**College Success
–- **

**A College ProfessorÕs
Perspective[i]**

By **Jerome Dancis**, Associate Professor
Emeritus, Math Dept., Univ. of MD

** Math Education Website: www.math.umd.edu\~jnd **

**0. Preamble.** This report will list actionable items
for MSDE, county school districts[ii] and the
University of Maryland (UMD) to do to increase college success in general and to
increase college success for STEM majors.

**Warning. **The views of college professors of
Mathematics on what is useful and correct Mathematics, are *very different *from those of Mathematics educators, education policy
experts and college professors of Mathematics education. [iii] [iv] To increase college success, the
opinions of college professors of Mathematics are the relevant ones [v].
Task forces on college success should include college professors of Mathematics,
science (sociology, physics, etc.), social studies (history, government, etc.)
and college instructors of remedial Mathematics, reading and writing as
stakeholders with relevant expertise.

**Ready for college**. To academically survive the first
year of college, students basically need the three Rs, Reading, wRiting and aRithmetic,
albeit all on high school levels. *No *Statistics needed.

Reading means
reading *with* understanding the
expository and descriptive text in science and social studies textbooks, *not* literature. This includes following written
directions. Writing means writing a coherent
summary of each chapter in the
science
and social studies textbooks, and relating the chapter to material previously
studied. Arithmetic means
Arithmetic, including fractions,
decimals, percents, measurement and multi-step Arithmetic word problems,
along with ÒgeneralizedÓ Arithmetic, better known as Algebra, but *not* the MD HSA on Algebra.

**1. Mathematics. **

As our 40+ Mathematicians' public
letter, "RACE TO THE TOP AND K-12
MATHEMATICS EDUCATIONÓ says:

For
the United States to remain competitive, every part of K-12 mathematics
education in this country must be strengthened: curriculum, textbooks,
instruction, assessments, and, above all, the preparation and continuing
professional development of those who teach mathematics and science, regardless
of grade level and the kind of school in which they teach. [vi]

All prospective K-8 mathematics and science teachers, coaches, and
supervisors should be required to pass a solid test on the core mathematical
material (especially arithmetic) for licensing. Mathematics supervisors and coaches should be required to
have at least the mathematics qualifications of those they supervise.

We need content-rich
professional development programs
for current K-8 mathematics and science teachers, coaches,
and supervisors, and for elementary
and middle school principals.

MD
should implement the recommendations of the rigorously researched National
Mathematics Advisory Panel's 2008 report that teacher licensing tests for all
K-8 mathematics teachers should fully address the foundational topics in
arithmetic (including fractions, decimals, and percents). It would be unfair to require Grade 8
students to add fractions, when the state does not require this of middle
school Math teachers. MassachusettsÕs Math content standards for its *elementary*
school teachers (1-5) are *higher* than MarylandÕs Math content standards
for Òhighly qualifiedÓ *middle* school Math teachers.

We
should follow MassachusettsÕs example of requiring aspiring elementary school
[Grades 1-5] teachers to pass a *math-specific*
test to earn their teaching license.

**Praxis II -- Too low level**. More rigorous licensing exams needed.

**ES. **Prospective teachers may *skip all* the Mathematics items on the Praxis
II Elementary School Content Exam, and still pass.

**MS.** MSDE uses the Praxis II Middle School Math Content
Exam as the ÒharderÓ option for their designating "highly qualified"
Middle School Math Teachers. But,
middle school Math teachers get to use *calculators*
on this exam, so *no* need for
"highly qualified" Middle School Math Teachers in MD to be fluent or
even knowledgeable in Arithmetic. My sense is that a well-trained sixth grader could pass this
exam.

**HS.** The Praxis II syllabus for high school math
teachers omits the entire second half of AP Calculus.

**Low
level College-ready ****Math Standard** (Ready to enroll in a college credit-bearing
Math course; this is *supposedly* Common CoreÕs goal**)**. Graduates should be
fluent in Arithmetic
and real (1980Õs) high school Algebra I, *without*
calculators. [vii]

College freshmen, not knowledgeable in Arithmetic or *real* high school Algebra I, are
relegated to remedial math courses; colleges are not very successful at
teaching these courses.
[viii]

MSDE
and counties should implement the rigorously researched report of the National
Mathematics Advisory Panel, which calls for appropriate instruction and
instructional time for Arithmetic in K-8.
[ix]

MSDE
and counties should use the arithmetic and Algebra I
questions on a college placement math exam as an end of Algebra I assessment
and/or as the ÒNo Child Left BehindÓ mandated Grade 10 math exam. Scoring
ÒadvancedÓ on the exam should mean that the student will *not* need remedial arithmetic or Algebra I, if and when he or she
enters college. The cut score for proficient (NCLB passing score) could be set
as low as the Maryland State BOE desires.

**Fully college-ready** **Math Standard: **To be ready for any Science, Technology,
Engineering and Mathematics (STEM) major in college a graduate needs to be
fluent in Pre-Calculus. This, in
turn requires fluency in Arithmetic
and Algebra II. A grade of C
is *not* sufficient; depending
on curriculum and teachersÕ standards, a grade of B (or even A) may *not* be
sufficient. My guess
is that a score of 600 on the Math SAT and on the SAT II advanced math exam are necessary, but
not sufficient, for success in college calculus (for engineers).

**High
school ready in Math for ****rigorous high school chemistry and physics classes** requires fluency in Arithmetic including
(*) measurement and (*) multistep word problems, as well as on (*)
fractions, decimals and percents and on (*) units and proportions. Also required is automaticity
on decimal equivalents of percents and fractions.

Counties and the MSA math curriculum should
include Arithmetic Word problems, which require critical thinking. [x]

**Problem 1
[xi].** (**Singapore Math ****Grade 5**) ÒEncik Hassan gave 2/5 of his
money to his wife and spent 1/2 of the remainder. If he had $300
left, how much money did he have at first?Ó

Adding
the Arithmetic and Pre-Algebra Math SAT and PSAT questions to the states and
counties middle
school Math curriculum would be a good step toward making all students more
college ready as well as ready in Math for rigorous high school chemistry
and physics classes. This would also make 600 a reasonable
goal for the average score of MDÕs graduates on the Math SAT. Instruction for such problems usually is
*not* included in the Math curriculum.

**Problem
2**. (**SAT – Level 3 ****on its scale of 1 to 5**) "How
many __minutes__ are required for a car to go 10 miles at a
constant speed of 60 miles per hour?"

**Probability and
Statistics** (before college) are **not**
needed for college readiness or success. The collegesÕ attitude to freshmen,
with **zero** K-12 Statistics, is: *No
Statistics; no problem. *[xii] Colleges are reasonably successful at teaching whatever Statistics a
student may need – but *just* to
those students who are knowledgeable in Arithmetic and Algebra. *Unfortunately*,
Probability and Statistics is a major strand in the middle and high school part
of the March draft of the Common Core Math Standards and in the MD (Voluntary)
State Math Curriculum. MSDE and
the counties should *remove* Probability
and Statistics from the Math
Curriculum; this would make these curricula more coherent and easier to
teach. Class time freed up, would
enable students to better learn Arithmetic.

**Guidance Counselors.** An eleventh grader, doing well in
Algebra II, has several math options for Grade 12. The guidance counselor should inform the student, that
taking Pre-Calculus will make him/her fully ready for all STEM majors. But, taking AP Statistics will likely
put them at-risk for college majors in statistics and engineering.

**Math should be correct on MSDEÕs and
countiesÕ assessments**. MSDE and counties should employ
Professors of mathematics to check state and county Math exams for Math
errors. They should employ
Professors of Statistics to check the Statistics, probability and data analysis
questions on state and county exams for Math errors

**2. Literacy**

**Goal** for English classes
Grades 4-12 should be that students can __understand__ their science and
social studies textbooks and be able to write a coherent summary of each
chapter (one page or less); this includes relating the chapter to material
previously studied. These are
summaries, *not* outlines or
reviews. Students need to be able
to paraphrasing what a teacher has said.
Reading includes paraphrasing a word problem
(from science or math), accurately and precisely, into mathematical
expressions, formulas or equations, as well as the reading of tables, charts
and graphs.

This would require *replacing* perhaps half of the literature in the Grades 4-12 English
courses with paragraphs from their science and social studies textbooks.
Proficiency in literature is important, but it is *not* necessary for college readiness.

**Writing and Speaking**.
Student need to be able to write and speak paragraphs coherently,
clearly, concisely, comprehensively, logically, accurately and precisely
without being cryptic, vague, ambiguous, obscure, redundant or repetitive. UMD should provide
professional development to train teachers to speak and write in these ways.
Counties should choose textbooks that model such writing. For Grades 4-12 counties should make such clear writing the *main* focus of English classes as
well as an important focus of social studies, science and mathematics classes.

<><><><><><><><><><><><><><><

**3. ****UMD.** The CEEB's
SAT II achievement tests are better predictors of college success than the
standard SAT and also better than High school GPAs. [xiii] UMD should follow the University
of California by requiring applicants to take the CEEB's SAT II achievement
tests; my preference is one each in Math, English composition, science and
history. This would send a message across the state
that the university expects high schools to provide rigorous courses. The state or the University of
Maryland could provide honorary scholarships of say $100/year to students, who
score say 650 or more on an SAT II achievement test.

The
UMD should cease to count pretend Algebra and pretentious Data Analysis courses
based on the MD HSA on [Some concepts from] Functions, Algebra, Probability and
Data Analysis as one of the two Algebra courses currently required of
applicants. IÕm told that the University
of California ÒcertifiesÓ rigorous high school Algebra I class as being
appropriate for college.

**Our children deserve viable instructional
programs, ones in which graduates trapped by remedial math in college will
become a rare exception, ones which will produce many more high school
graduates who are STEM ready and hence ready to fulfill President ObamaÕs and
Governor OÕMalleyÕs calls for more STEM college graduates.**

**Our teachers deserve viable instructional
programs, ones with coherent, teachable curricula and reasonable textbooks.**

[i] This article draws on and
complements my report, ÒCollege Readiness --
A Simple DescriptionÓ, on my website. The ÒCollege ReadinessÓ
report contains examples to illustrate items in this article.

[ii] ÒCounty school districtsÓ is my shorthand for Òlocal school districtsÓ.

[iii] This clash (between Math educators
and Math professors) is exemplified by the 1990Õs U. S. Dept. of Education's
Expert Panel (on textbooks), which produced a
list of just 5 exemplary mathematics textbooks. In
reaction, a cryptic public letter was published in the Nov. 18, 1999 Washington
Post claiming that several books on the list contained "serious
mathematical shortcomings". This letter was signed by about 200 college
professors, mostly of mathematics (including yours truly), and four Nobel
laureates. This letter is at: <http://www.mathematicallycorrect.com/riley.htm>.

One of this Expert PanelÕs exemplary textbooks was the Core-Plus
Mathematics textbook series. But,
using Core-Plus, in high school, has been sabotaging studentsÕ 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: "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.) The report is at
www.math.msu.edu/%7Ehill/HillParker5.pdf

Here
in MD, it was math educators who determined the syllabus for the MD HSA on
[Some concepts from] Functions, Algebra, Probability and Data Analysis. In opposition, 50 college professors of
mathematics and engineering signed the ÒPetition to Upgrade Maryland's
Mathematics StandardsÓ [2002]. 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."
Unfortunately, this prediction was realized. (See ÒMore Remedial Math
[at MD Colleges]? [YES]Ó at

www.facultyvoice.umd.edu/All%20past%20issues/2009-2010/FV_V23_N3.pdf).

(The
petition is on my website at www.math.umd.edu/~jnd/subhome/petition_w_sign.htm.)

[iv] Maryland and 44 other states,
have adopted the National Council of Teachers of MathematicsÕ (NCTM)
curriculum, written by Math educators with little consultation with professors
of mathematics. This curriculum
marginalizes arithmetic and emphasizes superficial statistics. It floods each grade (K-8) with so many
topics, that the curriculum is incoherent and very difficult to teach; before
any topic reaches deep memory, the teacher must change topics. MA, MN, MI, IN,
VA and CA (after 1999) did NOT
adopt the NCTM standards.

[v] College
professors of mathematics and Statistics expect that freshmen can graph a simple line without a graphing
calculator. In contrast, ÒThe head
of math instruction for the state, Donna Watts, disagreed. ÔThe technology is
there. It's not going to go away,Õ she said. "There is a limited
population who can do math symbolically, the way mathematicians do. ... Ô
Ò [Quote from ÒWith 'Pretend'
Testing, a Poor Imitation of Preparing StudentsÓ, Washington Post, December 25,
2003; Page GZ06] As noted in ÒCollege
Readiness -- A Simple DescriptionÓ, students lost points on a STAT 100 quiz at
UMCP for *not* being able to graph a straight line.

**Problem**. ÒIn a small town, 250 randomly sampled registered voters
were asked to state whether they would vote ÒYesÓ or ÒNoÓ on Measure A in the
next local election. The table below shows the results of the survey.

**VOTER
SURVEY RESULTS**

**Yes** **No** **Undecided**

96 34
120

There
are 5,500 people expected to vote in the next election. Based on the data, how
many people will vote ÒNoÓ on Measure A in the next election?Ó

Students
who answered 2,112, were marked *correct* on the 2007 MD HSA on [Some concepts from] Functions,
Algebra, Probability and Data Analysis.
But, students who answer
2,112, on a college sociology or political science exam will likely be
marked *wrong*; a correct answer would
be: *not* enough information is
provided for the list of reasons stated in ÒCollege Readiness -- A Simple
DescriptionÓ,

[vi] For
some data that using good textbooks (Singapore
Math), together with good Professional
Development led by a college professor of
mathematics, has been effective:

MASSACHUSETTS
COMPREHENSIVE ASESSESSMENT

Mathematics
Results 1998-2005,

Results
for North Middlesex Regional High School

Remarks to National Mathematics
Advisory Panel, Cambridge,
Massachusetts, September 14, 2006

www.ed.gov/about/bdscomm/list/mathpanel/3rd-meeting/presentations/waight.mary.pdf

Richard Bisk, Chair and
Professor Mathematics, Worcester State College wrote:

We were successful in North
Middlesex because the teachers got Professional
Development that improved their math
understanding and they got to use good materials (Singapore Math) with their
students. ... Most teachers will say up front that
they want the implementation knowledge and not the math as they don't realize
how their limited math background affects their ability to teach well. I've
been fairly successful in convincing them that the math needs to come first.

[vii] The MD/DC/VA Section of the Mathematical Association of America (MAA) issued its first
statement on the Ò[College ProfessorsÕ Concerns on] Mathematical Preparedness of
Incoming College FreshmenÓ. I paraphrase its key recommendation as:
Students should be able to perform basic calculations in Arithmetic and
in Algebra, without the assistance of calculators. [http://sections.maa.org/mddcva/HS_students.php]

[viii] ÒItÕs the math thatÕs killing
us,ÕÕ noted Donna McKusik, the senior director of remedial education at the
Community College of Baltimore County.
More than one in four college remedial students work on elementary and
middle school arithmetic. Math is
where students often lose confidence and give up on Community College. (The New
York Times, September 2, 2006) It is this necessary Arithmetic, which has
been *downplayed* by the MD MSAs on
Math and which is neither reviewed nor reinforced by the MD HSA on Algebra.

[x] Perhaps include my ÒA Grade by Grade Description of
Appropriate Arithmetic Word ProblemsÓ, which is Appendix B at:

www.ed.gov/about/bdscomm/list/mathpanel/5th-meeting/presentations/dancis-jerome.pdf

[xi] A simple Arithmetic (no
Algebra) solution, using Singapore Math strip figure appears in: ÒSolving
Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in
Grade 4–6 Texts Used in SingaporeÓ by Professor of Mathematics, Sybilla Beckmann.

[http://math.coe.uga.edu/tme/issues/v14n1/v14n1.Beckmann.pdf]

Her textbook, __Mathematics for Elementary Teachers__ is used on my
campus.

[xii] Exception, there are snippets
of data analysis, which would be useful for college freshmen.

[xiii]
My Faculty Voice
article, "How we use the SAT in admissions sends a message across the
state". February, 2002