Comments for Developmental Mathematics Revival!

Comment on Mathematical Literacy: How Did it Go? by Jack Rotman

Jack Rotman — Thu, 09 May 2013 17:56:59 +0000

Thanks. Good point about struggling students getting ‘recycled’ through again.

Comment on Mathematical Literacy: How Did it Go? by Sue Jones

Sue Jones — Thu, 09 May 2013 17:00:43 +0000

My experience here in the tutoring lab was that students felt like the online part took ***forever***. For some of them, it was over their heads — which meant the inevitable Assessment bounced them back down and they had to do Even MOre Exercises… but many of them also acknowledged that the serious immersion had made them a whole lot better at doing the stuff of math. Sometimes it transferred over to the classroom stuff and sometimes it didn’t.

Comment on Mathematical Literacy: How Did it Go? by schremmer

schremmer — Thu, 09 May 2013 15:29:19 +0000

Re. “One of the pleasant surprises is how well ‘dimensional analysis’ went.” Not a surprise to me but then I never use ‘naked numbers’ but only ‘numerator,denominator’ pairs as in 3 apples and then 3 apples • 5 cents/apple, cancel the apples and get 15 cents.

In other words, cents per apple is a dual denominator. Think “dual vector space”. And, in fact, there is really no need to stay in dimension 1 and not deal with ‘baskets’ and ‘price lists’. See <17. Fruit Salad and Linear Algebra>

Regards
–schremmer

Comment on Mathematical Literacy: How Did it Go? by schremmer

schremmer — Thu, 09 May 2013 15:13:46 +0000

Re. “students needed a symbolic rule for slope” Never noticed that. But then I let them plot two points, draw the segment of line and then the oriented rise and run arrows.

Re. ” Getting students to do [ ] homework!” Yes, that’s a problem with students with two jobs and a family and what not. I have no idea what to do about it.

Regards
–schremmer

Comment on Mathematical Literacy: Factoring in the Mathematics Curriculum by Sue Jones

Sue Jones — Thu, 25 Apr 2013 19:37:12 +0000

I was just reading yesterday in the NADE journal about the general condition of developmental mathematics and the conclusion of the article was: “We can no longer deny your weakest and poorest citizens the opportunity to obtain a college credential simply because we are unable to teach them how to factor polynomials.”
The article itself said absolutely nothing about that topic, and absolutely nothing about teaching students to understand math (it was the usual focus on Getting Students to Meet Math Requirements). I have this sinking feeling that there are all kinds of assumptions and judgements behind that closing statement.
I, too, have had a lot of students with a lot of confusion about multiplying vs. adding, and I start at the beginning of the year with stressing that the rules for adding and subtracting are really different than the rules for multiplying and dividing [interruption, I kid you not, to explain to a student that 1 2/3 is not 6/3 because where the plus sign is, you're supposed to add, not multiply]…
I think it’s worth spending the time on this, especially if I can build in time to show examples with good old fashioned numbers that yes, these are two ways of expressing the same thing.

Comment on Mathematical Literacy: Making Sense of Negative Exponents by schremmer

schremmer — Mon, 22 Apr 2013 17:27:27 +0000

Ah yes!, The (in)famous Hughes-Hallet, Andrew Gleason et al calculus book.

Given that the connection is a bit … incidental, I have always wondered how much grief it ultimately causes.

Regards
–schremmer

Comment on Mathematical Literacy: Making Sense of Negative Exponents by Jack Rotman

Jack Rotman — Mon, 22 Apr 2013 15:35:28 +0000

Only indirect … the course includes linear and exponential functions, so it is more a matter of ‘contrast’ than ‘connection’.

Comment on Mathematical Literacy: Making Sense of Negative Exponents by schremmer

schremmer — Mon, 22 Apr 2013 14:33:35 +0000

Re “The last class had two primary tasks: Integer exponents in problems, and equations of lines.”

What’s the connection?

Regards
–schremmer

Comment on Mathematical Literacy: Making Sense of Negative Exponents by schremmer

schremmer — Mon, 22 Apr 2013 14:26:10 +0000

In my experience, exponents should be defined from the start as integral exponents. Actually, it is the Laurent monomial Ax^±n that should be defined---as a shorthand for the longhand "A multiplied/divided by n copies of x". (Of course, when the coefficient A is 1, it can go without saying but only when the exponent is positive so I encourage the students always to write the coefficient, no matter what.) After the students have gotten used to go in and out of the shorthand, they should multiply/divide Laurent monomials for a while by expanding the shorthand into longhand, executing the longhand, and then writing the result in shorthand. After they get tired of it, one then points out that "oplussing" (adding signed numbers) the exponents takes care of multiplying Laurent monomials and "ominussing" the exponents takes care of dividing Laurent monomials. Regards --schremmer

Comment on Mathematical Literacy: Proportional Reasonng and Dimensional Analysis by schremmer

schremmer — Fri, 12 Apr 2013 17:37:38 +0000

Dimensional Analysis is a big word and one should first realize a few things:

A. That there are two very different situations:
1. When we are dealing with collections of items which we represent absolutely by number-phrases, that is by (numerator,denominator) pairs e.g. 3 apples.
2. When we are dealing with amounts of stuff which we can only represent relatively, that is only after we have decided on a unit amount of stuff e.g. 3 quarts of milk.

B. But that we can use (decimal numerator,metric denominator) in both cases, e.g. 2.3 KiloBytes and 2.3 KiloMeters. However, 2.3456 KiloBytes does not make sense while 2.3456 KiloMeters does.

C. That, sooner or later and in both cases, we need to involve the denominator dual to the original denominator e.g. cents/apple. Then, co-multiplication is rather nice: 3 apples x 5 cents/apple = 15 cents. (And that is where dimensional analysis really starts.)

D. That there is no real reason not to deal immediately with spaces, e.g. the space of “baskets” together with the dual space of “unit prices”.

Regards
–schremmer