Associate Professor Emeritus
University of Maryland
Office: MATH 3206
Phones: 301 345 2973 and 301 405 5141
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.
R U 4 teachers knowing Arithmetic?
RACE TO THE TOP
(Mathematicians' letter for good use of $5 billion stimulus money for improving education)
Articles on Teachers' knowledge of Math
College Readiness -- A Simple Description
College Success - A College Professor's Perspective
This report lists actionable items for MSDE, county school districts and the University of Maryland to do to increase college success in general and to increase college success for STEM majors.
Be Wary of H.S. Statistics
Stress On Analytical Reasoning (SOAR)
Suggested courses for College freshmen and Grade 12
Decline in Percent of MD HS Graduates Minimally Ready for College Math when they entered a College in MD.
1998 2005 2006
Whites 67% 60% 58%
African-Americans 44% 33% 36%
Asian-Americans 79% 74% 76%
Hispanics 56% 42% 43%
This is discussed in:
My Univ. of Maryland Faculty Voice Newspaper article: More Remedial Math at MD Colleges
scroll down to bottom of Page 1
also discussed in
"Pretend K-12 Mathematics Curriculum Produces Freshmen Who Know Less Algebra"
Morgan State University Mathematics Department Colloquium Talk (2011)
Leisure College, USA Homework and Learning Down; Grades and Tuition Up
Instruction in Arithmetic Devastated Under Superintendent Grasmick
Loopholes in NCLB
Mathematics instruction in Prince George's County Public Schools
Reading Instruction for Arithmetic Word Problems: If Johnny can't read well and follow directions, then he can't do math.
Simple unified methods for solving Supposedly Difficult Arithmetic Word Problems (2003) Its appendix is:
Algebraic Word Problems - Solutions for a few difficult Algebraic Word Problems
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.
Arithmetic Word Problems - The dangers of the Key-Word Method of instruction. Also Simple Methods for Arithmetic Word Problems (2002); this part is about half of Supposedly Difficult Arithmetic Word Problems , above.
On Pattern Mis-Recognition in Math InstructionPattern 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 examare Mathematically wrong.
High school Notes:
Computerized Tomography, a high school level explanation of CT scans (Uses logs and some trig.)
Student Modeling of Physical Phenomena as They Derivate Standard Integral Formulas
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.
My Newspaper articles on Education and Other Educational Articles
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 from Washington 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.
College Professors Should be on MD Task Force on the HSAs (High School Assessments)
Try Singapore Math K-6 Textbooks -- your students will learn Math, including how to do difficult Arithmetic word problems.
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.
Goals for high school - My Goals for high school math education.
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)
Two crucial steps toward Closing the Black-White Gap in Mathematics.
Jerome Dancis's Review of the Report of the Task Force on the Education of Maryland's African-American Males -- Useful Initiatives
A Hybrid, Small-Group, Guided-Discovery Method of Instruction -- A Rigorous, Non-Extremist Approach
The Texas Method and the Small Group Discovery Method by Jerome Dancis and Neil Davidson, printed by the Legacy of R. L. Moore Project at the Center for American History, Univ. of Texas, Austin.
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.)
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."
View sample questions from the MD HSA on the state website.
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.
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:
Really Qualified Math Teachers Should be Required (My presentation at the Oct. 28, 2003 meeting of the MD State Board of Education.)
Do the Math: Easy Test for Teachers Will Hurt Students Washington Post PG Extra Forum (December 4, 2003)
Relatedly, on the importance of having qualified teachers: Certified Teachers Needed .
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/A28031-2003Dec24language=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.
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 461 Introduction to Linear Algebra for scientists and engineers
Math 401Applications of Linear Algebra