: Yes, I am going to need to teach them some twitter etiquette (e.g. tweeting is not IMing), and I haven’t done that yet, but when I make that video for students I will post it around here somewhere, never fear.

Couldn’t students cheat? Sure, but they will have to remember to log 150 time-stamped hours spread over 15 weeks at a rate of at least 8 per week and it will have to correspond with the material that is being covered and their actual login hours in the LMS.  I think it would be easier just to report what they are doing as they do it.

There are some other benefits to twitter that I am hoping to see:  I want students to “plug in” to the network of other students while they study.  They do this with the discussion forums, but only when they need help.  However, they might find that other students in the course struggle with similar concepts without explicitly asking for help on a discussion board.  I am hoping this fosters more collaboration and a sense of “classroom community” that we still struggle with in online math.  Personally, I’ve struggled with ways to add more sense of community to my online classes in a way that is similar to student interaction that is face-to-face.  I think this could do it.

Another benefit I’m hoping to see is more students watching the videos before they do the homework.  I know they are well-watched in the process of homework completion, but there are some video lessons about foundational concepts that probably get light student coverage for lack of directly corresponding homework.  Perhaps when faced with an hourly requirement as well as an assignment completion requirement, this will make it more likely that the videos get watched before the struggles begin to complete problems.

I am also hoping that students begin to see the value of a learning network (as opposed to just a social network) and learn a method of accountability that can help them when they take on large projects (whether it is in school or for work).  In this “age of distraction” that we live in, it is important that we teach our students how to focus when they need to (and learn how to do this ourselves).

Of course, I have to wait until the fall semester to try it myself, but if you give it a try before then, let me know how it goes!  For now, I’m back to work on that pesky dissertation (and hour 228). You can follow me toiling away @busynessgirl if you’d like.

UPDATE: After thinking about this quite a bit, I am making one tweak.  I don’t want the need to count the hours to make this just another bad educational metric.  Therefore, although I will ask students to tally the hours, I will not require any specific amount – just a guideline that 8-12 hours per week would be what I would consider necessary to pass a 4-credit online calculus course.  I will prod students with low study times and low grades to try to put more time in, but I will hope that the social nature of the interactions will simply drive students to work hard.  At the end of the semester, I will ask students to write a 1-page summary of the experience and what they learned about their study habits.

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There’s a website-based equation editor at Sitmo.com, and for a little while, I’ve been trying to figure out what I would use it for.  This equation editor is built by a website that seems to focus on serious quantitative methods for financial calculations (spread options using Gaussian quadrature, exchange option pricing models, etc.).  I’m not sure that the folks who put up the Sitmo site intended for their equation editor to be used for math education in any way.

Here’s what it does.  You can build an equation using either LaTeX or a WYSIWYG editor and their widget displays both simultaneously as you build, right there on the website.

If I needed a quick string of LaTeX code, I could build it here.  Now, I could already do that from MathType, but if I were sitting at someone else’s computer, it might come in handy.

The other thing that Sitmo does is give you a “permanent link” to the equation.  For example, follow this link to see the permanent version of the equation that I generated in the image.  A great upgrade on this feature would be to provide code that would allow you to embed the equation into any webpage (like we do using Jing on discussion boards).

Now the point-and-click interface that sitmo has developed is not fantastic, but it is manageable.  I will give them points for coming the closest to a version of “Ming” (Math + Jing) that I’ve seen yet.

For students who do not have MathType or LaTeX, they would certainly be able to combine this with an image capture program like Jing to turn in mathematical work for an online course.  I’ve added the Sitmo equation editor to my iGoogle page in case I ever need an equation and am not at one of my native machines.

The other way you could use Sitmo would be to teach LaTeX coding to math students with no coding experience.  The ability to see the  WYSIWYG version and LaTeX version change simultaneously means that students could more easily learn by exploring how changes to the code look in the actual equation.

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