Some math ed tech links

Check out Hypernom, the new 4-D math game from Vi Hart and partners in (crime?) Andrea Hawksley (AH) and Henry Segerman. It’s pretty crazy — and beautiful. Nom nom nom. I can’t believe I missed this for so long. I got the link from a post on MathMunch, which is itself a very fun blog on math.

Hypernom and both make the marriage of math and computer graphics so cool….

I went to MathMunch today because I’ve been reading a bit about creating intellectual need in students. Today I read a post on Locked Doors, Headaches, and Intellectual Need, which linked to some earlier discussion happening at the blog dy/dan. So I checked out Dan Meyers’ more recent post and happened on Classkick Defeats The Mind-Reading Math Robots, which made me think of this blog. This post is about using the Classkick software to provide written feedback to students as they work through problems on their iPads. This seems really useful! It’s actually using tech to provide something that couldn’t be done before, rather than simply changing the medium of a traditional teaching method and making it more expensive.

Grammar Checkers for Writing Assignments in Math Classes

For the past few years there has been lots of talk about including writing assignments in college math courses. Writing assignments have been part of my teaching for many years now, including calculus labs, QL classes, MathCEP professional problems, and the much feared UMTYMP Calc 3 project.

Writing in math classes is tremendously valuable because it is the one of the few times we ask students to synthesize information, not just repeat computations. As an added motivation, I often hear people in industry say, “One of the reasons we hire mathematicians is because they are great writers”.  Yet, mathematicians are not trained in writing nor are we trained to teaching writing and most of the writing we do is in form of a proof. The proof writing is what people like about mathematicians: they can write a rock solid argument. However, honestly, many of us dread writing, and think we are terrible writers (myself included). Which brings me to the topic of this blog, grammar checkers!

When I was writing my thesis I spent an inordinate amount of time proofreading, re-proofreading, then proofreading again. My thesis, like nearly all math documents,was written in LaTeX, which doesn’t have the built-in spell and grammar check tools. Early mistakes took significant effort to correct later. I started to think “there must be tools to do this for me” and with a little searching, I found some. 

I think it is important to have the right approach to using a grammar checker. It’s not like spell check, which will detect every little mistake and suggest replacements. Grammar checkers will catch many mistakes, but should be viewed as a smoke alarm – if a sentence sets off grammar check, it is worth looking around for smoke and potentially rewriting the sentence. It doesn’t relieve you from needing to proofread, it just can direct your attention to obvious and embarassing issues that are easy to overlook.

  • After The Deadline. In my opinion AtD is the most sophisticated of the grammar checkers, although its also the most tricky to use. Atd is based on statistical analysis of bi-grams, and catches all sorts of missing verbs, passive voice, etc. The author describes it as “saving the world one passive voice at a time”. (Full Disclosure, the author of AtD is a good friend of mine and a remarkable programmer, but AtD is a fantastic tool and I’d use it even if I didn’t know the author).
  • TextLint. TextLint speaks tex out of the box, and has the best error messages I’ve seen. My favorite was “Qualifiers are the leeches that infest the pond of prose, sucking the blood of words.” Not only is that useful feedback on writing, its feedback presented in a way that is difficult to take personally.
  • LanguageTool. Rule based tool which was great for creating and applying a uniform style.

There are many other good grammar tools out there, including some specific to foreign languages. I haven’t investigated those in detail, but non-native english speakers make very common and predictable mistakes in writing. Common and predictable mistakes are the bread and butter of grammar checkers and if a computer can find them rather than a proofreader, all the better. Grammar checkers can also be tremendously useful enforcing a uniform style on a document. For instance, if you are a believer in the oxford comma, grammar checkers can easily find Oxford commas or tell you when you’ve forgotten them.

So, I’ve learned to love my grammar checkers. They mean less work for me, less annoying grammar mistakes for proofreaders and coauthors, and stylistically better writing. If you are struggling with an academic writing voice, its worth looking into a grammar checker. The next time I create a writing assignment, I intend to include to encourage my students to grammar check their work early and often. It lets them focus on the math and refining their understanding, rather than correcting its versus it’s errors.

And yes, I grammar checked this post, twice.


Reflections on the IMA Modeling Camp

I had the opportunity to help with this years IMA/MathCEP mathematical modeling camp a few weeks ago and wanted to share my thoughts on it. Daniel Schulthies organized the camp and followed the SIAM modeling guide fairly closely. We picked modeling topics which were local, current, and which there was enough data about. We did a cursory search to make sure there seemed like enough public data available, but students had to find the data on their own. 

We used the following projects:

  • What is the best location for a new MLS stadium in the twin cities (list of possible locations provided)?
  • How soon could Minnesota convert to 100% renewable energy sources?
  • What is the best light rail expansion route (list of possible routes provided)?
  • Find a good location for Wayzata to build a new middle school.
  • Following the poor air quality in early July due to Canadian wild fires, can you create a predictive model for air quality based on various observable events such as traffic, weather, wildfires, pollen, etc…?

Its was fascinating to see the wildly different models that different groups of students came up with, and it is always inspiring to see how excited these students are about math. I’m pleased that all groups got good results. Most of the models they used were simple, rank linear functions, graph models, and correlations. The tools they used for that were equally simple: google drive, docs, sheets, and slides. We provided goolgle drive folders to all the groups, and most of the students did all their work there. Early on, we had to force students to move their work from paper/blackboard into a spreadsheet. Once they moved into a spreadsheet, their models got significantly better, because they could refine their model and update data without doing significant computation. Interesting from a teaching perspective were which projects seemed to give interesting models. Itseemed to me like the most open-ended questions let students create more interesting models and had a larger variety of answers. Both “renewable energy” and “Wayzata middle schools” saw students use very different models to arrive at remarkably similar answers.

Having everyone in drive folders was great. We could see who was editing their spreadsheet at 1:15AM. Amusingly, it wasn’t just the students working late: I’m guilty too, one morning Daniel pointed out to me that my presentation had time stamps of 11:45pm one night and 7:00am that morning. The best story of the camp came during the presentations, when we called a group to present, only to discover they wern’t in the room. When we looked at the drive log, we saw that they were editing their presentation from the hallway.

If there was a flaw in this year’s camp it was the air quality problem problem. We asked for suggestions for topics from the returning students and they proposed air quality. They actually got interesting results, but it was a hard enough problem that they also left the problem discouraged. For next year’s camp, we are thinking models from this year’s students. See if they can build off an existing model to make it better. I’d also like to see a wider variety of models in next years camp. I suspect that is our own fault, some of the prompts were too similar and didn’t lend themselves to different models. Next year it would nice to have prompts which push students towards a greater variety of models. One thing which I think would help with that is having a variety of case studies to give the students. I gave a 15 minute presentation on moose and wolves on Isle Royale. I think would be neat to collect favorite mathematical models to include in classes and future modeling camps. Anyone have suggestions for models to use?

I was finally struck by how tricky it was to communicate to students what a mathematical model IS and what it DOES. Having to communicate that to students made me thing that mathematical models are not taught enough. I kept having flashbacks to casual conversations and industry work where the MO is “We must make a model that takes EVERYTHING into account”. I come away from the camp even more convinced that this is the wrong view, we don’t want everything – we just want to explain interesting behavior. I’ll close with a quote I was reminded of the yesterday at a conference:

“In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away.” –Antoine de Saint-Exupery

Surface Pro vs iPad

Recently I’ve been working with MCFAM to create supplementary online learning materials for probability. Tons of people take probability and need to learn it for professional exams, and we’d like to serve our U of M students and the wider community even better. Along the way I’ve been looking at ways to create this content. I’ve made videos of math problem-solving on my own personal iPad in the past, but got the chance to use a Surface Pro tablet at the university… and I like it better!

What’s going on here? I’ve successfully avoided Microsoft products for 15 years. Yes, last time I used Microsoft software regularly was freshman year or so. After that it’s been some Linux or Unix variant all the way, or a Mac. I liked the customizability and power of Linux and the way Macs “just worked.” I did not like all the unnecessary stuff involved with Windows. I never was an office user of computers: I use the web, I program, I do video processing, I type in Latex.

What a change, then, to feel that for recording instructional videos Microsoft products right now “just work”. No, I don’t know how to do scientific programming in that environment, but a lot of what I’ve been playing with recently is in the cloud anyway. And the Surface Pro is a beautiful machine that is made to be a tablet computer. The iPad feels like a toy in comparison, rather than a production machine.

I make PowerPoint slides or pdf files and display them on the Surface, then use Camtasia (a full-featured screen recording and video editing program) to record and then edit. It’s easy to export them to an mp4 and post them to Moodle or YouTube. I’ve made some cool math visualizations in PowerPoint, too. Yes, math equations are still a relative failure in Microsoft-land, but for less heavy probability and statistics I can manage.

By contrast, on the iPad I can record with several programs, but they aren’t very full-featured. I haven’t figured out how to make animated visualizations that I can also write on. The pen is less precise and I can’t get the control of writing that I have with the Surface, and then editing is a whole other question: need to import to another program or not edit, as far as I’ve figured out. Or I can mirror the iPad on my Mac and use Camtasia on the Mac, but then I need a certain wifi set up and so can only record at home, not at the University, and there can be a lag depending on the wifi speed.

I will keep doing research on how other folks record math screencasts, but I’m impressed at the extent to which the Surface Pro “just works!”

Desmos: a really fancy calculator, but much more

The Twittersphere recently made me aware of Desmos, a really fancy online graphing calculator. Fortunately, I was not introduced to it as such: I found it through a blog by a math teacher that now and then features a “maths gems” post — little tidbits of interest to mathy people and math teachers. The gems post that turned me on to Desmos also told me how minutes and seconds got their names!

Back to Desmos: this HTML5 web app is much more than a calculator. Their activities created by and for teachers include some winners. I checked out the “Polygraph: Parabolas” activity and it addresses vocabulary and understanding of quadratic functions in what looks to be an effective way. How do students learn to talk about parabolas using words like root, vertex, intercept, etc? By practice! And yet even with a group worksheet (and I love groupwork with worksheets!) structuring that conversation can be difficult. Here with a computer game we can get students to use their math vocabularies, without having to print out a lot of matching graphs, make copiers on the copy machine on another floor, cut them up using that paper cutter that gets stuck halfway, and then trying to collect them all after class so you can do the activity with the next group. A nice use of technology to lower the activation energy for a cool activity.

Besides activities for students, Desmos allows some nifty interactive demonstrations. This demo shows that if the complex roots of a quadratic are a+bi and a-bi, then the real roots of the reflection of its parabola are at x=a-b and x=a+b. This is easy to prove, of course. Look at the quadratic formula and see that the change of signs brought about by the reflection simply flips the sign of the discriminant. I knew this. But I had never seen it. Visualization can make a fact viscerally true.

Last advertisement for Desmos: a return to good old graphing calculator art. Did you, oh reader around my age, ever sit around drawing complicated pictures on your TI? Did you ever either make or give a beautiful polar coordinates Valentine’s Day card? If your student can use equations to draw Keroppi or a Disney-looking princess, I must say I think they’ve learned to play with math.

The flipped classroom: reports from the field

For those of us in academia, the fall semester is wrapping up. It’s a time when we reflect on the success or lack thereof in our fall classes, because it’s almost over, the final is coming, and we either feel pretty happy, totally depressed, or a sense of oncoming dread. These correspond to the feelings of the class going well and students learning, something wrong with the class that has been bothering us for a while, or a class that’s going alright but will soon implode due to the final. (I find that last feeling really only occurs in a class with a final exam shared with other classes or sections, which I can’t control. Otherwise a class is on the right track or started showing problems long before now!)

In this vein, I was reading some recent reflections on a flipped semester. These are from a college biology class with 600 students, and it sounds like the instructor has spent a lot of time setting up an effective educational environment for students. She writes about the preparation that took, though: flipping the classroom completely means all lecturing happens outside of class, and then class time is used for active learning. Even without the pain of technological snafus, that can essentially double the instructional time for a class. It doesn’t replace office hours or lecture prep, either. It is possible that in the future the videos can be used again, but the first semester of a flipped class involves an enormous time commitment.

I came to the article linked above via the blog of Prof-like Substance, a blogger I’ve been following for a while. Prof-like is at a research university and brings up questions about how such investments of time and effort are rewarded. We all live within a benefit structure largely imposed from outside, and focusing on innovative education can be a dangerous thing to do if you are ultimately judged by your research or grant-writing abilities. Traditionally in the US we have divided higher ed into research universities, small liberal-arts colleges, regional institutions, and community colleges. Research was primarily prized at research universities. Now research is emphasized more and more at institutions of the other types. Teaching is emphasized a bit more at research universities. I love bringing research to the undergraduate level and I think it’s great for learning. But if every faculty member at every institution has to do all the things, how can it be sustained?

One answer is for universities and colleges to provide support in the form of technology, tech experts, and educational design experts to those designing courses that lean heavily on new technologies. This is being done to various degrees at different institutions; I still hear a lot of, “It’s just making a video of you teaching… how hard can that be?”

How does your institution support innovative teaching using technology (or not)?


Lightweight math apps

Something I’ve seen more and more of lately is very lightweight apps that deal with algebra or other K-12 math topics. Last night I met the creator of Algebra Touch, Sean Berry. Algebra Touch is a pretty app that lets you play with algebra expressions: you can simplify, add, divide, factor, and more with a touch of the finger. I could see it being an enjoyable way to develop the algebraic equivalent of number sense — algebra sense? — especially for students who enjoy a tactile relationship with their mathematics.

Another app that’s been gaining attention: my brother told me about PhotoMath recently. Take a photo of an algebra expression and it will solve it for you and show the steps. On the one hand, a useful study tool; on the other hand, a testing nightmare. (Good thing it can’t do matrix factorization yet or I’d have to worry.) A current teacher wrote a letter to his department about the implications: “drill and kill” must be over when tools like this are available! But I still see facility with the basics as a gateway to success in college: students who can’t add fractions fluently have trouble figuring out the Jacobian matrix as well, not because they don’t understand it but because they can’t do it. The invention of the CD and Pandora and Spotify has not changed the fact that if you can’t play a scale, you can’t play Beethoven yourself. On the other hand, now people without formal musical training can have an app write sheet music from a sung melody. What’s the math equivalent of that?


Some interesting pre-calculus resources

My colleague Mike Weimerskirch at the University of Minnesota has set up a nice site of precalculus resources. It’s got videos, slides, and transcripts of short lectures on a variety of precalc topics, as well as links to appropriate sections of three free online textbooks. If you’re a current teacher, this is a great resource for students who might need review of trig, or summation notation, or sequences and series. The site also includes a number of in-class activities that go with the lectures.

Mike worked hard to make this precalculus class a more interactive class in person, shifting a lot of the lecture outside of class time in order to increase in-class work time. Students in college precalculus are often rather vulnerable to being derailed; they’ve often had trouble with math in the past and the learning strategies they have are often not great for the math they are facing. Shifting activities into class time allows teachers to model the math learning and experimentation process for students and help them learn new ways to learn math. It also helps keep them awake! I read a thought-provoking blog post this week about a veteran teacher who shadowed two of her high school students for two days, and was astounded at all the time we spend asking students to sit quietly and absorb without contributing. That prompts its own question: to what extent can online learning technologies create a space where students truly participate and feel that their presence is relevant to learning?

Math on the web: innovations from Khan Academy

The folks at Khan Academy are doing some very interesting things. Today I heard about an effort they’re calling KaTeX, math typesetting for the web. It is designed to be a fast alternative to MathJax, as far as I can tell — MathJax is great in some ways but can take a while to render. The syntax is based on TeX and when you load a page, it doesn’t reflow around the math expressions. It’s a Javascript library. Javascript is enabling some cool things…

So, my questions: does it play well with ebook standards?



Consumption and creation, K-12 discussion