I love to watch children learn. When people ask me why I like teaching, my answer is always the same: "I love to see that light bulb go off, to see that elation on a child's face when he 'gets it'". So there is a part of every math lesson I teach where I give students a chance to discover on their own.

But these are not huge, time-consuming tasks which involve groups of students. (I never figured out how you know which child is making the discovery when students are working in groups!) Instead, these are short moments built into every lesson where children begin with a known concept and are led to discover and figure out the new concept.

Later into the lesson, for the students who have failed to make that connection to the new, teacher intervention in a one-on-one basis with that student can pinpoint where the connection failed and the student has another opportunity to discover. I have many memories which I prize, memories of struggling children smiling with great joy. They got it. They figured it out without my actually telling them. I love these "light bulb" moments.

Dr. Wickelgren also acknowledges that students need these moments, but he also describes the perils of great units of time spent on "discovery learning projects".

The troubles of "fuzzy math" failures, which have created an uproar and lead to "math wars" around the country throughout the 90's and since the turn of the century are well documented. Parents have risen up to protest and to request changes in curriculum because of the failures of the programs to teach their children rigorous math.

Dr. Wickelgren describes the failures linked to Standards math (fuzzy math, new math) as follows:

"It dumbs down class content and lowers expectations for all kids. It doesn't adequately tests kids' knowledge. It wastes far too much time on activities that have little to do with math. And despite good intentions, it can actually decrease student participation.

"But the most important downfall of the approach is that it often results in only cursory knowledge of the nuts and bolts of math -- including basic aritimetic facts . . . and how to solve a variety of problems. This severely weakens the math curriculum because basic mathematical knowledge and problem-solving skill are the key ingredients of math proficiency. Mastering basic facts early is critical becase they form the basis for a huge amount of mathematics that follows. A child who doesn't know those facts by heart -- and how to use them in problems -- is at a serious disadvantage, even if he or she understands the concepts of addition, subtraction, multiplication, and division."

And this stunning statement from Dr. Wickelgren:

"The primary reason for the downfall: excessive reliance on student discovery of facts and principles instead of explicitly teaching them."

And another:

"Discovery sounds good on paper. In practice, it is time-consuming, inefficient, and results in little learning."

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