(no subject)
One thing that's bothering me about the curriculum for 10th grade I teach (Prentice Hall Math A) is the fact that students learn to factor trinomial expressions before they are introduced to equations that require factoring for a solution.
I think the most exciting thing about factoring is now you can solve this equation that you thought couldn't be solved.
I have memories of hacking away at an equation like x^2 + 2x = 8 before my teacher told us about the "zero product property" --it totally blew my mind that you could get away with that!
After that I was REALLY motivated to find a way to factor.
I feel as though we're teaching factoring as a computation skill-- There are conceptual elements to the "algebra tiles"-- but, it could easily just turn in to a kind of abacus-- speedy calculations-- meaningless results.
I'm teaching factoring now and I really want my students to have a deeper understanding than the text seems to allow. But people keep telling me that the conceptual approach will "take too much time" or "just confuse them."
Today, I had to cover a gym class. It was utter chaos and I feared for my life. As a result of this I left my lesson plan for the 10th grade in the main office. I had to "wing it" with my toughest class and I was pretty flustered.
I knew they were about to start factoring so I asked them to define the words "factor" and "product" We then factored some numbers and simple expressions as examples. Then I asked them "how do you know when you can't factor an expression anymore?" I let them think for a long time. They had some pretty good answers.
Then I asked "What are factors good for?"
Nobody had a clue. Till one girl suggested that factors can let you "Write things in different ways." So I asked "And what's that good for?"
"That's all you math people do you just write things in different ways."
I think this is an excellent description of much of mathematics.
I don't know if the whole conversation was waste of time or if it was the best lesson I've ever taught.
I think the most exciting thing about factoring is now you can solve this equation that you thought couldn't be solved.
I have memories of hacking away at an equation like x^2 + 2x = 8 before my teacher told us about the "zero product property" --it totally blew my mind that you could get away with that!
After that I was REALLY motivated to find a way to factor.
I feel as though we're teaching factoring as a computation skill-- There are conceptual elements to the "algebra tiles"-- but, it could easily just turn in to a kind of abacus-- speedy calculations-- meaningless results.
I'm teaching factoring now and I really want my students to have a deeper understanding than the text seems to allow. But people keep telling me that the conceptual approach will "take too much time" or "just confuse them."
Today, I had to cover a gym class. It was utter chaos and I feared for my life. As a result of this I left my lesson plan for the 10th grade in the main office. I had to "wing it" with my toughest class and I was pretty flustered.
I knew they were about to start factoring so I asked them to define the words "factor" and "product" We then factored some numbers and simple expressions as examples. Then I asked them "how do you know when you can't factor an expression anymore?" I let them think for a long time. They had some pretty good answers.
Then I asked "What are factors good for?"
Nobody had a clue. Till one girl suggested that factors can let you "Write things in different ways." So I asked "And what's that good for?"
"That's all you math people do you just write things in different ways."
I think this is an excellent description of much of mathematics.
I don't know if the whole conversation was waste of time or if it was the best lesson I've ever taught.