Feedback on bicycle / tricycle problem
1>> what would be appropriate
2>> more about setting standards
3>> thinks bike problem is ok
1>>
From: Self
To: @WAEDU.PML
Subject: 9th Grade Algebra Problem on WASL!
BCC to: @EDLOOP.PML,@EDU.PML
Send reply to: arthurhu@halcyon.com
Date sent: Fri, 16 Oct 1998 12:34:59 -0700
math01.gif
http://www.leconsulting.com/arthurhu/images/98/10/15/Page0001.html
At A.G. Bell Lake Washington, they had their 2nd annual "meet the
test"night, and this was their latest alleged 4th grade problem that they
showed off.
This is a 4th grade problem??? Even if a few kids _can_ figure this out by
some contorted guess and check method, we should not waste time teaching
kids, let alone assess for "skills" like this that are of ZERO value in
"real world" problems.
When IS the last time you had to figure how many
of bicycles and tricycles wer parked based on the total number of wheels
and difference in total number? It's pretty obvious that if you know the
difference is 4, she must have !@#$% counted them in first place!
Fact is, almost none of these "real life" problems have any application in
real life compared to straightforward math problems with one step and one
answer.
You have 4 more bikes than
tricycles, but 33 wheels total. How many bikes do you have? The only
reasonable way to solve this is middle or high school algebra. They
sent this home to kids and claimed that some of them had some
pretty remarkable solutions.
It's clear that they did _not_ teach kids how to solve this problem,
it's the old standards based "let's see if the kids can figure it
out, and if anybody actually gets it right on their own, we'll use
that student sample to 'set the standard'. That's the whole fraud of this
whole standards based thing because some kids will come to school knowing
this stuff from home without ever being taught at school things like
"proportion". If anybody can get it, we can assume that _all_ should be
expected to get it, or they don't pass their grade level??????
A 2nd grade teacher claims she showed her kids how to solve it too by
drawing pictures. If this is supposed to be from real life, somebody
deserves to be shot if we expect kids to solve real life problems this way
with guess and check or worse. Anybody that tries to solve problems like
this in real life deserves to be fired.
Solution:
High School Algebra (the only practical way to solve this)
x= bicycles
x-4 = tricycles
33 = wheels
x*2 + (x-4) *3 = 33
2x + 3x - 12 = 33
5x - 12 = 33
5x = (33 + 12) = 45
x = 45/5 = 9 bicycles
9-4 = 5 tricycles
Guess and check (not anything I'd ask any kid to do)
Make a table with these columns.
Pick the one with the desired difference
Tri= Number of Tricycles
TriWheels = Number of Tricycle Wheels
BWheels = Number of wheels left for Bicycles
Bicycles = Number of Bicycles
Diff = Difference between B - T
Tri TriWheels BWheels Bicycles Diff
1 3 30 15 14
2 6 27
3 9 24 12 9
4 12 21
5 15 18 9 4****
6 18 15
7 21 12 6 1
Match is 9 bicycles, 4 tricycles
It's one thing to waste a weekend getting kids to figure out
something that's completely useless as a math skill, it's quite
another to expect ALL kids to be able to pass this on a minimum
proficiency test, especially when there are NO 4th grade math
textbooks that show how to solve this problem, and solving for
unknowns isn't until the 7th grade benchmark anyways.
These are the algebra benchmarks:
http://cisl.ospi.wednet.edu/ComSL/MATHBMK.html
G4: solve simple equations using blocks, sticks, beans, pictures, etc.
G7: set up and solve single-variable equations
G10: create and solve equations and inequalities
G4: use standard notation in reading and writing open sentences, for
example, 3 x __ = 18
G7: understand and use variables in simple equations, inequalities, and
formulas, for example 3x > 18
G10: ***represent situations that involve variable quantities*** with
expressions, formulas and equations, and inequalities
This is a G10 problem by the state benchmarks.
There is no other standard for solving this sort of problem.
Date sent: Fri, 16 Oct 1998 14:57:47 -0700
From: Jim Keeffe
To: arthurhu@halcyon.com
Subject: Re: 9th Grade Algebra Problem on WASL!
> Arthur -
>
> You have a great way with words. I like how you come straight to the
> point.
>
> 'If this is supposed to be from real life, somebody deserves to be shot'
> 'Anybody that tries to solve problems like this in real life deserves to
> be fired.
>
> Send this one to Bergeson and copy to all members of the house/senate
> ed. committees and the members of the CSL and state board of ed. Keep up
> the pressure - the windshield will eventually cracked with all the bug
> shit accummulating on it.
From: Tami Matsumoto
To: wa-esslrngs@whitecap.psesd.wednet.edu
Subject: Re: 9th Grade Algebra Problem on WASL!
On Friday, Oct. 16, Arthur Hu wrote about a problem given to 4th grade
students in Lake Washington.
He was concerned that there were only two ways to solve the problem: 1)
guess and check, which he sees as too cumbersome and useless as a tool
for students to be taught, and 2) using a formal algebraic equation, in
his words "the only practical way to solve this".
There is a middle ground here that may have been overlooked. How about
a systematic list that allows the patterns to be seen? That is a step
above guessing and checking and a part of growth toward algebra.
Students who explore problems in this way get opportunities to see the
relationships between the variables, and gain some of the conceptual
underpinnings for algebraic thinking and reasoning.
A systematic list would look similar to his example, but would be
organized to show the patterns in the data. In this case, the
relationship of 4 more bicycles is held constant in the table, and the
number of tricycles begins at the lowest possible. Other organizations
are possible, but as long as they are systematic a useful pattern can be
seen.
Tri Wheels Bi Wheels Total Wheels
0 0 4 8 8
1 3 5 10 13
2 6 6 12 18
3 9 7 14 23
etc.
Some 4th graders will finish the table to 33 wheels. Others will see
patterns and "know" the solution after the first few lines of the table.
The patterns that emerge in this way are powerful and useful tools for
students BEFORE formal algebra is introduced. These types of problems
provide experiences that build "bridges" to the problems and strategies
that students will use in later years.
Mr. Hu sees a large number of items on the 4th grade WASL as being at
the 7th or 10th grade level. Perhaps some of them are similar to this
problem, in that they COULD be solved using 7th or 10th grade skills,
but COULD ALSO be solved with other methods that are accessible to
younger students and lead up to skills in higher grade levels.
From: "arthur hu"
To: destiny.esd105.wednet.edu@destiny.esd105.wednet.edu
Date sent: Mon, 19 Oct 1998 10:20:35 -0700
Subject: Re: Lake Washington's New OBE Standards-Based Report Card
Send reply to: arthurhu@halcyon.com
Copies to: wa-math-sci@mickey.esd113.wednet.edu,
wa-legislation@inspire.ospi.wednet.edu,
wa-esslrngs@whitecap.psesd.wednet.edu
Priority: normal
Texas TAAS is generally grade level appropriate. The problem with
TAAS, and I'm beginnig to agree is that standards easy enough for
ALL kids to pass are really pretty low when the top 20% CAN pass
these goofball high school level 4th grade tests even when the
school has taught them zilch about how to solve them
and 80-90% of
white kids are breezing past the TAAS while their SAT scores of
their top kids are slipping.
That's why we have to get back to norm-referenced tests, and
forget about what
you can expect all kids to do because you can't eliminate the
bell curve simply by chanting "all students will succeed" "all
students will suceed"..... A standard that fits all students is
useless for any purpose. With norm reference, you just make
the questions as easy or as hard as it takes to discriminate
between the worst and best students, and the pass point
all depends on what you want to do with your life ,because
good enough for McDonalds is not good enough for Microsoft
or MIT. That's how good is "good enough". Marc Tucker wants
you to think that one committee can set one standard for
everyone, and if you believe that one, you'll buy anything.
A version of the problem that would work for 4th graders would be
There are 4 bicycles and 3 tricycles. How many wheels are
there total?
Solution would require knowing how to compute the number
of wheels for each set, constructing (4*2) + (3*3) and
computing the answer in whole numbers. That's about the
extent of 4th grade level arithmetic. 5th grade gets into
decimals and multi-digit multiply an divide.
Most textbooks don't even
tell you how to use price per length to price out a materials
list priced by a length or area quantify at this grade level, which
is on the bird feeder problem.
In general, the NTCM math philosiphy is to take something
that looks very easy and change it into something about 10
times more difficult for real kids.
re - solve for number of bicycles in algebra problem
2>>
wa-math-sci@esd113.wednet.edu/CC
shadron@gte.net
Re: Lake Washington's New OBE Standards-Based Report Card (fwd)
the bicycle tricycle problem was a handout from the csl i got
from assessment night at ag bell kirkland elem school, it is
not on the web site
the 4th grade teacher who made the presentation had no problems
she said she was not in a position to sipute grade level, she juat
tried to work with whatever the system gave her. in fact the 2nd
grade teacher was confident rhat her kids coiuld do it by drawing
pictures
-the "standard setting " commitee only sets the cut score. Lyn
stuter was able to get the numbers on her site, they will be the
same every year. If you believe gordon ensign, the test difficulty
is designed by some "equating" method to be juat as hard each
year, but there is considerable evidence for both the wasl and
similar tests in califirnia and kentucky and ma that they
demonstrate progress by simply making the test easier and having
teachers spend all year gearing up kids to write bs that will
pass the rubrics
What is really nuts is that the "standard" was not set until
AFTER the 1st test (which was a "pilot" test) was constructed and
given. The committee never had a chance to even consider whether
not not the questions were even grade level appropriate (by my
analysis, at least 40% of problems require skills at grades 7,
10, or higher to complete, at least from my inventory of skills as
a grad of MIT with a masters in electrical engineering and
computer science). So it was up to whoever constructed the test
to set the grade level, and no one at the CSL has the foggiest
idea of who proposed that problems like the pizza (area =
height x width) flagpole (proportionality, indirect measurement)
or bicycle (construct and solve algebra problem) be put at the
4th grade. The idea is to "blame" it on consensus committees so
that they are not accountable, if "the people" said it's OK, then
it must be good.
So if it's a pilot test that we don't know if it was any good,
why is the "standard" based on a test that hasn't even been
proven to be valid? There's your whole problem.
on the infamous "bird feeder" question where you have to cost
a bird feeder based on a top and 3d dimensioned drawing based
on cost per length, the "4" point correct solution does not
even mention conversion from 60 inches to 5 feet. The EALRs and
test draft specifications don't mention unit conversions until
7th grade. The rubrics also specifically states that a full
4 points will be given even if all the math is wrong. A survey
of 5 different textbooks and every math benchmark I've seen
has no sign of this sort of problem, it's probably something
most middle school student could be expected to do.
On 1998-10-21 wa-math-sci@esd113.wednet.edu said:
>This is in response to James H. Klarich. I was very curious to see
>the "bicycle question." However, when I went to click on the site,
>it gave me an error message or saying it did not exist. Is anyone
>else having the same problem?
>[Moderator's note--In reformatting Mr. Klarich's post, I had to
>"split" the URL into two lines. What that means is that there is
>an invisible paragraph mark that a browser won't interpret properly.
>His URL is correct, but if you are trying to access the site from
>your browser e-mail, it probably won't work. Try copy and pasting
>it instead.--KS]
>James H. Klarich wrote:
>> I had promised myself to stay out of these discussions, I think
>>big brother is watching.....At any rate I can not remain silent,
>>I will probably regret this.
>> I know that this bicycle question is ridiculous! It is not
>>something I would expect my daughter to be able to do at age nine.
>>My daughter did take the fourth grade test last spring and she
>passed all four areas. >
>> Take some time to think about this:
>> One must remember that passing the test has no meaning with
>>regards to mastering the material in the essential learnings.
>>The only standard the students are being compared to is one which
>>was set by groups of adults thinking about what the "average"
>>fourth grader should be able to do. This could mean anything.
>Please take some time to visit: >
>> http://csl.wednet.edu/Web%20page/3%20Assessment%20System/
>> subdocuments/Technical%20Manual/E-SettingProc.html
>> This document presents the procedures followed in setting the
>>standards for the test. Please make comments regarding the
>>standard we (the State of Washington) have set.
>> James H. Klarich
>> Toppenish High School
From: Cmr1234@aol.com
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Date: Fri, 23 Oct 1998 23:24:44 EDT
To: arthurhu@halcyon.com
Cc: fredb001@spectra.net
Mime-Version: 1.0
Subject: Re: Defence of 9th grade algebra problem for 4th graders
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Arthur & Kurt: The table of possibilities is an interesting, but time-
consuming exercise for fourth graders who need to be learning other skills.
In my days of running a learning center which served, among others, secondary
remedial math students, the topic on which we spent the most time was
fractions. We also needed to teach the short and long division algorithms and
sharpen fluencies with the multiplication tables.
Of course we then had to go through decimals, percentage, ratio, scientific
notation, etc., to support their handling of Algebra.
My other reason for opposing the wasting of time on cute ways to find
solutions to problems that should be solved by Algebra is that the real
workplace would never condone such nonsense. It's only educrats who have
tenure that can get away with calling such drivel a "real-world" problem!
The real problem is their world is not real; it's grossly manipulated,
shielded from competition to do things the most cost-effective ways.
Charlie
.fredb001@spectra.net/CC
71524.2205@compuserve.com,
AHANDFHAND@aol.com
Re: math problem- need help
On 1998-10-27 fredb001@spectra.net said:
>Please send this to the math people in our group. I need help ASAP.
>Here is the problem:
>There were a number of bats in a cave. Two bats could see out of
>the right eye, three could see out of the left eye, four could not
>see out of the left eye, and five could not see out of the right
>eye. What is the least number of bats in the cave and what might
>their eyesight have been?
>How do you solve this problem We get problems like this from
>school all the time.
>Francine
pls forward to loop
do they include posting a request for help onthe
internet as a valid strategy or is this cheating??? Its
group solving, right?
maybe we need to keep a repository of stupid unreal life
nctm performance based not-math problems
in actual math, you simply take a formula and apply it,
you do not have to figure anything out assuming you have
been taught what it takes to solve the problem Otherwise
it is a test of iq and whatever the kid learned outside
of school.
you need to ask if your child was first taught how to solve
a similar problem before being asked to demonstrate they
know how to solve another one. If they did not, tell
your teacher to not assign any problems unless
they have been taught how to solve them. Your child
should not be graded onwhat they have not been taught.
Problem solving is just a blanket for testing kids on
skills that have not been directly been taught, thus
we find g7, g10, and college level problems at g4 and g5
tests and im the only guy onthe planet that has enough
sense to figure this out. The new tests deliberately
test for content known to not be taught at grade level
to insure "progress" as they force schools to attempt yo
teach to the test.
this bat problem doe no resemble any math problem that you
would have to solve in any actual job and
does not exercise any skill on any grade level textbook,
its the sort of thing you might find on an iq test
anyways
3+L 5-R dif = 2 blind bats
2+R 4-L dif = 2 blind bats (thank god this is consistent)
2R+ right eye
3L+ left eye
Arthur Hu "Fairness in Diversity" Kirkland WA
http://www.leconsulting.com/arthurhu/
Net-Tamer V 1.11P - Registered
+OK 1305 octets
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Date: Mon, 26 Oct 1998 18:40:01 -1000
From: Sandra and John Shadron
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Arthur,
Thank you for clarifying the bicycle problem. I think I know what kind
of problem it is.
Problems are really hard these days. I can't believe they give them to
kids. I have kids (8th grade) who don't even know their multiplication
facts. What happen to those standards?
I agree with you about tests being a "standard" with out having any
validity to them.
S. Shadron
.
most states have their curriculum standards on their web site
somewhere, is yours only available on paper or is it
on the web site? Most standards I found put the normal
curve as college track or advanced placement statistics
course, or college level statistics.
-----Original Message-----
From: Skoglund, Barbara [SMTP:Barbara.Skoglund@state.mn.us]
Sent: Wednesday, October 28, 1998 11:42 AM
To: 'Arthur T. Hu'
Cc: Wagner, Cathy
Subject: RE: Where are curriculum standards
I have forwarded your note to our statewide testing coordinator.
Barbara Skoglund, Communications Coordinator
Minnesota Department of Children, Families & Learning
barbara.skoglund@state.mn.us
651.282.5438
> -----Original Message-----
> From: Arthur T. Hu [SMTP:arthurhu@raima.com]
> Sent: Tuesday, October 27, 1998 8:19 PM
> To: 'barbara.skoglund@state.mn.us'
> Subject: Where are curriculum standards
>
> Hi, I spotted a gaussian distribution problem in your 5th
> grade test. Where are your curriculum benchmarks / standards that
> state that a 5th grader needs to know about the bell curve?
>
Subject:
Re: HS Algebra on 4th Grade WASL Math:??? Do we WANT this for our kids?
Date:
Fri, 16 Oct 1998 18:50:52 -0700
From:
"L. Anderson"
Organization:
WA State Spummeler
Newsgroups:
seattle.politics, wash.politics, ba.politics
References:
1
Arthur Hu wrote:
>
> math01.gif
> http://www.leconsulting.com/arthurhu/images/98/10/15/Page0001.html
>
> At A.G. Bell Lake Washington, they had their 2nd annual "meet the
> test"night,
> and this was their latest alleged 4th grade problem that they showed
> off.
>
> This is a 4th grade problem??? Even if a few kids _can_ figure this out
> by some
> contorted guess and check method, we should not waste time teaching
> kids, let
> alone assess for "skills" like this that are of ZERO value in "real
> world" problems.
>
> When IS the last time you had to figure how many
> of bicycles and tricycles wer parked based on the total number of wheels
>
> and difference in total number? It's pretty obvious that if you know
> the
> difference is 4, she must have !@#$% counted them in first place!
>
> Fact is, almost none of these "real life" problems have any application
> in real life compared to straightforward math problems with one step and
>
> one answer.
>
Perhaps you are missing the point of the problem. If the problem is to
come up with the one "preconceived answer" that's one thing. If it's to
teach the student "critical thinking" or "creative problem solving",
that's another. Unfortunately, it appears today's educational system is
doing little of these. In any case, your solution, below, shows me you
are thinking in "the box" and are expecting the one "preconceived
answer". Well, I'm here to tell you that your answer may just be
different but definitely, not unique! See below.
> You have 4 more bikes than
> tricycles, but 33 wheels total. How many bikes do you have? The only
> reasonable way to solve this is middle or high school algebra.
I disagree. Algebra is definitely worthwhile, but it isn't the only
legitimate way to solve this problem. A reductionist approach is not
usually the best way to approach a problem. Although it should be one
approach, just not the only approach. It has a tendency to put you in
"the box" and keep you there.
> They
> sent this home to kids and claimed that some of them had some
> pretty remarkable solutions.
I'll bet they did. I would love to see them. Essentially, children are
born intelligent, they have to be taught to be stupid. Unfortunately,
our society and educational systems does an excellent job of this!
Had the problem been part of a proper problem solving setting, what they
did would be a good thing. However, I'm afraid it's in a "touchy-feely,
self esteem, BS" setting so it's the worst of all worlds. As the
surgery patient lies dying, the surgeon thinks, "Hey, at least I feel
good about how well I made the cut, even if it was the wrong place to
cut. While I missed the appendix, god!, what a clean cut I made on the
brain stem. Now, where is that thing called the appendix, anyway?"
> It's clear that they did _not_ teach kids how to solve this problem,
> it's the old standards based "let's see if the kids can figure it
> out, and if anybody actually gets it right on their own, we'll use
> that student sample to 'set the standard'. That's the whole fraud of
> this whole standards based thing because some kids will come to school
> knowing this stuff from home without ever being taught at school
> things like "proportion". If anybody can get it, we can assume that
> _all_ should be expected to get it, or they don't pass their grade
> level??????
Perhaps they didn't teach the students how to solve the problem as you
perceive it should be solved. However, that doesn't mean that letting
the students try to "figure it out" is not legitimate. It borders on a
"meta problem solving" approach but I do take issue with them trying to
standardize that. It's one thing to standardize, teach, and test on a
problem solving tool like "algebra". It's another thing to standardize,
teach, and test on a problem solving approach like "lateral thinking".
Emphasis in the former being placed on using algebra to come up with the
one right "preconceived answer" while emphasis on the latter to
enumerate a number of solution approaches, how they lead to answers, and
what the answers are.
Unfortunately, I think the current educational system uses a mishmash of
both without understanding either. In the past, they at least handled
the algebraic approach reasonably well, but now, who knows?
>
> A 2nd grade teacher claims she showed her kids how to solve it too by
> drawing pictures. If this is supposed to be from real life, somebody
> deserves to be shot if we expect kids to solve real life problems
> this way with guess and check or worse. Anybody that tries to solve
> problems like this in real life deserves to be fired.
Again you may be missing the point. I draw pictures all the time to
help me solve problems. It's just another tool in my problem solving
tool box. So, should I be shot for drawing pictures? I hope not.
As an exercise, see if you can come up with the Pythagorean Theorem (a^2
= b^2 + c^2) just using drawings and a little arithmetic (mult, add). It
can be done, you know, and may have been the original insight into that
property of right triangles. If so, should Pythagoras have been shot?
Again, I think not.
Also, there is the solution using the sons of squaws and hippopotamus
hides. But that's another story :-) .
>
> Solution:
You mean one solution of many, not "the" solution.
>
> High School Algebra (the only practical way to solve this)
> x= bicycles
> x-4 = tricycles
> 33 = wheels
> x*2 + (x-4) *3 = 33
> 2x + 3x - 12 = 33
> 5x - 12 = 33
> 5x = (33 + 12) = 45
> x = 45/5 = 9 bicycles
> 9-4 = 5 tricycles
>
Very good Mr. Hu, that was an excellent solution. Class, can anyone
tell me what "approach" Mr. Hu used? Yes Cynthia, "algebraic", very
good. Now class, does anyone have another approach to solving this
problem? Yes Ralph? Guess and check? Proceed, Ralph.
> Guess and check (not anything I'd ask any kid to do)
(I certainly would, especially if problem solving was taught in a better
way to enhance the possible "solution set".)
>
> Make a table with these columns.
> Pick the one with the desired difference
> Tri= Number of Tricycles
> TriWheels = Number of Tricycle Wheels
> BWheels = Number of wheels left for Bicycles
> Bicycles = Number of Bicycles
> Diff = Difference between B - T
> Tri TriWheels BWheels Bicycles Diff
> 1 3 30 15 14
> 2 6 27
> 3 9 24 12 9
> 4 12 21
> 5 15 18 9 4****
> 6 18 15
> 7 21 12 6 1
>
> Match is 9 bicycles, 4 tricycles
>
Very good Ralph, but you really meant 5 trics and not 4. Can you tell us
why you said 4 instead of 5? Yes that's correct Ralph, you probably had
a "brain fart" and picked the difference and not the number of
trics--but you're making progress.
Now class, can anyone think of how this approach would be useful over a
purely "algebraic" approach. Yes, Lowanda? Ok, you want to write a
spreadsheet app on your pc so you can parameterize a time series
analysis of path use and the scanner can only count tire hits and give
you the difference between bike and tric and .... Very nice. (Perhaps
the problem is contrived, but that's not the point here.)
Ok class, now what would you do if the difference was 6 and wheels 40 or
the difference 12 and wheels 2? Hmmmmm? That's your next home work
assignment.
> It's one thing to waste a weekend getting kids to figure out
> something that's completely useless as a math skill, it's quite
> another to expect ALL kids to be able to pass this on a minimum
> proficiency test, especially when there are NO 4th grade math
> textbooks that show how to solve this problem, and solving for
> unknowns isn't until the 7th grade benchmark anyways.
If better problem solving techniques were taught, it wouldn't be a waste
and math skills would be only one of the tools available to the student.
Also, maybe the problem being solved is better served with an
"intuitive" approach rather than "algebraic". I have seen a lot of
folks with "book larnen" that couldn't "intuit" there way out of a paper
bag--I fondly refer to them as "learned fools". But that's another
story too.
I am in no way defending our current educational system--it's abysmal.
Teaching children to achieve their utmost potential is very, very
complex. We are not all created intellectually equal and
"standardization" can only deal with the "intellectual intersection" and
even that is a spectrum, e.g., in reading. Beyond that, it's "case by
case"--which is a hard problem.
I think the biggest problem with our educational system is that it's
structured to address only a subset of the "intersection" and not the
"utmost potential". Further, we're hypocrites--screaming for diversity
(read that skin color) but burning at the stake anyone who suggests we
support "intellectual diversity". But that's another topic.
Ok class, can anyone think of any other solution? Yes LA?
Mum, uhh, well the way I see it, you can't assume that the area where
the bikes and trics are only used by kids who can either only ride trics
or only ride bikes. Real life dictates a continuum which means training
wheels will be involved. Therefore, one member of the solution set
actually gives several separate solutions. Hence,
The following assumes all bikes and trics have a full complement of the
requisite number of wheels, so let:
x = # bikes with training wheels
y = # bikes without training wheels
z = # trics
(x+y)-4=z
4x + 2y + 3z = 33
4x + 2y + 3((x+y)-4) = 33
4x + 2y +3x +3y -12 = 33
7x + 5y = 45
So,
x = 5, y = 2, z = 3 Heavy transition from trics to bikes going on here
x = 0, y = 9, z = 5 A few days later when the kids get better
(So you see, the answer is not 9 bikes and 4[sic] trics :-), life's a
complex bitch, huh!)
Yes but what if some of the bikes had their wheels stolen?
But, but, but, ... you can't do this! It's, it's, well, it's n na na
nanon NON-STANDARD!
And so it goes!
Regards,
L Anderson -- munge mark '666'
>
> These are the algebra benchmarks:
> http://cisl.ospi.wednet.edu/ComSL/MATHBMK.html
>
> G4: solve simple equations using blocks, sticks, beans, pictures, etc.
>
> G7: set up and solve single-variable equations
>
> G10: create and solve equations and inequalities
>
> G4: use standard notation in reading and writing open sentences, for
> example, 3 x __ = 18
>
> G7: understand and use variables in simple equations, inequalities, and
> formulas, for example 3x > 18
>
> G10: ***represent situations that involve variable quantities*** with
> expressions, formulas and equations, and inequalities
>
> This is a G10 problem by the state benchmarks.
>
> There is no other standard for solving this sort of problem.
Subject:
Re: HS Algebra on 4th Grade WASL Math:??? Do we WANT this for our kids?
Date:
Sat, 17 Oct 1998 07:56:29 GMT
From:
postmaster@127.0.0.1 (Warrl kyree Tale'sedrin)
Reply-To:
warrl@blarg.net
Organization:
None -- just look at my desk!
Newsgroups:
seattle.politics, wash.politics, ba.politics
References:
1 , 2
I want to comment on this question:
An essential characteristic of an achievement test is that it must
cover a broad range of abilities. It should have a few questions that
almost every target person will get right, and a few questions that
almost no target person will get right, and a fairly even spread in
between.
I mean, suppose that your 4th-grade kid takes a 4th-grade achievement
test and gets every question correct, when the average 6th grader
taking that same test gets every question correct. Is your kid
slightly above average, or far above average, or ???
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Subject:
Re: Lake Washington's New Proposed OBE standards-based report card
Date:
Sat, 17 Oct 1998 08:33:06 GMT
From:
liberty@wolfenet.com (Mike Hihn)
Organization:
Wolfe Internet Access, L.L.C
Newsgroups:
seattle.politics, wash.politics
References:
1 , 2
On Fri, 16 Oct 1998 16:34:24 -0700, Travis Pahl
wrote:
>My expereience with OBE....
>
>
>Being young (which appperantly means I know nothing according to some in
>this NG, also means I am young enough to have expereinced first hand some
>of these new teaching methods such as OBE. I do not know what they are
>trying to do with it now, but I remember in 7th grade (about 8 or 9 years
>ago) I had a couple classes that were supposedly based on OBE. They never
>told us what exactly this outcome based education was, but what it meant
>to us was we would never fail. We were told that if we did not get 80% or
>better on an assignment, then we just had to do it again and again until
>we completed to a sastisfactory grade of 80%. This had two problems.
>
>1. The person who got 80% the FIRST time was not recognized as doing any
>better than the person that it took three times to get right.
That's the public school version of OBE, and indeed dumb.
But did those students also move on to the next level or whatever?
Or did they remain in locksetp with everyone else?
>2. The second problem and the problem that irritated me most, was that
>you could not pass if you did not get every assignment in at 80%.
Correction: the SCHOOL (or teacher) did not pass.
>To make a long story short... Even as a 7th grader, it was painfully
>obvious this OBE stuff is a joke and does not help teach (which you should
>all remember is the primary goal of education).
OBE has nothting whatever to do with teaching.
It's a discipline for designing curriculum, to acheive measurable
outcomes, and then assessing those outcomes to see if
teaching/learning even happened.
Needless to say, the public education bureaucracy ain't gonna
allow anything that says they have to actually reach something to get
a paycheck.
>This is fine that it is making a comeback. Maybe some people really
>truely beleive it will help. But they should do it with their own money
>not taxpayer money. However I beleive by abolishing public schools it
>would also get rid of these silly standards and things like OBE, because
>once parents have a choice, they will choose schools that focus on
>t4aching.
You've been bamboozled, Travis. OBE came out of the private sector,
and is still the norm in corporate and (later) military training.
I introduced it to a large corporate division in 1968 ($200 million in
$1968). As I recall, we got a 30% increase in measured learning,
from 50% lower costs, which contributed to a near doubling of
productivity and a small decline in turnover.
Teachers fought it for three decades, then figured out how to get the
wacko right to oppose it for them.
Mike Hihn, Executive Director
Libertarian Party of Washington State
"The party of principled solutions" -- http://lpws.org
3>>
Subject:
Re: HS Algebra on 4th Grade WASL Math:??? Do we WANT this for our kids?
Date:
Wed, 28 Oct 1998 21:57:12 GMT
From:
envirolaw@accessone.com (Kluck Roger)
Organization:
http://www.supernews.com, The World's Usenet: Discussions Start Here
Newsgroups:
seattle.politics, wash.politics
References:
1 , 2 , 3
On Wed, 28 Oct 1998 12:56:40 -0800, Arthur Hu
wrote:
>geez....
>
>The WASL is supposed to assess skills that ALL students are expected to know.
>Under outcome based education, there are NO more or less skilled students, all
>will be expected to achieve at the same idea. If you think that's a crazy
>idea, that's what the whole state reform program is based on. Performance
>based education _IS_ outcome based education, it said so in 1993 documents.
Arthur, I'm sorry but you really do not understand this. I understand
you are frustrated. But the examples you have given in the past are
readily done by many if not most 4th graders.
Outcome based education is a response to the complaints that
unqualified students were being passed on without proper understanding
of the basics. It requires that a student pass a test to move on.
Thus having a minimum score pass rate is the result. If you get less
than that score you stay behind till you learn the material needed to
pass. That in no way means all kids learn or are taught to the same
level. It means only that you have to pass the minimum score to go
on.
>Why can't you simply admit that this is an idiotic problem for 4th graders?
Because its not. Trial and error is a valid method for solving
problems and readily understood by fourth graders. I'll grant you its
not as efficient as algebra for this problem, but most fourth graders
should be able to quickly try a few mixes and see if they can get a
workable answer.
I help my kids with their homework, and I know if can be hard to keep
it at their level when you see a more efficient way to solve the
problem, such as algebra. But backing up and keeping it simple is
what is needed. The kids are learning basic skills. Approximation is
for example an important skill. If a kid does several trial "guesses"
to work it out, he's learning how to zero in on the correct solution,
and getting better at approximating.
And there is a real value to solving seemingly complex problems like
this with simple tools (in this case simple addition and repetition).
It gives kids the sense of the power of what they can accomplish with
these tools and encourages them to be creative in seeking solutions. I
think teaching and promoting this kind of creative thinking is in many
ways more important than learning the "wrote" way to solve a problem.
That creativity is what will serve them better in the future (provided
of course they know how to do the wrote method too when needed).
Anyway, maybe your time would be better spent on talking with your
son's teacher about helping you to help your son work on these
problems. I think your son would be better served by that than your
fight with the teacher, the school, and the district.
>Travis Pahl wrote:
>
>> You always have to have more advanced problems and less advanced problems
>> to serperate the higher skilled and lower skilled students. besides using
>> logic and organizing your thoughs and drawing pictures can solve this
>> problem quite easily and that is all part of math in elementry school.
>>
Roger Kluck, Attorney at Law. Seattle, WA (206)405-4373
Practicing law for 12 years; specializing in environmental law, but also handling general legal matters.
Free initial consultations. Reasonable and flexible rates
E-MAIL: envirolaw@accessone.com URL: http://www.accessone.com/~envirolaw
Subject:
Re: HS Algebra on 4th Grade WASL Math:??? Do we WANT this for our kids?
Date:
Thu, 29 Oct 1998 20:10:20 GMT
From:
envirolaw@accessone.com (Kluck Roger)
Organization:
http://www.supernews.com, The World's Usenet: Discussions Start Here
Newsgroups:
seattle.politics, wash.politics
References:
1 , 2 , 3 , 4
On Wed, 28 Oct 1998 17:15:12 -0800, Arthur Hu
wrote:
>The premise of standards and outcome based education is that all students
>can be
>taught to the standard of the best countries of the world, and when we do
>this, we
>will finally have slain the dragon of that evil bell curve. And if you
>believe that, boy do I have some social programs to sell you.
This is nonsense Arthur. The premise is that there has to be a
minimum standard of what is learned to move on to the next grade. If
you don't know or understand the minimal material needed to pass, you
stay put till you do. The trailing edge of the bell curve should not
be passed on to get further behind and hold back the rest of the class
in the next grade. Coupled with some good remedial education this
should be a big improvement for all the students.
Roger Kluck, Attorney at Law. Seattle, WA (206)405-4373
Practicing law for 12 years; specializing in environmental law, but also handling general legal matters.
Free initial consultations. Reasonable and flexible rates
E-MAIL: envirolaw@accessone.com URL: http://www.accessone.com/~envirolaw
No, the reform assumptions are nonsense. Marc Tucker, the original author of standards
based education has stated that he believes that all can pass the highest, not minimum
standards. ALL are expected to solve the algebra problem without ever being taught how
to solve the problem. How else can you explain a test that clearly tests content which is
known not to be covered in any present textbook or curriculum? Traditional tests are
limited to skills and methods known to be common to all (or used to be common before
all the schools adopted these crazy no-content curriculums)
Tucker stated that such a system will guaranteee that all students will be as good as the
average German or Japanese, but those are national averages - not even Germany has
ALL students at their average levels. He also says it will eliminate tracking, advanced, and
remedial courses. This taking marxism to an extreme so illogical not even Marxist nations
like China or Russia ever attempted such a nutty scheme.
Many experts like George Cunningham of Kentucky have stated that you cannot set a
"standard" independent of what actual students can do. The "standard" was in fact set by
a committee that was not told which problems were or were not grade level appropriate,
and they were not told the pass rates. Many other sample problems are even more
clearly and obviously taken from 7th and 10th grade benchmarks - area = height x width,
ratio, proportionality, frequency tables and histograms. Again, it stuns me when people
refuse to recognize a problem when it is this freaking obvious;.
The state reform version of outcome based education will destroy, not improve education,
most of the failures of the 90s is due to bungled reform movements, not traditional
educations, such as a generation of illiterate California high school students that whole
language was inflicted on.
Kluck Roger wrote:
On Wed, 28 Oct 1998 17:15:12 -0800, Arthur Hu
wrote:
>The premise of standards and outcome based education is that all students
>can be
>taught to the standard of the best countries of the world, and when we do
>this, we
>will finally have slain the dragon of that evil bell curve. And if you
>believe that, boy do I have some social programs to sell you.
This is nonsense Arthur. The premise is that there has to be a
minimum standard of what is learned to move on to the next grade. If
you don't know or understand the minimal material needed to pass, you
stay put till you do. The trailing edge of the bell curve should not
be passed on to get further behind and hold back the rest of the class
in the next grade. Coupled with some good remedial education this
should be a big improvement for all the students.
Roger Kluck, Attorney at Law. Seattle, WA (206)405-4373
Practicing law for 12 years; specializing in environmental law, but also handling general
legal matters.
Free initial consultations. Reasonable and flexible rates
E-MAIL: envirolaw@accessone.com URL: http://www.accessone.com/~envirolaw