3/11/99
http://www.leconsulting.com/arthurhu/99/05/math.txt
Houghton mifflin math central Grade 5
Scott forsman /addison wesley Grade 4
McDougall Little Integrated Math 1,2,3
Arthur Hu's Notes on new math textbooks on display at Lake Washington
Scott Forseman is on display at the Lake Washington district resource
center, there will be a meeting April 1 from 1 to 3 for interested
parents (yeah, right, nice work hour timing)
I took a quick 15 min peek. In general, books don't seem too
contructivist, they still have traditional content and methods,
though some seem a bit odd. For example, to multiply 1.3 by 3,
instead of just moving the decimal in the answer over by 1, you
"estimate" the result as between 1*3=3 and 2*3=6, therefore you get
3.9. That might lend itself to better understanding, but it's much
less efficient to require the student to do two more multiplies just
to figure out where the decimal goes.
I also saw strategies in Scott Forseman on how to "compute" addition
facts such as "doubles". Still, while it might help for kids who
don't memorize facts, memorization is still the most efficient way to
compute without a calculator.
Interestingly, where I found massive content simply missing from pre
1980 textbooks relative to the WASL examples, they also cover much of
the material found on the WASL math tests that are not explicity
mentioned in the benchmarks as 4th grade content. Unfortunately, they
still don't cover anywhere near what's covered in the WASL sample
tests. For example adding 1 burger + 2 fries is traditionally middle
school, but the WASL also asks you to add 60 inches of lumber at $5
per foot, which is a level of complexity I have yet to see even in a
middle school text. No ratio or proportion or rate or sorting a large
number of items.
Still the main concern is why they have added so much content.
Traditionally half of students didn't master basic math well enough
to continue on to algebra, so the the response is to teach even more
stuff? The Japanese standards are in line with old traditional US
standards in content.
I looked over the content summary for the McDougal Little high school
integrated math series,(so far I've heard it's already used in Lake
Washington and Issaquah) my jaw dropped. In a traditional sequence
you do nothing but algebra for a year, nothing but trig the next year
etc. In the integrated sequence, algebra is maybe 15% of content at
best, the rest is probability, statistics, graphics, problem solving
and god knows what stuff that I can only remember maybe 10% of.
It even requires students to use calculators to solve quadratic and
cubic equations graphically, use matrix inversion functions on
calculators to solve systems and do linear regression. These are
$100 Ti-8X calculators, not the old HP-35 or TI-30 trig and log
calculators we had in high school, and the schools have to buy a
calculator for every student. A teacher agreed with me that an
average student who traditionally had only a 50% chance of even
taking algebra now has to master not only algebra but perhaps 3 times
as much additional content isn't going to retain much. The integrated
sequence might actually be good for whiz kids who can absorb algebra
in 1 day, but I really wonder about it being used as the single math
track for all kids.
It's like the "higher standards" philosiphy has somehow proven that
the reason poor kids don't master multiplication and division is
because the rich kids get taught algebra and calculus. Yeah, right.
Heck, not even Bill Gates had to learn all this stuff in high school,
or K-6.
I have to wonder how, if not all kids could master the content of 20
years ago, how are modern kids going to be expected to master another
40% worth of material, much of it which was traditionally only seen a
college level math courses, being brought down not only to high
school, but early elementary (like frequency histograms and leaf /
stem plots, and if you don't know what they are, that's my point).
The public is being sold on standards that make sure everybody is
basically literate, but this is stuff that not even the top 1% of
kids would be expected to know, but the top 10% of adults might have
run into somewhere in k-career education.
I've never even seen stem and leaf plots before, and we were not
taught how to use guess and check tables in 4th grade when we were
taught in Algebra how to solve directly for such solutions.
Houghton mifflin math central
has a performance assessments book
- show how you calculated your answers
- shows "limited", good, and better answer "samples" in
standards based fashion.
level 5 (fifth grade)
dragonfly flies 24 miles in one hour
snail travels 24 inches in 3 min
how far can dragonfly travel in one minute? snail?
hint: 1 mi 5280 ft 1 ft 12 in
limited response 1 tortoise is faster
2 tortoise 8 in snail 40 in fly 126720 ft
(requires heavy unit conversion, WA test
specifications defer unit conversion to grade
7)
Where would each creature need to start to finish
at same time make a diagram and explain
Level 5 contents:
algebra style solve ax+bx=c (trad g9 algebra)
mixed add and multiply quantity cost list (trad middle school)
order of operations
greatest common factor
prime composite
mean range mode
line graphs
circle graphs
no frequency histogram
no lowest dist
problem solving work backward
reduce price by 25 then by half, now 23.50, what is
original price
elapsed time
4:05-3:55 regroup 3:64-3:55=9min
time zones
aug 22-july 10 - count on calendar
temperature
decimal mult
1.3*3
estimate answer between 1*3=3 and 2*3=6,
multiply as integer, but put decimal 39 as 3.9 based on estimate
(that's odd, why not just introduce rule of adding up decimal places?)
----------------------------------------------------------------
scott forsman /addison wesley
4th grade text book
Has added
- guess and check table
- line plot (frequency histogram)
- fraction of a set
- add up list of cost of parts
- elapsed time
- probability as fraction
- fraction of a set
Still lacking these WASL tasks
- sorting (scales)
- indirect measure by shadow
- find distribution with most items below a value
- cost of parts list with price by area / length
- work backwards from answer
- ratio (lemonade packet per cup)
- rate (cards per inch)
- use factoring to find lowest common denominator
- independent probability
- compare probability expressed as fractions
- elapsed time with regrouping minutes
line plot=frequency histogram
stem leaf plot
---------
2 0
3 3
4
5 0 0 8 50,50,8
6 5 2 0 65,62,0
7
8 2
uses place value to organize data
guess and check tables
(WASL requires this for bicycle tricycle problem)
time to minute
elapsed time 11:15 to 4:44
count hours, min write - no regrouping
(WASL requires elapsed time requiring regrouping minutes)
add sub money
add cost list 1 each item
(WASL requires adding up single, multiple, and quantity per
foot or inch total)
6,7,8 as factors
probability
likely
fair
outcomes list
predictions
(WASL requires independent probability)
probability as fraction
bonnie got 25/50 total votes = 1/2 prob
(WASL also requires comparing uncommon fractions
in marble example)
use fraction calculator simplify fractions
compare fractions with fraction strips
use equivalent fractions to compare fractions
fractions of a set
find 2/3 of 15
(WASL lawn mowing problem requires fraction of
a an area)
probability as fraction
4th grade guess and check
zoo costs $10 more for adult than child
1 adult + 2 children costs 37, how much is adult
10 students pizza $4 burger $5 total $46
solve how many each
table - pizza, cost, burger, cost, total=46?
-----------------------------------------
1st grade math
scott forseman math
This is very ambitious for 1st grade - it has certain and uncertain
probability, concrete division, elapsed time, cutting sandwiches and
pies into equal fractions, tallies and knowing when there is too much
information to solve a problem
place value to 99
change to 56 cents
evem odd
count by two
time to 30 min
elapsed time 3 to 4:30
adding 2 or 3 by counting
adding 3 numbers
add to 10 with counters 7+7
adding pattern
cups liters
sub facts 12
story adding
elevator 9 add sub
grid path
pizza equal parts
equal 2 4 parts 1/2 1/3 1/4
4 share 8 oranges
cut sandwich inhalf and fourths
certain uncertain events
add 3 numbers
double + 1
too much information
doubles to subtract
inches or feet
homework in packet
read 15 min every day
tally ||||/ ||||/
My comments
Thanks.
I looked over the scott forsman math series. The books I saw in use
at Holy Family looked fine, the grade 5 book looks like it actually
covers about 30% of skills found in the WASL that I complained about,
it tells you sort of how to do elapsed time and has "line charts"
which really are frequency histograms. What does concern me is the
sheer volume of content being moved down from what used to be college
level stat courses. I had never seen a "leaf and stem" plot in my
life before I saw the book. It also concerns me that all this new
content is far from standardized, if you took the sum of all of the
new textbook series, it still wouldn't cover all that's in WASL. The
benchmarks are worthless because they only cover what was in
textbooks 20 years ago for the most part.
Integrated math at the high school is far worse. The response to not
all kids will relate to algebra 1 is a year where algebra constitutes
only 15% of content, and the other 85% looks like it's lifted
straight out of a college level precalculus, statistics and trig
courses. The whole idea that the reason some kids can't master 7 x 6
is that we're not teaching them how to solve quadratic equations just
baffles me.
From: "Wilson, Nancy"
To: "'arthurhu@halcyon.com'"
Subject: RE: Tutoring on 4th grade WASL math?
Date sent: Tue, 9 Mar 1999 17:47:01 -0800
> Dear Mr. Hu,
> I was not able to reach you by phone at work today so I left a message. In
> case you need the information sooner, the meeting for parents on the math
> adoption will be held at the district resource center on Thursday, April 1,
> from 1:00 to 3:00 p.m. I think we should discuss your ideas again after you
> have had a chance to review these materials, which will be on display at the
> district office for a month before the school board makes a final adoption
> decision. Please call if you have questions about this.
> Nancy Wilson
>
> -----Original Message-----
> From: arthur hu [mailto:arthurhu@halcyon.com]
> Sent: Friday, February 12, 1999 10:16 AM
> To: Wilson, Nancy
> Subject: RE: Tutoring on 4th grade WASL math?
>
> You should see this. Here's a math teacher who actually
> teaches
> 5th graders to use algebra, none of this wimpy guess and
> check
> stuff.
>
> My response first.
>
>
> TEACHING ALGEBRA TO 5TH GRADERS
> \doc\web\99\03\alg5.txt
>
> Wait a minute, this is the first time I've seen somebody
> claim that
> it is reasonable for a 4th grader to use algebra, not guess
> and check
> to solve this equation. Considering that half of 9th graders
> don't
> even have their basic arithmetic proficient enough to start
> algebra,
> and that in a normal sequence of 9th grade algebra 1, you
> don't start
> solving equations until you've spent 2/3 of the year going
> over the
> 15 or 16 properties and operations one by one before you can
> apply
> them all (yes, I found where it explains the solution at the
> END of
> algebra one - only geometry problems and polynomials was
> after that),
> what' s the point of basing "higher standards" so that _ALL_
> students
> are expected to master these problems? What's wrong with a
> traditional sequence? I didn't take calculus until I started
> MIT, and
> I turned out just fine.
>
> Why force all students on a track where all are expected to
> master
> solving equations by grade 5 instead of traditional = half
> of
> students learn to master it by grade 9, and perhaps up to
> 65%
> including those who pick it up in college?
>
> The rigorous California math standards go out on a limb by
> saying
> students should be _ready_ for algebra by grade 8. Heck, I'm
> sure we
> can teach some 4th graders what the derivative of x^2 is
> too. Does
> that mean we teach them calculus and linear algebra?
>
> My 7 yr old can hack intermediate piano, two staff , two
> hands and
> accidentals. Do we then set a standard that all students
> should be
> "expected" to know and be able to play piano at such a
> standard?
>
> I don't think so, but that is what new new "higher"
> standards set in
> math and reading.
>
> Expected is no longer a range centered around 50th
> percentile
> performance. Required is now ALL students above something
> above the
> 75th percentile. That is madness.
>
>
> From: "Dave Cole"
> To: "ClearingHouse"
>
> Subject: [education-consumers] Re: Do your
> own thing, or, how to solve a problem the hard way
> Date sent: Fri, 12 Feb 1999 09:16:16 -0600
> Send reply to: "Dave Cole"
>
> >
> =====================================================================
> >
> >
> > I think Ken is underestimating his son.
> >
> > >There are 14 pieces of fruit in a bowl. There are twice
> as many apples as
> > >oranges, and half as many pears as oranges. How many of
> each type of fruit
> > >are in the bowl?
> > >
> > >Oh, and then my son really made me proud. I quickly
> showed him how the
> > >problem was solved using algebra. Not surprisingly, he
> didn't understand
> > >it. But he looked at me with a smile and said, "I guess
> that's why I need
> > >to stay in school, huh?" Can't teach that kind of comon
> sense.
> >
> > Last summer, I taught a 6 week mathematics class to 4th
> and 5th grade
> > students (actually they were just entering these grades so
> they would have
> > been 3rd and 4th grade students). The class met for 2
> hours every Saturday
> > and covered a number of "fun" mathematical subjects,
> including an
> > introduction to algebra concepts, fibonacci numbers,
> mental math skills, and
> > an introduction to the game of Equations. I gave this
> problem to my
> > daughter (a 4th grader now) and she solved the problem in
> about 2 minutes -
> > using Algebra. The problem is, she won't see algebra
> again in our school
> > district for 4 years, so now what does she do.
> >
> > By the way, although my daughter has been identified as
> gifted, this class
> > was not geared toward gifted children, nor were most of
> the 12 students
> > identified as gifted.
> >
> > Dave Cole
> >
> >
> >
> >
> =====================================================================
> >
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> >
> > Subscriptions & Archives: http://education-consumers.com
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> >
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>
>
> From: "Wilson, Nancy"
>
> To: "'arthurhu@halcyon.com'"
>
> Subject: RE: Tutoring on 4th grade WASL math?
> Date sent: Fri, 12 Feb 1999 07:20:54 -0800
>
> > Dear Mr. Hu,
> > I will be on vacation all next week, so I will give you a
> call during the
> > week of Feb. 22 to discuss your ideas. Thanks,
> > Nancy Wilson
> >
> > -----Original Message-----
> > From: arthurhu@halcyon.com
> [mailto:arthurhu@halcyon.com]
> > Sent: Thursday, February 11, 1999 2:53 PM
> > To: Nancy Wilson
> > Subject: Tutoring on 4th grade WASL
> math?
> >
> > Mail*Link¨ SMTP Tutoring on
> 4th grade WASL
> > math?
> >
> > Hi, it just hit me that I might be
> approaching this problem
> > with
> > the assessments the wrong way.
> >
> > SPI Bergeson says her experts have given
> another blessing on
> > the questions, so the chances of getting
> them to change
> > their
> > approach is just about zero.
> >
> > Now that I've figured out the skills that
> are needed to
> > solve these
> > crazy things, why not just give tutoring
> sessions to
> > interested
> > parents and teachers, and walk through all
> of the WASL
> > examples?
> >
> > It might take more than one night, but it
> would give me a
> > chance
> > to see if real kids can grasp the correct
> solutions and give
> > them
> > a better chance than a constructivist "let
> them be creative
> > and
> > figure out something" if they simply get a
> peek at
> > probability,
> > charts, proportionality, ratio and equation
> solving with
> > guess and
> > check if that's what the new math books are
> testing for.
> >
> > Very smart kids _can_ get this, a Kirkland
> crowd just might
> > be
> > smart enough to handle the normally middle
> school content
> > that's
> > hidden in this thing if they are given
> advanced instruction.
> >
> > I've also been informed that some 5th grade
> textbooks also
> > expect
> > students to use guess and check to solve the
> bicycle problem
> >
> > that we used to have to wait until 9th grade
> algebra to
> > solve.
> >
> > I've also seen samples from other state
> tests that are
> > likely to
> > appear on the WA tests. Whether or not these
> are too
> > difficult for
> > 4th graders, even after coaching, will
> become evident.
> >
> > MIght be interesting if we end up with AG
> Bell acing this
> > test
> > because you've got the one parent who knows
> the math
> > forwards
> > and backwards.
> >
> > phone day 206-748-5347
> >
> > arthur hu kirkland WA arthurhu@halcyon.com
> > "fairness in diversity"
> > http://www.leconsulting.com/arthurhu
> >
> > ------------------ RFC822 Header Follows
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> ADMIN;11 Feb
> > 1999 15:51:59 -0800
> > Received: from arthurhu (dhcp32.raima.com
> [198.206.247.141])
> > by
> > exchange.raima.com with SMTP (Microsoft
> Exchange Internet
> > Mail Service Version
> > 5.5.1960.3)
> > id 1P8YGF1J; Thu, 11 Feb 1999
> 15:34:21 -0800
> > From: "arthur hu"
> > To: nancy_wilson@qmserver.lkwash.wednet.edu
> > Date: Thu, 11 Feb 1999 15:35:16 -0800
> > MIME-Version: 1.0
> > Content-type: text/plain; charset=US-ASCII
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> > Subject: Tutoring on 4th grade WASL math?
> > Reply-to: arthurhu@halcyon.com
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> >
> >
>
>
> arthur hu kirkland WA arthurhu@halcyon.com
> "fairness in diversity"
> http://www.leconsulting.com/arthurhu
What I saw I could recognize as math, and I have the same concerns about
throwing in too much content at the expense of basics. I think they had the wierd "estimate" strategy for multplying .1 digit by no decimal. The 5th grade snail and dragonfly problem uses very heavy duty unit conversion.
I did not spend a a lot of time with it, but it is better aligned with the new NCTM assessments than the old books - you have to explain your answers, and content has been moved way, way up, I guess because they figure kids don't have to drill the basics anymore so they can master college level math instead (yeah, right)
This was the fault of the "new math", they tried to put college level
math theory on top of basic survival skills, and nobody ended
figuring how what the heck they were talking about. Like trying
to teach thermodynamics to drivers so that they can have a
"deeper" understanding of how their automobile works rather than
just how to drive and service the darned thing.
I would be happier with the more basic curriculum we had and shoot for lower stress and higher proficiency, not more content.
Problem is, if every kid is expected to know this stuff now after
the Bosheviks got done restructuring math education, will they
suffer if we only give them the basics? The smarter kids will
get this stuff, those at the bottom, I'm afraid will fall even further
behind. So much for "math for all". Are we really doing the kids
at the bottom a favor by requiring that all students get more math
than the top 1% used to get 40 years ago?
I see a major problem with the current education dissidents is they
say it is dumbing down the curriculum when in fact, content has
been moved up at the expense of basics. Like my kids' whole
music first piano lesson, forget about the boring one step per
lesson, let's start out doing some real life 2 hand music reading
from day 1. That's also the idea behind whole language, forget about
artificial Dick and Jane, let's expose them to Treasure Island right
off the bat. The fundamental assumption of a sequential traditional
eduation is that content should be simple enough for all but totally
disabled to keep up with, and any amount of learning is acceptable
for a passing grade.
Standards based education on the other hand
picks out the best samples as the "standard", and does not accept
mediorcre or average work as meeting that standard. Thus we have
tests that are widely accepted by the public even when 80% of
students fail high stakes tests, and even students with high IQs are
under strain to meet the standards and pass the tests.
What I keep on seeing is the assumption that what is good for the
top 10% must be good for everybody. Dag nab it, if the rich white
kids are doing algebra while the poor black kids are still stuck trying
to master arithmetic, we should simply force everybody to do algebra.
This is where I think I draw the line for grade level promotion. Elementary and middle school essentially put all kids
on the same track, and we should promote kids, no matter how
poorly they do, just give them remedial help to stay afloat. But
in high school, when you get to pick your classes, then use
entrance tests to gate people into tracks, not hold students back.
Date sent: Thu, 11 Mar 1999 20:04:34 -0800
From: Gloria Hoffman
To: arthur hu
Subject: Re: [education-consumers] Review of new math textbooks - Forget basics, go for the whole shooting match?
> Arthur,
>
> What was your impression of Houghton Mifflin's Math Central? My first
> grader is using it this year and has already been introduced to the
> calculator. It does not seem to stress the basics enough.
>
> Wonder what your opinion was?
>
> Gloria hoffman
>