Archive for the ‘Equations Online’ Category

Open and Close MathType Equations Quickly

Just in case some of you have made the migration to Office 2010 over the summer (I bit the bullet last week) … here’s an update to making the Ctrl-E hotkeys to open and close MathType without lifting your fingers from the keyboard.  This shortcut (which you should only have to install once per computer or Office upgrade) will save you so much time.

For those of you working with older versions of Word, there are videos for that too.

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Transforming Math for Elementary Ed

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

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:


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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Max-Plus Algebras

Someone asked for a copy of my Master’s Thesis Max-Plus Algebra: Properties and Applications (written in 2002 when I was finishing my Masters in Mathematics at the University of Wyoming). I thought I would just make it generally available in case anyone else is interested.

The thesis explains what max-plus algebras are, relevant theorems and definitions, and illustrates examples of how max-plus algebras could be used.  For example, you could use Max-Plus algebras to calculate the quickest traffic route or finding the bottlenecks in a production line.



For the record, not one character of LaTeX was typed to write this thesis.  I typset the whole thesis using MathType and Word.

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Impact of Wolfram Alpha on Math Ed

I’ve had almost two weeks to think about the impact of Wolfram|Alpha (abbreviated as W|A, and now pronounced by me as “Walpha”), and I’m ready to share some of my thoughts with you.

After spending hundreds of hours reading more than 200 papers on innovation in math instructional practices, change in higher education, and diffusion of innovation theory, it is strange to suddenly find myself observing the possibility of a sudden shift in math education caused by a new innovation. I liken it to being a vulcanologist who has, up until this point, been observing a dormant volcano and then quite unexpectedly, it begins rumbling.

What happens if there is sudden, random change all over the system?

What happens if there is sudden, random change all over the system?

Please keep in mind that these are my own predictions and thoughts, for better or for worse.

1. The adoption rate of W|A amongst students in higher education will be extremely fast.

I’ve examined the attributes and variables that affect the diffusion of innovations, and found that every single one points to a fast adoption amongst students.  Because W|A is free and similar to other technologies they know how to use (designed like a search engine), it has relative advantage over other CAS technologies.  With prior CAS technologies, you had to know exactly what series of steps or commands to write in order to extract the outcome you desired, but with W|A, the less you ask for, the more you get out.  W|A just assumes you want all relevant information it can generate.  W|A is easily trialable – anyone with Internet access can try it.  Not only that, but observability is also high – simply use a hyperlink to share what you’re doing in W|A with others. Compound this ease of observability with the incredible connectedness of the student population in the U.S. (Facebook, MySpace, etc.), and you can see why I don’t think it will take long for W|A to spread to the undergraduate population of math students.

Most students take their math classes for one reason: they are required to for their degree.  W|A will provide solutions to problems, relevant mathematical information, and in many cases, steps for how the solution was obtained.  Thus, for the reason that it appears to be a means to an end (getting through that math course with the least pain possible), using W|A to help complete assignments for math courses will be extremely compatible with the belief systems of these students.

2. There will be a sizable group of math instructors that immediately shifts to using Wolfram Alpha in instruction, and thus, begins to shift the curriculum in those classes away from computational mathematics.

I’ve already outlined many reasons why students will be fast adopters, and for the most part, these are the same reasons that instructors will be fast adopters (high relative advantage, low complexity, good trialability and observability).  The main difference between the student and instructor populations will be the compatibility between their beliefs systems and the innovation.  This is the only attribute where the adoption rate of W|A might be slowed.  For example, Computer Algebra System (CAS) technology (TI-89 calculators, Maple, Mathematica, etc.) has been around for at least 10 years, and yet CAS is not widely adopted in math courses (see the latest CBMS Statistical Report).

That’s not to say that math instructor beliefs aren’t compatible with the use of CAS Technologies.  I suspect that many, like myself, simply found that implementation of CAS in the classroom was too difficult.  In my case, I questioned how could I ask my students, who already had a non CAS-calculator in-hand from high school, to pay for extra software or another calculator to adopt the curriculum to CAS-inclusion.   To teach using software (before students all began buying laptops), we would require computer labs and site licensing, and this was not in the budget for many of us.  Whether it was calculators or software, either decision would require students to spend more money, and thus, these were decisions that would likely have required department buy-in.

What does this mean for the adoption of W|A today?  Instructors who already teach with CAS technologies will easily make the shift to using W|A.  Instructors who liked the idea of teaching with CAS, but were unable to implement for logistical reasons, will quickly also quickly make the shift to using W|A (you may think I’m full of it here, but I already know of several who have already changed their courses).   The real beauty of W|A being free is that individual instructors, under the umbrella of academic freedom, do not have to ask their departments or colleagues for buy-in.  Shoud they?  Yes. And if they are under some kind of contract to teach in a prescribed manner given by the department, then they should definitely ask.  But for the majority of us, if we just decided to change our courses tomorrow, very little could be done to stop it.

For my complete analysis of the rate of diffusion of W|A, you can download the 2-page analysis or view the slides that compare CAS and W|A.

3. There will be a sizable group of math instructors that attempt to either ignore W|A or put up an active resistance to it.

While some instructors will actively ignore the existence of W|A (look at the theory of cognitive dissonance), some will just passively miss it for a while (you know, by ignoring that email that they get sent that warns them to take a look at what W|A does).

However, given that there are still pockets of instructors and departments in the U.S. where graphing calculators are still not allowed, some instructors will likely react with resistance (i.e. we still don’t change anything) or possibly even with the charge that using W|A is cheating. For these instructors, compatibility of beliefs is not there.

What happens if there is well-planned similar change throughout the system?

What happens if there is well-planned similar change throughout the system?

4. We can change if we do so by focusing on areas of agreement instead of disagreement.

Mathematicians in higher education have been divided over reform teaching for 20 years now.  Much like some of the political hot potatoes of our time (which shall go unnamed here for fear of blog spammers), it is unlikely that the two camps of traditionalists and reformists will ever sway followers from the opposite side.   However, we can hope to agree on a middle ground.  I think we would all agree that we want to make sure that math instruction focuses on learning concepts.  I think we would all agree that some understanding of algebraic manipulation is important to lay the foundational structure upon which the rest of mathematical understanding is laid.  I think we would all agree that there is some set of fundamental skills that must be learned extremely well in order to progress to higher levels of mathematics.  Finally, I think we would all unanimously agree that we wish we had more time in our classes to be flexible in what we teach – to bring in interesting mathematical examples from the world around us even if the math doesn’t directly relate to the topic of the day’s lesson.

Perhaps this is the time for us to reach out and embrace a tool that might allow us to jettison some of the computational knowledge from the curriculum, and give math instructors greater flexibility in supplemental topics in the classroom.   Just like each English instructor has their own favorite books to teach with, math instructors have their own favorite topics they wish they could share with students: fractals, trend analysis, network theory, number theory, modern algebra … maybe these finally get a turn at the table.

One more thing.  You (my readers) have to understand how scary this whole thing might be for some math instructors.  I still think that anyone who is not a little scared by the changes that W|A brings hasn’t thought about it enough yet.  I’ve always been an instructor that lived for change, and I’ve been uneasy since W|A launched on May 15.   I have no doubt that I can change my courses to adapt to the new environment, and I know that in the end, the changes will be good ones – but the thought of changing so much across the board in all my courses is a daunting one.

We math folks were attracted to mathematics for its beauty, its power, and its logic.  In the classroom, we have always been the beneficiaries of its non-changing nature.  Algebra is algebra and calculus is calculus.  In all the languages of the world, algebra and calculus have been fundamentally the same for hundreds of years.  You can walk into any colleague’s class and cover for them as long as they tell you which topic to launch into.  This has been a fairly easy world for us to inhabit and teach in up to now.  So now, things change.  And probably, they change quickly.

My perspective, from my position inside the system.

My perspective, from my position inside the system.

5. We all need to keep the system in mind.

None of us teaches in a vacuum.  You cannot make major changes to your course without at least considering the impact that it will have when those students move to the next course, the next instructor, or the next college. Make sure that your course changes still provide sufficient “math backbone” to span students successfully to the next level of mathematics.  For more on this, view the slides starting on slide #13.

Personally, I do plan to change my courses to incorporate W|A in the fall, and let me tell you that I’m grateful to have another couple of months to think about exactly how to do it.  To those of you who are already using W|A this summer – you are the pioneers!  Please blog, write, comment, or email about how it is going and advice for making it work.

Note: Derek has also put up a WalphaWiki where we can all begin to document how W|A handles traditional math topics and the impacts this will have on our courses.

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MathDaisy 1.0 for Accessible Math

Last year, I posted about a product that could read math for blind, sight-impaired, or learning disabled students.  With the release of MathDaisy 1.0, it’s just gotten a LOT easier to produce accessible materials.  I’ve got thousands of pages of math materials built with MathType in Microsoft Word.  With MathDaisy, I can now just save these files in the MathDaisy “daisybook” format, give it a little time to produce, and then the produced file can be opened in a player (like gh player) and be read out loud to the student.

Before you read any further, you’re going to want to see just how easy this is.  As you know, I’m super busy right now with my dissertation, and don’t have extra time to mess with much else myself – but my friend Bob was nice enough to make me a short video to show me how MathDaisy works.  Invest five minutes of your time to see how MathDaisy works.


Want to use it now?  Once you’ve got the software set up, it should be pretty easy.  Here’s what you will have to do for software installation:

  1. You need to have MathType 6.5 (or use only the upgraded equation editor in Microsoft Office 2007).  For older files, you’ll want to first convert all the equations to the newer MathType 6.5 format using the Format Equations feature of MathType.
  2. Install the DaisyTranslater into Microsoft Word (30.5 MB download).
  3. Install MathDaisy 1.0 (a 30-day free trial is available if you want to play first)
  4. Install one of the two compatible readers to be able to play the produced files (gh Player or DolphinEasyReader)

Here’s what the student will have to do for software installation:

  1. Install one of the two compatible readers to be able to play the produced files (gh Player or DolphinEasyReader).

Got that done?  Just save your files as a DaisyBook and off you go!

Bravo to DesignScience for getting us some real help with making math accessible!  In my opinion, this should get them a nomination for the 2010 ICTCM Award for excellence and innovation in using technology to enhance the teaching and learning of mathematics.

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Prequel to MathType Tutorials

I should have anticipated this, but it was late at night.

You may need to first be convinced that MathType has its uses (if you are a LaTeX user). For the record, LaTeX has it’s uses too.

Here is my Equation Challenge! Type the following 15 problems using the program of your choice. (download it here in pdf)

I can type it in just under 5 minutes (watch that here). How long does it take you? If you can do it quickly in the equation editor you use, please record an example and comment it in.

I’m also giving you a link to a video in which I walk through the solutions to 20 derivative problems using MathType to write the math. You might be surprised to see that I can write the mathematics as fast as I can discuss it. I am (for the most part) not using the mouse.

(jump to the 1 minute mark to skip the mathematical explanations – and please keep in mind that this is not a pedagogical example – it is a video of the solutions to an exercise that the students work on after learning the derivative rules)

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MathType Video Tutorials

At the end of every traveling workshop I do, I like to do 30 minutes on using an Equation Editor. Everyone thinks they “know” how to use one. There’s not anything they can be taught. It’s one of the more fun sessions to do simply because everyone discovers something they didn’t know before. And it always would have saved them a lot of time.

One of the participants came up to me afterwards and confessed that he had written 150 pages of math text and he could’ve done it in half the time if he had learned these tips first. Several participants asked what they should be doing with all the free time they will have since typing their tests won’t take as long now (of course, they should be looking for some great interactive math stuff on the Internet with that extra time!).

Anyways, back in my hotel room that night, I again found myself wondering why the heck MathType doesn’t post video tutorials. Then I remembered that I actually have a set of tutorials that I recorded for the faculty on my campus.

Disclaimer: These videos are not great quality. They were some of the very first videos I ever recorded with Camtasia. The clicking sound is annoying (I figured that out later, but can’t remove it). And I’m really not compelled to re-record these because, well, it’s not my job!

However, as one last Bon Voyage gift to my readers, I’ve reproduced them so that I could post the tutorials on YouTube.

If you use equation editor or MathType, no matter how well you think you know how to use these, do yourself a favor and take 30 minutes to watch the videos. For 99.9% of you, it will save you far more than 30 minutes of time in the future. (the other 0.1% actually took the time to read all the MathType help files or have been to one of my MathType workshops)

MathType Tutorial: Creating the Ctrl-E Hotkey (for easily opening & closing equations)

MathType Tutorial: Using Hotkeys Part 1

MathType Tutorial: Using Hotkeys Part 2

MathType Tutorial: Formatting Equations and Alignment

MathType Tutorial: Tables and Formatting

MathType Tutorial: Formatting All the Equations in a Document

Just for the record, I could make much better videos today and I would actually add quite a few more tips (like nudging, Lewis Dot Diagrams, and miscellaneous other tips). But given that I’m in a time crunch, and there are many, many other things I should be doing right now, this is what you’re getting (my C-level video performances).

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When your MathType Toolbar Disappears

One of my assistants (Meg) was in a desperate panic today because her Ctrl-E command for MathType stopped working yesterday (and we are in the middle of a little project). Funny, because Jill (another assistant) got the MT Extra font error yesterday and it was driving her nuts.

Back to Meg’s story. To add insult to injury, her MathType toolbar was also (suddenly) gone. Falling back to old habits, she went looking in the Insert menu (on the object list) and sure enough, no MathType there either.

Okay, she thought … I’ll reinstall MathType. Nothing. What threw her over the edge was that Office kept telling her to reinstall the equation editor – which meant finding the CD – and she thought … this is silly, why the equation editor?

As it turns out, that is EXACTLY what you should do. If Office asks you to reinstall the equation editor, then do it. Now, clicking on the equation editor button will now open MathType and the Ctrl-E command works again. Yay!

Unfortunately, there is now a new problem (caused by Microsoft’s Equation Editor): the installation of the old equation editor has installed older fonts over the newer ones provided by MathType, so now you get a font error (which you can fix by following these directions).

Finally, the MathType Toolbar was still gone. Here’s how to fix that.

First go to the Tools menu, and choose Templates and Add-Ins

Under the Templates tab, you will see a check box line for “MathType Commands …” Check the box. Click on Okay.

What causes these “sudden” problems? My best guess is that each of them installed an update to Office (Meg’s on XP, Jill’s on Vista) and the updates interfered with or blocked the macro-nature of MathType. I’ve had similar things happen to me immediately following an update to Office or Windows.

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Sneaking Equations into Gmail

Here’s one I’ve been meaning to post for a while. Last month I figured out how to sneak equations into the text of email messages in gmail. It’s not ideal – ideal would be an equation editor built in to Gmail, but it does work and I’ve verified that the equations show up as intended on the receiving end of the emails in various programs (Outlook, Yahoo, Hotmail, etc.).

Here’s the principle: You know how companies are able to send you email that has lots of pictures and clickable text – just like a webpage? This is HTML-based email, and you can create it too using Google Page Creator as your editor.

If you already have a gmail account, you can use Google Page Creator to do the same things that these companies do when they build active HTML pages for email.

Create your equations with an equation editor (like MathType) and then use a screen-capture program (like Snagit or Jing) to create small image files of the equations you want in your email. Remember where you save the images, because you will have to find them again!

In Google Page Creator, create what you’d like to have in the email. One way to do it is to write the text in Page Creator and insert the images between the text lines.

A more efficient way to do it would be to write the text and equations in your equation editor, and insert the whole thing as an image in Page Creator.

When your document looks as you desire, copy the material in Google Page Creator, then paste the material (Ctrl-V) into a new email in Gmail. It should appear in the email exactly as it appeared on the page in Google Page Creator.

The reason this works (I think) is that both editors are WYSIWYG (what you see is what you get) editors built by Google and they are both writing the same back-end HTML code for everything you create.

Google Page Creator hosts the image files on the google servers, even if you never publish the web page. However, you can’t delete the images out of Google Page Creator, or they will disappear from the emails. I just have an unpublished page in Page Creator called “Sneaking Equations into Gmail” and I just keep adding new material to at the top.

Like I said at the beginning, it’s not ideal. Google should either build an equation editor that is compatible with all of its applications or integrate an existing equation editor into its applications. Google searching is optimized by mathematicians … you’d think that they’d be all over this!

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Lewis Dot Diagrams in MathType

I was discussing MathType with my officemate (who is primarily a chemistry instructor), and we got on the topic of Lewis Dot diagrams. She complained that its always been difficult to insert Lewis Dot diagrams into text, and I said that I thought I could figure out how to do it in MathType.

I remembered that Bob Mathews (from Design Science) had built Lewis Dot diagrams using MathType, and I asked if he could demonstrate his technique (which he has kindly provided in this little Jing video). His is the first diagram (he also shows you how to get the double and triple bond symbols).
Then I made a video of how I would do it too. Mine is the second diagram.
Anyways, if there’s a chemist in your life – pass these tips along please. You’ll make their day!

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