Re: memorizing formulas
In this "code" era one has to memorize frequently used simple formulae (and codes) to be quick in doing things. Cheers. Siddeek dennis roberts wrote: we memorize defintions of terms don't we? most feel that is helpful ... so, same thing applies to many formulas too ... and, if one uses then enough ... they usually CAN'T help but memorize them ... == dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = begin:vcard n:Siddeek;Shareef M. tel;fax:(907) 465-2604 Phone: (907) 465-6107 tel;work:P.O. Box 25526, Juneau, Alaska 99802-5526, U.S.A. x-mozilla-html:FALSE org:Alaska Department of Fish and Game;Division of Commercial Fisheries adr:;; version:2.1 email;internet:[EMAIL PROTECTED] title:Shellfish Biometrician fn:Shareef M. Siddeek end:vcard
Re: memorizing formulas
In this "code" era one has to memorize frequently used simple formulae (and codes) to be quick in doing things. Cheers. Siddeek dennis roberts wrote: we memorize definitions of terms don't we? most feel that is helpful ... so, same thing applies to many formulas too ... and, if one uses then enough ... they usually CAN'T help but memorize them ... == dennis roberts, penn state university educational psychology, 8148632401 http://roberts.ed.psu.edu/users/droberts/drober~1.htm begin:vcard n:Siddeek;Shareef M. tel;fax:(907) 465-2604 Phone: (907) 465-6107 tel;work:P.O. Box 25526, Juneau, Alaska 99802-5526, U.S.A. x-mozilla-html:FALSE org:Alaska Department of Fish and Game;Division of Commercial Fisheries adr:;; version:2.1 email;internet:[EMAIL PROTECTED] title:Shellfish Biometrician fn:Shareef M. Siddeek end:vcard
Re: memorizing formulas
Karl L. Wuensch [EMAIL PROTECTED] wrote:
I think that Bob Hayden is on to something essential here ("I noted that
Karl presented all the understandings he sought verbally on the list. Why
not do the same in class?"). I think of the "definitional formulae" just as
a convenient shorthand for the verbal definition of a construct. But it may
be the case that most of our students assume that something that looks like
a formula is just for use with mindless computations. They may have learned
this in their first 12 years of schooling, where formulas may indeed be
presented as nothing more than mindless recipes for getting some quantity
not really well understood. How can we break our students of that bad
habit? I do frequently verbalize the 'formula' after writing it on the
board -- for variance, saying something like "look at this, we just take the
sum of the squared deviations of scores from their mean, which measures how
much the scores differ from one another, and then divide that sum by N, to
get a measure of how much scores differ from one another, on average." The
shorthand is really convenient, I don't know how I would get along without
it.
I have always thought that success in stats courses was much more a
function of a student's verbal aptitude and ability to think analytically,
rather than mathematical aptitude. Has anybody actually tested this
hypothesis?
I think the problem here is that, at least in the US K-12 system,
"mathematical aptitude" really means "computational proficiency." In
"back to basics" math (and the overwhelming majority of K-12 math
curricula *are* "back to basics"; it's only in a few elite schools with
high-performing students that any of those educational innovations that
right-wingers claim are destroying the minds of our students have actually
been used, but I digress; see Alfie Kohn's writings), mathematical
notation is taught as a series of Taylorized (as in Frederick Winslow) job
instructions rather than as a language for precisely describing certain
types of relationships. IOW, it's taught as a bunch of hoops to be jumped
through without really understanding what you're doing; all that matters
is going through the prescribed motions. A student who is "good at math"
is one who can jump through those hoops quickly. The object of most K-12
math is to turn out human calculators (something that actually made
economic sense in the Old Days when a machine to do calculations cost a
lot more than an employee doing calculations longhand).
As John Allen Paulos pointed out in _Innumeracy_, the majority of American
K-12 students know *how* to add, subtract, multiply, and divide, but a
much smaller number of them know *when* to add, subtract, multiply, and
divide. They do just fine when given a spelled-out list of calculations
to perform, but they panic when confronted with word problems.
Over in comp.infosystems.www.authoring.html, there's a long-running and
acrimonious debate between those who see HTML markup as a *description* of
the structure of a document and those who see it as a bunch of commands
interspersed with text. The notion that formal notation can be a
description or explanation rather than a sequence of tasks to perform is
alien to a lot of people. It may very well be that some people simply
don't have the built-in cognitive ability to grasp the former, but I
suspect that a much larger number of people *could* develop that ability
if only they were taught how to think that way (and it is indeed a way of
thinking rather than a set of "skills"). Right now I suspect that most
who developed that ability picked it up through intellectual exploration
outside the formal system of schooling. I'm pretty sure I did (I was a
math major but am not involved in teaching).
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Re: memorizing formulas
"Wuensch, Karl L." wrote (inter alia): If you have read Edwin Abbott's "Flatland," you might recognize that the same concept (a mean) which looked like a point in one dimensional space now looks like a line in two dimensional space. Then you would be ready to leap into three dimensional space and even beyond, into hyperspace, but you might want to sit down and have a good beer first. I promise that we shall travel that space before the semester is out (as soon as we get started on multiple regression). Sorry? The natural generalization of a mean to a 2-dimensional space is surely the vector mean, which is a point. -Robert Dawson = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: memorizing formulas
I personnaly found a way to have the students memorize formulas without forcing them. I let them use their books for exams but I regularly ask questions on how the statistics calculated from the formula are affected when I change, say, the number of subjects, the homogeneity of a set of data, the range of the independent variable, etc. Therefore, they study the formulas before the exams because they don't want to be looking for it while their thinking about the question. -- Dr Julie Lamoureux, dmd, MSc Tampa, Florida [EMAIL PROTECTED] "Bob Hayden" [EMAIL PROTECTED] wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... - Forwarded message from Michael Granaas - I honestly believe that there is something to be learned from memorizing several of the basic formulas that are involved in defining statistics. I, less elegantly, tell my students that it is important to have this basic understanding so that it can 1) be utilized when we have the machines start doing the computations for us and 2)be drawn on for understanding when the mathematics is no longer so simple. - End of forwarded message from Michael Granaas - I doubt your students will gain ANY understanding from memorizing formulae. Once they have the understanding, then formulae MIGHT provide a summary or reminder -- but only for students who are VERY fluent at READING mathematics -- as opposed to mindlessly manipulating formulae. I do not see any such students in the undergraduate introductory course that I often teach. I noted that Karl presented all the understandings he sought verbally on the list. Why not do the same in class? _ | | Robert W. Hayden | | Work: Department of Mathematics / | Plymouth State College MSC#29 | | Plymouth, New Hampshire 03264 USA | * | fax (603) 535-2943 /| Home: 82 River Street (use this in the summer) | ) Ashland, NH 03217 L_/ (603) 968-9914 (use this year-round) Map of New[EMAIL PROTECTED] (works year-round) Hampshire http://mathpc04.plymouth.edu (works year-round) The State of New Hampshire takes no responsibility for what this map looks like if you are not using a fixed-width font such as Courier. "Opportunity is missed by most people because it is dressed in overalls and looks like work." --Thomas Edison = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: memorizing formulas
Hi Karl, With respect to memorizing formulas, i do not think it serves much of a purpose. I let my students use a single sheet with any formulas they wish to use. Afterall, in the real world they'd always have references available. The key is to know how to apply them. Al Ovedovitz = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: memorizing formulas
this came to me instead. I used to give my students a formula sheet. I'd expect them to know some basic formulas such as the mean and definitional formula for sigma -- Elliot M. Cramer PO 428 Chapel Hill, NC 27514 919-942-2503 815-377-1689 fax www.unc.edu/~cramer "Oved6" [EMAIL PROTECTED] wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... Hi Karl, With respect to memorizing formulas, i do not think it serves much of a purpose. I let my students use a single sheet with any formulas they wish to use. Afterall, in the real world they'd always have references available. The key is to know how to apply them. Al Ovedovitz = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: memorizing formulas
- Forwarded message from Michael Granaas - I honestly believe that there is something to be learned from memorizing several of the basic formulas that are involved in defining statistics. I, less elegantly, tell my students that it is important to have this basic understanding so that it can 1) be utilized when we have the machines start doing the computations for us and 2)be drawn on for understanding when the mathematics is no longer so simple. - End of forwarded message from Michael Granaas - I doubt your students will gain ANY understanding from memorizing formulae. Once they have the understanding, then formulae MIGHT provide a summary or reminder -- but only for students who are VERY fluent at READING mathematics -- as opposed to mindlessly manipulating formulae. I do not see any such students in the undergraduate introductory course that I often teach. I noted that Karl presented all the understandings he sought verbally on the list. Why not do the same in class? _ | |Robert W. Hayden | | Work: Department of Mathematics / |Plymouth State College MSC#29 | |Plymouth, New Hampshire 03264 USA | * |fax (603) 535-2943 /| Home: 82 River Street (use this in the summer) | )Ashland, NH 03217 L_/(603) 968-9914 (use this year-round) Map of New[EMAIL PROTECTED] (works year-round) Hampshire http://mathpc04.plymouth.edu (works year-round) The State of New Hampshire takes no responsibility for what this map looks like if you are not using a fixed-width font such as Courier. "Opportunity is missed by most people because it is dressed in overalls and looks like work." --Thomas Edison = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: memorizing formulas
I think that Bob Hayden is on to something essential here ("I noted that
Karl presented all the understandings he sought verbally on the list. Why
not do the same in class?"). I think of the "definitional formulae" just as
a convenient shorthand for the verbal definition of a construct. But it may
be the case that most of our students assume that something that looks like
a formula is just for use with mindless computations. They may have learned
this in their first 12 years of schooling, where formulas may indeed be
presented as nothing more than mindless recipes for getting some quantity
not really well understood. How can we break our students of that bad
habit? I do frequently verbalize the 'formula' after writing it on the
board -- for variance, saying something like "look at this, we just take the
sum of the squared deviations of scores from their mean, which measures how
much the scores differ from one another, and then divide that sum by N, to
get a measure of how much scores differ from one another, on average." The
shorthand is really convenient, I don't know how I would get along without
it.
I have always thought that success in stats courses was much more a
function of a student's verbal aptitude and ability to think analytically,
rather than mathematical aptitude. Has anybody actually tested this
hypothesis?
- Forwarded message from Michael Granaas -
I honestly believe that there is something to be learned from
memorizing several of the basic formulas that are involved in defining
statistics. I, less elegantly, tell my students that it is important
to have this basic understanding so that it can 1) be utilized when we
have the machines start doing the computations for us and 2)be drawn
on for understanding when the mathematics is no longer so simple.
- End of forwarded message from Michael Granaas -
I doubt your students will gain ANY understanding from memorizing
formulae. Once they have the understanding, then formulae MIGHT
provide a summary or reminder -- but only for students who are VERY
fluent at READING mathematics -- as opposed to mindlessly manipulating
formulae. I do not see any such students in the undergraduate
introductory course that I often teach. I noted that Karl presented
all the understandings he sought verbally on the list. Why not do the
same in class?
=
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=
Re: memorizing formulas
"Karl L. Wuensch" wrote: I have always thought that success in stats courses was much more a function of a student's verbal aptitude and ability to think analytically, rather than mathematical aptitude. Has anybody actually tested this hypothesis? 1. This clearly depends on the particular (type of) stats course. 2. I would find 'ability to think analytically' hard to distinguish from 'mathematical aptitude' - although I accept that some narrow definitions of both characteristics may have minimal overlap. Alan -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102Fax: +61 03 9903 2007 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
