**College
Readiness -- A
Simple Description**

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

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

**Ready for
college**. To survive
academically 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 "generalized" Arithmetic, better known as Algebra.

**1.
Mathematics. **

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

College
freshmen, not knowledgeable in Arithmetic or *real* high
school Algebra I, are
relegated to remedial math courses; colleges are not real successful at
teaching these courses. Some might
considered it *unfair* to require Grade
8 students to be able to add fractions, when MSDE does *not*
require this for its endorsement for "highly qualified" middle
school Math teachers.

As our 40+
Mathematicians' public
letter, "RACE
TO THE TOP AND K-12 MATHEMATICS EDUCATION" 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.

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

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.

**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 teachers' 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).

Adding
the
Arithmetic and Pre-Algebra Math SAT and PSAT questions to the middle
school
Math curriculum would be a good step toward making all students more
college
ready. This would also make 600 a
reasonable goal for the average score of MD graduates on the Math SAT. The SAT rated the following problem
a 3 for
difficulty on its scale of 1 to 5. Instruction
for such problems usually
is *not* included in the Math
curriculum.

**A
mid-level SAT Problem**.
"How many __minutes__ are required for a car to go 10
miles
at a constant speed of 60 miles per hour?"

Also,
competency with spread
sheets and graphing calculators would be useful.
(Not just type in a function and the hit graph.)

**Probability and
Statistics**. There are snippets of
data analysis, which would be useful for college freshmen.
These include knowledge and
understanding of means (averages), medians, deciles, box and whisker
diagrams;
also being able to read and draw a variety of graphs, charts and tables.

**Warning**. *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 Maryland (Voluntary)
State
Math Curriculum. The colleges'
attitude to freshmen, with **zero** K-12
Statistics, is: *No Statistics;
no problem*. Colleges are
reasonably successful at teaching Statistics ...
at least to those students, who are knowledgeable in
Arithmetic and Algebra.

For
example, on my campus (UMCP), psychology majors are required to
take PSYC 200, "Statistical Methods in Psychology", which builds on
PSYC 100,
"Introduction to Psychology". Business majors are required to take BMGT
230,
"Business Statistics". Sociology
majors take SOCY 201, "Introduction Statistics for Sociology", which
builds on
SOCY 100. This spring, we taught
41 classes of these three specialized beginning courses in Statistics. In addition the Mathematics Dept.
taught 8 classes
of STAT 100. "Elementary Statistics and
Probability".

Thus,
Probability and Statistics are NOT useful
for college readiness. Freshmen,
with a 5 on AP Statistics exam, and a
C in high school
Pre-Calculus, wishing to major in statistics (in college) will be *at-risk* in this major. Freshmen,
with **zero** K-12 Statistics, but aced high school
Pre-Calculus are fully
ready to major in statistics. (The
first college Statistics course, for students majoring in engineering
or
statistics, is based on calculus; it makes AP Statistics look like
child's
play.)

**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.

NOT
in the March draft of the
Common Core Math Standards for middle school.

**High
school ready in Math for ****high school personnel finance classes** requires fluency in decimal equivalents
of percents and fractions.

NOT
in the March draft of the
Common Core Math Standards.
For example, memorizing that 50% equals a
half, or even being able to figure out that 50% equals a half or
.5 are NOT included.

In
sharp contrast: "As his [Grade 5] students lined up
after lunch
outside his classroom, he popped questions before they could enter.
'Kayson,
what is two-fifths as a percent?' he asked. The boy hesitated before
correctly
answering 40. 'Next time,' Mr. Skeeter said, 'quicker.'"

College math professors
are *distressed* by the low level of
understanding of arithmetic and arithmetic-based Algebra by masses of
college
students. This is why the MD/DC/VA SECTION of the Mathematical
Association of
America (MAA) has broken tradition by issuing its first statement ever
on the
College Professors' Concerns on Mathematical Preparedness of Incoming
College
Freshmen [www.salisbury.edu/mddcvamaa/HS_students.asp]. I paraphrase its key recommendation
as: Students should be able to
perform basic calculations in Arithmetic and in Algebra, without the
assistance
of calculators. Thus, the Algebra
I, needed for college, is largely *excluded*
from the MD HSA on Algebra.

Also see my reports "**Comments on
Statement on Mathematical
Preparedness**" as well as my "**Notes on Remedial Math Problem**"
and "**A Review
of the Report of the Task Force on the
Education of Maryland's African-American Males -- Useful
Initiatives that should
have been included**"
on
my **Math Education Website.**

**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 these English courses
with paragraphs from their science and social studies textbooks.
Proficiency in
literature is important, but it is *not*
necessary for college readiness.

My
impression is
that high school teachers are required to pass a course on teaching
reading in
the content areas, but on my campus there is a single generic course,
but
reading history is very different from reading Mathematics. What is needed is that high school math
teachers are required to pass a course on teaching reading specifically
for
Mathematics; similar for other subjects.

**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. Unfortunately, for
students, the
writers of math textbooks do not model such writing, (perhaps true for
other
subjects). Such clear writing
needs to be made a *main* focus of English and social
studies classes in Grades 4-12.
Also, a focus of science and mathematics classes.

Also
see: "Literacy (writing and
reading) is crucial" on my website at __www.math.umd.edu/~jnd/Literacy.htm__.

**Our
children deserve a better instructional
program.**

**Lesser
notes****:**

"Along a wall [of the Dundalk campus of
the Community College of Baltimore County's Student Success Center] is
a rack
of handouts explaining points of grammar that might have last been
explicitly
taught in middle school, a measure of the immense ground to be made up.
One
covers comparative adjectives, explaining 'more' vs. 'most' or
'smarter vs.
'smartest.' Another discusses using pronouns and verb tenses." ["At
2-Year Colleges, Students Eager but
Unready", N. Y. Times, Sept.
2, 2006 www.nytimes.com/2006/09/02/education/02college.html?_r=1&sq=McKusik&st=nyt&scp=1&pagewanted=print]

Ezra
Shahn wrote ["On
Science
Literacy," in Educational Philosophy and Theory. Journal of the
Philosophy of Education Society of Australia, (1988).]: "In descriptions of many biological
phenomena " 'understanding'
means mastery of a sequence such as A then B then C then D " . It was
as though
in reading or hearing 'then' the student was understanding 'and'. "
[But] the
sequential relationship is more restrictive, hence more precise and it
is this
distinction that many students apparently fail to grasp." Shahn also
wrote: "it seems that students often misread conjunctions [including
the implication words 'because' and 'then' (as in 'A then B')] so that
they
mean 'and'. "

Arnold
Arons [A guide to
introductory physics teaching, Chapter I Underpinnings,
Section 1.16 Language]
wrote: "... essentially the same
problem frequently arises in connection with "if & then" statements
of reasoning." Arons elaborated: "Crucial to understanding scientific
reasoning and explanation [in beginning physics classes] as opposed to
recall
of isolated technical terms, resides in the use of [implication words]
words such
as "then" and "because".

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From
a Univ. of MD, College Park [UMCP] instructor:

I
... would like to comment in light of a recent quiz I gave in STAT
100 [Univ. of Maryland, College Park version of AP Stat].
Students were given a data set of five
ordered pairs and asked to calculate the least squares regression line. Most all obtained the [correct]
equation y = .52 + .7x, but many (over half of my class) missed points
because they
did not correctly graph the line.
Interestingly, many students omitted the scale of the graph, and
even
though most all plotted the ordered pairs, the line they drew on the
graph was
not y = .52 + .7x, but some arbitrary line. When
I returned the quiz and was talking to my classes about
this, a comment I received was, "Well, I graphed it on my calculator,
shouldn't I get credit for that?"
When I mentioned that I needed the scale, y-intercept, slope,
etc.
correctly graphed on the quiz paper for the student to receive credit,
the
reply was, ".... the calculator doesn't show the scale so I don't know
how
to do that." (By-the-way this was an assigned homework problem from the
text.)

Another question on the
quiz asked students to predict the volume of a tree with a diameter
equal to 20 given that the equation of
best
fit by least squares for the diameter vs. volume was y = -36.9 + 5.07x. I had more than one student who forgot
a his/her calculator say they couldn't do this problem because they
didn't have
a calculator (i.e. couldn't do decimal multiplication and addition).

FYI--I reviewed how to
graph a line in class (Algebra I) which the text assumes students know
before
taking STAT 100.

End email from UMCP instructor.

Relatedly
from Homeroom Column of Montgomery
Extra Section of Washington Post, December 25, 2003; Page GZ06: "With 'Pretend' Testing, a Poor
Imitation of Preparing Students":

And
I [Chenoweth] would like to know that kids
can graph a simple line without a graphing calculator before they
graduate from
high school.

The
head of math instruction for the state,
Donna Watts, disagreed. "The technology is there. It's not going to go
away," she said. "There is a limited population who can do math
symbolically, the way mathematicians do. If this is an exam for all
students,
we want to make it comfortable for however students learn."

**Problem**. You
borrow $100; you agree to pay ten
percent interest. How much interest do you pay?

A
Blair High School [Montgomery County] teacher of personal finance
wrote me: "... I
would not be at all surprised that it
would stymie 65% of my kids doing the problem with simple numbers and
no
calculator."

Towson
State University Professor of Biological Sciences, Virgina Anderson^{ }provides
extensive
training to her college biology students in the reading and drawing of
tables,
graphs and charts.^{ } The
general need for such instruction in college is indicated by a federal
study
conducted by the National Center for Education Statistics. " ... far
fewer
[Americans] are leaving higher education with the skills needed to
comprehend
routine data, such as reading a table about the relationship between
blood
pressure and physical activity, ... 'What's disturbing is that the
assessment is
not designed to test your understanding of Proust, but to test your
ability to
read labels,' [Mark S. Schneider, commissioner of education statistics]
added." ^{ }["Literacy of College Graduates Is on
Decline Survey's Finding of
a Drop in Reading Proficiency Is Inexplicable, Experts Say", Washington
Post, December 25, 2005; A12]

Just as fast
as students
can change 236 __cents__
to $2.36, they
should be able to change 236 __cent__imeters
to 2.36 meters
and 236 per__cent__ to
2.36.

To achieve
this, the
state standards for certification need to be raised.
Note:

"When Grant
Scott, a
biology teacher, had to teach (his chemistry students) at Howard High
School,
Howard County, MD, how to change centimeters to meters, he just
told them
to move the decimal two places -- rather than illustrating the concept.
...
'Forty-five minutes later, only three of them got it.' "
[Washington Post, February
15, 1999]

The
Arithmetic part of a two-line calculation
in a Chemistry textbook [Zumdahl, 5^{th} edition]: Simplifying the following messy
fraction [where "^" denotes an exponent]:

(1.0
x 10^1) (1.0 x
10^2)^2

---------------------------------------- = 4 x 10^5.

(2.0)^2 (0.50)^4

^{ }

Students
should
be able to simplifying this quickly, without a calculator, mostly doing
mental math. This type of
Arithmetic calculations is *not* part
of the high school math curriculum; it belongs in middle school math,
then it
will be reviewed and practiced in high school science classes.

Data
analysis is often tricky. Too
tricky for high school and too tricky for the writers of the MD HSA on
[Some
concepts from] Functions, Algebra, Probability and Data Analysis. Let's
look at 2007 Public Release Algebra/Data
Analysis Item #38 at

http://mdk12.org/assessments/high_school/look_like/2007/algebra/ftri38.html

This
is also Item #37 at

www.mdk12.org/assessments/high_school/look_like/2007/algebra/hsaAlgebra.pdf

"In
a small town, 250 randomly sampled registered voters were asked to
state
whether they would vote "Yes" or "No" 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 "No" on Measure A in the next election?"

To
obtain the correct answer, 2,112,
students are expected to make the following unwarranted and usually
incorrect
assumptions:

The
number of people, who will actually vote in the next election, is
exactly (not
just approximately) equal to the number expected to vote.

None
of the undecided people will make up their mind and choose to vote "No"
after
the survey. This is rarely a true
statement.

All
of the surveyed people, who answered, "undecided" were actually
undecided. Nobody said "undecided" as a
polite way
to say "None of your business".

None
of the people surveyed gave wrong answers, because it would be
embarrassing to
publicly say how they were really planned to vote.
This is often not a true statement.

The
fraction of people who will vote "No" in the next election is exactly
(not just
approximately) the same as the fraction of people who voted "No" in the
survey.

The
writers of the state math exams appear to have had little or no
training in how
to write Math precisely, without ambiguity and without loopholes. Writing Math correctly shares these
attributes with writing law correctly.

Again,
Data analysis is often too
tricky for high school: UMCP
Physics Professor, Tom Cohen's, observations of his child (a student in
Montgomery County Public Schools) doing her HSA "Algebra" homework on
"best fit" lines:

"However,
the
way data analysis is taught and tested troubles me. In particular, the
use
of linear regressions (done by a calculator) to fit lines is not
appropriate
for algebra one students, in my view. The students are NOT taught what
a
"best fit" line means mathematically, how to judge whether the model
fits the data well (i.e. chi square or other statistical measure) nor
even
given any clear way to understand whether the data ought to fit a line.
If you
ask the calculator for a line which will fit points which lie on a
parabola the
calculator will spit back a line and the students will dutifully write
it down.
The issues are subtle and algebra one students are not prepared to deal
with
them. Thus, the students are being miseducated in data analysis and
statistics."

"In
my view this
treatment is worse than useless, it is positively destructive. Students
are
told in essence to plug things in which they don't understand and then
to trust
the answers. This is diametrically opposed to the critical reasoning
about data
analysis that we need to instill in students."