Gradations of Content Quality, Depth and Variety in Math

Our school has their own "You Tube" account where students can upload content from their classes for sharing. I've been perusing this specific youtube page and noticing that teachers are creating content in a variety of different ways. As the amount of information that we are creating is doubling every seven years, it's no surprise that some of it is truly creative and some of it is a remix. Must the emphasis be on creating content or quality content?

Created Content that is the Same
In the following example, the fifth grade teachers used "Doceri" to have students animate their understanding of fraction operations but with a 2 dimensional model.


In this case, the student showed their skills of being able to multiply 5/6 by 4/5. What was really interesting was that a number of the kids had the exact same problem. See some more examples here, here and here. As a bank of instructional videos to help understand skills, having the exact same problem may be overkill, and we must ask ourselves: "Do we need 10 videos of the same thing when only 1 will do?" For a portfolio piece we may all want the same question but surely there can be some freedom for creativity and differentiation for product. Perhaps students want to do the same problem to compare different ways of solving or illustrating the solution which is now a standard with common core in the United States.

Created Content that is Different but with Similar Skills
In the following example, we see a student working out a problem that is different than the problem his peers are given but he applies the same skill. It was simply done by recording on the document camera which is now obsolete given our Ipads.

What makes this different from the first example is that problems can be scaffolded based on readiness and differentiated for mixed ability. You'll see some other examples here, here and here that are more or less easier or harder but serve more of a wider breadth of problems. Something like this will multiple skills could potentially serve as a summative assessment. However, although these problems are different, are they really that different?

Content to Serve as a Learning Resource
My collegue Zach Post has done some dynamite work in this regard. For his unit on algebra, he had students who were working together all create different video tutorials for a unit project.

Above, you'll see a couple of students working out a problem using PEMDAS which can serve as a nice resource for the other students. What was interesting though is the all students did a different skills some translated words into expressions, and another group focused on the distributive and associative property. These were invaluble for review later and students were "experts" in their particular domain. Are there enough principles of math to give a classroom of 22 students? Surely there is some repetitiousness.


Final Thoughts
As educators wade into or jump head first into the world of technology integration, I think asking ourselves these questions are particularly relevant. My wife last night and I were brainstorming a swimming project for her class in which she asked me how she should grade the use of "Explain Everything" in her project rubric to which I replied: "It shouldn't be graded. It's merely a tool to demonstrate the skills that you want them to understand in your class". Although making a good looking presentation makes it more watchable, we must be careful not to distort the learning outcomes with the packaging. 8 years ago, there was a push in our school for when students should start using Powerpoints. Can you guess what has happened to Powerpoints in my school?


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