5 ms·
It can be obvious in other ways. For example if you can see how a parabola is the product of two straight lines. And you can teach it that way.
by jonsen 5y ago
It can be obvious in other ways. For example if you can see how a parabola is the product of two straight lines. And you can teach it that way.
- civilized 5y agoI think, like the OP, this just dances around completing the square without actually eliminating the need for it. How do we know that all parabolas can be expressed as the product of two symmetrical straight lines?
- jonsen 5y agoThis is not about deep math. It's about pedagogics. How to generate some understanding and good feelings for solving quadratic equations.
- civilized 5y agoI just don't get why making some unsupported postulate about how parabolas can be generated from straight lines is better pedagogically than teaching completing the square and providing a geometric interpretation for completing the square.
- jonsen 5y agoThat's ok. I can't explain it here in a few lines. It's rather a pedagogic principle that permeates most of my teaching. It's not just a postulate. It's demonstrated. A style used from the start of algebra.
- SilasX 5y agoI honestly don’t see how this version is any more intuitive than regular completing the square.
- jonsen 5y agoPedagogically there's more to it than just the algebraic manipulations. The algebra here is basically as dull as all other algebra. It's the teacher's job to make it come alive.
- SilasX 5y agoYour previous comment just suggested that there's something pedagogically superior about this approach. If you don't believe that, you shouldn't have made the comment.