What math lessons would you offer to elementary teachers?
I may get to be part of a project that would help elementary teachers learn more math. Right now it's wide open. What would you teach them? Or if you're an elementary teacher, what would you like to learn?
One of the things I always taught my high school math students was the connection between early elementary school math and the algebra we would doing.
"You've been doing Algebra since elementary school. It just looked a little different. In elementary school, you got problems like this:
5 + ___ = 10 or 2 x ___ = 4
Your teachers would ask you, 'What number goes in the blank? What number is missing?' You would solve them quickly in your head. The only difference is that instead of a blank space or a box, we put a letter, a *variable*:
5 + x = 10 or 2y = 4
Now I'll ask you, 'What does x equal? What does y equal?' But the problems are really the same."
I like to think it was an eye-opening experience. If there was some way that elementary teachers can make that same kind of connection to algebra, it would certainly help us in the upper grades.
Also, they need to know their times tables, and be able to add and subtract simple problems without a calculator. So much time is wasted in upper grade because students lack in these skills.
Finally, in a more general sense, students come to middle/high school hating math, not believing in their ability to do it, and not seeing any sort of purpose for it in the grand scheme of things. These are problems that need to be addressed early; the message that this is important and applicable can't be understated.
It's not about numbers, per se; pointing out that numbers are everywhere around us is not the same as saying MATH is everywhere around us!
I think it would be helpful if elementary teachers really understood the place-value system. Teaching other bases is the way I check understanding of this concept with my students, so maybe it would serve teachers well also.
I wouldn't say it like this, but I would want them to realize that they probably don't know math well enough to teach it. As in, just because they can carry out an error-free multiplication or long division algorithm doesn't mean they actually know what they are doing. I'd want them to realize that it is not enough to get a kid to mimic a procedure. If that ignorance persists, it will seep into their classroom discourse, and perpetuate mathematical misunderstanding to another generation of American kids.
Then I'd want to back it all the way up and re-teach them the place value decimal system.
@Alison: I'm so tickled you said that! That's what I want to spend my first week with them on.
@Mr. D: With the simple calculations issue you bring up, it sounds like working with the teachers on mental math skills might be helpful. Maybe one goal would be for them to be fluent enough with doing things in their heads that they can take a more playful approach to it.
@Kate: Yeah, procedures are not what math is about. Hmm... Cornell is doing something called the Good Questions Project. I think I need to really know how to do that. (This teaching idea started in physics.)
Math Mama is Sue VanHattum, a community college math teacher interested in all levels of math learning, and the mama of a young son. I entered the blogging world as I began work on an anthology about learning math. Contact me at mathanthologyeditor on gmail etc.
One of the things I always taught my high school math students was the connection between early elementary school math and the algebra we would doing.
ReplyDelete"You've been doing Algebra since elementary school. It just looked a little different. In elementary school, you got problems like this:
5 + ___ = 10 or 2 x ___ = 4
Your teachers would ask you, 'What number goes in the blank? What number is missing?' You would solve them quickly in your head. The only difference is that instead of a blank space or a box, we put a letter, a *variable*:
5 + x = 10 or 2y = 4
Now I'll ask you, 'What does x equal? What does y equal?' But the problems are really the same."
I like to think it was an eye-opening experience. If there was some way that elementary teachers can make that same kind of connection to algebra, it would certainly help us in the upper grades.
Also, they need to know their times tables, and be able to add and subtract simple problems without a calculator. So much time is wasted in upper grade because students lack in these skills.
Finally, in a more general sense, students come to middle/high school hating math, not believing in their ability to do it, and not seeing any sort of purpose for it in the grand scheme of things. These are problems that need to be addressed early; the message that this is important and applicable can't be understated.
It's not about numbers, per se; pointing out that numbers are everywhere around us is not the same as saying MATH is everywhere around us!
I think it would be helpful if elementary teachers really understood the place-value system. Teaching other bases is the way I check understanding of this concept with my students, so maybe it would serve teachers well also.
ReplyDeleteI wouldn't say it like this, but I would want them to realize that they probably don't know math well enough to teach it. As in, just because they can carry out an error-free multiplication or long division algorithm doesn't mean they actually know what they are doing. I'd want them to realize that it is not enough to get a kid to mimic a procedure. If that ignorance persists, it will seep into their classroom discourse, and perpetuate mathematical misunderstanding to another generation of American kids.
ReplyDeleteThen I'd want to back it all the way up and re-teach them the place value decimal system.
@Alison: I'm so tickled you said that! That's what I want to spend my first week with them on.
ReplyDelete@Mr. D: With the simple calculations issue you bring up, it sounds like working with the teachers on mental math skills might be helpful. Maybe one goal would be for them to be fluent enough with doing things in their heads that they can take a more playful approach to it.
@Kate: Yeah, procedures are not what math is about. Hmm... Cornell is doing something called the Good Questions Project. I think I need to really know how to do that. (This teaching idea started in physics.)
ReplyDeleteAnd fractions! Won't someone please teach the children that fractions aren't evil!
ReplyDeleteYeah, if you help elementary teachers to deeply know three real-life situations modeling fraction division well, it will be a huge step forward.
ReplyDelete