Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: Another Precalculus Doorstop, Another Migrane
Posted:
Sep 1, 2010 3:24 AM
|
|
You have surfaced an important instructological principle that is well worth
serious (and better) attention.
Every professional exposition in mathematics tacitly presumes that its
readers already own a body of knowledge--- which is prerequisite for
comprehending that exposition.
In curricular mathematics instruction, each course is necessarily designed
on the premise that there exists a body of underlying (genuine) mathematical
knowledge that is in-common shared by all students who would undertake that
course. At the pre-calculus level, it always is presumed that we can rely
on students knowing that, among whole numbers, 2+3 = 5 ... and that same
presumption persists throughout school and college curricula. What else can
realistically be presumed --- at what curricular levels?
So arises the curriculum development (or textbook authoring) ... indeed, the
instructional ... challenge of realistically estimating the minimal,
maximal, optimal, and normal state of pertinent mathematical knowledge that
can expectably be held by all students who would follow a particular
course/path of personal mathematical growth.
As things now stand, our present mechanisms for screening students for
admission into specific courses badly fail to discern how well those
students are mathematically prepared to comprehend the mathematical essence
of that course ... so students arrive with diverse levels and areas of
"preparatory" education. Nonetheless, they normally are regarded as being
members of a "class" of students for whom that course is intended.
That leaves teachers (and authors) with the challenge of coping with the
differences in mathematical preparation for such "class" instruction in the
mathematics to be covered in that "course" of mathematical progress.
Ideally, the teacher could immediately give each student a mathematical
"shot", so that all could immediately be brought up to the mathematical
"par" from which the course could proceed, as the instructor/author desires.
Seemingly impossible -- unless we can realistically assign each student to
"go learn (whatever)". True, various kinds of "bridge" courses have been
created for bringing students up to par, for beginning various college
courses in mathematics. In fact, the entire "developmental mathematics"
program is justified on that basis. But the "enrollment below par" problem
for the "class" instructor of a particular mathematics course boils down to
how best to bring all class-students up to "entrance par", so as to enable
collective progress along that mathematical "course".
Every textbook authoring team has its own way of attempting to deal with
that dilemma of intra-class dispersive preparation. Every class-instructor
must do the same. You have objected to how one textbook tries to cope with
that dilemma ... suggesting that there exist better ways for textbooks to do
so. But each instructor has his or her own ways --- and there might be also
a better way of doing that.
So arises the scientific challenge of finding "best" ways for instructors
(or authors) for effectively attending the dispersive-preparation problem.
The starting point might well be to find a way of deciding when one way is
(as you suggest) not as "good" as some other ways.
Has our technological evolution reached the stage where it already is
possible to determine whether or not he or she is mathematically prepared
for academically successful entry into a (whatever) course in mathematics?
If so, has it reached the stage of being able to provide under-prepared
students with guidance on how to become duly prepared?
Is anyone interested in helping the nation to alleviate its
preparation-dispersal problem? ... or do we just sit back and moan about it,
until someone else makes progress?
Hopefully,
Clyde Greeno
--------------------------------------------------
From: "Domenico Rosa" <DRosa@post.edu>
Sent: Tuesday, August 31, 2010 3:35 PM
To: <mathedcc@mathforum.org>
Subject: Another Precalculus Doorstop, Another Migrane
> I am suffering from another severe migraine after examining the following
> doorstop:
>
> Larson Hostetler Edwards
> Precalculus with Limits: A Graphing approach
> Fifth edition, Brooks Cole
> 836 pages, plus an Appendix of 136 pages
>
> The first 100+ pages consist of review material involving mostly mindless
> algebraic manipulations and linear and quadratic equations.
>
> These types of doorstops are in sharp contrast with my 12th-grade Advanced
> Mathematics textbook that is discussed at:
>
> http://mathforum.org/kb/thread.jspa?forumID=206&threadID=478525
>
> Do the promoters of the latest propaganda campaign, Race to the Top, have
> any clue about the abominable doorstops that continue to be foisted on
> teachers and students?
> ****************************************************************************
> * To post to the list: email mathedcc@mathforum.org *
> * To unsubscribe, email the message "unsubscribe mathedcc" to
> majordomo@mathforum.org *
> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
> ****************************************************************************
****************************************************************************
* To post to the list: email mathedcc@mathforum.org *
* To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.org *
* Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
****************************************************************************
|
|
|
|
