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This morning's USA Today featured two seemingly contradictory stories. On page one, the headline is "School is too easy, students report." On page seven, an op-ed is entitled "Why our kids hate math." The first article, authored by their excellent reporter Greg Toppo, shares a report that included results of surveys where students were asked how hard or easy they found their classwork. Among the findings:
- 37% of fourth-graders say their math work is "often" or "always" too easy;
- 57% of eighth-graders say their history work is "often" or "always" too easy;
- 39% of 12th-graders say they rarely write about what they read in class.
We can all perhaps agree that schoolwork should not be "too easy." Every student should be challenged, in a way that moves them to the next level of accomplishment. Our task as teachers is to work with our students and figure out where they are, and design projects, lessons and assignments that engage our students in learning new skills, and gaining new understanding. The difficult part for us as teachers is finding ways to do this that place appropriate levels of challenge before each student, given that we may have a wide range of abilities and interests within any given class.
The second column reveals how difficult this is in practice. Author Patrick Welsh is a teacher, and writes from experience:
When summer school opened Monday at T.C. Williams High School in Alexandria, Va., where I teach, remedial courses in math had more students than any other subject.
That is because of the high failure rate not only in math courses, but also on the state's standard of learning exams in math. The summer school pattern is similar in most high schools around the country where kids will be trying to learn the math they never figured out during the year.
I worry that we're pushing many kids to grasp math at higher levels before they are ready. When they struggle, they begin to dread math, and eventually we lose thousands of students who could be the scientists and engineers of tomorrow. If we held back and took more time to ground them in the basics, we could turn them on to math.
He goes on to attribute this to a national trend:
Pushing students to the next level of math before they are ready is endemic in schools across the country, and is most pronounced in the move to have younger and younger children take algebra.
The National Center for Education Statistics reports that from 1990 to 2007, the percentage of eighth-graders taking algebra went from 16% to 31%. California has been in the forefront of pushing kids into algebra: By 2009, 54% of its eighth-graders were taking algebra, the result of an initiative by California's State Board of Education.
I shared some concerns about the Algebra for all 8th graders plan in California four years ago. Also back in 2008, Greg Toppo shared similar worries.
But here is the seemingly paradoxical question: Is it possible that school is too easy in some ways and too hard in others?
My own classroom experiences teaching middle school math and science were similar to those of Sally Miller, a math teacher Welsh quotes.
Miller, like every math teacher I talked to, says schools are pushing too many middle-school kids into algebra. "Many of the concepts in algebra are abstract," Miller says, "and if children are not developmentally ready to deal with abstraction, you can turn them off to math forever. Even the best students who can pull off A's in eighth-grade algebra by just memorizing eventually end up realizing they did not really learn it."
I recall an attempt I made to teach my 8th grade science students to figure out the scale of a map. They could use the formula in a direct way, where they were given the variables and some direction about how to multiply and divide to get the answer. But when they were given the challenge of applying this knowledge, to actually determine the scale of a map using this approach, many of them were flummoxed. And I tried five different ways of teaching them - we would practice, go back and forth with various models, and many of them could not work with the level of abstraction that was needed - the deep understanding of what proportion is all about.
So one big issue is what is an appropriate level of challenge for the average student at a given age. And Welsh is sharing evidence that California, and other places pushing Algebra down to the 8th grade, may be missing the mark and causing damage as a result.
But the other challenge, is that even though there is some average student out there for whom the standards might be written, a lot of students are above average and many are below average. So even if we get the average set about right, we still will miss the mark with lots of students. How do we solve that problem?
This is where I question the wisdom of the whole benchmarking enterprise. This comes back to a question posed by a commenter here a few months ago, "I don't see any harm in requiring all students to be able to recite their multiplication tables from memory up to 12 X 12 by the end of third grade or they don't go to fourth grade." And by this same logic, we can have a whole series of benchmarks on up the grades, which every child must master before they move to the next grade. And if school is "too easy" at any given grade level, we respond by raising the bar, and lowering the grade level for whatever skills or concepts that could be mastered at an earlier age.
In spite of our best intentions, we may do great harm when we decide with absolute certainty that all 8 year olds must know X or Y. We can justify this with all sorts of claims that if we do not do this, our students will not be prepared for college, and we have to intervene to make sure everyone is on grade level. However, I think a far greater number of students will be helped if we have a looser set of definitions of what grade level is, and less reliance on benchmarks and all the curriculum and tests designed to march us through time to all these required outcome.
I also think we end up here with a far too simple concept of "easy" and "hard." I think the way we need to make school "harder" is not by increasing the number of facts that students need to memorize, or the age at which they learn math concepts. I think we need to deepen their ability to apply these concepts in meaningful ways.
I worked with a teacher in Oakland who taught sophomore Biology. His students had Earth Science the year before, and were taught by a teacher who believed in thorough preparation for tests. My colleague was doing Project Based Learning with his students, and giving them much more open-ended challenges, to conduct research and come up with proposals on how to restore endangered species in the state. His students complained to him that this work was too hard. "Why don't you teach us the way Miss G. did last year? Tell us what will be on the test, help us study, and then we take the test and do well. This is way too hard!"
We could make these students work harder by making their test longer, requiring them to memorize more and more. That would be harder, just as moving Algebra to lower grades makes it harder. Or we could make their studies more challenging by making them more open-ended, requiring more creativity and problem-solving. I think the latter approach gives teachers a lot more ability to gauge the appropriate level of challenge for their students, and also allows us to make their schoolwork more meaningful.
What do you think? Is school too hard or too easy? How should we find the right level of challenge for our students?