Dr. Wickelgren, author of Math Coach, A parent's Guide to Helping Children Succeed in Math, explains that it is not possible for children to "discover" much of what is important for children to learn in elementary grades. How, he asks, can a student deduce, through discovery, the meaning of "3 to the 4th power" or that there are 5,280 feet in a mile. There are many things which must be taught by the teacher and then memorized by the student. Now you may avow that these are things that a student could conceivebly discover, so let Dr. Wickelgren describe how a typical "discovery" session works.

"Using the discovery method, students are given very little of the information necessary to solve problems. Solving problems thus requires gigantic leaps of intuition that virtuallly no students possess, so they flounder. A class typically spends half an hour -- and sometimes as long as two and a half hours -- on a single problem."

Because the "discovery" time is largely unsupervised by the teacher, it proves to be a very inefficient use of students' time.

Dr. Wickelgren tells of a student who "complained to me that his class spent an entire week on one problem before the teacher told the students how to solve it."

And remember that in addition to the inefficiency of this procedure, students are also asked to spend time discussing what to do, and then to spend more time writing about how they arrived at their solution. And what if their solution isn't even correct??!! Remember, the teacher is not involved, is not guiding students back on track when they wander off on a rabbit trail.

As a result of all of the wasted time, very few problems actually are solved by the students. Teachers are giving little or no information, and student proficiency takes a nose-dive.

Contrast this scenerio to the traditional classroom, where children are taught by direct instruction. Students are given most, not all, but most of the information needed for solutions. Smaller amount of insight is needed and thus some students, though not all, solve the problem quickly. Several of these problem-solving activities are given throughout the course of the lesson, affording students additional opportunities to use small bits of insight to solve other problems. (And a teacher steps in to help, giving additional information when needed, if the problem takes too long.) Many students gain confidence because of the successes they make each lesson. And they see the point in what they are doing. The goal is short ranged.

Solutions are found quickly, not hours later, and students do not lose interest because the problem's answer is so long in coming. I'd rather have students engaged for several small problems they have hopes of solving than disengaged for an hour because they see no point in what they are doing.

## Wednesday, June 18, 2008

### Perils of Discovery Learning, Part II

Posted by Concerned Teacher at 5:19 PM

Labels:
direct instruction,
discovery learning,
Fuzzy Math,
traditional classroom

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