
Re: Teaching Dev Mathematics Conceptually: practical ideas
Posted:
Feb 4, 2009 6:22 PM



Laura,
Thanks for attempting to get us to focus on the practical.
Here's one I used yesterday, that is an odd, surprising one.
I did order of operations, which almost all of them mostly remembered, even though they are in math 010, developmental prealgebra, the lowest of the low classes. They drilled it a lot in high school, I think.
So... I told them I would show them WHY this was the order.
I wrote on the board 2+3 2 x 3 2^3
and asked them to calculate each one. There was a little discussion on the last one, that 2^3 was not 6 (sigh) because it really means 2 x 2 x 2. Then the punch line:
The order of operations goes from most powerful to least powerful  from the thing that matters most and makes the most difference (exponents), to the thing that matters least.
Then we went on to talk about Please Excuse My Dear Aunt Sally, and how it's misleading because Multiplication and Division are actually tied, as are Addition and Subtraction. But it's a nice mnemonic as long as you remember that. And then we practiced a bunch singly and in pairs.
So... there you go.
I always thought the order of ops was arbitrary, and always taught it that way. But then I remembered that my dad had once told me that in programming, addition was last, because it made the least difference to what you were doing. So I've been pointing this out to students, and I think it makes what looks like an arbitrary idea a little less pointless.
I'll try to add some more of these sometime soon. I hope other people will pitch in.
Kathleen Offenholley Borough of Manhattan Community College
________________________________ From: Laura Bracken <bracken@lcsc.edu> To: wmackey <wmackey@uark.edu>; Philip Mahler <mahlerp@middlesex.mass.edu> Cc: mathedcc@mathforum.org Sent: Monday, February 2, 2009 6:28:17 PM Subject: RE: Teaching Developmental Mathematics Conceptually
There are a lot of "what ifs" that we can think about...
What if our students did not come to us with their past math experiences and past school experiences  what if they were motivated, knew how to study, did not have learning disabilities, did not have problems at home, did not have money trouble?
What if we could assume that all of our students read at the 9th grade level?
What if all of our students had access to free oneonone or small group tutoring by appointment from a qualified tutor?
What if we could change the college math curriculum, prealgebra through whatever, without worrying about whether our courses still prepared our students for their work in all majors (including STEM) and without consideration for our colleagues who are not ready for change or for the impact of these changes on students who will transfer to a more "traditional" program?
What if our institutions had enough money so that math classes were only taught by fulltime instructors? (I know my institution is facing at least a 10% budget cut and enrollment is also increasing. Things are getting worse, not better.)
As far as I can tell, these things are not going to happen anytime soon.
I think it is good that we talk about learning theory and brain development and the ways we might go if we could start over and redesign everything. But, I also think that we should spend much more time on this list talking about what we are doing now to try to help students develop better conceptual understanding and to become persistent learners who take responsibility for their own learning. My sense is that we have a lot of colleagues who need specific suggestions for things they could do now, within the constraints of the status quo.
So, my question to you all  assuming that you are teaching a relatively standard curriculum in prealgebra, elementary algebra, and/or intermediate algebra and you are using, at least for exercise sets, a mainline textbook  is what are you doing to help your students improve their conceptual understanding? What assessment strategies or teaching strategies are you using? What works? What doesn't? Do you think your students are doing better in their next courses as a result of these efforts?
Laura
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