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Topic: Teaching Developmental Mathematics Conceptually
Replies: 71   Last Post: Feb 11, 2009 10:11 AM

 Messages: [ Previous | Next ]
 Aguilar, Darla Posts: 19 Registered: 9/12/05
RE: Teaching Developmental Mathematics Conceptually
Posted: Feb 2, 2009 4:01 PM

I teach the Math for Elementary Teachers course. I have them finding formulas for linear problems for 4 months and they still don't connect it to what they learned in algebra class. All of the students can write an equation of a line given two points and even recognize that the data goes up by the same amount in a table but they don't connect the two because the context is not similar. When I show them, they are amazed. Most of them have actually developed a method to find the formula but it seldom relates to y=mx+b.

It is great to talk about memorization vs conceptual but applications are where most students fall apart because they only understand the concept in a math context.

Darla Aguilar
Desert Vista Campus
Mathematics Department Chair
520-206-5160

- -----Original Message-----
From: owner-mathedcc@mathforum.org [mailto:owner-mathedcc@mathforum.org] On Behalf Of Jonathan Groves
Sent: Sunday, February 01, 2009 3:53 PM
To: mathedcc@mathforum.org
Subject: Teaching Developmental Mathematics Conceptually

Dear Fellow Mathematicians and Mathematics Educators,

I am wondering how we can teach developmental mathematics courses conceptually, that is, how to teach them so that the students understand the reasoning behind the computations (why the procedures work) and how to use their knowledge to solve new problems and how to find concrete meanings in the symbolism. In other words, developmental math courses should not be taught by rote or as a "cookbook" (or "bag of tricks") course. This doesn't mean we throw away algorithms like those used to solve equations, but we make sure the students know where they come from and why they work. Most of these students learned math this way, and it didn't work. So why should we teach it that way, too?

It is hard to teach such a course this way (to emphasize, I should say that this is a class that meets in a traditional classroom, not online) because of lack of time. Often, a year-long high school math course is crammed into one college semester, which is usually several weeks shorter than a high school semester, not to mention that developmental math courses meet only 2-3 days a week as opposed to 5 days a week. We often are tempted to lecture and reduce everything to rote by not taking the time to explain where concepts come from and why the procedures work since we usually don't have the time to explain this after we explain the procedures and go over examples. How do we make time for both?

I can imagine finding the time to do this for classes that meet online isn't anywhere as hard. But this depends on how conceptual the curriculum and textbook are for the course you are teaching, how flexible the school is in letting you choose assignments and tests and discussions online (actually, it is possible to get around this even if discussion questions are already prechosen since the teacher still has the flexibility in adding to the discussion). If the book and curriculum are mostly rote and so are the assignments and other graded stuff and the teacher has little or no flexibility in designing assignments and other graded stuff, then the teacher will find it nearly impossible to teach the course conceptually since the lack of graded stuff on conceptual questions makes it hard to motivate students to go beyond rote learning. In general, I discover that if students know they will not be graded on something, very few of them will bother to learn it (exceptions may e!

xist in advanced courses perhaps). If the course is predesigned and is highly rote, how can we encourage the students to learn conceptually and not by rote?

Jonathan Groves
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Date Subject Author
2/1/09 Jonathan Groves
2/1/09 Prof Martin Weissman
2/1/09 Jonathan Groves
2/2/09 Alain Schremmer
2/1/09 Bret Taylor
2/2/09 Tom McClure
2/2/09 Larry Stone
2/2/09 Alain Schremmer
2/3/09 Jonathan Groves
2/4/09 Beth Hentges
2/4/09 Alain Schremmer
2/4/09 Jonathan Groves
2/5/09 Larry Stone
2/5/09 Beth Hentges
2/6/09 Phil Mahler
2/6/09 Alain Schremmer
2/6/09 Phil Mahler
2/3/09 Jonathan Groves
2/2/09 Alain Schremmer
2/2/09 Hart, Rose
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2/3/09 Jonathan Groves
2/2/09 Phil Mahler
2/2/09 Alain Schremmer
2/3/09 Phil Mahler
2/2/09 Wayne Mackey
2/2/09 Laura Bracken
2/2/09 Alain Schremmer
2/2/09 Phil Mahler
2/3/09 Wayne Mackey
2/2/09 Bret Taylor
2/3/09 Phil Mahler
2/3/09 Jonathan Groves
2/3/09 Jonathan Groves
2/4/09 Joan Bookbinder
2/4/09 Beverly R. Broomell
2/4/09 Phil Mahler
2/4/09 Jonathan Groves
2/5/09 Phil Mahler
2/5/09 Jonathan Groves
2/5/09 Phil Mahler
2/5/09 Jonathan Groves
2/5/09 Revathi Narasimhan
2/2/09 Wayne Mackey
2/2/09 Alain Schremmer
2/3/09 Jonathan Groves
2/4/09 Jonathan Groves
2/5/09 Wayne Mackey
2/5/09 Laura Bracken
2/5/09 Jonathan Groves
2/6/09 Phil Mahler
2/6/09 Alain Schremmer
2/6/09 Jonathan Groves
2/6/09 Alain Schremmer
2/7/09 Jonathan Groves
2/7/09 Alain Schremmer
2/8/09 Jonathan Groves
2/10/09 Wayne Mackey
2/7/09 Phil Mahler
2/7/09 Jonathan Groves
2/8/09 Phil Mahler
2/10/09 Wayne Mackey
2/10/09 Alain Schremmer
2/11/09 Wayne Mackey
2/10/09 Wayne Mackey
2/10/09 Wayne Mackey
2/10/09 Alain Schremmer
2/11/09 Wayne Mackey
2/2/09 Aguilar, Darla
2/2/09 Alain Schremmer
2/2/09 Phil Mahler
2/3/09 Jonathan Groves