Friday, September 20, 2013

Why is Investigation so Hard?

At the end of the second week, with one week left to go in the unit, I wanted to get a better sense of where my students were. 

I knew roughly where they each were based on individual interactions in class, but as a whole I wasn't sure how the class was progressing. I'm also still not convinced that many of the students themselves know where they are in the unit, even though most classes start with a review of the "master list" and thinking about where we need to be to get things done on time.

So I made a large coloured chart with each student's name on the left side, and their progress through the unit's "hand in" tasks. Here's where we are (with names omitted). One student per line - the colours are only to distinguish between students.

What immediately jumped out at me was something I had suspected all week: about half of the 28 students (2 more have been added since my last blog post) stalled on the first Investigation of the unit. On the chart above, they have the first four squares coloured in, and little else.

First three exit slips and quiz? No problem. All knowledge-based tasks... practice and perform. Asked to do an investigation of how parabolae are stretched or compressed? Suddenly a task that should take one class at most, is taking the better part of THREE classes to finish. 

Students became hesitant, unsure of how to test what the investigation was asking, or how to interpret what they were doing. Most teachers (including myself) would not be surprised by this. Students often find this type of activity tough.

What did surprise me though, was how little the students tapped into the resources at their disposal to help them complete the investigation. Instead of working together (or asking each other for help), or turning to the Internet (they were all using graphing calculator apps or websites), or even picking away at it for homework when it took longer than one class (there were learning resources listed in the master document for them to consult), they chose instead to just stop working. They became distracted by conversation and online games. When I checked in with them, they would ask me about the question they happened to be on, but would then be reluctant to go further.

As a result, for some students, most of the week was spent on this single activity. With four classes left until the unit test - and one of those will be designated a review period - they will have a very tough time catching up. We'll be discussing strategies on Monday... it will be interesting to see how the students approach the week.


  1. I love the graphic representation of students' progress here--it really makes it clear where they're stalling!

    I have a question, though--can you explain what an "investigation" task is in the context of your course, and especially how it differs from a "knowledge-based" task? I teach philosophy at a university, and just am not familiar with these terms for some reason (guess we don't use them like this!). So if you could explain that, I could think further about why I think it could be the case that students are having difficulty with that sort of task. Thanks!

    1. The students LOVE the coloured chart... they migrated to it immediately yesterday morning, and referred back to it throughout the class. I'll take a new picture today to show their progress.

      To answer your question, the knowledge-based tasks are simply demonstrating that they have mastered the learning goal. For instance, Learning Goal 4 is "Using a, h and k, I can describe a quadratic function in vertex form." To test this, I would give them the general equation f(x)=a(x-h)^2+k and they would have to identify what a, h and k are. They would also have to match equations in this form to graphs. They could learn this (and memorize it) through a mini-lesson, reading, other resources, etc.

      For the same learning goal, the investigation has them actually figuring out how a, h and k transform the function by trying things on their graphing calculator apps. Instead of giving them a lesson (and simply telling them the answer), and instead of just reading about it, they have to try f(x)=3x^2 and f(x)=0.5x^2 and f(x)=-2x^2 etc. to see how the parabola is changed as a is changed. They come up with the "rules" themselves, and then apply what they've learned to other scenarios.

      I hope that helps!


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