Dick is working to implement a systemic initiative, as opposed to a mechanistic view of education. This means, first of all, that piecemeal approaches to fixing schools don't work. Schools are integrated social systems, so "tinkering" with little pieces can't effectively change the entire school. What's more, in this new view, knowledge is likened to a living organism (complex, adapting, self-regulating), and not to a machine. In other words, and this I believe is his main point, we must focus on teaching big ideas, ways of thinking, or MODELS that are inseparable from their real-world applications.
In working towards these goals, Dick and others have come up with a series of questions/group projects which provide a sort of assessment that is entirely different from testing. The group today tackled one such problem, as you'll see below.
Dick outlined five trends influencing theory and practice:
There are four types of instructional goals: behavioral objectives, process objectives, affective objectives, and cognitive objectives. Dick claims that our school systems tend to bounce back and forth between the first two, and occasionally touch the third, but have largely ignored the fourth.
It's only in reaching for cognitive objectives that you provide students with the chance to form constructs, tangible thought processes that apply to entire areas of mathematics. It's pretty clear that in the natural sciences kids invent metaphors and models to explain phenomena. These may or not be right, so to get them to learn, you introduce kids to a complex system where they are forced to apply, test, and re-evaluate their theories.
This is true for math too!! We must focus on complex systems so that students can learn how to describe situations. It's our job as math educators to get kids to form models. Before doing so, of course, we must first figure out, for example, what the 8-10 BIG IDEAS are at a given grade level.
Since the world today is composed of complex systems: communication, economic, etc., students need to be able to relate appropriately.
This does not mean testing! From a systemic viewpoint a teacher does best to examine rather than test, to describe rather than measure, and to assess rather than evaluate.
The creation of good problems, activities, and means of assessment.
When broader understandings and abilities are recognized and rewarded, a broader range of students naturally emerges as having math potential. Two main goals are EQUITY to help identify and encourage previously neglected children and QUALITY to provide equal access to powerful ideas.
The process of thinking out a problem like this is what Dick calls Model Construction. In a normal classroom, he advises preceding this step with a series of warm-up questions. After spending about 45 minutes in our groups we reconvened for discussion. Our six groups came up with very distinctive ways of going about the same problem, and a lot was learned from sharing our results.
One thing that Dick stressed was that assessment can take many forms. Discussion that may have occurred at the beginning of a unit can be a form of assessment. In fact, he suggests that until teachers are more comfortable with these types of projects they should use them at the beginning of the year to help them learn something about how their students think.
I hope I have done Dick's talk justice. If you have any questions, feel free to send them on.
Home || The Math Library || Quick Reference || Search || Help