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LostInParadise's avatar

What changes would you make to K-12 education?

Asked by LostInParadise (28550points) December 18th, 2008

I would make changes to the mathematics curriculum. In math education there are basically two sides – those pushing back to basics and those who want a more project and discovery approach. The discovery approach seems to be preferred mainly by educators, meaning that the general public wants the basics.

The general public is wrong. There are some interesting studies showing that a more open ended approach results in better scores on standardized tests and greater appreciation of mathematics by the students. Some students actually switch from hating math to loving it. If someone wanted to deliberately discourage people from appreciating math, they could not do much better than to copy the way it is currently taught.

Another change I would make is to give a brief introducation to non-Euclidean geometry when teaching Euclidean geometry.

Non-Euclidean geometry represented a major philosophical change in the way the Universe is perceived. It came as a major shock that there might be other geometries that describe our Universe and although Euclidean geometry works on a small scale, it is quite possible that on a large scale it does not apply. Our Universe may, for example, be something like a finite 3 dimensional surface of a 4 dimensional object.

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8 Answers

dynamicduo's avatar

I would have more education about the Internet. I believe the Internet is the biggest step forward humanity has made since the printing press. Since teachers commonly teach students how to do research via books, it clearly makes sense that they should also be teaching about how to use the Internet wisely and smartly.

cwilbur's avatar

Eliminate grade levels. I’d have primary education, which would last from 3 to 5 years, and would cover grades 1–3; then elementary, which would last another 3 to 5 years, and would cover grades 4–6; then junior high, which would last 2 or 3 years, and would cover grades 7–8; then finally high school, which I’d leave much as it is now.

The idea is that there would be standards for leaving each group. You don’t leave primary education until you can read, add, subtract, multiply, and divide, for instance. The difficult part is determining criteria that are both reasonably objective (so that two teachers evaluate the same child the same way, within a reasonable margin of error) and that are actually a good reflection of what the child is supposed to have mastered by that point.

My rationale is twofold: I’ve seen that tracking is one of the problems with teaching. Once you get on the “advanced student” track, you’re stuck there; but if you have a bad six months, and you wind up not on the “advanced student” track because of that, you suffer. And different students take different amounts of time to master skills—and it changes as the student grows. So instead of having a 12-year program and including social promotion, by eliminating grades you eliminate the need for social promotion. Most students will take four years to master the primary school skills, which is fine; some will do it in three, and some will take five, and all that is just fine too.

As far as pedagogy goes: I’m not familiar with math pedagogy, but I know that in music theory pedagogy the sweet spot is a balance between drills and rote practicing and exploring projects. You need to have the fluency with the basic materials match the explorations and projects you’re doing: the way to do this with college students is to alternate exploring and drilling, so that the exploring leads to understanding the underlying rationale while drilling leads to fluency with the materials that you need for the next phase of exploring. I think math is likely to work the same way.

(If you teach just exploration and projects, the students understand the theoretical principles but can’t apply them because they don’t have the fluency with the materials. Eventually the fluency catches up, but it’s frustrating and slow. If you teach just drilling, the students have perfect fluency with the materials but can’t apply them because they don’t understand the theoretical principles.)

ben's avatar

Sounds like you should read A Mathematician’s Lament. He tears about the way math is taught in schools.

See previous discussion:
http://www.fluther.com/disc/27439/what-do-you-think-of-a-mathematicians-lament/

steelmarket's avatar

Want a quick turnaround in the success of today’s classrooms? Lift the huge burden of administrative BS shouldered by all public school teachers and let them spend all their time on their students and curriculum.

LostInParadise's avatar

@cwilbur, I did read the article. It came out before I joined Fluther. I agree with it very strongly.

Sometimes it seems as if schools go out of their way not to reveal patterns. For example, students are sometimes taught that the sum of the external angles of a convex polygon is always 360 degrees. This seems a bit odd until you imagine rolling the polygon along the ground one full turn. The polygon turns about each external angle and it travels in a circle, which is 360 degrees.

augustlan's avatar

I like CWilbur’s ideas and would combine them with your approach, but apply it to other subjects as well. I think education should be much more ‘open-ended’ and taught in a more exploratory way. There will always be a need for basics, but they should be supplemented with active discussion and exploration.

LostInParadise's avatar

I also like @cwilbur’s ideas. In particular I like the idea of eliminating grades, not just to get rid of social promotion, but to keep education from being viewed as a competitive activity.

What horrible things we do to children. They are born eager to learn and explore, curious about everything. There is for them no distinction between learning and play. Schools ruin all of this by regimenting, lecturing and grading and giving homework even in the lowest grades. Is it any wonder that they soon come to hate school? There is a better way that is not only easier on them but more effective. Children learn best in a relaxed environment where they can harness their creativity, learn from their mistakes without being penalized and rely on the teacher as a resource to guide them when they get stuck.

cwilbur's avatar

There’s also The Six-Lesson Schoolteacher—well worth reading.

I think the optimal learning environment is in free or Sudbury-style schools, but that requires an incredible investment of teacher resources. My idea of getting rid of grade levels is based on keeping current teacher-student ratios while importing a lot from the free/Sudbury style approach.

Also, in free schools, the idea is for the teacher to find teachable moments in the things the student is interested in—the theory is that if the student is curious about something enough to learn about multiplication learning the multiplication tables (for instance) is going to seem like a reasonable thing to do, and that combination of curiosity and motivation is going to make learning the multiplication tables easy. But this requires the teacher to be looking for teachable moments and responding to the student’s interests—as soon as you have more than about 5 students per teacher, this is not going to be feasible. So you keep some of the exploration, but add a bit of drilling and rote learning to balance it out—with the idea that by the time you get to studying the multiplication tables, you’ll have done at least one exploratory project where you saw the usefulness of multiplication.

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