College Success –-
A College Professor’s 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 “generalized” Arithmetic, better known as Algebra, but not the MD HSA on Algebra.
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. [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. Massachusetts’s Math content standards for its elementary school teachers (1-5) are higher than Maryland’s Math content standards for “highly qualified” middle school Math teachers.
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.
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 “harder” 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 Core’s goal). Graduates should be fluent in Arithmetic and real (1980’s) 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 “No Child Left Behind” mandated Grade 10 math exam. Scoring “advanced” 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 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).
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) “Encik 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?”
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 MD’s 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 colleges’ 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 MSDE’s and counties’ 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
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. I’m told that the University of California “certifies” 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 Obama’s and Governor O’Malley’s 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, “College Readiness -- A Simple Description”, on my website. The “College Readiness” report contains examples to illustrate items in this article.
[ii] “County school districts” is my shorthand for “local school districts”.
[iii] This clash (between Math educators and Math professors) is exemplified by the 1990’s 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 Panel’s exemplary textbooks was the Core-Plus Mathematics textbook series. But, using Core-Plus, in high school, has been sabotaging students’ 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 “Petition to Upgrade Maryland's Mathematics Standards” . 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 “More Remedial Math [at MD Colleges]? [YES]” at
(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 Mathematics’ (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, “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. ... ‘ “ [Quote from “With 'Pretend' Testing, a Poor Imitation of Preparing Students”, Washington Post, December 25, 2003; Page GZ06] As noted in “College Readiness -- A Simple Description”, students lost points on a STAT 100 quiz at UMCP for not being able to graph a straight line.
Problem. “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?”
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 “College Readiness -- A Simple Description”,
[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
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 “[College Professors’ Concerns on] Mathematical Preparedness of Incoming College Freshmen”. 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] “It’s the math that’s killing us,’’ 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 “A Grade by Grade Description of Appropriate Arithmetic Word Problems”, which is Appendix B at:
[xi] A simple Arithmetic (no Algebra) solution, using Singapore Math strip figure appears in: “Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4–6 Texts Used in Singapore” by Professor of Mathematics, Sybilla Beckmann.
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