First of all on the issue of transparency. Most rubrics come in one of two varieties. Either they are extremely didactic in a step-by-step hold-your-hand IKEA instruction manual sort of way or they are touchy-feely rubbish where you get a ‘1’ for ‘not demonstrating significant understanding’ but a ‘5’ for ‘demonstrating unique depth and content mastery’. Rubrics of the latter variety are meant to satisfy the political needs of institutionalized learning, while rubrics of the former are theoretical expressions of teaching to the lowest common denominator.
I’m pretty solidly on board with everything he says here. I don’t want my students to think that the one true way to do anything is to haul out my rubric for the assignment and fill in all the squares completely. I want them to think critically, to creatively synthesize ideas that we have learned together and to develop analyses, ideas and outcomes that are novel and unexpected — and well-supported, thoughtful and demonstrate clear connections to the ongoing work of the class. I don’t want my students to think that life is simply about checking off boxes on someone else’s list.
But here’s the rub, he goes on to attack the idea that rubrics can act as a tool that promotes objectivity by the teacher:
I don’t want students to do ‘what I want’. I don’t want students to follow ‘objective’ rules. In fact, that’s entirely the type of behavior I’m trying to break my students out of.
I hear his argument that it’s counter-productive to educate our students for their lives to come by aiming them at expectations based on our own experience. Clearly, new contexts require new ideas and new expectations, and our goal should be to help our students learn to develop those new ideas free from the constraints of our own, out-dated thought patterns.
But, we also need to help our students develop skills and techniques for critiquing their own work, for judging whether or not it is objectively good for what it was meant to do (or even serendipitously good for something unexpected — therein lies a window into the power of portfolios, but I digress). A number of commenters suggested working with students to develop collaborative rubrics.
And, I say, this is exactly what we are doing whenever we challenge a student to identify their audience, to present their ideas, to argue for and support their own efforts and creativity and analysis and learning. In fact, there is an implicit rubric at play every time we work with our students to develop qualitative understanding of how they can improve their work.
In this case, the rubric is not a checklist, and it is not an attempt to trample the students’ learning with “my” objectivity: it’s a contract that I am making between myself and my student. “Here, this is what I am looking for in your work — and what you should be looking for in your work.” I believe that there is real value in making this contract explicit where possible, by developing rubrics for and with my students to anticipate what areas of their work I should be focusing on when evaluating drafts and final submissions.
And I think that this idea of the rubric as contract is particularly important because what it really represents in a covenant between the party with power (myself) and the party with less power (my student). I didn’t choose to set the stage this way, but at the end of the day, I’m the one who is entering grades for this student, and it is my evaluation of this student that will be definitive for this course. By making this covenant, an agreement between a party with power and a party lacking in power that effectively binds both parties, I am helping my student not only to focus their efforts, but hopefully alleviating distracting pressures by agreeing not to evaluate on certain aspects of his or her work.
The flip side of this rubric conundrum is that not everything that I teach (or that is worth learning) exists without an objective, clearly-defined, body of specific facts and skills that must be mastered by the student. For example, if I were teaching Latin, I would need to work through at least some specific grammar, vocabulary and idiom as a foundation for more open-ended and creative learning. And I would have an objective standard for determining whether or not a student gets it — why would I not communicate that standard to my students? Why would I not give them a target to aim for?
I recall my high school graphic design teacher putting forth what I believe to be a sensible argument during a discussion of the rules of composition. Someone had pointed out that there were great works of art that violated all of these rules, and yet were still great: why should we have to follow them? And Denny Heck responded: “You don’t get to break the rules until you understand the rules.” Yes, she wanted us to learn the rules of composition, but she also expected us to be creative and find ways to violate them and still achieve successful compositions. But those violations would be educated, conscious decisions, aware of the challenges that we were facing — decisions made thoughtfully, well-supported and judiciously.
For assignments at lower levels and earlier in my courses, I do favor rubrics as a way of framing the goalposts for my students. I think that giving them a target to aim for when working to master concrete concepts and facts is a solid support of the education. In providing the rubric, I am also acknowledging that I am not looking for a total understanding of everything, that there could be some confusion in some areas, without the student being entirely at sea when it comes to building on that knowledge. The rubric lets me show my students that there is a “good enough” knowledge of the subject matter that will let us converse about more complicated concepts fluently and without distraction by their confusion.
Seth Battis August 21st, 2009
Posted In: Teaching
Shelly Blake-Pock just posted a question on his blog about teaching math in a paperless environment (in fact, since I started gearing up to respond, he’s posted some follow-ups as well).
Last year, wearing my math teacher hat (nominally given to me as a member of the Math & Computer Science department — normally only worn on the most formal occasions), I got involved in a project with my department trying to work with our students to develop a mathematical Wikipedia. The idea was that kids would write up their mathematical knowledge for the younger students and their classmates, creating a review site focused on what the students thought was important to know about the material we were covering in class.
The big idea was that this would push the students to both reflect on what they knew (as they worked to articulate it for less experienced students) and take part in some independent learning (as they researched their topics to figure out how to write them up). It wasn’t really a rousing success, for a number of reasons, not the least of which was that the kids were assigned topics (rather than selecting their own) and ended up mostly parroting their textbook into the wiki. There wasn’t any real collaboration or peer-review going on, at least not in a really critical sense (“Why did you explain it the way the text book does? I didn’t get it then and I don’t get it now… do you get it?”)
MathML requires a plug-in for Internet Explorer 7 (no idea about 8, but I’ll bet it still needs the plug-in), but Firefox can read and parse MathML natively. Peter Jipsen has links to some helpful fonts to download to make it all look a little nicer, but they’re truly optional. Once it’s set up on your server, you just include a magic incantation at the beginning of the page to invoke the translator, type in your calculator equations, and whamm-o: pretty equations!
Now, this only handles equations on the web. We didn’t get to graphs or diagrams in our experiments last year. But I can tell you where I would look for graphs — Google has an embeddable chart generator that might work. I hope there are other similar tools.
Again, all this is with the stated goal of readable, editable, shareable mathematics online. This doesn’t address doing the exploratory work: this is the write-up and reflection after the exploration. Without a tablet, I’m not convinced that one can do general mathematical work on a computer. And with a tablet, I’d add FluidMath (still in beta, I think) to the list of must-have applications.
Seth Battis August 4th, 2009