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Re: Mathematical understanding
Posted:
Nov 8, 2010 5:15 PM
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On Nov 8, 2010, at 4:05 PM, Laura Bracken wrote:
> This question applied to a developmental prealgebra class is "how
> does one actually lead students to an adequate conceptual
> understanding of number, arithmetic, very basic algebra, and
> problem solving in 39 hours"?
>
> I think one of the inherent difficulties in the college environment
> is the limited contact time. I see my prealgebra students three
> hours a week for one semester. Their attendance tends to be less
> than consistent (for a variety of reasons, often out of their
> control) so they don't get all of the 39 hours.
>
> They need to develop number sense, the ability to round and
> estimate and compare estimations, the ability to read critically
> and identify needed and extraneous information, they need to
> understand how units of measurement work and are related to each
> other, they need to understand positional notation, they need to
> understand what a fraction or decimal number represents, they need
> to understand when it is appropriate to add, subtract, multiply or
> divide whole numbers, integers, fractions, and decimals as well as
> do those procedures, they need to understand what a variable
> represents and why we can do the things we do to solve an equation
> in one variable, and they need to understand that a graph, a table
> of ordered pairs, a list of ordered pairs, and an equation in two
> variables are multiple representations of the same thing -- a
> relationship.
>
> Many of my students in this class do not read well and can barely
> write a paragraph. One of the issues in having students do "rich"
> applications and activities is that they read very slowly and they
> do not approach what they are reading analytically.
>
> Please, I don't need an idealistic or philosophical answer to this
> question; I need a realistic practical answer that can be applied
> to my classes and to the same classes that will be taught by
> adjuncts next semester. Remember that I teach four sections of
> developmental math every semester, that I am accountable for my
> students' performance on a common department final, that my student
> success rate (percent with C or better, withdrawals after tenth day
> count as F) is calculated every year, that I am not protected by
> tenure, that my class size may be going up because of budget cuts,
> that the amount of tutoring available in the math tutoring center
> (staffed only by students) will probably be going down because of
> budget cuts, and that there is no money for professional
> development or release time.
Elementary my dear Watson:
The answer is not to take the students for morons and take advantage
of the fact that in appropriate circumstances---which excludes
dealing with a succession of isolated independent topics, the
learning curve is exponential. In other words, the connective
tissues, not memory, are what holds the stuff together.
Towards an implementation, see http://www.freemathtexts.org/
Standalones/RDA/Contents.php
And of course, keep in mind that the stuff on FreeMathTexts.org is
under a GNU Free Documentation License which means that you can take
anything you want and do whatever you want with, and to, it.
Best regards
--schremmer
P.S. The common departmental final is the only sticky issue. The one
I protected my students from was more than moronic. Had it been semi-
sane, I believe that I could have let my students take it with very
little if no coaching. What you are facing is, at best, an extremely
fine balancing act.
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