APPENDIX II : CORE PLUS IN TRAVERSE CITY
In this appendix there are several articles from The Traverse City Record-Eagle. The one relating to Bloomfield Hills is in the body of the update.
By
MICHELLE
KELLEY
Record-Eagle staff writer
TRAVERSE CITY - Complaints to the Traverse City Area
Public Schools' Board of Education about math curriculum deficiencies were not
ignored Monday.
In a unanimous decision, the board approved short and
long-term changes to the district's math curriculum, which offers students only
the Core-Plus Mathematics Program.
Core-Plus math teaches students how algebraic formulas
apply to real-life situations, as opposed to traditional math that stresses
rote learning of formulas.
Before the decision was made, the board heard testimony on
both sides of the math debate.
"I've been downright disgusted with the math program
here," said Jessica Stoltz, a recent Traverse City graduate.
Stoltz, who chose to complete her high school math
requirements at Northwestern Michigan College, said she often came home from
school in tears because of difficulty in her high school math classes.
"That's not right," she said.
Mike Wilson, a teacher at East Junior High School and a
Traverse City graduate himself, supported the Core-Plus program.
He explained his experience in traditional math classes as
a student and as a teacher using Core-Plus.
"I'm learning more about math as a teacher than I did
as a student," he said.
Parent Deborah VanWagoner was not for one program or the
other.
"I want my children to have a choice," she said.
Board members and administrators acknowledged the gaps in
learning faced by some students, and after a number of meetings with the
district's math department came up with a proposal that may solve the
deficiencies.
The approved proposal includes short-term (one to four
weeks) changes for this year's seniors. They are:
- Identifying students with algebra/geometry deficits
based on the 1999 ACT test, and other information available.
- Developing and implementing a pilot algebra/geometry
class(es) option for these students.
- Administering an appropriate diagnostic test to students
with perceived deficits in algebra/geometry.
Other short-term (one-12 weeks) changes for freshmen,
sophomores, juniors include:
- Complementing the Core-Plus Mathematics Program
curriculum with units that will prepare student for ACT, PSAT, SAT, TIMSS and
MEAP tests as well as college level mathematics.
- Planning with staff and train for the implementation of
above units.
- Aligning the curriculum in the Academically Talented and
Accelerated core math program. Use a combination of Core-Plus and academically
talented curriculum.
- Administering a diagnostic test to all students.
- Providing support to at-risk and special needs students.
Long-term (three to nine months) changes for grades seven
to 11 include:
- Identifying, recommending and implementing an
alternative choice (besides Core-Plus) in the secondary mathematics curricula
that research has demonstrated to be successful elsewhere.
The alternative choice will be developed by a task force
comprised of students, staff and community members.
"I'm so thrilled we're going to have a choice for our
students, parents and teachers," said Dianne Walker, a Central High School
math teacher.
Related stories:
Pros and Cons of Core-Plus
Core Math is result of decade of development
Math controversy rages in Bloomfield Hills
By MARJORY
RAYMER
Record-Eagle staff writer
TRAVERSE CITY - Communities nationwide are being divided by a new way of
teaching math.
Horror stories of top high school math students placed in
college remedial classes, calculator dependency and lack of basic algebra
skills have led to demands for a back-to-the-basics approach here and
elsewhere.
"You cannot replace algebra with a calculator,"
said Gregory Bachelis, a math professor at Wayne State University and leading
critic.
Advocates for the new form of mathematics, such as the
Core-Plus Mathematics Project used in Traverse City since 1994, will outperform
traditional - if only given a chance.
"Core Math isn't a bizarre new math. It is a
sophisticated math. We're doing things we've never done before," said Dan
Fouch, math curriculum coordinator in Traverse City.
Gone is the math most people remember: pages of formulas,
followed by problem after problem for students to solve using memorized
formulas from algebra, geometry, trigonometry classes.
In its place are "investigations" with teams of
three and four students working together to solve real-life problems that
combine multiple traditional classes, often using graphing calculators.
Formulas are taught as concepts. Students learn how and why they work but don't
necessarily memorize them.
This develops critical thinking and problem-solving
skills, instead of encouraging robotic formula application, reformers say.
Mathematicians on both sides of the academic debate are
armed with numbers, theories and studies attempting to prove not all ways of
teaching math are created equal. Which is greater, however, appears to be a
function of who backed the study.
This much is obvious: The most aggressively reforming
school districts - like Traverse City - are being forced to backpedal.
The first class of all-Core instructed students won't
graduate from Traverse City until next year.
Yet, critics of reform math won a major concession in
Traverse City last week: No longer will Core-Plus be the only option and some
of those old worksheet-style assignments will return.
"We need to respond to parents," explained Jim
Rossi, interim superintendent who began his career in education as a math
teacher.
There will be choice. Yet, this real-life story problem
remains unsolved: Is new better than old?
PERCEIVED PROBLEMS
"I feel cheated," said Lindsay Dilloway, a 1999
Traverse City graduate. "It was my education, and they didn't prepare me
well enough to go on to college."
Dilloway got A's in her high school math class but scored
so low on her placement test at the University of Michigan that she will take
remedial math this fall.
"I was thinking about becoming an engineer, but I
just don't know now," said Dilloway, who believes she might have scored
better had she been allowed to use a calculator as she frequently did in Core
Math.
She took an algebra class at NMC this summer to prepare
her for U-M.
"I had things I'd never seen in high school math and it
was equal to ninth-grade math," Dilloway said, but added, "I aced
it."
There are countless other stories. Chris Eichenlaub, a
senior, paid tuition to Northwestern Michigan College to take traditional math
classes after trying Core-Plus for one year.
"I got so frustrated, because I was just so
bored," Eichenlaub said.
Lauren Kruer, also a senior, is studying geometry,
trigonometry and fractions by CD ROM because she misses the step-by-step
instruction of traditional math.
"Each thing has its orderly step. Each thing has its
time and place," she said. "Why change something that was already
working?"
There also are complaints about too much essay writing,
heavy pressure to cheat within the group atmosphere and not enough specialization
for more advanced students.
"You've got kids with incredible intellect with kids
that are remedial," Eichenlaub said. "They say there is a
philosophical concept for that. That's just like communism. It's a wonderful
philosophy, but the reality just isn't there."
One local student went so far as to convey his resentment
of the reform math program through two bumper stickers: "Friends don't let
friends take Core" and "Core Happens."
Dianne Walker, a 30-year veteran teacher, said she sees
too many of her students struggling.
"I get calls weekly for tutoring," Walker said.
"My personal opinion is we need to do something different. There are lots
of reform maths out there. We just chose the wrong one."
George Weber, a local CPA, led a self-described
"uprising" of parents that successfully demanded Traverse City offer
an alternative to Core-Plus.
He was appalled by stories he heard from other
dissatisfied parents of mostly college-bound students.
And, he wasn't happy about the prospect of paying for
additional college courses for his children to learn what he believes should
have been covered in high school.
"They tell us, 'Your kids will always do fine.' Well
we don't want our kids to do fine. We want them to excel," Weber said.
STORIES VS. STATISTICS
Core supporters say early indications are that the program
is preparing most students well.
"We are instantly held accountable," said Julie
Faulkner, curriculum consultant for Traverse City schools. "Over the long
haul, if given time, we could really prove ourselves, and we already have
indicators that we are going in the right direction."
One of the key indicators: class enrollment. More students
are taking more math.
At Traverse City West Senior High School alone, the number
of math sections for seniors has increased from seven to 11 sections this year,
teacher Tamie Rosenburg said.
That is more than 100 additional students taking a full
four years of math, even though graduation requirements only mandate two.
In traditional math, usually only a small fraction of
seniors chose to take any form of math.
"They were more or less the survivors, the people who
could do math," Rossi said.
There are other early successes being reported:
- Of this year's seniors, 88.6 percent will receive
endorsed diplomas in mathematics by passing the Michigan Educational Assessment
Program test. Scores are broken into four levels with the first three receiving
an endorsement. Nearly 30 percent more Traverse City students scored in the top
level than the state average.
- More Traverse City students received college credit by
passing advanced placement calculus tests last year than ever before. In 1995,
eight students (34 percent of those who took the test) received credit. In
1998, 27 students (more than 40 percent) passed. In 1999, early returns
indicate about 50 students will receive college credit.
- Average scores on the math portion of the ACT test have
stayed relatively constant, rising from 21.7 in 1993 to 22.5 in 1998.
"I wouldn't say we're doing any better, but I'd say
they are holding their own," said Rossi, the interim superintendent.
Admissions experts at Northwestern Michigan College
support Rossi's view.
According to data collected for its math placement test, a
slightly greater percentage of students are being placed in remedial classes -
but not what the college considers a significant number.
In fall 1998, 63 percent of Traverse City students were
placed in remedial math classes (any course lower than college algebra). That
compared to 62 percent in 1997, 54 percent in 1996 and 58 percent in 1995.
Also in 1998 and 1997, fewer students took math at the
college because the public schools began offering more advanced placement
courses.
"The trend data shows that Core students do as well
or better than traditional math students," said Christian Hirsch,
Core-Plus Mathematics Project director at Western Michigan University. "All
that we needed was a chance to get the curriculum developed and give it a
chance to work. (Critics) wanted proof of the curriculum's success before it
had even been developed."
Statistics, of course, even in a debate about mathematics,
are always doubted by the opposing view.
As for all the horror stories, well, there always have
been and always will be students who score lower than expected on tests,
administrators said.
As the NMC figures indicate, more than half of Traverse
City students never exposed to Core-Plus were placing in remedial math.
REFORMING REFORM
"I don't think people are proposing going back to the
way we taught math 20 years ago," Weber said.
And, yet, the bitter debate - which some scholars have dubbed
the "math wars" - has raged on.
Why?
"For some parents it might be just a fear of change,
a failure to recognize in the world in which we live, the only thing that is
constant is change," Hirsch said.
The students say their anger stems from a resentment over
being used in what they term an unsuccessful math experiment.
"How dare you play gerbil with me?" Eichenlaub
said. "This is a public high school, not some science lab."
Students remain especially bitter that they were not given
a choice on whether they wanted to participate.
Traverse City first offered Core Math in 1994 to a select
group of about 100 students.
The next fall students were given the option of Core or
traditional math but were not allowed to switch after selecting which path to
take. The student body split 50-50.
During the next year, the 1996-97 school year, Traverse
City began phasing out traditional math. Only Core was offered to
ninth-graders, who are now seniors.
"If a high school is going to offer this, and if you
want to take the risk of taking this program, then fine," Dilloway said.
"I didn't have a choice."
Critics say the program's failures are exhibited in its
own revisions of the curriculum, which have added basic algebra computation and
supplemental worksheet-style booklets to help struggling students.
Hirsch, the Core-Plus Mathematics Project director, said
these are signs of improvement - not of failed beginnings.
"I would say that students who studied the pilot
version probably studied a version that is not as good as the second
version," Hirsch said.
"But it is not at all clear that the pilot version
wasn't better than what they would have been studying. I would maintain that it
was at least as good."
Schools like Traverse City led the way, but Core Math soon
will become commonplace.
Some 100 schools are expected to use the Core-Plus
curriculum this fall. Hundreds of others follow similar course work, in classes
sometimes called connected or integrated math.
Walker, the teacher, said she sees first-hand that
students can't complete basic algebra problems. Students need calculators to
subtract negative numbers, she said.
"This new reform mathematics is saying there are
skills students don't need to know, and to some extent maybe I would agree with
that, but not to the extreme they are taking it," Walker said.
"Colleges still expect students to have these skills."
Yet, Diane Moore, who has taught for more than 25 years,
said she sees students who are actively exploring math, something she never saw
in her traditional math class.
"I walk around the room and hear students talking
about problems, solving problems. They are engaged in math, and they are doing
it for an hour," Moore said. "There is no way I could go back."
Traditional math was failing students, Fouch said. The
school district simply tried and will continue to try to offer students the
best curriculum available, he said.
"We are obligated to make sure our kids are prepared.
Our students need to be competitive on a national and international
level," Fouch said. "Our kids need to learn how to learn how to take
a problem and solve it even if it is something they've never seen before."
Related
stories:
Pros and Cons of Core-Plus
Core Math is result of decade of development
Math controversy rages in Bloomfield Hills
Mathematics Achievement for Andover and
Lahser Students at the University of Michigan 1995-98
Source: Data from U-M registrar's office. More than half
of Bloomfield Hills students go to U-M.
- Math grades steadily climbed for Andover students from
1995 when the average was 2.76 (B-) on a 4.0 scale to 3.07 (B) in 1998. Lahser
students' did not show the same consistent growth. Their math scores started at
2.14 in 1995, peaked at 3.15 in 1996, eventually dropped back down to 2.57 in
1998.
- In 1998, Andover students' average math grade was a half
point better than their Lahser counterparts.
- A similar percentage of students from both schools
placed into pre-calculus - math 105 the lowest course offering at U-M - in
1998, 8.3 percent from Andover and 8.6 percent from Lahser. Students are
expected to take calculus or higher courses in their first year.
- Placement in pre-calculus stayed consistently near 8
percent for Andover students, in all years except 1997, the first class taught
entirely by Core-Plus. Lahser students also stayed close to the 8 percent mark
being placed in pre-calculus, except the first year 1995, when more than 20
percent were placed there.
Study's conclusion: Andover achievement for the years 1995
and 96, when a traditional curriculum was in place, is not as strong as that of
the years when the Core-Plus Mathematics program is in place.
Author: Arthur F. Coxford, math professor at the
University of Michigan, co-director of Core-Plus Math Project
Criticisms of study: The study includes a small number of
students. It only includes students who went to U-M and took math in their
first year. At most the study is based on 36 students in any given semester.
Study done by researcher with personal bias.
Outcomes Analysis for Core Plus Students at
Andover High School: One Year Later
Source: Data comes from an analysis of results from a
survey of students.
- Although both groups of students maintained nearly
identical grade-point averages in high school, their college achievements
showed drastic differences.
- 15 of 23 Core-Plus students who attended Michigan State
University were placed in remedial math. Two others who placed in math 103,
intermediate algebra, withdrew to take remedial math instead. Only 1 in 23
placed in a standard pre-calculus course.
- The average grade-point average for Core-Plus grads was
1.9 compared to 2.6 for traditional math students.
- Andover students on average ranked the usefulness of
high school math in college at 1.75 on a scale from 1 to 5. Lahser ranked the
usefulness of high school math at an average 3.46.
- Andover students report dropping to near the 50th
percentile in the math portion of the SAT test, compared to the 76th for Lahser
students. Verbal scores were 74 at Andover, 79 at Lahser.
Study's conclusion: Students felt Core-Plus failed them.
Extreme care is needed before adopting a program of this type.
Authors: Analysis by R. James Milgram, Stanford University
professor. Survey by Gregory Bachelis, math professor at Wayne State
University. Both are active in Mathematically Correct, a national opposition
group to reform math movement.
Criticisms of study: The data, including grade-point
averages and standardized test scores, is all self-reported by students which
leads to inaccuracies. Researchers used invalid generalizations by referring to
the pilot curriculum as Core-Plus, which has gone through several improvements
and modifications since the survey was conducted. Study done by researchers
with personal bias.
By MARJORY
RAYMER
Record-Eagle staff writer
TRAVERSE CITY - It takes a bit of a history lesson to fully understand Core
Math.
The reform math curriculum taught in Traverse City is the
culmination of a decade of study, development and application.
The ideas behind the Core-Plus Mathematics Project were
actually developed and debated on the national level in 1989 when the National
Council of Teachers of Mathematics set new standards for math education.
Focus then shifted to creating an interactive learning
atmosphere, developing students' critical thinking and problem-solving skills,
incorporating technology and making all students mathematically literate.
"Mathematics continues to grow and change," said
Christian Hirsch, director of the Core-Plus Math Project. "People need to
know more and different mathematics than they did in the past. Quantitative
thinking is the new literacy.
"Can you recall yourself being in social situations
in which a person admitted they didn't at all feel comfortable with basic
computation? They never would have admitted that about reading. People need to
recognize that quantitative thinking is as important as reading."
In 1992, three years after the new math standards were
unveiled, the National Science Foundation funded the development of four
curriculums based on the new standards.
One of those five-year grants went to Western Michigan
University, which produced the Core-Plus Math Project and put Michigan and
several of its communities in the center of the debate between new and old.
High schools had to apply for a chance to serve as one of
more than 30 Michigan schools to pilot the curriculum. Traverse City was
accepted in the second year and began using the curriculum on a limited basis
in 1994. Two years later the school system adopted Core-Plus as its sole math
curriculum.
In 1997, WMU received another five-year grant to develop a
fourth year of the core curriculum for high school seniors.
Early on, Core-Plus met criticism that it did not fully
develop students' basic algebraic and geometry skills. Many of those criticisms
remain today.
"We have in each revision placed more attention on
algebraic skill," Hirsch said. "The whole idea for piloting is to
find out what works well and what doesn't so it can be improved."
Also, new this year is a supplemental packet of exercises
that closely resembles traditional math problems.
"I think it is important to understand that this
curriculum is tested and evaluated, and improved and tested, and evaluated and
improved again so that the final published curriculum has gone through several
series of tests and refinements - which stands in contrast to most book that go
into use virtually untested," Hirsch said.
This fall, about 100 schools in Michigan are planning to
use the Core-Plus curriculum, he said.