Monthly Archives: November 2013
There’s a joke in here somewhere along the lines of the Java ProblemFactory joke, but I digress.
Wolfram, the folks who make Mathematica, Wolfram Alpha, and various oddities, have come up with a Problem Generator for certain branches of mathematics. If you don’t want to sign up for a trial of Alpha Pro to try it out, I’m going to give you a quick overview here.
The short version is that they’ve created a random problem generator that takes a template, fills it with random numbers, and asks a straightforward procedural problem similar to back-of-the-textbook practice problems. No word problems, just “find where this is discontinuous” or “find the median of this list of numbers” or “factor this expression.” You can ask it for easy, medium, or advanced problems. Advanced problems involve doing a little more of the work yourself (unfactored expressions in rational functions, for example) and more intimidating numbers with square roots and such. They provide step-by-step solutions that use the exact random values given to you.
In terms of drilling exercises, this is fairly handy. Some of it is higher-level material, so that’s nice. There’s arithmetic, number theory (very basic – factor this, LCM of that), high-school algebra, single-variable calc, linalg (add, subtract, cross, determinant), and super-basic statistics (avg, mean, mode, and range).
The lack of educational sophistication, however, is what makes this less than impressive to me. It’s more of an aid to textbook manufacturers than it is to students or teachers. You can practice doing integrals until your hands fall off, and lord knows people need practice with their skills, but as we all know at this point, Students do not overcome conceptual difficulties after solving 1000 traditional problems. (Yes, that’s in italics because it’s the title of a paper.) You won’t know what an integral is any better afterwards than you did before.
It’s also not extensible. Where’s the tool that allows us to make our own problems? How do we create our own templates? Will this list ever get expanded, or is this just something that someone came up with on their 10% time?
This might be a good product for textbook manufacturers, so they can create books faster and more accurately. It might be good for math teachers as a way to get quick problems for their tests, things they can wrap words around to make real problems and not just exercises. It’s good for drill-and-kill practice, to the extent that such things are necessary. If you’re saying “But we already have all of that stuff in thousands of books and practice sheets…” then you’re hitting on the exact reason I don’t think this is very useful.
We should be working to figure out good ways to use tools like Alpha in the classroom. Right now I just have this bizarre image of someone just sitting there with the Problem Generator open on one page, and Wolfram Alpha open on another page, plugging questions from one into the other and returning the answers.
For those who aren’t yet familiar with him, the rarely-updated blog of Edward “Joe” Redish:
Redish is a very big name in physics education research. My favorite post so far is “The World is an Ill-posed Problem”.
Teaching in the classroom requires a fairly broad set of skills. As an absolute minimum, it requires two: the ability to relate to your students, and knowledge of the subject material you’re teaching. We can break these down in all sorts of ways (classroom management and lecture delivery are both part of relating to your students), and add many other skills (lesson planning and knowledge of misconceptions, for example), but relatability and subject knowledge will do as a minimum.
When you’re in an online environment, putting together a course on your own brings in other skills. Not many people have all of them, so online courses are typically designed by a team. You need one person to handle technical matters, one to write, one to supply subject knowledge, one to interact with the students, and (assuming you’re using video) someone to edit the videos and someone to appear in them.
It’s not unreasonable to replace that last person with someone who has no content knowledge. After all, in a molecular biology course, your techie doesn’t need to know how to… uh… yeah, I know nothing about molecular biology, so I can’t even come up with a reasonable example. Your video editor doesn’t even need to know what protein biosynthesis is, let alone how it works. (Thanks for the example, Wikipedia!) So why should the person delivering the speech need to know anything? They just need to stand and deliver, and do so in an entertaining and captivating manner. Your writer and subject knowledge expert can handle the scripting.
If this seems strange, it’s because we expect a lot from classroom teachers, and we consider the production of an online course to be something quite like teaching. In fact, it’s something quite different. So if Matt Damon wants to do a guest lecture for PoetryX, or Tilda Swanson wants to put a few hours on film for Fundamentals of Neuroscience, why would we say no?
I understand that there’s a concern about this appearing… less than genuine, I suppose. If the content is accurate and the delivery more stirring, I say go for it anyway.
You might have heard about a month ago that George Washington University has been lying about its admissions process.
I have difficulty writing about this while keeping my temper, so I’ll try to be brief. This is not an issue of one person’s definition versus another’s. This is not an “everybody does it” issue or a “internal process, not a public matter” issue. This is a school that advertised one thing, told it to even its own workers, and then went and did something else.
There’s nothing wrong with considering a student’s ability to pay when you take them in. It sucks, but you have to pay the rent. (And the salary, and the overhead, and benefits, and and and…) But you can’t say “I’m covering my eyes” and then peek through your fingers.
Now, to compound their… it’s not a mistake, it’s an outright lie… they’ve decided to double down on the “Oh, this is just a matter of definition” defense.
No. It’s a lie. Own up, get honest.
To jump right to the italicized punchline:
…we are convinced that Common Core is so deeply flawed that it should not be adopted by Catholic schools which have yet to approve it, and that those schools which have already endorsed it should seek an orderly withdrawal now.
I find this very interesting, not so much from the religious angle as from the “whole student” angle.
It’s very well-phrased: the people writing the letter acknowledge that the Common Core proponents genuinely want to improve education, but they disagree that this is a good way to do it. In fact, they’re not even taking issue with the idea that the CC would improve the things at which it is aimed! They instead focus on the things that the CC doesn’t focus on, and thus pushes out of the core of education:
Promoters of Common Core say that it is designed to make America’s children “college and career ready.” We instead judge Common Core to be a recipe for standardized workforce preparation. Common Core shortchanges the central goals of all sound education and surely those of Catholic education: to grow in the virtues necessary to know, love, and serve the Lord, to mature into a responsible, flourishing adult, and to contribute as a citizen to the process of responsible democratic self-government.
It goes on to say some things that I agree with and some that I don’t. It is defensive and protective of religion to a level that is both understandable and unfortunate.
I’m not religious, so I couldn’t care less what the Common Core says about it (hint: it says practically nothing about any religion). I care deeply when I see that these religious officials and professors are worried that their schools – focused around a particular philosophy and goal – won’t have the time to pursue that goal. I really love schools with a philosophy and a goal. I might not love every philosophy or every goal, but I love that different schools can do things differently and pursue what they see as best in humanity.
The cynic in me says that the secular parts of the letter might have been added as afterthoughts, but I don’t think they’re wrong. This quote hits it on the nose for me:
Professor Anthony Esolen, now at Providence College … “We are not programming machines. We are teaching children. We are not producing functionaries, factory-like. We are to be forming the minds and hearts of men and women.”
Very much so.
I’ve taken some time to recharge the blogging batteries. Let’s start with this one.
I was doing some brainstorming the other day, trying to think about a course I’m helping put together for HarvardX. I wrote a little chart like this:
Assets | Methods | Objectives -------+---------+----------- | |
The left-hand side is for listing the good things about our topic, and the resources we have, anything that would help us improve our students’ learning. In this particular case, the big thing we had going for us was that the topic is inherently cool. It’s also fairly recent, and
The right-hand side is for listing what we want students to come out being able to do, or appreciating, or thinking. Any sort of objective is ok – learning objectives, affective goals, etc. We had a good number of content goals; the sorts of things one usually finds in the bottom of Bloom’s taxonomy. We also wanted people to come away with an appreciation for the importance of being multidisciplinary, and a greater interest in the space program.
In the middle part, you draw lines from your assets to your objectives and label the lines. It’s a way of saying, “here’s how we’re going to take advantage of this asset and use it to forward our course.”
I got stuck. I got completely, utterly stuck. There was a total disconnect between the assets on the left-hand side and the course’s objectives on the right-hand side. Even after a lot of experience in teaching and a lot of educational research, I really hit a brick wall here.
I would have had a much easier time listing challenges instead of assets. The material is disconnected from our daily experience. It requires some math, and draws from multiple topic areas. It’s cutting-edge information, which means it’s inherently a little uncertain. There are a lot of challenges to overcome, and looking at how we might overcome them would have been an easier exercise… but that’s the kind of thing I’m used to doing. Teachers spend a lot of time looking at our challenges and figuring out how to overcome them. I don’t think most of us are used to looking at our course’s assets and figuring out how to use them.