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Interview
with University of MD Mathematics Professor
Jerome Dancis
The “Math Wars” have
been fought since the 1980s. The
debate centers on what Mathematics
should be taught and how it should
be taught. In the following interview,
Dr. Jerome Dancis talks about the
math wars, why mathematics education
standards are so low in Maryland,
and what we can do about it. Dr.
Dancis is an Associate Professor
Emeritus in the Mathematics Department
at the University of Maryland,
College Park.
The
following is an abridged version
of the interview with Dr. Dancis.
The full version is available at
http://www.baltimorecp.org/newsletter/jerome_dancis.pdf.
(PDF file)
Q: The following quote from
Education World describes the Math
Wars:
On
one side of the conflict are the
traditionalists who claim that
students should learn math by
memorizing and practicing basic
facts and skills. On the other
side are proponents of what is
often called “whole math,”
who deride the old “kill
and drill” methods of education,
claiming that children learn best
when they discover, understand,
and integrate knowledge through
independent exploration.
[1] |
Would you say this is an accurate
depiction of the longstanding debate
over math education?
A: It is a
common way the Math Wars conflict is misrepresented
by many advocates for the Reform Math
Movement. It only mentions differences
in teaching styles while not mentioning
the more important differences in curriculum
(much weaker under Reform Math) and
the even more important differences
in the amount of mathematics learned (much
less under Reform Math).
In
fact, mathematicians advocate the importance
of both conceptual understanding (Reform)
and basic skills (Traditional). They
are not mutually exclusive. Basic skills
are necessary for conceptual understanding
and problem-solving. [2]
In theory, the Math Reform Movement
places great emphasis on conceptual
understanding, but, in practice, the
Math Reform conceptual understanding
is at a very low level. Some of the
Math Reform conceptual understanding
is wrong and some of it is misleading.
Math reform often mistakes vocabulary
knowledge for conceptual understanding.
However, there is a place for the
good elements of both traditional education,
such as learning the usual method of
multiplication and having a coherent
curriculum, and a few aspects of a
Math Reform education, such as group
work, in an effective mathematics program.
Is the Reform Math movement
an attempt to address the ineffective
math curriculum of the 1980s?
Partially, but the Reform Math curriculum,
including the Maryland State Department
of Education’s curriculum (MSDE),
is far more underachieving, very repetitive,
even more ineffective, and even more
inefficient than the 1980s math curriculum.
Some of the Math Reform curriculum
is wrong and some of it is misleading.
The Maryland School Performance Assessment
Program (MSPAP) exams were an example
of the Math Reform curriculum’s
lowering of math standards. Former
head of the Maryland State Board of
Education, Robert Embry, wrote:
| I
realized … how fundamentally
serious some of MSPAP’s
deficiencies were. For
example, one question had students
manipulating a dozen small pieces
of paper to figure out the area
of a room--seemingly to avoid
making a simple calculation using
the traditional paper and pencil … Perhaps
no issue about the MSPAP concerns
us more than the clear lack of
substantive knowledge required
for the test. [3] |
Why is it important for students
who do not plan to pursue math or
technology in college to learn real
algebra?
As
1960s civil rights icon Dr. Robert
Moses says, Algebra is the next civil
right. Moses (Ph. D. in the philosophy
of mathematics [Harvard]) states that “the
most urgent social issue affecting
poor people and people of color is
economic access. In today’s world,
economic access and full citizenship
depend crucially on math and science
literacy.”[4]
Not knowing Algebra significantly
prevents many students from obtaining
their first or second choices for a
career or college major.
Who decides what will be taught?
An
administrator from Prince George’s
County summed up how state exams shape
what is taught in the public schools.
This administrator cautioned the State
not to include "any
item in the Core Learning Goals
for the high school assessments
that it did not then plan to
use in the test. 'Forget
about us teaching anything you’re
not testing. All anybody cares
about anymore is if the material
is going to be on the test.'" [5]
If
a student does well on the Maryland High
School Assessment
(HSA) Algebra exam, will the student
do well in college math?
Not
necessarily. Furthermore, it does
not provide the background for even
college remedial algebra (real Algebra
I or II); or for high school Algebra
II or for high school physics. As University
of Maryland, Baltimore County President
Freeman A. Hrabowski III noted: “the
[Maryland state] standards [are] woefully
inadequate.” [6]
As
40 Maryland college Math faculty
have noted: “Maryland’s
mathematics standards … neglect
the math skills [like arithmetic] and
conceptual understanding that are essential
for real algebra” and “teaching
to such a low standard will increase
the already high number of students
taking remedial math [that is, real
Algebra] in college.” [7]
What about NAEP [National
Assessment of Educational Progress]?
Will a student who does well on NAEP
be prepared for college math?
Not necessarily. Most of the questions
on the Grade 12 NAEP belong in Grade
8.
Is
real arithmetic or algebra being
taught at all in Maryland schools?
Arithmetic has been marginalized.
Knowing
that x + 2x = 3x or
solving 2x = 8, without the aid
of a calculator is not on the
syllabus for the Maryland Algebra exam.
This is why I nick-named it Maryland’s
pretend Algebra Exam. "Even
one of the people responsible for the
[Maryland Algebra] test, Maryland State
Education Department official Gary
Heath, said, 'We would be the
first to tell you it doesn’t
have a lot of algebra, nor was it intended
to.'" [8]
Maryland schools are replacing their
real Algebra I course, with MSDE’s
pretend Algebra syllabus.
Why are the standards for
K-12 math education so low in Maryland?
Because MSDE is not willing to set
appropriate standards for teacher certification.
In order to learn Real Algebra, students
need to be fluent in arithmetic. But
many students leave middle school not
fluent in arithmetic. To achieve fluency
in arithmetic, students need teachers
who are fluent in arithmetic. But fluency
in arithmetic, especially calculations
with fractions and decimals, is not
required for MSDE’s endorsement
as a “highly qualified” middle
school Math teacher. So what
to do? Option #1 is for MSDE
to raise its Math standards for “highly
qualified” middle and elementary
school Math teachers; this would enable
MSDE to raise its Math standards for
students.
Option #2 is to marginalize Arithmetic
and “reinvent” Algebra
as “pretend” algebra, wherein
students do all calculations on calculators.
MSDE chose Option #2. Maryland
school systems are revamping or replacing
their traditional Algebra I curriculum
with MSDE’s pretend algebra.
Do public school math teachers have
a strong background in mathematics?
Many teachers have very good knowledge
of Mathematics. Unfortunately for our
children, many others do not. We would
like to assume that MSDE’s teachers’ certification
guarantees appropriate and correct
knowledge of Mathematics. This assumption
is not correct.
A child of mine had mathematically
correct answers marked wrong on Algebra
I and II exams and on a Geometry exam.
This occurred at Blue Ribbon schools,
which received national honors from
the first President Bush as “Schools
of Excellence”
At a University of Maryland seminar
for Math Education graduate students,
the question came up: why is it that
a negative times a negative equals
a positive. A math education professor
from Harvard explained it as follows: If
we consider good to be positive and
bad to be negative, then doing bad
things to bad people is considered
good. This is a cute answer,
but it has no connection to
a correct explanation.
How do Maryland teachers
become “Highly Qualified” under
No Child Left Behind?
One way teachers may earn the “highly
qualified” middle school math
teacher endorsement from MSDE is by
passing the Praxis II “Middle
School math content” exam. Teachers
may use calculators on this exam, so
fluency in fractions and decimals is not required.
Alternatively, middle school math
teachers can use (pretend) college
Math courses, specifically designed
for elementary school (K-5) teachers,
to partially fulfill the college math
requirements for MSDE’s endorsement
as a “highly qualified” middle
school math teacher. The level of these
Math courses is so low that college
students, majoring in basket weaving,
cannot get credit for these courses.
Is Maryland’s
high school Math curriculum effective
at all?
Maryland High Schools had an effective
high school Math curriculum, at least
for many students. Of course, it was
not effective for the many students
who did not know Arithmetic. The overuse
of calculators (this century) has resulted
in students being less well prepared
for college. As Maryland High Schools
replace Real Algebra with Maryland
(HSA) Pretend Algebra, students will
be even less well prepared.
What prompted California to
drop the Reform Math curriculum?
California developed its current math
curriculum after experiencing the disastrous
impacts of the Reform Math movement. Eight
years of Reform Math in California
public schools resulted in the remedial
math (Algebra) rate, at the California
State College System, skyrocketing
from 22% to 52% among entering students.
The drastic drop in student math achievement
contributed to a counter-revolution
against the Reform movement and led
to the creation of the California Math
Framework (1999).
What can be done to improve
K-12 math education in Maryland?
I would recommend the following changes
in order to improve math education:
- MSDE must first bite the bullet
on standards for teacher certification.
Especially raising Arithmetic content
standards for K-5 teachers and Arithmetic
and real Algebra content standards
for Middle school Math teachers.
- Institute new state certifications
for combined middle school math and
science teachers and for AP Calculus
teachers. An AP Calculus teacher
could provide math expertise and
math leadership for his/her high
school’s math teaching team.
- Provide serious professional development
in Arithmetic and real Algebra for
those K-8 teachers who would benefit
from it.
- Provide bonuses for elementary
and middle school principals and
vice-principals who are fluent in
Arithmetic and Real Algebra. They
could provide their teachers with
leadership in Arithmetic instruction
and could accurately evaluate Arithmetic
instruction.
Raising the math standards for math
teachers will enable the state to
raise math standards for students.
- Replace
the counterproductive Maryland
Content Standards with the 1999
California Standards. Better yet,
use the Singapore standards for
K-7 or use a cut-down version of
Achieve’s K-8 math
curriculum standards [9] by
moving its Grades 6-8 probability
material and much of the Geometry
to high school. Maryland is one of
18 states that joined Achieve’s “Mathematics
Achievement Partnership”. Singapore
textbooks were used with great success
in College Gardens Elementary (Montgomery
County). [10]
- For High School use textbooks approved
by the state of California for this
Century or academic math textbooks
from the 1950’s.
- Use
the PSAT Math exam for the states
standard Math exam for Grade 8,
required by NCLB. The bulk
of the PSAT Math exam consists of
Arithmetic and pre-Algebra questions.
Teaching to the PSAT Math exam would
considerably raise the level of teaching
mathematical thinking and analysis.
[11]
- Replace the Maryland pretend Algebra
exam with the Algebra I questions
on the common Math placement exam
of Maryland community colleges.
- Require
that Maryland Hope scholarship
recipients be able to enter college,
without the need to take any remedial
course. This would pressure
high schools to raise standards.
- Starr,
L. (2002). Math Wars! Education
World. http://www.education-world.com/a_curr/curr071.shtml
- Dr.
H. Wu’s great article, “Basic
Skills Versus Conceptual Understanding – A
Bogus Dichotomy in Math Education” in
The American Educator, American
Federation of Teachers, Fall 1999.
- Robert
C. Embry, Jr.’s, (former
head of the Maryland State Board
of Education), 1996 memorandum
to Nancy Grasmick, Maryland State
Superintendent, on the web at
https://listserv.umd.edu/cgi-bin/wa?A2=ind0108&L=ctetch-l&P=424 ;
it was an MSDE state secret until
summer 2001.
- Dionne,
Jr., E.J. (6 March 2001). Into
the Math Mix. The
Washington Post,
pg. A.23. As leader of the Mississippi
Voter Rights Project, Dr. Moses
was one of the ten most important
civil rights activists in the1960s.
Moses has a Harvard Ph.D. in the
philosophy of mathematics. For
the past decade he has been organizing
the Algebra Project.
- Robert
C. Embry, Jr.’s, (former
head of the Maryland State Board
of Education), 1996 memorandum
to Nancy Grasmick, Maryland State
Superintendent, on the web at
https://listserv.umd.edu/cgi-bin/wa?A2=ind0108&L=ctetch-l&P=424 ;
it was an MSDE state secret
until summer 2001.
- Bowler,
M. (31 March 2004). A call to raise
the standards; Expectations: UMBC’s
president urges state education
officials to push schools toward
academic excellence. The
Baltimore Sun, pg. 2.B.
- Petition
to Upgrade Maryland’s Mathematics
Standards. http://www.math.umd.edu/~jnd/subhome/petition_w_sign.htm
- Mathews,
J. (19 August 2002). Algebra =
X in One School, Y in Another;
Teaching Inconsistent as Standards
Waver;. The
Washington Post, p.
A.01.
- Achieve
Initiatives/MAP: MAP’s K-8
Expectations. Achieve Website: http://www.achieve.org/achieve.nsf/MAP-k-8?OpenForm
- Singapore
textbooks are written in English
and can be found at: http://singaporemath.com.
- Bowler,
M. (31 March 2004). A call to raise
the standards; Expectations: UMBC’s
president urges state education
officials to push schools toward
academic excellence. The
Baltimore Sun, pg. 2.B. “When opponents
of the SAT, for example, tee off
on its purported bias against minorities,
[University of Maryland, Baltimore
County President Freeman A. Hrabowski
III] replies that he has been writing
SAT test questions for years --
and that minorities can, and many
do, ace the SAT.”
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