Educational Homepage of Jerome Dancis

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

Educational Resume of Jerome Dancis

My interview by the newsletter of the Baltimore Curriculum Project contain many of my views on Math education.  For the summary "spotlighted" in the Feb. 2006 newsletter.    The last question was "What can be done to improve K-12 math education in Maryland?"; my nine answers follow in the interview.

Teaching Word Problems and Fractions

    Simple unified methods for solving Supposedly Difficult Arithmetic Word Problems  (2003)  It's 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.

College Class Notes:

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 - Calculus background useful for differential equations.

 

Commentaries on education and mis-education.

My Newspaper articles on Education   and  Other Educational Articles

Masses 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) is crucial.  ( Excerpts from Washington Post of July 13, 2006.
  • Masses of high school students are not able to read and comprehend their textbooks.
  • College professors are distressed by the low level of understanding of Algebra and Arithmetic by masses of students as they enter college; even students, who have taken calculus in high school. This 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 effective mandates the exclusive use of calculators for Arithmetic and Algebra.

    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


    Goals for high school - My Goals for high school math education.
      Reading Instruction for Arithmetic Word Problems: If Johnny can't read well and follow directions, then he can't do math.

      On Pattern Recognition in Math Instruction

    Treismans Calculus Project - My paper ALTERNATE LEARNING ENVIRONMENT HELPS STUDENTS EXCEL IN CALCULUS -- A PEDAGOGICAL ANALYSIS
    Math Workshops - More Treisman type workshops needed.
    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 Amer. 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.

    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 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 does 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 which in turn, will result in more students needing to take remedial math when they enter college as well as high school graduates not fluent in Arithmetic. 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 writes:  "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.  Large numbers of students should not be flunking a math exam because of reading.      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.  Absurd.

    7.  Cover-up for the Algebra the students are not learning.

    As stated, the official title "MD HS A on Functions, Algebra, Data Analysis and Probability" is such a gross exaggeration as to 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 461 Introduction to Linear Algebra for scientists and engineers
     
    Math 401Applications of Linear Algebra

     
    Notes for various Math classes


    Mathematical Research in Numerical Linear Algebra and Linear Algebra  and in   Geometric Topology