![[IMP]](implogo1.gif)
The Interactive Mathematics Program Listserver
January 1997 Archived Messages
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Date: Thu, 2 Jan 1997 08:43:01 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: "Janice A. Bussey"
Subject: Re: My next question
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I wanted to give a quick response to some of Carol Berland's comments.
I've noticed that others have given very lengthy responses but I shall be
brief.
I have found (and I visit lots of IMP schools) that no matter how long you
and your school have been teaching IMP, it still seems like a "new" program
to your students and they will always have these emotional questions. I
believe that it's part of an IMP teacher's responsibility to encourage
these questions and discussion. An IMP teacher has to believe in the
program and its philosophy well enough to defend it and support it when
students and parents feel insecure. Yes, in IMP 1 when they are starting
out, they are concerned when things in the classroom seem so different and
the work they are being asked to do seems different. In IMP 2 when
students are faced with "Solve It", they need a lot of encouragement again
because this unit presents symbolic algebra differently from what their
friends in Algebra 1 got (and they are concerned because they are getting
it a year later). I find students in IMP 3 and IMP 4 especially concerned
about IMP and their math experience because they are headed towards SATs
and college and competing with others from more traditional math programs.
Seniors get especially agitated when they anticipate going into a
university with who-knows-what kind of program. They aren't sure they will
survive. These are all valid concerns and the teacher needs to keep
channels of communication open with her students so that the students are
aware of their own mathematical power and capabilities. To avoid these
discussions in the classroom is to do a diservice to these students.
There. I guess it wasn't as brief as I thought it was going to be.
Janice Bussey
>I'm still cleaning up loose ends on the Null Hyp. and Need for Stats. questions
>. Thank you for your responses. Surely you must have questions of your own, o
>r have you all got it figured out? Anyway, I always have lots of urgent questi
>ons. My next:
> Teaching Imp 1 is a year long hassle reassuring kids that yes you are lear
>ning math, yes this is algebra, Euclidian geometry,college entrance math, advan
>ced calculus, etc. - you must know what I mean. No this is not math for dummi
>es, remedial math, non-college track math, etc. Now I see a great change in my
> sophomores in their maturity and acceptance. Some are still bothered by
> the same conflicts, but they are not at all vocal to me while last year someti
>mes they even get insulting (I'm so sensitive). All kidding aside, in our 3 ye
>ar use of Imp, we usually experience one full class of freshman dropping imp
>at the year's end while very few year 2 or 3 drop and now we have a strong dema
>nd for imp 4 (which is why I was requesting stats on imp success).
> Also, being among the very top high schools in the Chicago area, drawing on
>ly from the city, but from the city's top test scorers, our incoming students a
>re well-prepared and looking for a challenge. Not that Imp doesn't give them a
>nd me a challenge - but they come in with these fantasies of hard algebraic
>equations to solve, hard math problems to quickly and mysteriously put down the
> answers for, hard multiple choice tests to come out on top of, etc.
> So my question to you veterans and authors of imp is: Do you experience th
>is emotional struggle with new imp students verses older ones? I do believe it
> is emotional, because many of them come in to our prize high school with wishe
>s and dreams for themselves which imp kind of busts up a bit. It's tough. Do
>we just struggle all year with it trying to keep it just a dull rumble? Or do
>things get better as people's perceptions of what math education should be
>changes? Is the Imp curricullum changing to meet the better preparation in mid
>dle schools?
> Background on my school Whitney Young. Something like 60-50% African-Amer
>ican, 20-25% Hispanic, 15% Caucasian, 15-% Asian or something like that. Only
>25-30% poverty level - the main factor really. Kids travel 1 hour or more by p
>ublic transportation to get here in all kinds of Chicago weather and we have
>excellant attendance. Most kids do homework and most do POW's. Of course what
> is "most"? But does it matter that our kids have these conflicts about whethe
>r Imp is real math or dummy math? I think all teachers even in the so-called u
>nderachieving high schools have this same conflict.
> This year (only my second try at Imp 1), I've adjusted the challenge level
>a bit by fiddling with the pow's or pace, but I don't want to lose vision of ho
>w I should be in the classroom and what the curricullum could be. I'm kind of
>flying blind except for whatever chance comments Margaret Small gives me.
> I'd appreciate any thoughts you have on this. Thanks.
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Date: Sat, 4 Jan 1997 22:40:25 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: ChichaL@AOL.COM
Subject: Re: Imp 4 final
Comments: To: djohnson1@telis.org
Thanks Dan, I'll hold off till the inservice.
Chicha
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Date: Sun, 5 Jan 1997 20:30:27 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Dan Fendel
Subject: Los Angeles Times article (fwd)
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There was a big article on math ed in today's LA Times (Sunday). I just
got back from vacation and haven't read it, but was asked to forward it,
so here it is. It's poorly formatted, and I may have it later as an
attachment.
As far as I know, the statement about IMP in Japan is false, but we heard
that mentioned initially several weeks ago, so we're trying to track down
the source.
I'm asked to relay the infor that the actual press clip ( with photo)
will be sent to all the regions soon.
Dan Fendel
Director Professor of Mathematics
Interactive Mathematics Program San Francisco State University
Los Angeles Times
LOS ANGELES TIMES Jan. 5, 1996
COLUMN ONE
Formulas for Math Problems
U.S. educators jump from fad to fad as
students continue to lag those in
other countries. As a backlash to Reform method
builds, experts try to come up
with answers.
By RICHARD LEE COLVIN, Times Education Writer
Scientists, doctors, engineers--you leave the
room. While we're at it,
mathematicians and MBAs, you join them.
It's math time. And for once, the rest of
us--not merely the numbers whizzes--have to pay
attention.
Today's problem is a two-parter: 1) How many
times will we redesign math classes before U.S.
students measure up to the rest of the world? 2) Will
doing so, again, finally get Americans over
their aversion to math more
complicated than balancing a checkbook?
Stumped? Don't feel bad. So are many experts.
In November, Americans brought home a report
card from the Third
International Math and Science Study, the most
comprehensive comparative test ever. Graded on a curve, eighth-graders in
this country averaged about a C-minus, far back of such honor roll
nations as Singapore, Japan and Belgium.
The result hardly surprised American
educators--it merely repeated what had long been known.
Back in 1957, though, when the Russians blasted
Sputnik into orbit,
Americans were shocked. They realized their
children were being taught math less suited for space travel than
figuring how much seed to buy for the springplanting. As a result, the
nation was dangerously short of top scientists and mathematicians.
Thus came the revolution known as New Math. Only
to be toppled later by Back to Basics. Which was supplanted by Reform
which, even now, is giving rise to. . .
Backlash.
For four decades, the United States has
skittered from one math fad to another--each bringing rewritten
textbooks, new training courses for teachers and new homework assignments
to befuddle parents schooled under an earlier orthodoxy. Today's parents,
who were forced to memorize multiplication tables in their school days,
may find their own kids being handed calculators in the first grade.
Our math instruction oscillates between the same
poles that shape and
reshape our culture, politics and even our
morality. We are torn between
discipline and liberation, between demanding
performance and promoting
self-esteem--a two-step that, in education,
causes us to fixate on facts and
formulas one moment, then complain the next that
such "rote learning" fails to produce "true understanding."
The mood of the moment places greater value on
getting kids to feel good about math than on improving their test scores.
But we're reevaluating, of course, worried that things have gone too far.
Here in California, a state panel is about to take yet another look at
guidelines for teaching math.
Meanwhile, what you see as we begin 1997 is:
* Fantasy Lunch. Trying to make numbers fun, the
Mathland lesson
series has second-graders spend "math time"
creating paper versions of favorite foods. All the cutting and pasting
makes it more art lesson than charting exercise, some teachers complain.
* The same philosophy has university consultants
telling high school
algebra teachers that students must work in
groups on problems that will
"reveal" concepts. One class in Ventura County
grows so frustrated trying to "discover 1,000 years of math" that the
students beg the teacher to explain the material. So she lectures--but
keeps the desks in groups so the principal won't find out.
* Districts, including Los Angeles Unified, ban
purchases of certain math books though teachers say they lift test
scores. The problem? Reform philosophers find them too packed with
formulas.
Such conflict among professional educators would
be unthinkable in a country like Japan, where instruction changes slowly,
guided by classroom successes.
In the United States, no central education
authority, national curriculum or performance standards show the way.
Philosophies of "teaching go back and forth, but there's no sense of
progress," said James Stigler, a UCLA psychology professor who has
compared math teaching around the world.
Reacting to November's report card, U.S.
Secretary of Education
Richard W. Riley urged that we not simply
abandon the current orthodoxy--the Reform agenda that spawned Fantasy
Lunch--without having given it a real try.
But Riley is enough of a historian to know that
competition is more
American than consensus.
So a San Gabriel Valley school may be a
microcosm of how the nation might sort it all out.
At Rosemead High, the math department proudly
refuses to decide
between the "reformers" and "traditionalists."
In some classrooms, you find the teacher conspicuously in the back while
students up front present the nightly homework problem on an overhead
projector. But down the hall, a teacher is at the chalkboard, firmly in
control, leading the class through geometry exercises.
Students and parents decide which class works
for them.
The key is, teachers at Rosemead do both methods
well--with adequate training and with passion.
That has not always been the case in America's
math classrooms.
Launching of Sputnik --and New Math
Though Sputnik was the turning point, the seeds
of New Math were
planted years earlier during World War II. New
technologies such as radar
exposed the weakness of U.S. soldiers' math
skills.
After the war, mathematicians at the University
of Illinois and Yale,
helped by the National Science Foundation,
looked for ways that children still riding bicycles with training wheels
could be taught math concepts such as sets--the idea that numbers can be
grouped by characteristics, such as whether they are even or odd.
If students understood, for example, that our
numbering system is based on 10s (there are ten 10s in 100, ten 100s in
1,000, etc.), they would appreciate the brilliance of math and be able to
use it in advanced classes--or on the job.
The approach sputtered along until Sputnik
elevated math and science
instruction to a national crisis. Overnight,
thousands of teachers--many
inexperienced--were asked to introduce new
topics to classes packed with baby boomers.
New Math landed Philinda Denson in the Los
Angeles Times in 1964.
She was a newly minted math major from the
University of Redlands who not only understood the approach but "loved
it."
"I thought it was very rigorous and true and
honest," recalled Denson, now one of the teachers at Rosemead High.
Thirty-three years ago, she was recruited to
help ease parents' anxiety over not understanding what their children
were learning.
"The old math is not being discarded," Denson
was quoted as saying.
"We want to teach children why as well as how.
Instead of starting out by
'borrowing' and 'carrying,' we want children to
understand what they're
doing."
But even teachers, especially in elementary
grades, were lost. Lynn
Steen, a math professor at St. Olaf College in
Northfield, Minn., said that led to absurd lessons in which students were
drilled on how to spell terms such as
"commutative," as in the "commutative
property"--which simply means that 2 + 3 equals 3 + 2.
By 1966, the movement was unraveling amid
concerns that students were not learning basic skills. Over the next
decade, New Math was satirized as "hopelessly abstract, elitist,
confusing and impractical," said San Francisco writer Jeffrey W. Miller,
who studied the history of New Math after deciding he was one of its
victims.
Back to Basics was the reaction.
A National Hero Emerges
Opinion polls showed that Americans wanted
discipline and a familiar curriculum to offset the social disruption
shaking the country. So even as dress
codes were being liberalized and requirements eased in college--meaning
students did not have to take much science, for instance--elementary
schools returned to old-style arithmetic drills.
The approach eventually produced a national
hero, East Los Angeles'
Jaime Escalante, who showed that hard work
mastering formulas could lift
low-income students into the math elite. His
Garfield High students passed
Advanced Placement calculus exams at astounding
rates.
But many math educators were not convinced. They
agreed that Escalante was a brilliant motivator, but how many were like
him? They simply were not
willing to concede that math instruction had to be top-down--or that
calculating was the same as understanding.
In 1983, this group got the ammunition it
needed. The National
Commission on Excellence in Education released
its "Nation at Risk" report, showing that too few high school students
were taking math. Each year after the
ninth grade, the number fell by half.
Another problem: women and non-Asian minorities
were overwhelmingly being filtered out. Why couldn't math be a sponge,
soaking everyone up?
That was the language of Reform.
In a sense, it turned New Math upside down.
Where New Math presented the students with theories ("sets"), Reform
started with games, designed so students would discover such concepts.
And why did math have to be so abstract? Why ask
students to divide the fraction 1/2 by 1/4? Why not ask: How many
quarters are there in a half-dollar?
Easier, right?
Under the Reform philosophy, students were given
calculators, freeing up time previously spent number-crunching for
"higher order thinking." They
were to work in groups to get a feel for how math was used on the job.
Students might figure out what products a bakery
should have to maximize profits. The solution traditionally required
complex equations. But the students here can draw diagrams and the answer
is less important than getting them to "think about strategies, talk with
other kids and then pull the math out of that," said Judy Anderson, who
directs a National Science Foundation project helping Southern California
teachers develop nontraditional lessons.
The reformers won a big victory in 1985, when
California adopted a
framework for math instruction that promised to make students
"mathematically powerful."
The Reform movement remains on top: Education
journals highlight ways to teach "African American math." Conferences
attracting 5,000 teachers suggest downplaying the difficulty of classwork
by basing problems on fairy tales.
One missionary in the Reform cause is consultant
Ruth Parker, who
rejects long division and multiplication tables
as nonsensical leftovers from a pre-calculator age. She urges audiences
to "let kids play with numbers," and they will figure out most any math
concept.
Parker has spoken before 20,000 people over the
last six months at the behest of school districts. But there's an ominous
reason for that: The districts are worried.
About backlash.
Reform now is facing the same sort of
scrutiny--and ridicule--that killed New Math.
Why? The feel-good language presents an easy
target. And the test score gap with other industrial nations is not
closing.
This fall, the National Assessment of
Educational Progress said
17-year-olds are no stronger in math than 20
years ago. Only six of 10 high
school seniors can compute with decimals,
fractions and percentages. Fewer than one in 10 can use beginning
algebra.
Math professors shake their heads at the skills
of freshmen--54% in the CSU system have to take remedial math. "Things
the average students would know backward and forward 12 years ago, these
students don't know at all," said Jerry Rosen of Cal State Northridge,
lamenting how students now use calculators to add single-digit numbers.
Performance in elementary grades is shaky as
well. Last year, after many California schools began using Reform lesson
plans, test scores immediately plunged in Santa Barbara, San Francisco
and elsewhere--stirring parent revolts.
"I don't think parents would be skeptical if
they thought the new ideas were firmly anchored in their kids being able
to balance a checkbook when they're older," said Miller, the San
Francisco writer. He put his daughter in a Catholic school where she is
expected to memorize multiplication tables by the end of the third grade.
Just as California led the way to Reform, so is
it experiencing backlash first. Critics compare the state's math
curriculum to its disastrous experiment in
reading instruction. Officials embraced the "whole language" approach,
downplaying fundamental phonics skills in favor of trusting that students
would learn them through exposure to interesting stories.
In math, those leading the backlash say it's a
difficult subject, whether reformers admit it or not. And it is practice
adding and subtracting--with a pencil--that prepares the mind for complex
work such as calculus.
The fight gets ugly at times.
At San Fernando High, Dan Hart is following the
example of Jaime
Escalante. He touts "real academic standards"
and uses the same texts and cram sessions to teach low-income Latino
students Advanced Placement calculus.
Of 19 who took the AP test last spring, eight
passed. Francisco Garcia also scored a perfect 800 on the college
entrance SAT test.
But Hart is an outlaw in the Los Angeles
district because he uses
structured Saxon Publishing books, which
reformers have stricken from
approved lists. His students have them only
because the publisher donated
them.
"It's astounding to me that these books are so
vilified, because kids learn so much better," Hart said.
Hart is optimistic, though, because the state
now is rewriting its
guidelines for the teaching of math and reading.
In fact, the appointment of
outspoken backlashers to the math panel enraged
reformers, with 3,000 teachers signing protest petitions.
So what to do? Were we to repeat the patterns of
the past, policymakers would order a retreat to traditional practices and
declare the war won . . . until the next counterrevolution.
But no one--neither reformers nor their
critics--believes that would
improve our international standing.
Voices as prominent as Albert Shanker, the
president of the American Federation of Teachers, say we need to decide
exactly what math students should know at each level. And we should not
flee from testing performance because failure may hurt some.
That still leaves room for different approaches.
The nations high on the international report
card do not use one method.
Japanese teachers use many Reform-type lessons,
but students also attend
private programs for extra drilling.
What's more, Japanese lessons are better crafted
and more likely to
include challenging math ideas. That was the
conclusion of Stigler, the UCLA professor, who supervised videotaping of
eighth-grade classes in various
nations.
American lessons, in contrast, were unfocused
and often interrupted.
Stigler said 95% of the teachers espoused Reform
ideas, but the vast majority offered lessons not unlike those of the
1950s.
That finding was one reason that Education
Secretary Riley urged
Americans not to give up on Reform philosophy.
Parents, he said, should
demand classes that help kids really
"understand."
But Riley, a former governor of South Carolina,
noted that unlike other ountries, authorities here have limited power.
Americans "don't like the federal government to
come in and tell them how to teach," he said.
The last four decades back him up. Ordering all
teachers to teach a certain way--or taking away textbooks they
like--seems futile. There are too many teachers to indoctrinate them all.
There's too much room for misunderstanding.
And a disgruntled few can scuttle any method.
"The nature of our people, their diversity, the
freedom that Americans enjoy has made this country great," Riley said.
"But another thing that's made
the country great is competition."
That's what you see at Rosemead High.
Competition Among Approaches
Even before the students settle in, it's clear
that Melody Martinez is in control of her math class for freshmen and
sophomores, but not dictating to it.
"The bell's going to ring, have your calculators
ready," she says from the back of the room. "Presenters, get ready."
A student named Claudia is ready to talk about
the homework--devising a strategy for guessing what will be on the back
of three cards: one with an X on
both sides; another with an O on both sides; the
third with an X and an O.
Students flip the cards 100 times as a trial,
then work up a probability formula: Two-thirds of the time, the back will
match the front.
Martinez is in the Reform vanguard. She and a
few other teachers at
Rosemead use the Interactive Mathematics Program
(IMP), which replaces the usual high school sequence (algebra to geometry
to advanced algebra) with a series of problems that each can take eight
weeks to solve. Developed with grants from the National Science
Foundation, it is used in 178 schools nationwide--and also widely in
Japan.
"You don't feel you are doing math most of the
time but . . . when you put it all together it's the same," said senior
Rene Cardona.
This is not "feel-good" math. If "you miss your
homework, you're
busted," Cardona said. "She'll call your
parents."
In trials across the country, IMP students have
done no worse--but no better--on college entrance exams than students
taught traditionally. Still,
Martinez believes weaker students stick with
math longer because they enjoy the unconventional approach.
Linda Boyd teaches geometry down the hall. Her
classroom brings back memories.
She starts by handing back the previous night's
homework and then
going over the problems. She's at the front of
the room. The desks are in rows, not pushed together for group work.
Then she calls students' attention to a lesson
on how to tell whether two geometric shapes, such as triangles, are the
same.
"Suppose that polygons QRPNL and ZYWXS are
congruent. List all
pairs of congruent angles and all pairs of
corresponding sides."
Boyd acknowledges that the lesson is abstract.
But students "are learning to develop their minds." And that is the way
that two shapes would be
compared in, say, construction jobs.
Rosemead's teachers have reached a truce:
Respect each other--but
compete for students.
This school year, only a quarter enrolled in
Reform classes.
"It's been a struggle because people have very
strong feelings on both sides," Martinez said. "Some of them you can
understand. They've been through so many new programs and . . . they find
it hard to see that this one is going to be any different."
Denson, who was featured 33 years ago as a New
Math pioneer, now is among the traditionalists. But she borrows Reform
methods.
Her biggest worry? That tomorrow's math gurus
will "want to make a big change and pretty much throw out what went
before."
* * *
One lesson--and 3 Ways to Teach It
The Pythagorean Theorem, A + B = C , is one of
the best known
concepts of mathematics. Attributed to the Greek
philosopher Pythagoras, who died in 495 B.C., it shows how the two
shorter sides of a right triangle compare to the longest side--known as
the hypotenuse. Part of a high school geometry, it has practical uses in
many fields--carpentry or industrial design, for example.
Here's how it is taught by:
TRADITIONALISTS
* In a book commonly used in the mid '70s, the
teacher would describe the theorem, talk about its history and state it:
"In any right triangle, the square of the length of the hypotenuse is
equal to the sum of the squares of the lengths of the legs."
Sample problem: A man walks 2 miles north, 3
miles east, and then 2 more miles north. How far is he from where he
started?
Step 1: Diagram the man's walk then determine
length of dotted line.
Step 2: To do this, create a right triangle.
Step 3: Apply the formula.
Answer: 5 miles
* * *
REFORMERS
* The theorem is the first geometry lesson in
the College Preparatory
Math curriculum used in about 750 schools.
Students plot points on graph paper to create different size triangles.
Then they experiment to understand what "squared" means: drawing squares
off the three sides of a triangle. Then they can see the truth of the
statement that A-squared plus B-squared equals C-squared.
Create squares to see how the size of A
(squared) + B (squared) in fact equals the size of C (squared)
* * *
RADICAL REFORMERS
The Interactive Math Program introduces the
theorem with a game. Two students arrange square "rugs" of various sizes
to create a right triangle. One player gets points equal to the area of
the largest rug. The second gets points equal to the combined area of
the two smaller rugs.
Step 1: Students get rugs.
Step 2: They arrange the rugs three at a time,
to form triangles.
Step 3: They discover that, when the triangle is
a right triangle, both
players receive an equal number of
points--because the two smaller rugs equal the size of the larger one.
* * *
Changing Math Fashions in Math Education
Since the World War II, math instruction in the
United States has changed course time and again--with little improvement
in test results.
Early 1950s: Students are grouped by ability and
memorize multiplication tables in early grades, using timed drills. But a
majority drop math after the ninth grade.
1952: Committee on School Mathematics is formed
at the University of Illinois and begins developing one version of what
would become known as "New Math." Idea is that students should learn the
laws governing math as well as how to calculate.
Mid-1950s: Small number of schools test
committee's curriculum,
weaving together lessons in algebra and
geometry. Students work with
sets--groups of numbers having common
characteristics.
October 1957: Sputnik is launched by Soviet
Union.
Summer 1958: National Science Foundation begins
funding four-week summer institutes on college campuses to train high
school teachers in New Math. They are told that instead of giving
students a rule--for instance that a series of multiplications can be
combined if they have a common element--the youngsters should figure out
for themselves that (6 X 4) + (7 X 4) is the same as 13 X 4.
1958: National Science Foundation funds School
Mathematics Study
Group at Yale University to write another
version of New Math. Sale of Yale books, completed in 1959, jump from
23,000 the first year to 1.8 million after three years.
1962: Articles opposing New Math begin appearing
in scholarly journals.
1964: Max Beberman, one of the founders of New
Math, warns that
because teachers had not been adequately trained
in it, the nation is "in danger of raising a generation of kids who can't
do computational arithmetic."
Mid-1960s: Many schools sponsor classes to
explain the new teaching methods to parents. Though there are concerns
about whether students are earning basic skills, California downplays
drills in favor of encouraging students to "discover" math.
1967: Five-year study of 12 Western nations
finds U.S. 13-year-olds and high school seniors far behind those in other
countries. New Math is blamed.
Early 1970s: Gallup Polls show public concern
about lack of basic skills and discipline in schools. Schools begin
rejecting New Math materials in favor of a back-to-basics approach.
1974: "Why Johnny Can't Add," an indictment of
New Math, is
published.
Mid- to late-1970s: Back-to-basics approach
spreads, but it has its critics as well, planting seeds of the Reform
movement: Math conferences beginfeaturing sessions on how to help
students gain understanding by solving problems on their own.
1983: "Nation at Risk" report warns that America
is in danger because of the weakness of its schools.
1985: California's issues a "framework" for math
instruction that is the most advanced statement of the Reform agenda.
Emphasis is on problem-solving, applications and student understanding.
1986: U.S. Dept. of Education releases a
17-nation comparison showing that America's best students--those in the
top 5%--last in algebra and calculus
when matched against top students elsewhere. Back-to-basics movement is
blamed.
1989: "Curriculum and Evaluation Standards for
School Mathematics" the bible of Reform math, is published.
1992: Revised California math framework is
published, further
de-emphasizing teaching of basic skills in favor
of greater thinking and
understanding.
1994: Reform textbooks are adopted by state's
Board of Education.
Critics say approach is filled with "fuzzy
crap," signaling start of backlash.
1995: State Supt. of Public Instruction Delaine
Eastin appoints a panel to examine math instruction. It concludes that
changes are necessary to restore emphasis on basic skills as part of a
balanced approach that also includes conceptual understanding.
November 1996: Another state panel is created to
rewrite the state's math guidelines to carry out that vision.
November 1996: The Third International
Mathematics and Science Study, comparing students in 41 countries, finds
U.S. eighth-graders below average.
Copyright Los Angeles Times
=========================================================================
Date: Mon, 6 Jan 1997 09:32:40 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: IMP
Subject: Evidence
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Content-Transfer-Encoding: 8bit
IMP teachers, parents, and administrators would like more evaluation
data. During a past workshop we brainstormed ideas for gathering such
data at the local level. Following are suggestions of evidence that could
be gathered about the success of IMP in your community, with ideas in
parentheses about where/how to gather the information. Good Luck.
* numbers of schools, teachers, students in IMP (count them)
* numbers of schools who have shown interest in teaching IMP
(applications, phone calls, visits, ...)
* numbers of parents/families at IMP family nights (count them)
* number of IMP family nights, including comments, ....(count them, make
copies)
* retention data, that is, percent of IMP students going on to IMP 3 and
IMP 4 compared to students in traditional classes going on to Algebra II
and Pre-calculus (from class lists currently, from transcripts in the past?)
* teacher growth, teachers as leaders (list presentations done by
teachers, lists/pages from local, state, and national conferences)
* show how enrollment patterns have changed - fewer sections of
traditional and more of IMP (math department schedules present and past)
* SAT data (from May of 11th grade, using matched pairs; numbers of
students taking the tests compared to students in traditional sequence)
* number of students going on to higher education, or, number of students
having taken three years of college preparatory mathematics compared to
the past (count them now and pre-IMP)
* questionnaires - teacher, parent, student, administrator (from Dr.
Norman Webb, others from sites)
* support letters from principals talking about the changes since IMP has
arrived (ask them to write them now)
* RwonderfulS letters of support from important people in industry,
education,... (copy them)
* support letters from admissions officers at colleges and universities
(copy them)
* mathematics curriculum is aligned with the NCTM Standards (reports to
school boards, ...)
* number or percent of teachers using IMP within a school, and the trends
(count them)
* percent of classes using graphing calculators in a school (count them)
* reduction in number of tracks (mathematics department schedule of
classes now and pre-IMP)
* focus of department meetings (agenda for now and agenda for pre-IMP)
* grades (mathematics, overall, science, English, ...) of IMP compared to
traditional (transcripts)
* attendance patterns of IMP compared to traditional (on school computers?)
* Compare IMP with local, state or national statistics using any of the
variables (NAEP, ...)
* Student work while students are in high school (from IMP work)
* letters from IMP students once they are in college (copy them)
* histories of graduating students (communicate with them while in college)
* comparison of IMP and non-IMP students on New Standards performance
tasks, or other state performance tasks
Lynne Alper
=========================================================================
Date: Mon, 6 Jan 1997 09:36:06 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: IMP
Subject: College acceptance
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
Now that you are back in school, please check with the IMP seniors in
your classes....did any of them hear from more colleges to which they
might have applied early? Let us know about any new colleges or universities
to which IMP students have been accepted. Just include the full name of
the college or university and the state in which it is
located....Thanks..Lynne Alper
=========================================================================
Date: Mon, 6 Jan 1997 09:51:01 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: IMP
Subject: Photographs
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
Attention IMP 3 and IMP 4 teachers.....we need photographs of your
classes in action....during the next months, take as many photographs as
you like...close ups of students working on specific activities in the
units...Remember, just include a post-it on the back of each photo with:
* your name and school
* student names from left to right
* unit and activity
* suggestion for a caption
AND, MOST IMPORTANT OF ALL...., PERMISSION SLIPS FROM ALL STUDENTS FOR
WHOM KEY DOES NOT ALREADY HAVE THEM.....
Some schools have found that sharing the IMP 1 text with the IMP 3 and
IMP 4 classes in your school gives the students the impetus to want to be
featured in future texts....
Just send everything (no paper clips, please) to me...
Lynne Alper
IMP
P.O. Box 2891
Sausalito, CA 94966
Thanks....cheers...Lynne
=========================================================================
Date: Tue, 7 Jan 1997 02:06:38 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: ChichaL@AOL.COM
Subject: Re: College acceptance
Add Ball State University and IUPUI from Capuchino
=========================================================================
Date: Wed, 8 Jan 1997 18:07:10 CST
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Carol Berland
Subject: Bees POW
Next week our 3 imp 2 classes will be assigned the Life of Bees POW. I was thi
nking that many students would be scrambling to use the same reference material
. I'd like to have some do Bees, but some do other insects or ?? Do any of yo
u veterans have any suggestions for varying the topic? Of course there are the
so-called African bees and the current threat to the survival of the
agriculturally important honeybee. Any more suggestions would be appreciated.
Tomorrow and th next day my students will be presenting their chi square P
OW. It's been beautiful and such a pleasure! Imp is still severely threatened
at our school
=========================================================================
Date: Thu, 9 Jan 1997 03:16:44 GMT
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: DeeAnne Doseman-Flaws
Subject: People perceptions of Reform math
MIME-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 8bit
To all IMP teachers,
Here is a rather unique letter, not to mention a rather
confusing letter to the editor that was published in the Orange County
Register, 1/8/97. With all the confusion regarding the New/New Math,
this article brings to the surface just how confused the public is in
regard to what students really need.
In case anyone actually wants to respond to this letter, the addresses
are:
Snail Mail: Letters to the Editor
The Orange County Register
P.O. Box 11626
Santa Ana, CA 92711
Fax: 714-565-3657
Email: letters@link.freedom.com
The article follows: (hopefully without too many typos)
New Math Counts for little in the real world
By Bruce Crawford (a free-lance writer who lives in Fountain Valley)
Recently significant strides have been made in strengthening
our public-school curriculum regarding phonics. Now the time has come
to focus on math. I consider math to be a vital job skill for
everyone. Yet I see good students who, accustomed to using
calculators, have to count on their fingers when they dont have one.
I have taken honor-student Boy Scouts to the grocery store to buy food
for a camp-out, and the cant keep a running total in their heads.
These are warning signs.
A quote from R. Buckminster Fuller, best known for his
geodesic domes, comes to mind., He said, "You dont replace the old,
you make it obsolete by introducing a superior methodology."
In Fullers contest, New Math, and its latest variant, New-New
Math, dont meet muster. They havent made traditional math obsolete;
they arent superior. New Math and New-New Math are all hope and hype.
America leads the world in math-based technological
developments. The innovators who have been producing them learned
math the traditional way. How could all of the math-intensive
technologies have been developed at warp speed if the traditional
methods of teaching math did not work We also have empirical
evidence that NM/NNM are failures. A month ago the Third
International Math and Science Study (TIMSS) released its latest
results for middle-schoolers. Its not pretty. The United States
scored in the second-lowest group. Strife-torn post-communist
countries such as the Czech Republic, the Slovak Republic, Slovenia
and Bulgaria all scored much higher than U.S. students did.
The top three countries, Singapore, South Korea and Japan, all
scored more than 20 percent higher. Singapore scorched us, almost 30
percent higher. The report said that our math instruction is a mile
wide and an inch deep. But the cottage industry that depends
on New Math and New-New Math says we cant return to the old math.
The traditional methods wont work, cant work, they cry. If we try to
go back, things will only get worse., Wrong! Things may get worse
for them, but things will get a lot better for students.
The reports of successes where schools have returned to
traditional math instruction are coming in faster than they can be
compiled. Jaime Escalante didnt use New Math/New-New Math; Marva
Collins doesnt. The Barclay School in Baltimore, the Frederick
Douglass School in New York and the School for Arts and Sciences in
Chattanooga dont all NM/NNM near their classrooms. The Barclay
students perform at parity with a nearby private school charging
$10,000 tuition a year. The Frederick Douglass School has a waiting
list. Arts and Sciences has a 95 percent college matriculation rate.
So much for wont work, cant work.
All three examples are inner-city public schools. Their
students come from "at-risk" families, and they had been considered
uneducable, suitable for care-taking and social promotions only. That
is, until someone set high standards for them and implemented a
traditional curriculum. Voila!
David Drew, author of "Aptitude Revisited: Rethinking Math and
Science Education for Americas Next Century," describes a study done
at the University of Texas, El Paso.
One of his doctoral students had observed that the school had
not been hiring American students to tutor in its remedial education
center.. The majority of tutors came from Mexico, Malaysia, and
India. She set out to discover why. It came down to attitude,
expectations and standards. These three "backward" countries dont use
NM/NNM.
Some people argue that "one size doesnt fit all" and that all
children dont need the rigors of traditional math because they arent
going to be engineers, doctors or accountants. All they really need
to be able to do is balance their checkbooks.
Thats wrong. At a practical level, they have to know math
if they want to be able to earn a "livable wage." No law can change
that.
Drew cites studies that show that mastery of math is the
single best indicator of future earning potential. Math, not
legislation, is the way to close the income gap between the advantaged
and the disadvantaged. More and more blue-collar jobs will require
math proficiency. Those who dont have it will be relegated to
minimum wage jobs. They wont need a checkbook. Today lathe
operators have to run computerized machine tools. Production-line
workers have to be able to operate small industrial computers called
PLCs. Electricians now have to make calculations involving
trigonometry and vectors.
At his academy, Plato, a philosopher, put the highest emphasis
of all subjects on mathematics. He felt it was a survival skill. In
"The Republic," he used a military anecdote to demonstrate his point:
Palamedes became a hero during the Trojan War by defeating
Agamenemnon, who couldnt count his feet. Palamedes was able to count
Agamemnons soldiers and ships and used his math advantage to defeat
the hapless Agamemnon and his larger forces.
Even in Platos time, math was divided into two parts:
"arithmetike" and "logistike." Arithmetike" had to do with the
attributes of numbers. "Logistike" had to do with calculations.
There in the crux of the problem.
New Math and New-New Math focus almost entirely on
"arithmetike." The real world deals primarily with "logistike." One
needs to understand both. But to ignore "logistike" is a travesty.
The results of doing so have been quantified empirically and
they are irrefutable.
The timing is right to restore traditional math. Sacramento
is preparing to release new funds for textbooks. Not a penny should
go toward sub-standard New Math and New-New Math materials. Lets
reinstate traditional mathematics until, in Buck Fullers words, a
superior methodology makes it obsolete.
**End of letter**
My comments on this letter:
Well to start off, I agree with Mr. Crawford at many points.
I agree with him that we need to stress the basics. Many of the new
curriculums will not be effective if the student does not have basic
skills or the want/need to learn. One cannot do high order thinking
if they are incapable of doing the low level thinking. Between the
lines, Mr. Crawford is basically saying that we should want to emulate
the teaching and life styles of Singapore (whipping, torture, fines
for spitting, censorship), South Korea, and Japan ( highest suicide
rate for teens). This is hardly want I would want, but we are all
entitled to our opinion, which is not necessarily true in these other
countries. As to the other countries mentioned, these are still left
over from the soviet style of teaching and learning. Do we really
want to emulate these countries?
One point that Mr. Crawford seems to miss, when he talks about
those inner cities schools that have succeeded, is that these schools
also, with all probability have instituted severe discipline and
consequences for students who dont tow the line. ( Does this
perchance refer to the countries he wishes to emulate). Just for his
information, the NM/NNM was probably NEVER taught in these schools,
they simply changed the way in which thing were done. Also, the fact
that there are waiting lists for these schools, you dont suppose that
the parents might actually care about if their children learn, thus a
higher rate of success? Duh???
He also makes reference to tracking of students (He argued
about not all people are going to become doctors, engineers or
accountants, but they still need to know high levels of math), or
rather that we shouldnt track students (According to Mr. Crawford,
ALL students should take high level math). I guess Im a little
confused at this point. On one hand, he states that we all need to do
hand calculation, but a few paragraphs later he states that they need
to use high tech. tools. After all, we all know that long division is
key to running a computer. I dont know about most of you that use
computer, but it seems to me, that higher order thinking skills are
needed to use and program a computer, not just doing the basic four
operation to lists of numbers. Well, which does he want? I however,
do agree with him, in that math is key to a high earning potential.
On a final note, I wonder if Mr. Crawford has actually seen or
observed the new curriculums. I sincerely doubt it. He more than
likely has been reading propaganda from such groups as HOLD (Hold Open
Logical Debate), which do not offer both sides of the argument.
Another point Mr. Crawford seems to miss is that if the
current system does not work, we shouldn't replace it until we find a
better, superior method. A slight problem here though, how are we
supposed to find these new, better methods, if they are not tried out
in the real world. I guess he has no need for prototypes, or
experimentation?
Please excuse my rambling in many directions, but it basically
is because people such as above make me quite angry. I do realize
that people are entitled to their opinions, but lets be sure of the
facts, before we make such generalizations!! (Gee, like I'm one to
speak! ;-) )
DeeAnne
DeeAnne Doseman-Flaws
deeannef@deltanet.com deeannef@hotmail.com
deeannef@juno.com
=========================================================================
Date: Thu, 9 Jan 1997 14:47:04 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: hessnesh@HUGSE1.HARVARD.EDU
Subject: Re: Bees POW
Comments: To: Carol Berland
In-Reply-To: <199701090012.SAA52294@piglet.cc.uic.edu>
MIME-version: 1.0
Content-type: TEXT/PLAIN; charset=US-ASCII
This morning we had a "beekeeper" visit our IMP II classes. Being a
veteran beekeeper and a prof of genetics at harvard, he was a wealth of
information. But, here are some of the topics he covered.
The different roles of the queen, the drowns, and the worker bees
The ways bees "communicate" (movement, sound, smell, direction,
magnetism,etc.)
Construction of the hives (double layered, 3/8" apart, sloping down
prisms,etc.)
Climatic adaptation of different species of bees
TEmperature control of bees
Effects of being stung by bees
Comparing honeybees, yellowjackets, hornets, etc.
Economics of being a bee keeper
Life cycle of bee
Bee eyes (with hexagonal parts)
Effort to make wax vs. effort to make honey
Natural vs. commerically-started hives
Hope this is a start.
Sharon Hessney
Fenway Middle College High School
=========================================================================
Date: Mon, 13 Jan 1997 20:56:18 -0600
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Jane Kostik
Subject: Re: College acceptance
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
Lynne,
I have some additional colleges to which our IMP-4 students have been
accepted. I haven't yet heard from other Mpls high schools.
Gustavus Adolphus--St Peter, MN
Luther--IA
Winona State--Winona, MN
St Cloud State--St Cloud, MN
Mankato State--Mankato, MN
Metro State--Mpls, MN
University of Minnesota--Twin Cities Campus (Mpls)
Minneapolis Business College--Mpls, MN
University of St Thomas--St Paul, MN
I'll let you know when I hear more.
Jane
Jane M. Kostik Henry High School
Minneapolis Public Schools 2020 43rd Ave No
IMP Co-Director Minneapolis, MN 55412
(612) 627-2897 ext 8325
=========================================================================
Date: Fri, 17 Jan 1997 07:28:48 CST
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Carol Berland
Subject: Pennant Fever Assessment (In-class)
I am asking this question for two IMP 3 teachers who disagree on the answe
r. They want to know from others who've worked through this before what you th
ink the answer is to question 3 of the In-Class Pennant Fever Assessment. Also
, do you need the information from the question 2 above?
Here's the question shortened. Q2. Hirk ...(is setting up from a list of
ten day-long bike trips) five day-long bike trips. He wants to do a different
trip on each day of his 5 day vacation. How many different schedules does he
have to choose from? Q3. Hirk ... has 8 different pairs of biking shorts
and 12 different biking shirts. .....He will wear different clothes each day..
..How many choices does he have for different ways to plan his wardrobe?
=========================================================================
Date: Fri, 17 Jan 1997 09:20:23 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: "Janice A. Bussey"
Subject: Re: Pennant Fever Assessment (In-class)
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
> I am asking this question for two IMP 3 teachers who disagree on the answe
>r. They want to know from others who've worked through this before what you th
>ink the answer is to question 3 of the In-Class Pennant Fever Assessment. Also
>, do you need the information from the question 2 above?
> Here's the question shortened. Q2. Hirk ...(is setting up from a list of
> ten day-long bike trips) five day-long bike trips. He wants to do a different
> trip on each day of his 5 day vacation. How many different schedules does he
>have to choose from? Q3. Hirk ... has 8 different pairs of biking shorts
> and 12 different biking shirts. .....He will wear different clothes each day..
>..How many choices does he have for different ways to plan his wardrobe?
Dear Carol,
The answer to question 3 is 638,668,800 choices. I've seen tons of
ways that students have solved this which are all correct. I can't even
remember all of them so I'll at least present my way of thinking:
The only reason that you may need question #2 is to realize that Hirk
has a five-day vacation. Now to figure out how many orders he can make
with his 8 pairs of shorts over 5 days, you can take the permutation of 8
things taken 5 at a time. (6720) Then you can take the permutation of 12
shirts taken 5 at a time. (95040) Now for each 5-day arrangement of
shorts, you can match it up with each of the arrangements for shirts. So
that's 6720 X 95040 which is 638,668,800.
This is certainly not the only way to solve the problem. I hope you
get a lot of interesting responses.
Janice Bussey
=========================================================================
Date: Fri, 17 Jan 1997 12:33:51 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: DRobathan@AOL.COM
Subject: Re: Pennant Fever Assessment (In-class)
Carol,
Most of my students that answered question #3 of the Pennant Assessment did
as Janice suggested: Calculate 8P5 * 12P5
=========================================================================
Date: Fri, 17 Jan 1997 12:39:19 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: DRobathan@AOL.COM
Subject: Re: Pennant Fever Assessment (In-class)
Carol,
I'll try again! Most of the kids answered question #3 of the Pennant
assessment the following way: 8P5 * 12P5 . I did have some other solution
methods, one of which was 12*8 variations for Monday, 11*7 for Tuesday, ...
8*4 for Friday. This also gave the correct answer.
Take care,
Dave Robathan
=========================================================================
Date: Fri, 17 Jan 1997 17:13:56 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: hessnesh@HUGSE1.HARVARD.EDU
Subject: Mid-term exams
In-Reply-To: <199701171336.HAA03272@piglet.cc.uic.edu>
MIME-version: 1.0
Content-type: TEXT/PLAIN; charset=US-ASCII
WE have found in our files an IMP Year 2 = First Semester Exam with a 1994
copyright. Are there a group of exams that go with IMP that are not the
take-home and in-class assessments? If so, may we have a set?
Sharon Hessney
Fenway Middle College High School
=========================================================================
Date: Sat, 18 Jan 1997 17:17:00 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Fullerosh@AOL.COM
Subject: Re: Pennant Fever Assessment (In-class)
It seems to me that the answer may depend on how you interpret the question,
"How many choices does he have for different ways to plan his wardrobe?"
Suppose, for example, that Dirk will only have two days of vacation. Is
wearing shirt 1 with shorts 1 on Monday and shirt 2 with shorts 2 on Tuesday
different from wearing shirt 2 with shorts 2 on Monday and shirt 1 with
shorts 1 on Tuesday? (Same outfits, worn on different days.)
If you say yes, then it seems to me that using permutations in the way Janice
and others have indicated is appropriate. If you say no, then you've got to
take a different approach. Allowing permutations of both shirts and shorts
causes the same sets of shirts and shorts to match up on different days of
the week. This effectively counts each matchup of shirt with shorts twice,
in the situation I have described.
On the other hand, using only the number of combinations for both does not
allow shirt 1 and shirt 2 to be matched with both shorts 1 and shorts 2
(shirt 1 and shorts 1 on Monday, shirt 2 and shorts 2 on Tuesday; or shirt 1
and shorts 2 on Monday, shirt 2 and shorts 1 on Tuesday.) It would seem that
what we need to do is to match each combination of shirts (or shorts) with
the number of permutations of shorts (or shirts), or vice versa. For Dirk,
this would mean (12C5)(8P5), or the equivalent (8C5)(12P5).
Don't you love interesting questions like this?
=========================================================================
Date: Mon, 20 Jan 1997 09:19:22 CST
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Carol Berland
Subject: Around Horn POW
Does anyone know any similar problems from "real life" that involve a situation
similar to around the horn? It's such a fun problem; some of my kids always
want to know to what does this apply even though they do like it and are having
some fun with it. Thanks.
=========================================================================
Date: Mon, 20 Jan 1997 08:56:00 -0800
Reply-To: "Jerry C. Neidenbach"
Sender: Interactive Mathematics Program
From: "Jerry C. Neidenbach"
Organization: Gooey
Subject: To Sarah
In-Reply-To:
MIME-Version: 1.0
Content-type: text/enriched; charset=us-ascii
Content-transfer-encoding: Quoted-printable
9Sarah,
The article appeared in the LA Times on Sunday, January 5, 1997.
Jerry10
_/_/_/_/ _/_/_/_/ _/_/_/_/ _/_/_/_/ _/ _/ Camarillo, CA
_/ _/ _/ _/ _/ _/ _/ _/ gooey=40gooey.com
_/ _/_/ _/ _/ _/ _/ _/_/_/_/ _/ Admin: Dave Burns
_/ _/ _/ _/ _/ _/ _/ _/ (via FC SMTP/NNTP)
_/_/_/_/ _/_/_/_/ _/_/_/_/ _/_/_/_/ _/ Gooey 805.445.1012
=========================================================================
Date: Tue, 21 Jan 1997 09:13:23 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: "Janice A. Bussey"
Subject: Re: Mid-term exams
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
>WE have found in our files an IMP Year 2 = First Semester Exam with a 1994
>copyright. Are there a group of exams that go with IMP that are not the
>take-home and in-class assessments? If so, may we have a set?
>
>Sharon Hessney
>Fenway Middle College High School
Dear Sharon,
During the course of curriculum development for the Interactive
Mathematics Program, there have been many versions of the in-class
assessment and the take-home assessment for each unit. I don't know if
anyone has all of them. After working with IMP focus groups and the
publisher, we settle on the version we like the best and that will be the
version which goes into the published teachers guide from Key. In
addition, many teachers design their own end of unit assessments and exams.
If you want to give me a call at my toll-free number (1-888-MATH-IMP), we
can compare what exam items are going in to the Year 2 published version
with the 1994 exam you are looking at and go from there.
Janice Bussey
=========================================================================
Date: Wed, 22 Jan 1997 11:57:20 -0800
Reply-To: Dan Fendel
Sender: Interactive Mathematics Program
From: Dan Fendel
Subject: Posting about IMP from Kim Mackey of Valdez, Alaska
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; CHARSET=US-ASCII
For your information, I am posting below a statement that appeared on the
Math Forum's discussion group about the NCTM Standards.
I will follow this with a copy of the reply I sent to that list. You
should all be aware of the kind of comments that appear on the internet
about math ed in general and about IMP in particular. We try to keep the
truth available but it's a constant struggle.
Incidentally, if you are interested in joining that list-serve, I think
all you have to do is send the message "subscribe" (without quotes) to
the math forum address.
Also, if you are interested in the ancient history of the "Wu report"
mentioned in Mackey's posting, contact the IMP office.
Dan Fendel
Director Professor of Mathematics
Interactive Mathematics Program San Francisco State University
>From mackeys@alaska.net Sat Jan 18 08:07:36 1997
Date: Sat, 18 Jan 1997 00:17:41 -0900 (AKST)
From: Kim Mackey
To: nctm-l@forum.swarthmore.edu
Subject: IMP, a standards-based curriculum
INTRODUCTION
When looking at curricula that purport to be standards-based,
it is best to keep in mind two things. One is what Sherman Stein calls, in
his book "Strength in Numbers", the Action Syndrome.
"The Action Syndrome helps a person cope with the stress of
action. It reduces several options ultimately to one. It enables the doer
of an act, the "actor", to commit to this one option, to suppress doubts,
and to sustain dedication."
"Nothing is so persuasive as the force of conviction. Those who
cannot convince themselves certainly cannot convince anyone else. The
Action Syndrome therefore enables the actor to draw others to the cause."
The other thing to keep in mind is the Hawthorne Effect. In analyzing a
math curriculum the Hawthorne Effect might occur when it is not the
curriculum that produces improved mathematics achievement, but the
_enthusiasm_ teachers have when using the curriculum.
============================
Last week I suggested that standards-based curricula can be distinguished
from traditional curricula in four ways: 1) integrated curriculum, 2) a heavy
emphasis on group learning, 3) extensive writing about mathematics, and 4)
a heavy emphasis on "real-world" problems. The curriculum I propose to
analyze is the Interactive Mathematics Program or IMP.
FIRST QUESTION: Who wrote the curriculum?
The authors of IMP are two professors at San
Francisco State University, Diane Resek and Dan Fendel, and two
professional developers, Sherry Fraser and Lynne Alpert. A search through
the million volume catalog at Amazon.com reveals that Fendel and Resek
co-authored a book entitled "Foundations of Higher Mathematics,
Exploration and Proof", which is currently used in a 100 level math course
at Simon Fraser University (and perhaps others).
An Alta Vista search on Diane Resek produced a number of interesting hits
including a short talk she gave at ICME 8 on the role of calculators in
the classroom. Another web page was her article "Techniques for
Cooperative Group Work" in the Focus on Calculus documents at the
University of Arizona. In the paper she discusses a number of common
sense suggestions for using cooperative groups with the Harvard Calculus
Consortium text. For example she says, "I feel the CCH text is certainly
lively, but not lean. Following my department's syllabus, I was able to
have students work in small groups for about 20 minutes a week out of a
total of 150 minutes."
SECOND QUESTION: Is IMP a true reflection of the NCTM standards?
The publishers, Key Curriculum Press, certainly think so. In a section
titled "A Model for Mathematics Education Reform" on their web pages they
say:
"The IMP curriculum is designed to make the learning of a core
curriculum more accessible, especially to those groups, such as women and
minorities, who traditionally have been under-represented in college
mathematics classes."
"The IMP is designed to be used with heterogeneous classes. The developers
of the program believe that virtually everyone can gain a deep
understanding of the curriculum and can make valuable contributions as a
member of a learning group."
"...students are organized into small groups (usually four students to a
group), and much of the classroom learning is done in the context of
these groups."
"...the role of the teacher changes from that of "imparter of knowledge"
to that of observer and facilitator."
==================================
The reform-minded PROMPT group (Professors Rethinking Options in
Mathematics for Prospective Teachers) had this to say about IMP on one of
their web pages.
"Some of you may recall that IMP was a part of the first-year PROMPT
workshops as an example of a reformist, standards-based high school core
curriculum."
==================================
IMP was also listed in the 1994 Promising Practices list
developed by the regional Eisenhower consortia funded by the US Department
of Education's Office of Educational Research and Improvement. "The
criteria used to evaluate each program included innovativeness, support of
national standards, effectiveness, and transferability."
================================
Finally, IMP is listed in the Fall 1996 Annenberg/CPB Guide of Reform
Initiatives. Some excerpts from the abstract are:
"IMP is a four-year mathematics curriculum for secondary students that
focuses on open-ended explorations of complex problems. The program was
designed in 1989 to fulfill the national mathematcs standards and those of
the California Mathematics Framework."
"Teachers must learn new ways to manage a classroom, since IMP does not
use the traditional model of a teacher lecturing to students who then
complete a number of paper and pencil exercises."
"Teacher training is essential for the success of this program, as
teachers must not only master new instructional strategies, but new
mathematical content and assessment methods as well. Success in an IMP
class is measured more by how well a mathematical tool or idea can be used
in a meaningful context than by the traditional approach of computation
tests."
=================================
It seems clear therefore, that IMP _does_ represent a curriculum
that incorporates the major aspects, both mathematical and instructional,
that are at the heart of the NCTM standards.
THIRD QUESTION: So what does it look like?
I recently purchased the 1997 student edition of the year 1
IMP text and have been working my way through the problems. Some initial,
non-judgemental observations:
1) There is no index.
2) There is classwork for a total of 137 days.
3) There is a _lot_ of writing by students.
4) Homework problem sets are short, often 5-8 problems.
5) Lots of pictures.
6) There is no procedural drill in the text.
7) There are 19 POWs (problems of the week) for an entire year. The POWs
typically do not have a single correct answer.
===============================
The text, which represents the entire first year of high school
mathematics, centers around 5 sections:
1) Patterns -- a 24-day unit of introduction, integers, angles,
and in-out tables.
2) The Game of Pig -- a 29-day unit dealing with probability.
3) The Overland Trail -- a 30-day unit dealing with graphs,
variables, rate, and lines of best fit.
4) The Pit and the Pendulum -- a 28-day unit dealing with graphing,
equations, and statistics.
5) Shadows-- a 26-day unit dealing with basic geometry including
similarity and triangles along with some basic trigonometry.
=============================================================
==========================
QUESTION FOUR: How is IMP perceived by the students being taught with it
and the teachers who are teaching it?
There are a number of IMP web sites on the Internet. One which has access
to most of the others is http://www.azstarnet.com/~quesnel/imppage.html.
This web page is maintained by Jerry Quesnel, a 20 year veteran math
teacher at Desert View High School in Arizona whose mean mathematics ITBS
scores are in the 27th percentile. Here are some of Jerry's comments:
Do Not allow too many below-level students into the program. This will make
it impossible to work.
Pros and Cons
1) more fun for teachers and students.
2) much more time consuming to prepare for.
3) more students can be successful when compared to a traditional
approach.
4) standardized test scores have shown no real change yet.
5) students do not get enough computation practice.
It is interesting to note that some of Jerry Quesnel's comments about IMP
mirror those of Professor Hung-Hsi Wu's in his review of IMP at Berkeley
high school. At other IMP sites there are letters from students extolling
IMP. At the Mathematically Correct website there are several anecdotes
about problems with IMP including its inability to prepare students for
higher level math and science classes and the remediation sometimes
necessary for college-bound students.
=============================================
Some Judgemental comments on the IMP year 1 text.
As a high school math teacher who has taught for ten years, there are a
number of areas in the IMP text that I have difficulty with. On the minor
side, when dealing with 9th and 10th graders, telling them to write "Some
ways to..." or "all you can think of..." on an assignment as occurs
fairly frequently on IMP classwork, POWs, and homework, is a recipe for
low quality work due to teacher subjectivity and student desire to do the
minimum amount of work for the maximum grade.
2) There is an incredible amount of writing required of students in the
text. To adequately and honestly grade and provide feedback to this
writing would eat up a tremendous amount of time.
3) The lack of an index is very irritating.lack of an index is very
irritating.
4) The topics seem disjointed and I often have trouble seeing the
connection between one section of a unit and another.
=============================================================
Comments: It is clear that IMP is a discovery-oriented, constructivist
curriculum. Students are encouraged to find their own meanings of
mathematical subjects while conversing with their peers and being
facilitated by the "guide on the side" once known as a teacher.
Unfortuntely, as developmental psychologist David Geary explains in his
book, "Children's Mathematical Development" "one of the implicit
assumptions of the constructivist approach is that mathematics is a
biologically primary domain."
Geary explains that this is true of some areas such as number,
counting, and some features of arithmetic, but is definitely not the case
for more complex mathematical skills. In an area in which IMP is decidedly
lacking, drill and practice, Geary has this to say.
"Finally, the argument that drill and practice and the development of
basic cognitive skills, such as fact retrieval, are unnecessary and
unwanted in mathematics education fails to appreciate the importance of
basic skills for mathematical development. As noted earlier, drill and
practice provide an environment in which the child can notice regularities
in mathematical operations and glean basic concepts from these
regularities. Much of mathematics involves being able to use procedures,
equations, and so on. Except for basic numerical and arithmetical skills,
most children are not likely to be able to develop mathematical procedures
solely on the basis of their conceptual knowledge."
To me it is clear that IMP represents a curriculum which is
standards-based. Thus its flaws rest either with the standards themselves
or with the philosophical orientation of reformers in the mathematics
educational community.
=========================================================
=================
But what about the TIMSS results? Don't they show that the Japanese are
using constructivist techniques and conceptual problem-solving a la the
NCTM standards?
According to Professor Wayne Bishop, who gleaned much of the following
information from an extensive phone conversation with James Stigler, the
UCLA professor overseeing the TIMSS video studies, Japanese mathematics
classrooms do not resemble either IMP or the traditional mathematics
classroom in the US.
"The lessons are of a "problem solving" nature but they are usually not
so-called "real world" problems. They are mathematics problems in a verbal
setting with a definite right answer implied. Students are actively
invloved in solution approaches and formulation with alternative solution
ideas discussed extensively. These are not, however, student directed
situations. The classrooms are very teacher directed. The instructor has
studied the problem extensively and is aware of the various approaches
that will be offered. An important part of the lesson is discussing these
various solutions, including their strengths and weaknesses. These are not
independent projects that are expected to be accompanied by a lengthy
student essay on the various strategies failed and ultimately successful
as is common in reform movement pedagogy in the US today. The instructor
knows and the instructor weighs the various strategies offered and all
students are expected to know the optimal ones and why to reject inferior
ones."
"Along the way, some of this instructor direction is done in a lecture
mode although it would not be fair to characterize the setting as
primarily lecture. The current reform movement cliche, to be "a guide on
the side" instead of a "sage on the stage", is simply not an apt
description of instruction in Japanese classrooms. The instructor is
clearly the "sage" whether guiding or lecturing. During the student
solution stage, instructors are well aware of the approaches being chosen
and offer helpful advice and critical comments. Overall, Japanese
instructors do more traditional lecturing than is common in US
precollegiate classrooms."
regards, Kim Mackey
=========================================================================
Date: Wed, 22 Jan 1997 11:59:43 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Dan Fendel
Subject: Re: Word Problems and the NCTM Standards (fwd)
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
Here is the reply I sent to the Math Forum discussion list.
Dan Fendel
Director Professor of Mathematics
Interactive Mathematics Program San Francisco State University
---------- Forwarded message ----------
Date: Wed, 22 Jan 1997 08:10:29 -0800 (PST)
From: Dan Fendel
To: nctm
Subject: Re: Word Problems and the NCTM Standards
Kim Mackey posted a fairly long commentary on the Interactive Mathematics
Program (IMP) on Saturday, January 18. As one of the directors and
authors of the program, I want to respond in order to clarify some
misleading assertions and correct some misinformation in this posting. I
apologize for the length of this reply, but Mackey's posting requires
detailed comment. (Mackey posted another, briefer comment that referred
to IMP on Sunday, January 19. That one reflects such major misconceptions
about the program that it is beyond specific comment.)
Mackey poses four questions and gives replies to each. In responding, I
will basically follow the outline of those questions, without quoting the
entire posting.
For those who are not familiar with IMP, let me provide some basic
background. Our program is a four-year integrated mathematics sequence
intended for grades 9 through 12. Although the material has been in
development and classroom testing since 1989, it has just begun appearing
in published form, beginning with the Year 1 book, which was released
last summer. Years 2 through 4 will be released one at a time in
succeeding years.
In addition to the student textbooks for each year, there are extensive
teacher guides that provide detailed daily lesson plans, background
mathematics, pedagogical suggestions, sample questions to pose to the
class, and so on. For additional information about IMP beyond what I
supply here, you can call 1-888-628-4467.
>FIRST QUESTION: Who wrote the curriculum?
Mackey's basic information here is correct, but some minor clarifications
are in order.
1. Most of the actual writing was done by Diane Resek and myself. For
those who are interested in formal credentials, I would add that Diane
and I have Ph.D.'s in mathematics from UC Berkeley and Yale University,
respectively.
2. Mackey refers to our colleagues, Sherry Fraser and Lynne Alper (not
Alpert), as "professional developers." Although I'm sure no confusion was
intended, let me clarify that "professional developer" in this context
means someone with experience in professional development of teachers
(inservice workshops and the like) rather than someone who develops
textbooks professionally. Sherry and Lynne are both experienced
secondary school mathematics teachers with many years of experience
developing and leading workshops for teachers. They have played a major
role in working with teachers to help them make the transition from a
traditional program to the IMP curriculum.
>SECOND QUESTION: Is IMP a true reflection of the NCTM >standards?
Nothing much to add here, except that I would prefer to see IMP reviewed
on its own merits rather than in terms of whether or not it "reflects the
NCTM Standards." (I don't mean to suggest that Mackey thinks otherwise on
this.)
>THIRD QUESTION: So what does it look like?
Mackey starts the response to this question with seven statements about
the IMP Year 1 text labeled "initial, non-judgemental
(sic) observations." These statements reflect oversimplifications and
misunderstandings that appear to be (at least in part) the result of
Mackey looking only at the student textbook and not examining the teacher
guides. This is a major error in trying to understand a curriculum that
is also a professional development program. I will comment on several of
these "observations."
Mackey writes:
>2) There is classwork for a total of 137 days.
This is a very literal interpretation of the student textbook and an
inaccurate one. The IMP teacher guides are organized into "days" (like
lesson plans) to assist teachers with planning, and the numbering of
these days is referred to in the student textbook.
Our experience is that these 137 "written days" translate fairly well
into a standard school year, taking into account time for testing,
special events, and so on, allowing for the fact that material planned
for one day will occasionally take longer than a day, and providing time
for teachers to use the substantial collection of supplemental problems
we provide that go beyond the daily lessons.
Mackey writes:
>4) Homework problem sets are short, often 5-8 problems.
This is a very misleading statement. The written length of an assignment
is hardly an adequate measure of its scope. If "problem" meant the type
of mechanical exercise found in traditional textbooks, these would indeed
be short assignments. But in fact, most of the individual questions are
not routine exercises but involve thought-provoking and challenging
problems. They require students to apply concepts to complex situations,
to analyze data and to draw and justify conclusions, to make connections
between concepts, and to synthesize ideas.
Mackey writes:
>6) There is no procedural drill in the text.
I don't know how Mackey defines the term "procedural drill," but I would
disagree with this statement. Although "drill" is hardly our idea of good
homework on a regular basis, we do provide, as appropriate, substantial
opportunity for students to use concepts and to practice skills both in
the context of complex problems and in more context-free situations.
Here are just two examples of the latter:
In an assignment on rules for order of operations, students do the
following task:
None of the statements below is correct as
written. Rewrite them, inserting parentheses
so that the resulting statements are correct
equations.
a. 12 - 8 * 1 + 7 = 32
b. 8 - 15 + 6 3 = 1
c. 7 + 3^2 = 100
d. 24 + 16 8 - 4 = 10
e. 20 7 - 2 + 5^2 * 3 = 79
(I here use * to represent multiplication and ^ to represent
exponentiation. Standard notation is used in the text.)
In an assignment on how to work with the concept of similarity, students
do the following task:
In each of the four pairs of figures below,
assume that the second polygon is similar
to the first. In each case, do these steps:
* Set up equations to find the lengths
of any sides labeled by variables.
* Find the length that solves each equation.
* Explain how you found the solutions to
the equations.
Note: Measuring the diagrams will probably
not give correct answers, because the diagrams
may not be drawn exactly to scale.
(These instructions are followed by four pairs of figures, with sides
labeled by either numerical values or by algebraic expressions.)
Mackey makes four other statements labeled "Judgemental comments" that
appear after "Question 4" but that I think are better dealt with in the
context of "Question 3." I will quote them in full and then respond to
them as a group.
>As a high school math teacher who has taught for ten
>years, there are a number of areas in the IMP text that
>I have difficulty with. On the minor side, when dealing
>with 9th and 10th graders, telling them to write "Some
>ways to..." or "all you can think of..." on an
>assignment as occurs fairly frequently on IMP
>classwork, POWs, and homework, is a recipe for low
>quality work due to teacher subjectivity and student
>desire to do the minimum amount of work for the maximum grade.
>
>2) There is an incredible amount of writing required of
>students in the text. To adequately and honestly grade
>and provide feedback to this writing would eat up a
>tremendous amount of time.
>
>3) The lack of an index is very irritating.
>
>4) The topics seem disjointed and I often have trouble
>seeing the connection between one section of a unit and another.
These comments reflect the danger in simply picking up a textbook off the
shelf and using the written pages alone as the basis for judgment.
Teachers who use this textbook receive extensive support that Mackey
appears to be unaware of. The teacher guides that go with the student
textbook are just one element of that support. Most IMP teachers receive
very substantial workshop experience that helps them to see the
connections that Mackey misses. In addition to summer and school-year
workshops, they are provided with time to meet with each other during
school so that they can discuss what's happening in the classroom, plan
lessons together, and assist each other in developing the mathematical
connections.
Mackey "has difficulty with" the fact that the curriculum requires "an
incredible amount of writing." As IMP teachers know (from workshop
discussions), we don't expect teachers to read everything that students
write. Students can learn from the process of writing even if teachers do
not read all their work or provide feedback about all of it. I would also
note that we give teachers assistance in developing techniques for
reading and evaluating large amounts of student writing without getting
bogged down in all the details.
Mackey comments for a second time here about the lack of an index. This
student text is not intended as a reference work (which seems to be
Mackey's idea of what a textbook should be). The teacher guides and
workshops provide teachers with considerable guidance as to what
mathematics they will find where, so the lack of an index is not the sort
of problem it would be in a traditional text.
As to Mackey's (unnumbered) item 1, consisting of comments on the
specific language used ("Some ways to..." or "all you can think of..."),
I think it makes more sense to judge what the quality of the student work
produced by the work itself rather than by nit-picking the language of
the assignment.
Finally, Mackey's fourth question:
>QUESTION FOUR: How is IMP perceived by the students
>being taught with it and the teachers who are teaching
>it?
Mackey begins by quoting from a web page maintained by Jerry Quesnel, an
Arizona teacher:
>Do Not allow too many below-level students into the
>program. This will make it impossible to work.
Let me clarify what this means: One of IMP's goals has been to provide
meaningful mathematics courses to a broader range of students than has
been done previously, and therefore we suggest allowing some students into
IMP Year 1 who would otherwise have been placed in remedial classes. I
think all that Quesnel means is that if there are too many such students,
it will sink the class. I would venture to say that the same is true of a
traditional algebra class.
Mackey continues to quote from the Quesnel web page:
>Pros and Cons
>1) more fun for teachers and students.
>2) much more time consuming to prepare for.
>3) more students can be successful when compared to a
>traditional approach.
>4) standardized test scores have shown no real change yet.
>5) students do not get enough computation practice.
I assume that we all would consider items 1 and 3 as "pros," and I don't
think they need further comment. I consider item 2 as "mixed" and item 4
as neutral. Item 5 is a "con," but worth some comment.
I consider item 2 (a statement with which I agree) "mixed" because, of
course, teachers already don't have enough time to prepare for their
work, and so adding to their burden is negative. On the other hand, IMP
strongly recommends to schools that they provide extra time for teachers
to do this extra work (and most schools have done so). One of our major
goals is to assist teachers in upgrading their understanding of
mathematics, and many teachers regard their experience teaching the IMP
curriculum as the most successful and rewarding mathematics learning
experience of their careers. Most say that they would never go back to a
traditional style of teaching.
As to item 4: First of all, the school where Quesnel teaches began using
IMP in the 1995-96 school year, so the fact that "standardized test
scores have shown no real change yet" at that school doesn't mean much.
The fact is that we and individual schools have done several studies of
standardized test scores, and all show IMP students doing as well as, and
sometimes better than, students in traditional programs. For instance, at
Philadelphia's selective Central High School, both 1995 and 1996 analyses
of PSAT scores showed statistically significant higher scores for IMP
students than for students at Central in traditional programs.
But it was not our goal to raise scores on standardized tests. What we
have done is keep those scores at least at their existing levels while
adding substantial new content and skills to the curriculum that are not
measured by those tests. For example, our students learn far more about
probability and statistics than students in traditional programs (our
evaluation data confirms this) and our students have more experience
writing about mathematics and dealing with complex problems than students
in traditional programs.
Now for item 5. I guess the key word here is "enough." My guess is that
most educators would say that students in a traditional program don't
have enough mastery of "computation skills" either. IMP does not try to
"out-practice" the traditional programs. We have made the decision that
it's more important to give students meaningful experience with real
mathematics than to drill them in computation so that they can achieve
high scores on timed tests. (This comment needs to be modified, but only
slightly, if "computation practice" is taken to include drill on such
skills as multiplying or factoring polynomials.)
Mackey then makes the following strange statement:
>It is interesting to note that some of Jerry Quesnel's
>comments about IMP mirror those of Professor Hung-Hsi
>Wu's in his review of IMP at Berkeley high school.
I'm not sure what the point is. Two comments only:
a. Which of Quesnel's comments does Mackey mean?
b. Wu wrote the Berkeley report nearly five years ago, based on a
preliminary draft of some of the materials. IMP's rebuttal to this report is
available to anyone interested.
Mackey goes on:
>At other IMP sites there are letters from students
>extolling IMP. At the Mathematically Correct website
>there are several anecdotes about problems with IMP
>including its inability to prepare students for higher
>level math and science classes and the remediation
>sometimes necessary for college-bound students.
Gee whiz! Mathematically Correct has "several anecdotes" about problems
with IMP and has found that remediation is "sometimes necessary." Is
Mackey suggesting that students in traditional programs are always
prepared for "higher level math and science classes" or that they never
need remediation? I doubt it, so what's the point?
(For those who don't know about Mathematically Correct, this organization
is dead-set against the NCTM standards.)
I won't comment on the last components of Mackey's posting except to say
that Wayne Bishop is another vehement opponent of the NCTM standards, as
well as a vigorous advocate of John Saxon's texts, and is hardly a
reliable interpreter of the TIMSS study.
Once again, I'm sorry for the length of this reply, but I saw no alternative.
Sincerely,
Dan Fendel
Professor of Mathematics Director
San Francisco State University Interactive Mathematics Program
=========================================================================
Date: Thu, 23 Jan 1997 09:13:04 -0600
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: David Turkington
Subject: What is a listserv
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
Someone wrote:
>what the heck is a listserv??
Well, a listserv is really nothing more than an interactive electronic
bulletin board. Very similar to the bulletin boards i see on the wall at my
local grocery store. People post messages on it that they would like others
to see and read.
So that people don't have to read messages that are of no interest to them,
each particular listserv is dedicated to one particular topic. There are
currently THOUSANDS and thousands of listservs worldwide. Different
people/organizations maintain them for almost every conceivalble topic. If
you are interested in something in particular, i almost guarantee that there
is a listserv dedicated to that subject somewhere on the internet.
On the technical side a listserv works like this. A computer at some
organization will maintain a list of all the addresses for everyone who has
asked to subscribe to a particular listserv. When one of the subscribers
sends a message to that computer (sends a message to the list, as we say) it
will automatically echo that one message out to all the addresses subscribed
to that list.
There are always two addresses associated with each listserv. One is for
administrative use and the other is for posting messages. If you want to
subscribe/unsubscribe to/from the list you send a message to one address. No
one else will see this message. If you want to post a message so that
everyone else will get a copy you send your message to another address.
In the case of our IMP Listserv, the computer that maintains the list of
subscribers is at the University of Illinois at Chicago. The addresses you
use to subscrive/unsubscribe and post messages can all be found on our IMP
Web pages at http://www.math.uic.edu/~cpmp/imp.html
If you have other questions, or would like me to try and make this clearer,
feel free to send me a note at dturk@uic.edu. I'm the impteach list owner.
Thanks for your interest.
=========================================================================
Date: Thu, 23 Jan 1997 10:36:27 -0600
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: David Turkington
Subject: IMP Web pages
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
I'm sorry. I told you the wrong address for the IMP Web pages in the last
message i posted.
The correct address is http://www.math.uic.edu/~cpmp/index.html
Sorry for the mistake! :-)
=========================================================================
Date: Fri, 24 Jan 1997 12:37:14 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Dan Fendel
Subject: Washington Post
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
Marianne Smith (IMP Director of Communications) asked me to forward this
article from the Washington Post to the listserve.
Dan Fendel
Director Professor of Mathematics
Interactive Mathematics Program San Francisco State University
U.S. Struggles To Solve Its Math Problem Time, Teaching Style Appear to Be
Factors
By Rene Sanchez and Robert O'Harrow Jr.
Washington Post Staff Writers
Thursday, January 23 1997; Page A01
The Washington Post
The eighth-graders at Jackson Middle School in Fairfax County knew what
they were in for as soon as they walked into math class. On a screen in
front of the room, their teacher, Eugene Pair, had projected six
equations next to the words "No Calculators."
The class began with groans and complaints. But Pair was unapologetic.
"You guys have been doing this since the fourth grade," he said, "so it
should be no problem."
For the next half hour, writing on an overhead projector, Pair showed how
to solve the problems. Then he gave the students 20 more equations to
tackle in seven minutes. He spoke, they listened. Then they took to the
task with pen and paper.
This is the traditional approach to teaching math, an integral part of
schools across the nation. It relies on textbooks, repetitive
problem-solving and drills to gauge what students know. Like many
educators, Pair believes in it. "The structure is good. It works," he said
one recent afternoon after class.
But now, those venerable classroom habits are under attack.
A landmark study comparing how American students fare in math to their
peers in other industrial nations, such as Germany and Japan, recently
directed sharp criticism at schools for what they expect of students, and
at teachers for how they instruct them.
Relying on math formulas or drills in class, the study suggests, bores
many students and undermines their performance. In many other nations,
teachers are putting more emphasis on creative learning exercises that
challenge students to discover math concepts on their own -- not just plug
numbers into equations.
Since its release late last year, the study has ignited widespread debate
about what schools ask of students and teachers in math. President
Clinton took up the issue during a visit yesterday to schools in suburban
Chicago, where he urged educators to raise math standards and to improve
how they teach the subject.
"What our students learned in math in the eighth grade is learned in Japan
in the seventh grade," Clinton said. "Even more troubling to me . . .
students in Germany and Japan learn 10 to 20 math subjects in depth; our
students are asked to cover 35 math subjects and, therefore, don't learn
any of them in depth."
As part of the study Clinton referred to, a half-million eighth-graders in
41 countries were tested in math. Researchers also surveyed teachers,
analyzed curricula and videotaped class instruction around the world.
What they found was distressing.
"American students are taught very quickly how to do things in math,"
said Eugene Owen, an analyst with the Education Department who helped
coordinate the study. "In a country like Japan, there's more emphasis on
getting students to understand underlying concepts in math. If an
American student forgets a formula, he tends to be up a creek."
Nationwide, many schools are reexamining their math programs and making
changes in style and rigor. For the first time, some are now requiring
ninth-graders to take algebra, for example. Nationally, math scores are
creeping upward.
Yet the study contends American students still rank below the
international average in math, even though they spend more class hours on
math and get more homework. That suggests the roots of the problem are
deep. Solving it, educators say, will present at least one profoundly
difficult task: changing the mindset of teachers.
"If you want teachers to lead children in hands-on learning, teachers have
to experience that themselves, and few have," said Richard J. Murnane, an
education professor at Harvard University. "Most have been taught with a
chalk-and-talk method. Changing that is not easy, especially if the only
training you get is a workshop now and then. It takes much more time and
perseverance."
The experience of Fairfax County is a microcosm of the struggles facing
many school systems as they try to teach math, a subject educators and
employers often rank second only to language and reading in terms of
importance.
Student math scores in Fairfax are higher than those in most other
districts. Yet even in this prosperous system, the challenge to change
teacher habits is immense.
"Teachers tend to teach the way they were taught, and they were all taught
by a teacher giving three examples and saying, `Now you practice,' " said
Tom Nuttall, Fairfax's math coordinator. "We're talking about a cultural
change here."
The difficulty of achieving that is most apparent in elementary schools,
where educators say teachers tend to have the least familiarity with math,
and show little inclination to learn more.
Last year, Fairfax offered elementary math teachers two training courses.
In the easier session, the emphasis was on teaching "methods." About 600
teachers signed-up. In the other, they had to learn the "content" of what
they teach. Six teachers came.
"If you suffer from math anxiety, I don't know how you can teach the
subject, other than following the book," Nuttall said. "We still hear
stories about teachers who say to students, `If you're good at recess
today, you won't have to take math.' "
Fairfax officials began overhauling math instruction four years ago.
First, they pared back the material students were expected to learn, to
give teachers more time to focus on lessons. One of the faults the study
found is that even the best American teachers have to race through work to
keep pace with school curricula.
Fairfax teachers were encouraged to be creative by using geometric blocks
or other props to illustrate math concepts. Middle school students were
urged to take algebra, a subject traditionally reserved for high school,
but which other countries teach earlier. In the last five years, the
proportion of Fairfax eighth-graders taking algebra has soared from less
than one in five to almost half.
But even teachers promoting this revamped approach say having it take root
is a constant battle. Consider Deborah Gutman. She helped develop the
county's math curriculum and she teaches at Jackson Middle School.
Her students rarely use textbooks. When she assigns equations, she rarely
solves them at a blackboard. Instead, she encourages students to analyze
problems with brightly colored blocks that represent abstract equations.
Then she asks them to defend their solutions. The problem: It takes time.
Gutman does not have much of it.
One recent afternoon, she wanted to teach the concept of proportional
reasoning. Rather than work through a series of equations, she asked the
12-year-olds to imagine baking batches of chocolate chip cookies. She held
up cartons of sugar, flour and butter and asked them to calculate the
lowest possible cost per dozen.
Students were intrigued. But by the time they had tried a few practice
problems and divided into groups, there were only 12 minutes left in the
47-minute class. Gutman dashed around the class to encourage the
experiment. Several students became frustrated. "I don't get it," said
Erin Baumann, 12. Other students nodded in sympathy. Disappointed, Gutman
had to repeat the lesson before moving to new material. To save time the
next day, she showed students how to find the solution instead of letting
them do it. Because of the way her school schedules it classes, on some
days Gutman has twice the time to teach the lesson. But even then, it's
often not enough.
"I'm always looking at the clock," Gutman said. "If I had these kids an
hour and a half a day, five times a week, I know their test scores would
be higher."
Nationwide, many schools have begun raising their standards in math. But
the study has raised cautions about that charge. Higher standards will not
be meaningful, it contends, if teachers are chronically short of time in
class and are judged largely by how well they get through a textbook each
year.
Using a textbook is not an inherently bad idea; most are selected to match
the goals schools have for students, and they lend structure to a class.
But a teacher who focuses too much on plowing through material can lose
sight of whether students are learning. There are often more creative
ways to engage students,
the study suggests.
It also reveals differences in teaching styles. One of its chief features
was videotaped analysis of how American math classes are taught, compared
with instruction in nations where schools seem to be having more success.
Researchers said they found striking consistency in the habits of
American teachers, even though, unlike most other industrial nations, the
United States does not have a strict national model for curricula or
teaching training.
"When you look at it, you really think there is a formal American style,"
said James Stiegler, a psychology professor at UCLA who coordinated the
videotaping project. "We found that American teachers develop concepts far
less frequently. We tend to practice routine math procedures more than
anything else."
There were other distinctly American habits: Teachers put great emphasis
on praising students. Many also created drills to give students some taste
of academic success, in part by deliberately asking questions with obvious
answers.
Those tactics, in moderation, are not all bad, the study contends. Some
students can be served well by the approach, and some of the teaching
traits found in other nations -- like the total absence of praise for
students -- struck researchers as too harsh.
Still, they worry that American teachers dwell too much on praising
students for simple accomplishments and lack the patience to let students
gradually discover lessons on their own -- a process some educators dub
the "Aha!" phenomenon.
"American teachers were very uncomfortable with having students confused
for even a little while," Stiegler said. "You see them stopping a lesson
and rushing over to a student saying, `Let me show you how.' In Japan and
other countries, teachers like to let kids struggle, even have the wrong
answers for a while, to try to get them to discover something. When they
do, they seem to have more mastery of a lesson."
There is still great tension among math educators about which approach is
best. Some say the study overstates the benefits of teaching "concepts"
and ignores the value of other methods. Some school systems are still
designing curricula that stress equation-solving skills and abstract
thinking. Those methods, they insist, have been successful for generations
of students.
At Fairfax's Jackson Middle School, the curriculum includes much of what
the study advocates. Even the length of classes has been expanded. Yet how
material is taught still varies. The reasons for that, teachers say, are
compelling: lack of time to prepare, lack of training, and too much
material to cover.
Pair, the eighth-grade teacher, said the need to prepare students for high
school often overwhelms his effort to try new teaching styles. But Jackson
Principal Michael Doran said teachers sometimes feel that pressure too
keenly.
Jackson is narrowing the aims of math instruction to give teachers freedom
to try new approaches. But Doran said that too often math is merely one of
many pressing priorities in schools. "We try to do too much," he said. "If
we're going to be so good at math, we might have to give up something as a
nation. And it might not be worth it."
There are other hurdles. Pair said he is torn between his desire to
applaud the effort of struggling students and the need to push them harder
to master fundamentals. That tension is exacerbated by the county's new
grading philosophy, which requires educators to assess a student's
progress, not just test scores. Pair also said there is a philosophical
issue: Should teachers focus on topping international comparisons, or work
harder to improve students who struggle? He worries the newer methods
could leave some students behind.
"I like to think of myself as a teacher who can raise the bottom rather
than lift the roof off," Pair said. "What matters to parents is, `Do you
know my kid? Is my kid doing better? Is my kid going to be prepared for
the next step?' "
@CAPTION: At Jackson Middle School, Deborah Gutman, right, helps Erin
Baumann, left, and Tricia To solve problems with blocks representing
equations.
@CAPTION: Eighth-grade teacher Eugene Pair, center left, goes over pop
quiz results with, from left, Jerman Yassin, Vinh Thach and Carlos Duron.
@CAPTION: Jackson Middle School teacher Deborah Gutman, who helped plan
the Fairfax County math curriculum, works with seventh- graders, from
left, Jesus Falcon, Jessica Bolling, and Luis Viayrada.
Copyright 1997 The Washington Post Company
=========================================================================
Date: Sun, 26 Jan 1997 20:20:26 CST
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Carol Berland
Subject: Update Need Stats
Thanks to everyone who responded to my note, "Need for Stats". I used everyone
's response, but to no avail. We are still offering IMP years 1 to 3, but we c
ould not yet get permission for year 4. Despite all the evidence, our principa
l can not believe this is college preparatory and she still must see our state
IGAP scores. Strange, but of course there is a lot more to the story
but not for public laundry washings. We still have a teeny slim chance and we'
re not giving up yet. However, I just wanted to thank everyone for their suppo
rt.
I'm still having a good time in the classroom at least.
=========================================================================
Date: Sun, 26 Jan 1997 22:42:13 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: ChewCK@AOL.COM
Subject: Re: Update Need Stats
Carol, did you point out the Eaglecrest data - the difference between year 3
and year 4. Year 4 ties everything together.
=========================================================================
Date: Mon, 27 Jan 1997 10:38:15 -0600
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Margaret Small
Subject: videos
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
We have been using Buck and the Preacher for Overland Trail. It is more
engaging than just PBS specials on westward expansion. I am trying to get
good videos for each of our schools. Has anyone used other videos besides
the Powers of 10 (Alice) and Bees? Suggestions? Also, a few years ago we got
a color animated version of the Game of Pig for IBM machines. Now we only
seem to have access to the dos based pretty boring software. does anyone
have a cite for the more active version of the game? It showed graphic dice
rolling. Also, since we don't have LOGO in the published version, has anyone
developed other computer applications for IMP 1? Using spreadsheets or WEB
sites?
Thanks for your assistance.
====================================================================
Margaret Small Interactive Mathematics Program
Chicago Secondary Mathematics Improvement Project (CSMIP)
Institute for Math and Science Education (IMSE)
University of Illinois at Chicago Chicago, Ill
email: msmall@uic.edu
home phone:312-588-4016
=====================================================================
=========================================================================
Date: Mon, 27 Jan 1997 20:51:44 +0000
Reply-To: brlawler@ccsd.k12.co.us
Sender: Interactive Mathematics Program
From: "Brian R. Lawler"
Organization: Cherry Creek Schools
Subject: Is it statistics you need?
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
I'm making a guess about your situation. You're principal will not
change her mind no matter what statistics she sees.
I have another idea. In the past several months I've heard so many
statements from my Year 4 kids to the tune of "now I see why we did
these things the past 3 years" or "I wasn't so sure, until this year."
Many of these students would be excited about an opportunity to write
letters describing their experiences in the Year 4 curriculum. Many
already have. And believe me, their writing elegant (no suprise after
IMP) and from the heart.
would this be a help?
=========================================================================
Date: Tue, 28 Jan 1997 15:46:21 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: IMP
Subject: Photos
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
Hi IMP teachers....
Yes, we could still use some photos for IMP 2 (Alice and Cookies) and for
all units in IMP 3...and for any wonderful, clear, generic IMP photos of
students working....
Remember the system.....
Send only photos for which we have all student permissions, or include
the new student permissions along with the photos...
Number the photos with a circle dot on each photo.
On a separate sheet...write the following for each numbered photo:
Your name and school on the top of the list...
Names of people in the photos..left to right
unit
activity
photographer
Please send all good quality photos to:
Lynne Alper
IMP
Box 2891
Sausalito, CA 94966
Also, remember that Key will reimburse you for all expenses...just
include the receipts to me...and, no paper clips...actually post-its are
terrific...
Thanks...looking forward to including more schools in IMP 2, IMP 3, and
IMP 4 texts...and...we always need additional photos for the Teacher
Editions...even of teachers working at the inservices...
Cheers...Lynne
=========================================================================
Date: Wed, 29 Jan 1997 20:36:33 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Kathy Juarez
Subject: State Board appointments
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
The following letter appeared on another listserv but seems relevant here.
You may wish to join your language arts colleagues in writing Lockyear and
your state senator.
------------
(snip, snip)
Subject: Letters re appointment of Dronenburg & Hume
I just wanted to remind CATENet members that this is the month
in which the Senate Rules Committee will make its recommendation to the
Senate on Wilson's reappointment of Dronenburg and Hume. A two-thirds
vote of approval is required for such reappointment. I am attaching a
sample letter to Lockyer with his address included. He also has an
email address: blockyer@kcp.com
Senator Bill Lockyer
Tenth District
22634 2nd Street
Hayward, California
Dear Mr. Lockyer:
Two members of the SBE are up for reappointment this month: Kathryn
Dronenburg and Jerry Hume. These are two of the members who want to
change the make up of the Instructional Resources Panel for Mathematics
to reflect their agenda....an agenda which would deny higher order math
skills to most kids and keep math in its historically ineffective mode
of mind-numbing, repetitive, and meaningless tables of problems. They
were also active in the removal of two publishers from the recommended
list for language arts adoption and the attempt to add two totally
unbalanced programs, again reflecting their fear of programs which
support self reliance and emphasis on thinking and personal response.
As chair of the committee which will recommend action on these
appointments, you are in a position to suggest new members who have a
better understanding of the professionalism required to make decisions
that impact children all over our state. It is unfortunate that almost
anyone who ever learned to read and add considers him or herself to be
an expert in those fields. I do not want my child's education
influenced by a few petty bureaucrats with an agenda of their own.
Please give your most serious attention to this urgent situation. Your
appointments will affect children in California for better or for worse
for years to come.
Sincerely,
I hope we can flood the committee with letters. Writing to your
own State Senator would also be a good ideas as the entire Senate will
be voting on these reappointments. Thanks, Joann Kersten
Kathy Juarez
Fulton Valley Prep at Piner High School
Santa Rosa, California
kjuarez@metro.net
=========================================================================
Date: Thu, 30 Jan 1997 05:58:55 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: ChichaL@AOL.COM
Subject: Re: videos
Are you familiar with the Cal Poly Videos entitled Project Mathematica? The
have several really goo computer generated videos such as one on the Theorem
of Pythagoras, one on PI , and another on Similarity. Actually bits and
pieces of the one on Polynomials is good too.
The cost about $20 a piece.
I do not have the address at home...I can bring it tomorrow.
=========================================================================
Date: Thu, 30 Jan 1997 15:37:58 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: hessnesh@HUGSE1.HARVARD.EDU
Subject: Re: videos
In-Reply-To: <970130024732_2025042867@emout01.mail.aol.com>
MIME-version: 1.0
Content-type: TEXT/PLAIN; charset=US-ASCII
The Cal Tech videos are excellent and fit in very nicely with IMP. The
ones we have used are: The Story of Pi, Similiarity, Pythagorean Theorem,
Sine & Cosine I, and Sine & Cosine II. Each comes with a teacher guide.
The cost is now closer to $30 each and is sold through the Cal Tech
Bookstore. The provide very quick service. (NCTM no longer offers them
for $20 each.) WE expect to have some students do research projects using
them as a step-off point. The graphics is terrific.
On Thu, 30 Jan 1997 ChichaL@AOL.COM wrote:
> Are you familiar with the Cal Poly Videos entitled Project Mathematica? The
> have several really goo computer generated videos such as one on the Theorem
> of Pythagoras, one on PI , and another on Similarity. Actually bits and
> pieces of the one on Polynomials is good too.
>
> The cost about $20 a piece.
>
> I do not have the address at home...I can bring it tomorrow.
>
=========================================================================
Date: Fri, 31 Jan 1997 05:57:22 -0800
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: Linda Steiner
Subject: GSDMC
Mime-Version: 1.0
Content-Type: text/plain; charset="us-ascii"
I am giving a presentation at the Greater San Diego Math Conference
entitled "Changing Parent Concern to Parent Involvement". My portion deals
with the topic "If I could do it over, knowing what I know now, I
would....."
If you have any ideas that have been successful in your District, please
forward them to me.
Thanks
Linda Steiner
Orange Glen High School
Escondido, Ca.
=========================================================================
Date: Fri, 31 Jan 1997 09:38:35 -0500
Reply-To: Interactive Mathematics Program
Sender: Interactive Mathematics Program
From: ChewCK@AOL.COM
Subject: Re: GSDMC
Linda, I have some ideas - but first clarify the "if I could do it over"
part. Who is the "I" part - teacher or parent?
Sheryl Chew
=========================================================================
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