In light of current controversies around testing and teacher evaluation, let’s do a little thought experiment. How would Miss Snug have handled this lesson if it were occurring just before a round of standardized testing? Would she not have had to interrupt the children’s speculations and instructed them that actual circumstances in word problems must be completely disregarded, because the point is to arrive at the answer the test designers have in mind? After all, how could test designers anticipate the lines of thought that spontaneously erupted in her classroom? Real life, and real thought, are too complicated to be foreseen – and so need to be put aside at testing time.
We … are concerned about education because our adult citizens need to be flexible thinkers, ready to adapt to the ever-changing circumstances of the global marketplace. But making standardized tests the center of our curriculums tells children the most important thing they need to learn in school is how to arrive at predetermined answers on the tests. …
So in fact the test doesn’t reflect at all what kids should learn in school. What they really need to master is the kind of imaginative, adaptive thinking Miss Snug encourages in the passage from “The Trumpet of the Swan” – skills that cannot be assessed in any way other than actually knowing the children.
This little episode captures what volumes of education research have shown: we are born curious, and the best education models do not proceed on the basis of “what we want them to learn,” as Mr. Bloomberg correctly describes the goal of test-oriented education, but on the assumption that our job is to foster children’s ability ultimately to shape a world different from what we leave to them.
Now I agree that basic skills in mathematics are important. To learn mathematics effectively, you need to have your multiplication facts at your fingertips, and also your trig identities (if you’re learning at a higher level). However, the problem is that our assessment systems are skewed towards what is easy to test, especially what is easy to test using standardized tests. When resources are strained, as they are now, what is easy to assess ends up dominating the entire educational enterprise.
The best way to engage students is to ask them what they wish to learn. What is it that makes their hearts sing? (However, we should begin asking them early in life; if you wait until 12 or 16 years of the standard education system has crushed the spirit of our children, then you might not get a very satisfying answer to what makes their hearts sing.) And then create an environment where they are lovingly supported in pursuing their own goals. This is the only way to nurture creative and critical problem-solvers that we need so much to confront the serious problems facing civilization. Assessing their work can never be done using standardized tests.
In pursuing their own goals, many students will have need for some mathematical technique or other. With 21st century technology, it should be possible to create a system, a repository, of lessons that teach all of the basic techniques. (I’m sure that the internet is already chock full of such material, albeit scattered and of uneven quality.) When students need them, they can be guided and supported in learning what they need. Making students sit through 12 years of mathematics through high school, and then even more afterwards, in case they should need it, is a terrible waste of effort. Students would be better off doing something of value.
I cringe every time I think about the excellent teachers out there spending precious class time teaching 500 students how to work the product rule for derivatives and such things. Such things are best learned by doing, with feedback, in a combination of small groups and alone. I would much rather see our excellent lecturers spending precious class time on modelling the kind of critical and creative thinking that can’t easily be transmitted in other ways.
A final note: The inhumane standardized testing that is consuming the education landscape like a plague is infecting teacher evaluation as well. Tim Clifford’s article at the same SchoolBook blog is a powerful argument against this horrible practice.