The end of the semester is approaching, and I’m a bit crunched for time this week. But I do have one more brief thought about integration to share.
A few years before I left my full-time work as a curriculum developer, a freelance journalist interviewed me via email about mathematics word problems and my theories on why students often say they hate them. I told her that my years of curriculum development work really opened my eyes to just how inauthentic word problems can be. Is it possible to write word problems that target a particular mathematics concept and also are meaningful to children? Yes, definitely. Is it possible to write 50+ such problems targeting that same mathematics concept? I can tell you from experience that it gets really tough, really fast.
And that’s before applying the list of constraints that comes along with the task in large-scale curriculum development. During our latest round of development, we were not allowed to reference any junk food in our problems. We also had to stick to round objects when we talked about fractions, because our chosen manipulatives for fractions were circles. How many round items can you think of that aren’t considered junk food, but are round and make sense to divide into parts? It starts out easy: oranges, tortillas, cucumber slices. But then come the descriptors that help make semi-junky food sound ok: veggie pizzas, whole-wheat pita. By the tenth problem or so, I promise you’ll be grasping at straws. I’m pretty sure we wrote some fraction problems about cans of cat food.
My point is simply this: Starting with some form of disciplinary content and back-tracking to a reasonably authentic task is difficult after the first few times. And when tasks start to lose authenticity, kids notice. The activities they complete start to feel like busy-work (because they are).
The issue I’ve been thinking about this week is whether the task of contextualizing content becomes easier or harder when you’re thinking about two disciplines, as in integrated curricula. On one hand, it seems like finding a task authentic to both disciplines might be more difficult. But on the other hand, I think part of the difficulty of generating authentic tasks is that usually authentic tasks require multiple kinds of component skills. Finding one that gives kids exposure or practice to one particular thing, but does not require any other skills they don’t yet have, is a challenge. So I think it is possible that considering two disciplines might actually open up some space to move in task development.
Take the number grid activity I discussed last week. I’ve written other activities before asking kids to map out paths on a number grid. And I’ve asked them to limit their movements to moving in rows or columns — adding or subtracting 10s or 1s. But I never had a great reason for that restriction, other than a desire to focus on place value, so often the task felt inauthentic. But when I added the element of programming a robot, suddenly the restriction in movements had new meaning: Programming languages are made up of a limited set of commands. So a very similar activity became more authentic — along one dimension, at least — through integration.
I’m hoping to find more of these happy compatibilities as I continue to think about integrated curricula.