Jerome Dancis
Associate Professor Emeritus
University of Maryland
Mathematics Department
Office: MATH 3206
Phones: 301 345 2973 and 301
405 5141 jdancis@math.umd.edu
Many of my views on Math education policies are contained in an interview
for the Baltimore Curriculum Project. For highlights, see the summary
"spotlighted" in its newsletter of Feb. 2006. My
answer to the question, "What can be done to improve K-12 math
education in Maryland?" can be found near the end of the interview.
Fractions - "Toward
Understanding and Remembering -- How to do Hand Calculations with
Fractions" This paper presents a method for teaching calculations
with fractions in a manner that is easily understood, easily
remembered, and which will considerably reduce the need for
memorization and homework. Also, it will reduce students making "dumb"
mistakes.
On Pattern Mis-Recognition in Math
Instruction Pattern Recognition is a popular topic in the
Reform Math Curriculum. Questions on this topic on the NAEP exams
and on the state of MD HSA math exam are Mathematically wrong.
Linear Equations - Linear
Operator and Linear Algebra Theory for Linear Differential Equations.
(A second year calculus course.) These notes may
be used for both a discovery method and a lecture method of
instruction.
Background from Calculus - Aspects
of Calculus, which are useful for differential equations, but often
fall through the cracks in Calculus class.
Large numbers of college students are relegated to remedial Algebra I and Arithmetic
classes.
"More than one in four remedial students work on elementary and middle
school arithmetic. Math is where students often lose confidence and
give up." (New York Times)
"Algebra
and
reading
competence vital for all students", Prince
George's Gazette Dec. 14, 2006
Literacy (writing and reading)
instruction is crucial. (Excerpts
fromWashington Post of July 13, 2006
And from Reading
Instruction for Arithmetic Word Problems:
"Some 70 percent of [fourth - twelfth graders] require remediation [in
reading]. Very few … need help to read the words on a page; their
most common problem is that they are not able to comprehend what they
read." This results in large numbers of students not able to
read
and comprehend their textbooks. From a report published by the
National Association of Secondary School Principals
(NASSP): "Sadly, if students two to three grade levels behind [in
reading] do not receive intensive literacy instruction, the results can
be devastating because the struggling reader will not experience
success [in many classes]."
College professors are distressed by the low level of
understanding of Algebra and Arithmetic by large numbers of students as
they enter college -- even students who have taken calculus
in high school. This concern prompted the local college math
professors' professional association [ the MD/DC/VA section of the MAA]
to issue its statement "ON MATHEMATICS
PREPAREDNES [NOT]" College math professors decreed: "Students
should be able to perform Algebra and Arithmetic calculations, without
the assistance of calculators." This is the opposite of the
MD HSA on [pretend] Algebra, which effectively mandates the exclusive
use of calculators for Algebra I.
The Arithmetic curriculum should include (See my public presentation to
the National Mathematics Advisory Panel [which
starts
at
the bottom of Page 36]):
1. Fluency in Arithmetic word problems, especially,
non-trivial, multi-step Arithmetic word problems, with a Stress On Analytical Reasoning (SOAR).
2. Fluency in measurement including measurement
problems with a SOAR.
3. Arithmetic-based science lessons, especially those with a
SOAR and which make use of estimation and measurement.
4. Instruction in reading comprehension and following directions,
specifically for word problems. In
contrast, the popular Math Reform curriculum emphasizes wordy
"real world problems", usually with little math content, problems,
which Avoid Analytical Reasoning.
Treismans Calculus Project - My
paper "Alternate Learning Environment Helps [Black] Students Excel In
Calculus -- A Pedagogical Analysis" (long version) Math Workshops - More Treisman type workshops
needed. (short version)
The Math Wars - Reform vs.
Traditional Math Instruction, how each mucks up math education.
A fun, critical video on how two popular Reform math textbook
series: TERC and
EverydayMath (used in Montgomery County, MD) muck up the teaching
of Arithmetic.
The Core-Plus Mathematics textbooks will sabotage your child's college
Mathematics education. It sets up students to need remedial
Algebra and Arithmetic when they enter college and it sets up students
to do poorly in their first college Math course. Read this smoking gun type report:
"A Study of
Core-Plus Students Attending Michigan State University" by Michigan
State University Professors of Mathematics, Richard O. Hill and Thomas
H. Parker, in the American
Mathematical Monthly (Dec. 2007) , an official publication of
the Mathematical Association of America [MAA]. (The MAA is the college
math professors professional association for college math education.)
MD's Pretend Algebra and Pretentious Data
Analysis Exam
Our MD college faculty "Petition
to Upgrade
Maryland's Mathematics Standards" was signed by 50 math and
engineering college professors. One of its main points is
that "the State of Maryland's mathematics standards neglect the math
skills [like arithmetic] and conceptual understanding that are
essential for real algebra." It also notes: "Teaching to
such a low standard will increase the already high number of students
taking remedial math [that is, real Algebra]
in college."
The implementation, of the MD HSA on Algebra
(and Data Analysis) test as an end-of-year exam and and as a
graduation requirement, will likely result in a major dumbing down of
math education in Maryland. Read: Beware
the
MD
Algebra Test - (Presented at the Nov., 2002 MD-DC-VA
Sectional Meeting of the MAA.) Montgomery County Public
Schools may be taking the lead:
"State
and county math standards hurt student performance" in Silver
Chips, (Dec. 18, 2003), the student newspaper of Blair High
School (Silver Spring, MD) Two quotes: "MCPS
[Montgomery County Public Schools] mandated changes to the Algebra I
curriculum to align the course with the tested material [MD's Algebra
Exam]. 'We don't think the material is what they need to know to be
successful [in Algebra II and Precalculus],' said Blair H.S. algebra
lead teacher Maria Costello".
"Changes in the curriculum are cited as a main cause for students'
deficiencies in basic algebra, which are manifesting themselves in
higher level math courses that require an understanding of concepts
taught in Algebra I. 'Our Algebra II students are worse than ever. Our
Pre-Calculus students are worse than ever. It's falling apart as we go
up the ladder,' said Costello."
STOP MARYLAND'S PRETEND ALGEBRA EXAM AND
PRETENTIOUS DATA ANALYSIS EXAM
Stop the Maryland's (MD) Pretend Algebra and Pretentious Data Analysis
exam, which is part of the Maryland High School Assessments (HSA)
program and the pending proposal by the Maryland State Board of
Education (MSBE) to require that
students pass the HSAs as a graduation requirement.
1. Pretend "Highly Qualified" Math Teachers
The MD standards for middle school math teachers do not guarantee math
teacher fluency in the many middle school math topics on MD's
Pretend Algebra and Pretentious Data Analysis exam. It
was supposed to be the No Child Left Behind Act (NCLB) to the
rescue. NCLB mandates that states set standards for "highly
qualified" middle school teachers. But Maryland is setting
the bar for middle school math teachers below its bar for
students. Some details in:
2. Much wrong Algebra and misleading Data Analysis.
The MD Pretend Algebra and Pretentious Data Analysis exam includes much
misleading and wrong Algebra and Data Analysis. Some
examples in Beware the MD Algebra Test
(Items
4
and 6 and end of #3)
3. Adding 3 + 5 and solving
2x = 200 without a calculator not required. MD's Pretend
Algebra Exam
Versus Students Learning
Simple Math The overuse of trusty calculators on the
exam will lead to their overuse in MD high schools and middle schools.
This in turn, will result in more high school graduates not fluent in
Arithmetic and more
students needing to take remedial Algebra I and Arithmetic when they
enter college.
Relatedly, "With 'Pretend' Testing, a
Poor Imitation of Preparing Students" by Karin
Chenoweth in her Dec. 25, 2003 Homeroom column in Montgomery Extra
Section of Washington Post
(http://www.washingtonpost.com/ac2/wp-dyn/A28031-2003Dec24?language=printer)
She
wrote:
"I now call the test a 'pretend algebra' exam and fear
that it will undermine mathematics instruction throughout the state."
4. If Johnny can't read, then he can't pass MD
Algebra exam. The reading level of the students
demanded by the MD "Pretend Algebra and Pretentious Data Analysis" exam
is higher than
the math level required of the students. This is producing false negatives, that is, students,
who understand the math but still flunk MD's HSA on math due to their
reading difficulties in comprehending the exam questions.
Two reading problems masquerading as an Algebra
problem and a data analysis problem are listed in "When It Comes To Math, Words Count",
Washington Post. Outlook Sunday September 8,
2002.
5. Math Level
on HSA Algebra Exam NOT a Step Up
The math level required of the
students is not clearly a step up from that of MD Functional
Math exam. It should be. If one looks at just the
level of the math done by the students, then the MD Pretend Algebra
Exam is a step to the side. The exam sidesteps the math; this
includes, but is not limited to leaving the bulk of the math to
the hand calculators. Also the exam includes misleading and wrong
Algebra and Data Analysis, which is counterproductive. Students
no longer need to be able to add 3+5 without a calculator.
6. The
California Path to Remedial Math. The math section, of
the Maryland State Dept. of Education (MSDE), has been colonized by the
MATH Reform movement, which is lead by the National Council of Teachers
of Mathematics (NCTM). During the period, when "Reform" instruction was
becoming official state policy and was being increasingly used in the
California
schools, with "pretend" Algebra replacing real Algebra, the remediation
rate in mathematics (Algebra) skyrocketed from 23% in
1989 to 54% in 1998 for freshmen in the Cal. State
University System.
7. Cover-up for the Algebra the students are not learning.
As stated, the official title "MD HSA on Functions,
Algebra, Data Analysis and Probability" is such a gross exaggeration as
to be highly misleading to parents and students. Needed a "Truth
in labeling" law for state exams. At least rename it the MD
Math Exam.
Related reading:
Arithmetic problems are also Masquerading as Algebra on the
MD Algebra test, in Free For All
in
Washington Post Saturday, September 7, 2002.
"State math test dumbs down
curriculum", Viewpoint, Prince George's Journal, July 3, 2001
Easy arithmetic solutions to five of the more
difficult problems on the sample MD HSA
Algebra (and Data Analysis) test are presented in Supposedly Difficult Arithmetic
Word Problems mentioned below.
Math 461Introduction to Linear Algebra for
scientists and engineers