Examples of baccalaureate requirements in quantitative literacy (QL) on various campuses, including programs that support student achievement of QL and efforts at assessment. Comments, corrections, and additions are welcome by e-mail toLynn A. Steen. (QL Home Page)
Amherst Babson Bates Bowdoin CSU Fullerton |
Clark DePauw Hamilton Harvard New York Univ. |
Rhode Island Sam Houston Skidmore Trinity (CT) UColorado Denver |
UMass Boston UNevada Reno UOregon Wellesley |
No specific degree of quantitative literacy is required at Amherst since Amherst has no requirements beyond taking a Freshman Seminar, completing a major, and taking 32 courses. Although we don't have requirements, we do have guidelines which are stated in the catalog. Every student is urged to take courses in each of six areas, two of which are "employ abstract reasoning" and "work within the scientific method." But these are only voluntary guidelines; it is up to the student (with advice from his or her advisor) to follow them.
Since we have no quantitative literacy goals per se, we don't make any effort to assess quantitative literacy on campus. Every now and then, a study is made of how students distribute their courses. Most recently, this was done for Amherst's ten-year reaccreditation. For example, among the classes of 1995 and 1996, only 60% took a laboratory science course and 63% took a mathematics or computer science course. (This data does not consider the students who took calculus in high school but not at Amherst.) Many students graduate from Amherst with no course, or perhaps just one, in mathematics and science. The reaccreditation report suggests that given these low percentages, Amherst should "either reconcile the rhetoric of non-mandatory course distribution guidelines, or adopt requirements." Quite a while ago, Amherst did have a pretty tough math/science requirement. Nobody talks about reinstating that, but some people do wish for a return to distribution requirements.
At Amherst, our real focus has been on quantitative support (in both mathematics and science) rather than on quantitative literacy. This is because students who want to take mathematics and science courses often encounter serious difficulties, usually because of poor high school preparation. One strategy by which this support is provided is through the Quantitative Skills Center (QSC) which is led by the Quantitative Fellow, a recent graduate who serves a one- to two-year appointment. The QSC concerns itself less with quantitative literacy than with helping students (at many levels) succeed in whatever math/science/economics courses they choose to take.
Many professor hope that the Quantitative Skills Center can address analytic and inferential, not just informational, deficiencies. The college's Committee on Academic Support is currently studying a proposal to significantly expand the Center by hiring a permanent professional as director who could focus on the students' reasoning deficiencies. Right now, though, the Center provides tutoring, organizes study groups and topic-specific workshops, and hosts discussions on succeeding in science. Related programs include a pre-first-year summer science program and a January-term pre-calculus course. (Top)
As a result of recent changes in graduation requirements, students at Babson College are called upon to exercise and develop pervasive across-the-curriculum competencies throughout their academic and co-curricular program, rather than in a single area, division, or discipline. The pervasive competencies fall roughly into five areas: ethics and social responsibility; international and multicultural perspectives; leadership, teamwork, creativity; rhetoric; and numeracy.
The Mathematics/Science Division has identified eight competencies that fall into the numeracy area: Graduates who have met this competency are:
All students take courses in quantitative methods including calculus, probability, and statistics in their first year. This is followed by a course in applied quantitative modeling and applications taught in the intermediate management core courses in the sophomore year. All material is delivered in a "software intensive" environment in which heavy emphasis is placed on statistical software and spreadsheet modeling. Assessment is currently handled by traditional measures (projects, in- and out-of-class exams, homework, etc.). Plans for the immediate future involves processes intimately related to competency based assessment. (Top)
Bates expects that its graduates should have "an appreciation for the manner in which quantitative techniques can increase one's capacity to describe and analyze the natural and social worlds." The general education requirements for the baccalaureate degree implement this objective by requiring at least one course in which "the understanding and use of quantitative techniques are essential to satisfactory performance." Designations of these courses are made by the departments and cited in the college catalog. Some courses designated as meeting requirements in the natural or social sciences may be also be designated as satisfying this quantitative requirement.
Recently, the Bates faculty spent over two years debating possible changes in general education requirements. A stronger QL requirement was proposed and debated, but nothing was passed. What all this means in practice is that departments are free to designate courses satisfying this requirement. However, as some faculty admitted in the discussion of requirements, they often just use the quantitative designation as a flag to let students know that numbers will be used in the course. There is, in fact, no college-wide commitment to teaching quantitative literacy. The mathematics department has a course "Working with Data" that is designed to address these issues. But, in my opinion, the college as a whole is woefully behind in addressing the quantitative literacy of its graduates.
There is some hope on the horizon. A "Math Center," which has been proposed in various incarnations for over ten years now, has finally been approved by the administration. As some of us envision it, this Center could provide rich resources for improving quantitative literacy (not just remedial skills). (Top)
The faculty of Bowdoin College established a Quantitative Skills Program to serve all students because such skills are often required for careers that lead to administrative positions, for further study in professional fields, and for problem-solving, committee or organizational work and everyday life. Although most Bowdoin students enter college with excellent quantitative skills, not every student has a strong background in all the areas covered by the program. For example, many entering students chose to take calculus in high school instead of statistics, while others attended high schools not offering either.
All incoming students take a test during orientation to demonstrate their current proficiency in four areas: computation and estimation, probability and statistics, graphical analysis and common functions, and quantitative reasoning. The Quantitative Skills Program director analyzes the test results to determine areas of weakness and sends the results to each student's academic advisor.
Although there is no requirement for students to enhance their quantitative skills, the Program strongly recommends particular quantitative ("Q") courses to students who would benefit from applying the quantitative reasoning required for that particular class. Q courses are offered in both the natural and social sciences; many students satisfy the mathematics/natural science requirement with a quantitative course.
The Quantitative Skills Program also provides non-credit independent study plans customized to a student's needs. For students who need special help, a mentor is assigned to the Q courses the program recommends. The mentor leads weekly study group sessions and exam review sessions. He or she gives study strategies and may occasionally do some individual tutoring. For many courses, evening "brush up" sessions on quantitative techniques are available preceding their use in the class.
Courses that have received support from the Quantitative Skills Program include: Introductory Biology, Comparative Neurobiology, Introductory Chemistry, General Chemistry, Introduction to Computer Science, Introduction to Social Research, Microeconomics, Quantitative Analysis in Political Science, Introduction to College Mathematics, Statistical Reasoning, Differential Calculus, Introduction to Statistics and Data Analysis, Contemporary Astronomy, Physics of the Twentieth Century, Introductory Physics, Sociology Research Methods, and Women in Science. (Top)
At CSU-Fullerton, the general education requirement in mathematics is 3-4 units. The goals of this requirement are for students to:
Assessment of student performance is based on grades: to graduate, students must complete a general education mathematics course with a grade of C or better. (Top)
All students at Clark University are expected to pass at least one "Formal Analysis" course selected from such options as calculus, statistics for psychology, or other similar courses. However, before students can take any of these courses they need to score above 520 on the Math SAT or, if their score is below 520, then they must pass our locally written Formal Analysis (FA) exam. Students who fail to pass this FA exam (while scoring below 520 on the Math SAT) are routed to a proficiency course called Quantitative Thinking which they must pass prior to enrolling in an FA course.
As far as I know, these requirements have been in place for some time. However, this is my first year in a newly created position as Director of the Mathematics Center. By creating this Center and budgeting my position as a satellite to these requirements--although my responsibilities are not limited strictly to this role--the College is signaling a more proactive response to students needs.
The goal of the Mathematics Center is to provide support for all courses offered at the university where mathematics, quantitative reasoning, or mathematical applications arise. In this respect, we provide tutoring and workshops on (quantitative) course topics. In particular, our goal is to reach those students who require greater assistance and attention and to involve them in a friendly, supportive environment. We attempt to facilitate conceptual understanding of the topics involved, not merely help student prepare for exams or get through their homework (although these services are also provided). I'm a strong believer in cooperative learning, having worked with Uri Treisman at UC Berkeley a long time ago, and at UCLA and Cal Poly Pomona in their problem groups.
Since students are tracked based on results of the SAT and FA exams, we can assess their progress by monitoring their grades in the Quantitative Thinking course and subsequent Formal Analysis course. It may take some time, now that the Center is established, to develop more formal approaches to assessment. (Top)
The quantitative reasoning program at DePauw University was instituted in the early 1980s when the faculty voted to include three competencies as part of the graduation requirements for all liberal arts students--one each in writing (W), quantitative reasoning (Q), and seminar (S). Courses meeting these competencies are offered across the curriculum. Because writing is so pervasive in the college curriculum, students are expected to gain this competence early in their career. The Q competency is expected to be completed by the end of the junior year; often students meet this requirement with a course in their major. The S requirement is often met in senior seminars, again commonly in the major.
In order for a course to be labeled as "Q," faculty teaching the course must be Q-certified and their proposed courses must be approved by the Q faculty committee. Curriculum, instruction, and assessment must include significant quantitative components such as quantitative reasoning, problem solving, interpretation of quantitative data accompanied by decision making, and critical assessment of quantitative reasoning models. Evaluation for Q-competency is separate from the course grade: students do sometimes, however, successfully pass the course but fail to be Q-certified. Faculty members must describe to the Q committee (and later to their students) the criteria for earning a Q in their particular course.
Before offering a course as a W, Q, or S course, faculty members must first complete a one-week summer certification workshop for the particular competency they wish their course to address. During the Q workshop, faculty members discuss quantitative reasoning, hear presentations on various aspects of the Q program, listen to Q-certified faculty discuss their Q courses, and experience quantitative reasoning situations. As part of the workshop, and during a follow-up period, faculty members are expected to start work on developing their particular course as a Q course. In some cases, such as mathematics, science, or economics courses, it may be mostly a matter of documenting the inherently quantitative nature of the course. For other courses, faculty members may find the need to change or supplement their previous course in significant ways to meet the requirements to be a Q course. Faculty members have regularly considered the competency workshops to be a very valuable experience because it is one of few opportunities to work fairly intensely with, and learn from, colleagues from different disciplines.
Examples of recently offered Q courses include:
Astronomy Calculus Communication Research Methods Computer Science Contemporary Society Development of Modern English Discrete Mathematics Family and Community in America Introduction to Economics |
Logic Oceanography People and Politics in the US Physical Geology Physics Physiology of Exercise Psychology Statistics and Research Methods Research Methods in Political Science Sociology Research Methods |
Placement in the Quantitative Reasoning course was originally done by a combination of SAT-M scores and an in-house placement test. Although it is nice to have multiple criteria for placement, it became clear that the placement test was not adding enough information to be worth the cost of administering it to all students. So now placement is done on the basis of SAT-M scores alone, except for a borderline group for whom the placement test is required. The placement test contains 25 multiple-choice questions to be answered in 25 minutes. It is scored as "rights minus 1/4 of wrongs;" a passing score is 14.5. Any student who questions their placement into the developmental course may take the placement test to be exempted from this course. Generally, students with SAT-Math scores below 500 rarely succeed, but they have the right to try.
The issue of whether the developmental course in Quantitative Reasoning should be required or recommended still plagues us. Many students are often highly math anxious, math avoidant, or math incompetent. Forcing such students into a course that they view as remedial is educationally questionable, although it is fairly clear that they need some preparatory course before enrolling in a Q course. We are now trying to offer them other options within the framework of having to take an introductory level course before being eligible for a Q course.
For example, the mathematics department has added a "slow calculus" course to the curriculum, taking two semesters to cover Calculus I. For students who are interested in pursuing mathematics, science, or economics careers, taking the first half of this course instead of Introduction to Quantitative Reasoning and then taking the second half as their Q course seems like a possible option. Evidence shows that this may be a good option for selected students, but probably not for the weakest students.
Likewise, a "baby" statistics course designed as a pre-Q course for students interested in the social sciences is in the development stage. Also in the list of possibilities is a third option designed to be of interest to humanities majors. The current course could possibly be altered to meet this need, dropped altogether, or kept as another level in the Q program for the weakest students.
Introduction to Quantitative Reasoning is basically a problem-solving course with problems chosen from the "big ideas" of number, size, and shape (i.e., geometry and measurement), data and chance (i.e., statistics and probability), and algebra. Because the focus is on reasoning, the mathematical content is intentionally kept at a low level so that students can develop their reasoning and problem solving skills. Most of the students have had three, four, or even five years of college-prep mathematics in high school, but they have obviously never been asked to make sense of what they were learning nor to communicate their thinking and reasoning about mathematical ideas. For many this is the first time that mathematics has made any sense to them. Their mathematics autobiographies, written the first day of class, reveal anxieties, loathing, and misunderstanding of the subject. (One student reported emphatically that mathematics is the "most illogical subject in the curriculum!" One wonders what kind of mathematics teaching that student has been exposed to.)
Pedagogy is very important. Students spend most of their class time working together to reason through problems without the professor showing them the path to the solution. Students must reason in order to learn how to reason; watching the professor lecture isn't a very successful way to develop student's quantitative reasoning power.
The Q Center, part of a comprehensive Academic Resource Center, supports students in mathematics, science, economics, Q, and pre-Q courses with trained peer tutors, organized study sessions, and help with study skills in those courses. Tutor training is a semester long, credit-granting course, after which students may continue to work in the center for pay. (Top)
Following an investigation of quantitative skills among Hamilton students, a written examination was devised and given to all incoming first-year students to test quantitative skills necessary to make informed judgments about problems that have an essential numerical content, skills that should be part of the "intellectual equipment of any educated citizen." Subsequently, the committee recommended that the college establish a Quantitative Literacy Tutorial Center. Students scoring below a cutoff would be advised to pursue studies, including tutoring at the center, to improve their quantitative skills. Student tutors, all of whom have a firm mathematical background, are selected from majors in biology, chemistry, economics, mathematics, and psychology.
In 1995 the faculty voted to make QL a requirement for the class of 2000. Now, by the end of the first year, each student must demonstrate basic quantitative literacy either by scoring at least 50% on the Quantitative Skills exam (which each first year student is required to take during orientation), by passing a course having a significant quantitative/mathematics component, or by completing a non-credit-bearing tutorial through the Quantitative Literacy Center.
Qualifying quantitative courses include general biology, introduction to chemistry, ocean science, physics of architecture, as well as several beginning courses in mathematics and physics. In addition to the QL requirement, Hamilton requires students to take two courses in mathematics or science--many of which also fulfill the QL requirement. The faculty is now in the process of restructuring the goals and requirements for graduation, so the mathematics requirement (or perhaps the QL requirement) may change.
The mission of the Quantitative Literacy Center (QLC) is (a) to provide academic support to students who have failed the Quantitative Skills exam, and (b) to support, with peer tutoring, students who are taking courses with a quantitative component. QLC tutors serve as mentors for the non-credit-bearing tutorial chosen by some students as a way of fulfilling the QL requirement. (I interview students who take the non-credit-bearing tutorial, assessing their mathematics backgrounds and their feelings about taking mathematics.) The goal is to help students develop skills that would allow them to pass a retake of the Quantitative Skills exam. Drop-in tutoring at the Center is available to help first-year students who are taking courses to satisfy the QL requirement, as well as self-identified and referred students from all classes who need help with the quantitative, mathematical, or statistical components of a course. (Top)
Twenty years ago Harvard introduced a Core program of consisting of eight courses on broad themes required of all students. In addition, the Core legislation mandated that students demonstrate "competence in quantitative reasoning." Although the legislation did not define the meaning or level of this competence, faculty who implemented the quantitative reasoning requirement (QRR) decided to focus on two very important areas--data analysis and computer use--that were not part of the traditional sequence of mathematics. The goal of this requirement was that each Harvard graduate be "an intelligent reader" of reports and articles containing arguments "which are allegedly backed up by numerical data" and have "first-hand experience with both the strengths and weaknesses of the computer."
Two serious constraints limited the QRR right from the beginning. First, since the requirement was extracurricular (imposed in addition to a student's regular four courses), it could not be too demanding. Second, the possibility of serious opposition from people uncomfortable with quantitative thinking cautioned against a challenging requirement. Given these contraints, the faculty who implemented the requirement in the early 1980s decided just to equip students with rudimentary quantitative skills, hoping that this would encourage other faculty to make more use of quantitative ideas across the curriculum. By 1989, ten years after the requirement began, QRR was fully accepted. By then there were even calls for a more rigorous requirement.
The data interpretation part of the requirement was implemented by a 25-item multiple choice examination. The computer programming component was implemented by a test problem to be solved by writing and implementing a computer program (in any language). Both tests were offered several times each year. To prepare, students were encouraged to study brief review booklets written expressly for the requirement and to consult with QRR staff who were specifically assigned help students meet the requirement. Courses in statistics, quantitative reasoning, and computer science were allowed as alternatives to either or both components of the requirement.
Harvard students are very bright. Nonetheless, each year nearly half the students failed the first data interpretation test. The biggest challenge, it turned out, was to convince them "not to turn off their brains." Too many had been conditioned to think of mathematical techniques as formulaic, memorizable procedures that lead to one right answer. For example, many students had to relearn how to work with decimals and percentqages. Many don't think of number as meaningful; saying that 83% of 60 is 4.98 is, to many, just as acceptable as 49.8. Quite a few students will reach for their calculators when asked what 10% of 100. (And these are Harvard students!) Once they are engaged intellectually, however, many raced through the material with surprising ease.
In 1987, the report of Harvard's accreditation review recommended that the QR requirement be made more substantial. By being extracurricular, the requirement conveyed the message that the College does not take QR all that seriously. Because the requirment is met by passing tests, it was often perceived as a meaningless hurdle rather than as a meaningful set of useful skills. Finally, the extracurricular nature of the requirement limited significantly the amount of time students could be expected to invest.
Deductive Logic Health Economics The Magic of Numbers |
Uncertainty and Statistical Reasoning Algorithms and Data Strcutures Choice and Chance: The Mathematics of Decision Making |
During 1991-95, with support from the National Science Foundation, a task force of distinguished faculty at NYU created a multidisciplinary three-course curriculum intended to show how science works rather than provide hasty coverage of a large number of topics. This sequence, called Foundations of Scientific Inquiry (FSI),became a graduation requirement for all arts and science freshmen entering in the fall of 1995. FSI is one of two main components of general education, the other being a four-course sequence on Foundations of Contemporary Culture (FCC).
FSI was designed to address certain pervasive problems of the distribution requirement system that was in place in 1991. These include:
The program that emerged for FSI had three components which are taken in sequence:
For each component students are offered a very limited number of choices. For Quantitative Reasoning, the choices are mathematical patterns in nature, mathematical patterns in society, or mathematics and the computer. Quantitative Reasoning is designed to teach students to recognize mathematical patterns within verbally presented problems. The emphasis is not on technical skills--"Kafkaesque algebraic manipulations high school teachers are so fond of"--nor on memorization of facts. Instead, it approaches mathematics as the art of pattern recognition, which means:
Since the FSI courses are taken in sequence, they build on each other so that course content gradually becomes more sophisticated. All FSI courses have substantial lab components, and students make heavy use of scientific calculators in all aspects of the course. All courses have a significant quantitative component, and the two natural science courses emphasize the nature of scientific reasoning but also draw together knowledge from several areas of science. The FSI program, and especially the Quantitative Reasoning course, have been studied and adapted in many institutions. Texts for the course have been published by McGraw Hill.
From the beginning, the greatest barrier to success in the FSI program is students' intimidation by its quantitative dimension. A great many students are poorly prepared in mathematics, and fear it. Typically, 20% of entering students must take a remedial course called "Mathematical Thinking," which is an absolute prerequisite for entry into Quantitative Reasoning, the first course in FSI.
At the other extreme, from the time FSI began a small number of well-prepared students were permitted to bypass Quantitative Reasoning by substituting instead a main-line mathematics course such as calculus or statistics (or by scoring a 4 or 5 on AP Calculus).
Despite these efforts both to prepare weak students for Quantitative Reasoning and to encourage students who might be bored to take a course more appropriate to their preparation, many students were still intimidated by the atmosphere of the course. So beginning in 1997, the top 20-25% of incoming students (identified by FSI placement tests) were simply exempted from the Quantitative Reasoning Requirement. The result was astonishing. Morale and performance of the remaining students in all versions of Quantitative Reasoning improved significantly.
Once the very best students were removed, other more subtle problems remained. The mathematical topics in FSI are fairly elementary, but the way they are used is not. This created in some better prepared students a curious mixture of hubris and dismay. "I've seen these topics ever since junior high school," complained one student. "Now, because I'm forced to take this course, I've got a C on my transcript that's killing my grade point average." Such comments, often from students who have taken calculus in high school, revealed that most of these accelerated student do not know even these elementary topics at a level that would justify exemption.(Top)
Rhode Island College has long had a general education requirement including a mathematics course, a lab science course, and a third course either in mathematics or science. The pure liberal arts course is a survey course that is a variation of COMAP's For All Practical Purposes. We also have beginning courses for management majors, elementary education majors, a "technical math" course for medical technicians and some life science majors, a precalculus course emphasizing graphing functions and trigonometry, and beginning statistical methods. These courses all satisfy the general education requirement but, in my judgement, none of them can be described as a QL course.
We also have a for-credit course similar in content to high-school algebra II and a new non-credit remedial course called "Basic Math Competency" that does some arithmetic, elementary geometry, statistics, and algebra. This latter course was introduced in response to complaints from some departments, especially science and economics, that some students lack minimal quantitative skills. Students are forced into it if their SATs in mathematics are low enough and they fail a short-answer test on this material given to all students with low SATs, regardless of high-school record. This course, which replaced a traditional non-credit course that only covered the contents of elementary (first year) algebra, does have some QL-related goals. Completion of this "competency" requirement is a prerequisite to our general education mathematics courses.
Through the minimum skills requirement we want to ensure that all students have the minimum skills needed for success in courses in science, nursing, elementary education, etc., whereas through the general education requirement we want to ensure some exposure to the broad nature of mathematics. But we also have to be sensitive to program requirements in management, elementary education, and other areas. We do not officially use the term "quantitative literacy." Our assessment of students' quantitative skills (or "competency") is based on their success in the new low-level Basic Math Competency course and feedback (still indefinite) from instructors of general education courses in mathematics and in other departments.
It is my view that QL elements (by which I mean, working more with large numbers, with multiple step problems, with problems drawn from real societal issues, with problems involving comparisons, with problems where the directions are not completely specified, where the reasonableness of the answer is important) should be more extensively used in all the lower division courses that are used to meet the general education requirement. I do not think the College will officially establish a QL course, but some of us are thinking of trying it out with a special section of our existing liberal arts course--if we can find a textbook that we think will work. (Top)
All students at Sam Houston State University are required to meet a two-semester (6 hour) quantitative literacy requirement as part of their core requirements. In practice, most students meet this requirement by taking one mathematics course (College Mathematics) and one computer science course (Introduction to Computers). College Mathematics is taught predominantly by lecture in sections of 90 students, makes no use of technology, has little structured teamwork or writing, and is assessed almost entirely by means of traditional short answer or multiple choice tests. Introduction to Computing uses software that lacks real world context, fails to emphasize the importance of selecting appropriate software tools, and hardly mentions the common characteristics of application interfaces or the relationships among applications such as word processors, spreadsheets and databases.
This will soon change. The total number of semester hours for the core has been reduced from 52 to 42; one of the casualties was a 3-credit hour reduction in the quantitative literacy core, although individual departments or programs can continue to require more. To address deficiencies in the current offerings and to prepare for the reduced requirement, we decided to develop (with support from NSF) an integrated, introductory course in mathematics and computer science that creatively adapted key components of exemplary courses.
The goal of the new course is to develop problem solving skills through the judicious application of mathematical and technology tools. It extends student skills in interpreting and analyzing problems from a quantitative perspective, in identifying appropriate quantitative tools, in applying these tools in the construction of a solution, and in communicating solutions. In meeting these goals, the course is designed to provide a comprehensive and lasting foundation for the students' academic and professional career.
In achieving the goals of the course, students will be expected to identify appropriate quantitative and technological tools for use in problem solving, manipulate both qualitative and quantitative data using appropriate software, and use technology as a means of communication. Throughout the course, students will be helped to develop computer skills in a mathematical framework and vice versa. In addition, they will learn to represent and interpret quantitative information symbolically, visually, numerically and verbally.
Conducted in a PC laboratory setting, this team-taught course is activity driven, with professors serving as facilitators rather than as lecturers. The new course stresses group work to develop teamwork and communication skills, student projects to develop problem solving skills and a feeling for scientific inquiry, and active learning experiences. We expect to use a variety of assessment tools consistent with national trends and course goals.
Since it is important to start with students' experiences, topics have been chosen that are accessible to students with weak mathematical and technologically disadvantaged backgrounds. An important consideration in the choice of mathematical topics is whether they are applicable to real-world problems and whether a natural connection with current software exists. Based on these criteria, we have selected topics in word processing, presentation, and graphics software; spreadsheets and functions; linear programming; descriptive statistics; geometry and trigonometry; finance; modeling, curve-fitting, and forecasting; and Internet services and e-mail.(Top)
Three years ago the quantitative requirement at Skidmore was increased to include a second level, bringing it into complete parallel with the college's writing requirement. Upon entering, every student must demonstrate basic quantitative skills (what we call QR1) by scoring 20 out of 25 on an in-house Quantitative Reasoning exam. First-year students have up to four chances to pass the exam. Otherwise, or if they prefer, the requirement may be satisfied by passing a course in Quantitative Reasoning (Mathematics 100) before the end of the sophomore year. In addition, before the end of the junior year, every student must pass one course designated as Quantitative (or QR2). These courses are distinguished by employing some quantitative tool such as mathematics, statistics, or computing in a way that is central to the course. Such courses are offered in mathematics, computer science, economics, chemistry, physics, geology, psychology, sociology, and even in music and liberal studies.
The goal of QR1 is fundamental quantitative skill (arithmetic; simple measurement geometry; consumer issues; interpretation of simple data, charts and graphs; simple probability). The goal of QR2 is either to apply those fundamental skills in an academic discipline or to gain further quantitative skills, or both. Fundamental to both of these requirements is that students gain the confidence to confront quantitative questions and try to seek their answers.
For QR1, assessment is quite direct: Pass the test or pass MA 100. Since the content of those is very clear, so is the goal. For QR2, assessment is a much trickier question which we are now mulling over, among other things, in the face of a forthcoming Middle States review. Although we believe the variety of QR2 courses is a strength, this variety makes assessment of QR2 difficult. The only goal which is common to all QR2 classes is "QR-confidence," and how do you assess that? (Any ideas you have here for us would be most welcome!) (Top)
Trinity's faculty established a Mathematics Proficiency (QL) Requirement in 1987. The Math Center was established at the same time to administer the requirement. The proficiency of incoming students is determined by a test given each fall as part of the new student orientation program. The skills and concepts tested are grouped into four areas (numerical relationships, statistical relationships, algebraic relationships, and logical relationships) corresponding to Trinity's four proficiency courses:
Math 101. Contemporary Applications: Mathematics for the 21st CenturyAll the courses offered by the Math Center stress the transferring of mathematical skills and attitudes in the service of problem solving and anchor quantitative ways of analyzing and solving problems in contexts using Hartford data.
The proficiency exam and the QL program at Trinity have changed, of course, in the eleven years since the requirement was established. Four years ago the only QL course offered by the Center was Math 101, the foundations course described in the CUPM report "Quantitative Reasoning for College Literacy." In last four years we have created three additional half-semester courses for those students deemed "quasi-proficient" who needed work in some, but not all, of the areas tested. We think the courses are more in the spirit of the report than the drill-type exercises formerly administered (like medicine!) by the Center.
We are pleased with this palette of four innovative foundations courses, which provide a varied introduction to quantitative reasoning. The Math Center has been less successful in instituting a college-wide program to reinforce the "habits of mind" we try so hard to establish in these introductory courses, which are taken before students complete their second year at Trinity. As far as college requirements go, a student is deemed proficient (read quantitatively literate) upon completing the appropriate foundations course. We of course know better.
The role of QL at Trinity has been significantly enhanced by the work of Helen Lang, chair of the philosophy department, who has instituted an extensive program of mathematics and science laboratories in humanities and social science courses with the help of substantial funding by both the NSF and the NEH. Historically, philosophy, mathematics, and science have always been closely related and a major part of philosophy's task as a discipline has been to account for the successes and failures of mathematics and science. Under these grants Trinity has worked to develop specific problem-solving skills in mathematics and science settings appropriate to the humanities and social science disciplines.
These grants have enabled me to partially realize one of my goals as Director of the Center: to increase the quantitative content of non-math courses at the college. For example, I have created labs for a Latin American history course exploring Mayan mathematics and astronomy, and mathematical analysis of historians' arguments concerning the size of the indigenous population of the New World at the time of European discovery. I am currently working with a classicist to create similar labs for an archaeology course. Other mathematicians and scientists have created labs on the physics of sound for a linguistics course, on epidemiology for a history course, and on the chemistry of pottery for a philosophy of art course. Similar laboratories have been attached to courses in ancient, medieval, and modern philosophy, medical ethics, philosophy of science, philosophy of art, and philosophy of sport. Laboratories and Literacy: Mathematics and Science in the Humanities contains a complete list of these courses.
I see the extension of quantitative thinking throughout the curriculum and throughout a student's four years at Trinity as the most important--and elusive--long term goal of our program. So far, I have only been able to achieve an "ad-hoc" approach, giving guest lectures in courses and co-curricular programs, and working with the laboratories project. Quantitative literacy is not seen by the mathematics department at Trinity as its concern. I have hopes that with the addition this fall of another staff member to the Math Center, there will be more opportunity to support quantitative work by colleagues in other departments. To this end, the sessions sponsored by the MAA and the proliferation of programs at other institutions are valuable both as models and examples to help convince others at Trinity about the value and necessity of quantitative literacy for all students. (Top)
The Mathematics Department at the University of Colorado at Denver teaches a one-semester QL course called "Mathematics for Liberal Arts Students" which is currently based on the book Using and Understanding Mathematics: A Quantitative Reasoning Approachby Bennett and Briggs. This course is one of two courses required of students who are not in the algebra-calculus track; the other is a solid computer literacy course. This QL requirement for the campus has not changed in several years.
The goals of the course are to provide liberal arts students with a (possibly last) opportunity to understand how mathematics impacts their everyday lives, their future courses at the university, and their future careers. We teach a very practical course that is designed to illustrate mathematics in context. The course relies considerably on news articles, real data, and practical problems.
Quite honestly, we have not made much progress on systematic and comprehensive assessment of quantitative literacy. At the moment a student who passes the QL course meets the goals of the program. This is not an adequate process and needs much more attention. One of the dilemmas of designing and offering QL programs is finding faculty members--particularly mathematics faculty members--who are interested in devoting any time to QL courses and programs. For most faculty members, it is simply an unrewarded, low-priority way to spend one's time. I contend that QL courses should be one of the highest priorities for a mathematics department, if only because it impacts so many students (especially if we reroute students who are currently in college algebra courses, when they really should be taking good QL courses.) (Top)
The University of Massachusetts is in the process of instituting new general education requirements. As part of our "first year experience" we are introducing a Math/QR requirement that students can meet either by passing a test or by taking one of two courses in either mathematics or quantitative reasoning. The mathematics course is roughly equivalent to traditional college algebra and serves as a prerequisite for precalculus. The vanilla version of the QR course (which we're piloting now) will serve as a prerequisite for other mathematics, statistics, and methods courses. Both are intended to be foundation courses, not terminal courses.
The QR course contains some basic statistics and both linear and exponential models. Like all such courses, it lies somewhere in the intersection of college algebra, statistics, and liberal arts mathematics courses. Some sections are using Kime and Clark's Explorations in College Algebra(Wiley) and others Bennett and Briggs' Using and Understanding Mathematics: Quantitative Reasoning Approach (Addison Wesley). In the future we may offer more versions of the QR courses. (Top)
The University of Nevada at Reno requires one mathematics course of every student, the lowest being a "math for liberal arts" class taught from Johnson and Morwey's Mathematics: A Practical Odyssey. Other courses used to fulfill this requirement are college algebra and trigonometry, elementary statistics, and calculus. The goal of this requirement is that students should receive a basic education in mathematical skills and concepts; should take other courses that utilize these skills and concepts; and that as a consequence they will be helped to learn how to learn.
In addition, through an NSF-supported Mathematics Across the Curriculum (MAC) project, the University is seeking to improve the quantitative and mathematical skills of all students and to help them better appreciate the importance and utility of mathematics. This is done primarily by working with faculty in various disciplines to assist them in enhancing the quantitative and mathematical content of their courses, and then providing them and their students with the necessary support.
One component of MAC is a series of Gateway Exams intended to test the mathematical skills students will be required to have for success in various courses in many different departments. Gateway exams involve no more than basic mathematical skills that students should reasonably be expected to have already mastered. Therefore, a passing score is usually 80% or higher. Gateway exams are intended to inform and diagnose, not to punish or discourage; they inform students about the mathematics that will be used in a particular course and diagnose students' ability to handle that mathematics. Based on the results of this diagnosis, help is provided to those who need it. Generally, students must pass the appropriate Gateway Exam in order to complete the course. (Top)
Most graduates of the University of Oregon either get a B.A. (which requires two years of some foreign language) or a B.S.(which requires instead some degree of mathematical literacy). The latter can be certified by taking three quarters of mathematics or computer science. Historically, the lowest mathematics class that qualified was College Algebra (Math 111) which leads to a course on functions (trigonometry) and calculus (either scientific or business-oriented).
The mathematics department has known for a long time that this is a tedious and often irrelevant sequence for the weaker students (who don't want to take a foreign language either). So about ten years ago we developed an alternative sequence that would be new, different and more interesting--and not require even College Algebra. Since this would be the final mathematics course for almost all students, we also wanted it to convey that mathematics is a living subject.
The new sequence, Math 105-106-107, begins with a two-course survey of practical mathematics and concludes (in Math 107) with an introduction to the "ideas of calculus." In the beginning, classes were limited to 28 students and taught by both regular faculty and graduate students; the method of teaching, different from all other courses, stressed group work using worksheets. Ultimately the teaching was turned over to graduate students (who were assisted by undergraduates).
This did not work as well. Although a few of the graduate students enjoyed the challenge and recognized that this was a good course to add to their resume, many resented the extra work required to teach the course and to learn material they didn't already know. This resentment was fueled by some faculty who felt that the graduate students' time should instead be focused on their own coursework and research. Many in the department came to resent that we were putting more resources per student into these general education courses than we were in mainstream courses like calculus.
Faculty attitudes were not the only problem. So were students'. Although Math 105-106-107 was designed as a freshman course, students put it off as long as possible. Typically, two thirds were juniors or seniors who entered with hostility and thwarted any effort to make it an effective course. The course became famous as a "mickey" and students resented any effort to retain substance.
A few years ago, under further financial pressures, the mathematics department decided to offer this course in large sections taught by faculty with undergraduate (not graduate!) assistants, many of whom are really excellent. Unfortunately, the course did not improve. Now no one wants to teach it. The course isn't working for the students or the department. The mathematics department has talked about killing it, but if it did that it would lose a lot of credit hours and alienate a lot of faculty in other departments whose students are served by this course. But if the course is to be retained, it needs to be changed to something that faculty and students can tolerate. (Top)
"The ability to think clearly and critically about quantitative issues is fundamental to effective citizenship in the modern world. Further, mathematical reasoning is important in a wide range of disciplines. The College wants to ensure that mathematics does not serve as a barrier to those students who might otherwise consider courses or careers that require basic quantitative reasoning skills." With this as rationale, in 1997 Wellesley College established a quantitative reasoning requirement for all students consisting of two parts: basic skills and overlay courses. The college was concerned that some students might avoid quantitative courses because they feel that they lack the needed quantitative skills. The QR requirement seeks to ensure that no student avoids courses (or careers) solely because they entail mathematics.
The basic skills component is intended to help students gain the mathematical skills they need for courses with a quantitative focus. These skills include arithmetic and basic algebra, reading and preparing graphs, and the ability to draw conclusions about the world based on quantitative information. This component can be satisfied either by passing the QR assessment (taken by all incoming students during orientation) or the basic skills course QR 140. This is a full-credit course that includes a review of algebra, geometry, and the analysis and interpretation of data. Basic skills are stressed, but emphasis is placed on conceptual understanding and the relevance of mathematics to everyday life. Spreadsheets are used in weekly computer labs to explore various mathematical models of real-world phenomena. (The basic skills component must be satisfied before a student can register for a course that satisfies the overlay component as well as certain other courses at the discretion of individual departments.)
The overlay component is designed to engage students in the analysis and interpretation of data in a scientific or social context and to provide an understanding of the statistics used in everyday life. This component can be satisfied by passing a QR overlay course, offered by a number of departments, that emphasizes the analysis and interpretation of data. More than a dozen different QR overlay courses are offered by the departments of astronomy, biology, chemistry, economics, geology, mathematics, political science, psychology, and sociology. (Normally, a single course cannot be used to satisfy two separate distribution requirements. However, a single course can be used by a student to satisfy a distribution requirement and an overlay requirement.)
The quantitative reasoning program at the College administers the quantitative reasoning requirement; provides instruction for the QR basic skills course, QR 140; provides tutorial support to students in quantitative reasoning overlay courses; and offers curricular support to faculty interested in modifying existing courses, or designing new ones, so that these courses will satisfy the overlay component of the quantitative reasoning requirement. (Top)