In math, big ideas are defined this way (R. Charles, Journal of Mathematics Education Leadership, Vol. 7 No.3) :
" a statement of an idea that is central to the learningand here's an example:
of mathematics, one that links numerous mathematical
understandings into a coherent whole."
"Any number, measure, numerical expression, algebraicNow that idea can be a beautiful thing to a mathematician and it's clearly an underlying understanding or concept that we aim for students to develop over time, but having that knowledge hasn't helped me see it's value or importance or usefulness outside the walled garden of math.
expression, or equation can be represented in an infinite
number of ways that have the same value."
One of the higher ed bloggers I follow is working on how to make the big ideas of physics and computational computing more accessible to his students.
Lately I've been doing quite a bit of reading about how the folk in higher ed are struggling with the why's, how's, and what's of improving their teaching skills. Similar to the way that many K-12 educators have been reluctant to adopt new technologies, some higher ed folk are finding it challenging to change their way of thinking about learning and teaching. I think perhaps in both cases the reluctance may stem from not seeing the why's -- or perhaps it's because that for many educators, figuring out our why's is something that takes place in the formative years of our careers. Maybe it's like developing a personal fashion sense or a look when you're young and after that you always dress the same way unless/until something forces you to see yourself in others' eyes and you don't like what looks back at you.
I think 'getting to why' is perhaps one of the biggest big ideas of our profession. Perhaps under all the reasons people give for not wanting to engage in this kind of educational overhaul (too much work for too little return, just a fad, no time, too much important content to cover, won't help on the test, doesn't work in my subject) lies these two simple facts:
- those of us who have made the paradigm shift have not done the work of making the why's explicit in as enticing and elegant a way as John Burke has done with his one simple idea and his one big idea.
- my why's (I'm an adult; I liked math; I didn't struggle in school) are not everyone else's (especially my students').
Hmmmm ........ sound familiar?