Enhancing Entry-Level Mathematics Student Success at

Oklahoma State University

A Report of the Committee to Explore Enhancements to the Mathematics Education

Curriculum at Oklahoma State University

June 20, 2011

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Table of Contents

Introduction

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Identification of the Problem at OSU What Some Universities Do to Address the Math Success Rate Problem Are Students "Ready" for College-level Study of Mathematics? A Fundamental Premise A General Strategy for Solving the Problem

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Committee Recommendations MLRC - Mathematics Learning Resources Center Placement Exam Placement Based on Exam Results Advising Recommendation The ALEKS Web-Based Placement and Learning System The Calculus Sequence A Pedagogical Model to Teach the Learning and the Doing of Mathematics

within the Mathematics Course Faculty Oversight Position Increased Mathematics Staffing Outreach Program to High Schools Additional Considerations

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OSU Data and Attributes of At-Risk Students

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Implications from a Statistical Analysis of the Data

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References

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Appendices Appendix A - Descriptions of OSU MATH Courses Appendix B - Assessment and Placement through Calculus I at the University

of Illinois Appendix C - PREPARATION for COLLEGE READINESS: A PreK-16

APPROACH Appendix D - Attributes of At-risk Students

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Enhancing Entry-Level Mathematics Student Success at Oklahoma State University

A Report of the Committee to Explore Enhancements to the Mathematics Education Curriculum at Oklahoma State University

Introduction In mid October 2010, Provost and Senior Vice President Robert J. Sternberg invited mathematics professors Douglas B. Aichele and Benny Evans to serve as co-chairs of the Committee to Explore Enhancements to the Mathematics Education Curriculum at Oklahoma State University; both agreed to serve. Provost Sternberg invited the individuals below to serve as Committee Representatives; all agreed to serve. Dr. Brian Adam, Professor, Ag Economics Mr. Chris Campbell, Assistant Director, University Academic Services Dr. James Choike, Professor, Mathematics Dr. John Gelder, Professor, Chemistry Ms. Linda Hall, Mathematics Curriculum Specialist, Edmond Public Schools Dr. Tim Krehbiel, Professor, Finance Dr. Brenda Masters, Professor, Statistics Dr. Jeremy Penn, Director, University Assessment and Testing Dr. James Smay, Associate Professor, Chemical Engineering Dr. Juliana Utley, Assistant Professor, Teaching and Curriculum Leadership Dr. Jim West, Professor, Electrical and Computer Engineering The organizational meeting was held on November 30, 2010. At this meeting, Provost Sternberg charged the committee to seek better ways to reach learners in entry-level mathematics classes. He spoke about: (1) more effective pedagogy; (2) curriculum organization; (3) effective intervention strategies; (4) interface with K-12 schools to better meet the needs of entering freshman; (5) investigate new mathematics courses in the transition; (6) investigate ways to more effectively reach students by teaching them at the level where they are. The desired outcome of these enhancements should be greater success rates for students as learners. Provost Sternberg also mentioned that the committee's study should not be limited by budget constraints but rather to think "big" about ways to enhance student success. He expressed a desire to have the committee's report completed by June 2011.

Identification of the Problem at OSU Following the organizational meeting, the Committee to Explore Enhancements to the Math Education Curriculum began regular meetings starting with a review of the DWF rates for all of the OSU entry-level mathematics courses. This review included the following mathematics courses: MATH 1483: Mathematical Functions and Their Uses

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MATH 1493: Applications of Modern Mathematics MATH 1513: College Algebra MATH 1613: Trigonometry MATH 1715: Precalculus MATH 2103: Elementary Calculus MATH 2123: Calculus for Technology Programs I MATH 2133: Calculus for Technology Programs II MATH 2144: Calculus I MATH 2153: Calculus II MATH 2163: Calculus III MATH 2233: Differential Equations A special thanks is accorded to Dr. Brenda Masters, Professor of Statistics, for obtaining OSU DWF Rates for these courses. The following tables summarize DWF Rates for these courses by Fall term, by Spring term, and by Academic year (Fall plus Spring term) beginning with Fall 1999 and including Fall 2010. Table 1 displays percent of DWFs for each of these courses. Table 1.

DWF Rates for Entry-level MATH Courses

Course Percent

of DWFs in Fall

Percent of

DWFs in

Spring

Percent of DWF

in Acad.

Yr. MATH 1483 34.3 36.5 35.3

MATH 1493 33.3 34.3 33.8

MATH 1513 36.5 44.8 40.5

MATH 1613 34.7 35.7 35.2

MATH 1715 32.3 50.1 40.8

MATH 2103 36.5 33.2 34.9

MATH 2123 41.7 44.5 43.0

MATH 2133 30.8 34.6 32.6

MATH 2144 43.3 52.0 47.4

MATH 2153 40.4 38.6 39.5

MATH 2163 28.1 28.0 28.1

MATH 2233 31.3 29.5 30.5

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Table 2 displays the same data but arranges the courses in descending order by DWF rates. Table 2.

Entry-level MATH Course DWF Rates in Descending Order

Course Percent

of DWFs in Fall

Percent of

DWFs in

Spring

Percent of

DWFs in

Acad. Yr.

MATH 2144 43.3 52.0 47.4

MATH 2123 41.7 44.5 43.0

MATH 1715 32.3 50.1 40.8

MATH 1513 36.5 44.8 40.5

MATH 2153 40.4 38.6 39.5

MATH 1483 34.3 36.5 35.3

MATH 1613 34.7 35.7 35.2

MATH 2103 36.5 33.2 34.9

MATH 1493 33.3 34.3 33.8

MATH 2133 30.8 34.6 32.6

MATH 2233 31.3 29.5 30.5

MATH 2163 28.1 28.0 28.1 Examining Table 2, we notice that the course with the greatest DWF rate is MATH 2144, Calculus I, the entry-level calculus course for engineering, science, and mathematics majors. This course is the fundamental entry-level course for most of the degrees offered by OSU in the so-called STEM majors. The four courses that have DWF rates greater than 40% are either Calculus I (MATH 2144 is engineering Calculus I and MATH 2123 is Tech Calculus) or courses that directly relate to mathematics preparation leading to STEM majors at OSU (MATH 1715 is Precalculus and MATH 1513 is College Algebra). To provide some national perspective in interpreting these OSU DWF rates, we feel it is appropriate to cite the following studies. The Mathematical Association of America's (MAA) Task Force on the First College-Level Mathematics Course reported that the DWF rate for College Algebra ranges between 40% and 60% nationwide ( see URL: http://www.maa.org/t_and_l/urgent_call.html). The MAA's report Algebra: Gateway to a

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Technological Future, edited by Victor J. Katz indicates that nationwide the DWF rate for College Algebra is in excess of 45%. Thus, many college and universities experience greater DWF rates than we have here at OSU. To highlight the particular issue with DWF rates in Calculus, we note that AP Calculus AB scores over the last six AP exams show that 40.9% of the AB test takers score less than 3, the equivalent of a D or F [AP Report to the Nation, 2005 - 2011]. As we examine the DWF rates for Calculus, whether at OSU, or nationally at other universities, or even at the exemplary AP Calculus program, the fair and the underlying assumption is that students enroll in Calculus, either in college or in AP, because they have the appropriate transcript prerequisites for Calculus. But transcript prerequisites, as OSU and AP data suggest, do not automatically translate into being ready for success in Calculus. This situation raises the question "are students really ready for calculus at the college level," and, more generally, "are students really ready for college level mathematics?" While OSU's DWF rate is not excessive in comparison with national data, it is entirely appropriate for the Committee to Explore Enhancements to the Mathematics Education Curriculum to examine the question of enhancements and strategies that will lead to increased student success in mathematics at OSU. What Some Universities Do to Address the Math Success Rate Problem As we have indicated earlier, the problem of DWF rates in entry-level mathematics courses exceeding 40% is not unique to OSU. In this section of the report, we describe what some colleges and universities are currently doing to increase success rates in entry-level college mathematics courses. Our list of colleges and universities are:

University of Illinois at Champaign-Urbana University of Texas at Austin Arizona State University University of Arizona SUNY at Potsdam.

This list contains a Big 12 university, a Big 10 university, two of the comprehensive universities in the state of Arizona, and a smaller school, SUNY at Potsdam. For a general comparison and an overall description of these colleges and universities compared to OSU, see Table 3 below. The data in Table 3 was obtained from College Results Online, a site located at the URL http://www.collegeresults.org.

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Table 3.

College

2008 6-Yr Grad Rate

% Pell Recipients among Fr.

% Minority

Est. ACT

Score

Student Pop

Carnegie Classification

Student Expenditures/Total

FTE

U of Illinois 82.0% 16.0% 13.9% 28 30,435 Research

Very High $11,978

U of Texas 77.8% 23.0% 22.9% 27 35,560 Research

Very High $13,796

OSU 59.8% 22.0% 15.8% 25 16,856 Research High $9,687

U of Arizona 57.2% 19.0% 21.6% 24 26,509 Research

Very High $12,671

Arizona State U 56.0% 20.0% 18.9% 24 34,117 Research

Very High $15,096

SUNY at Potsdam 49.3% 34.0% 6.3% 23 3,525 Masters Large $11,092

University of Illinois at Champaign-Urbana The University of Illinois used the ACT score to recommend placement in an appropriate entry-level mathematics course. But, prior to 2007, the use of the ACT score as a placement tool still resulted in high proportions of students failing to complete Calculus I at University of Illinois. In 2007, the University of Illinois developed a program to deal with high DWF rates in lower division mathematics courses. This program focused on the placement issue for calculus and precalculus. Basically, the program that was adopted was an exclusionary model. That is, a placement test is used to determine a student's readiness for calculus, and students who fail to make a pre-determined cut-score are not allowed to enroll in calculus. A second cut-score is established for precalculus. Even if students can demonstrate that they have met all other prerequisites, enrollment is blocked until a pre-assigned cut-score on the placement exam is reached. During the first week of class, the Registrar will as a matter of policy drop students who have not achieved the required cut-score. While the University of Illinois placement program is largely exclusionary, students are given help and support to raise their placement scores. The placement tool and the support system is the online ALEKS program. The following description of the ALEKS software is provided by its web site.

ALEKS , Assessment and LEarning in Knowledge Spaces, is a web-based, artificially intelligent assessment, and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained. ALEKS courses are very complete in their topic coverage and ALEKS avoids multiple-choice questions.

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Students pay $10.00 each time they wish to take the placement exam at the University of Illinois. If additional help is needed, students can purchase an ALEKS learning module for $35. A report on the ALEKS program implementation at the University of Illinois is in the Appendix (see the paper entitled "Assessment and Placement through Calculus I at the University of Illinois" by Alison Ahlgren and Marc Harper). Further information about the ALEKS system for higher education can be obtained at http://www.aleks.com/highered/. University of Texas at Austin The University of Texas also uses the ALEKS system both for placement and for remediation, following pretty much the implementation program developed and instituted by the University of Illinois. In addition to the use of the ALEKS web-based system, the University of Texas also offers a Mentor Academy, which assigns to each incoming student an undergraduate mentor. The mentor, among other things, is expected to "engage their freshman mentees and teach them the skills they will need to become successful both in and outside of the classroom, and prepare each one to be dynamic, engaged and accomplished students at The University of Texas." Further information about the Mentor Academy at the University of Texas is available at http://www.utexas.edu/tip/MentorAcademy/. Arizona State University In 2006, the ASU provost commissioned a multi-disciplinary faculty committee to examine and recommend possible solutions to persistence problems in Arizona State University’s freshman programs in science, technology, engineering, and mathematics (STEM). This committee issued its report, Failing the Future – Problems of Persistence and Retention in Science, Technology, Engineering, and Mathematics (STEM) Majors at ASU, a year later in 2007. One of the committee's findings that they termed as "chilling" in their report was the following:

Forty-three percent of students who receive an A in precalculus and who had declared a STEM major that requires calculus chose not to take calculus. In other words, even the very best students in precalculus who thought they wanted to enter a STEM major are leaving STEM.

In addition, this ASU committee found that during the period fall 2001 through fall 2006, • 43% of engineering majors, • 54% of mathematics majors, • 51% of physical science majors, and • 50% of technology majors

who enrolled in Calculus I at ASU and whose intended majors required Calculus II never earned credit for Calculus II. In this report the committee placed a focus on persistence and retention of students in

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the STEM majors. The committee defined persistence as "the rate at which students in a major succeed in (get credit for) the next course in a sequence that is required by that major. Among the recommendations that this committee made to the ASU provost for improving ASU's freshman STEM programs were:

• Establish a system that rewards departments for high persistence rates and high retention rates;

• Establish a system that rewards instructors of entry-level courses for adopting and modeling student-centered methods of instruction as measured by best practices observation protocols and for achieving high persistence rates among their students from one course to the next;

• Create a virtual college for tenure-track faculty who have declared a scholarship of teaching as their primary emphasis;

• Encourage departments to adopt and use a learner-centered pedagogy in place of the traditional content-centered lecture style pedagogy;

• Provide workshops for instructors, teaching assistants, and faculty that address issues of scientific teaching and best practice in STEM pedagogy, and expand opportunities for undergraduates to participate in research mentored by a faculty member.

University of Arizona The Arizona State University 2007 report "Failing the Future" cited University of Arizona, its sister institution, as an example of a university that was able to improve student success in mathematics. In 1983 the University of Arizona’s mathematics department initiated a self-study due to attrition rates reaching 50% in some beginning courses. After initial assessment of its undergraduate education, the mathematics department initiated a five-year implementation plan to address the problems, based on five premises:

• Students must be placed in courses commensurate with their abilities; • Students must be provided with a supportive learning environment and a caring

instructor committed to undergraduate education; • Entry-level courses must be structured to meet current student needs • Future success of the program relies on effective outreach programs to local

schools • Students need exposure to technology to enhance the learning experience.

The University of Arizona's action plan included the following key recommendations:

• reduce class size; • institute a mandatory math placement and advising program; • institute a new precalculus course; • offer a calculus I course with five credit hours; and • replace the self-study intermediate and college algebra courses with a two

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semester sequence in college algebra taught in small classes. The above action plan began the process of change in 1985, which over twelve years resulted in a dramatic improvement of the educational environment. The University hired a dozen new faculty members, instituted a Mathematics Center with computer facilities and special services, and augmented the budget to improve undergraduate education. (A historical note that is worth citing is that the Mathematics Center at the University of Arizona was modeled after the OSU Mathematics Learning Resource Center (MLRC) that was conceptualized, designed and developed by the OSU Mathematics Department and is still in existence today, operating and serving OSU students.) Changes were spearheaded by administration, faculty, and lecturers. In 1997, all freshman level mathematics courses were taught in classes of size 35, and passing rates improved by up to 40%. The mathematics department had excellent relations with other University departments, high schools, and with the local community college. The Math department became a national leader in calculus and differential equation reform and technology usage. The number of mathematics majors dramatically increased. SUNY at Potsdam SUNY at Potsdam is not a peer university of OSU, nor is it a peer university of the other universities being considered in this section of "best practices" relative to entry-level college mathematics courses. However, SUNY at Potsdam is included in this report because of its spectacular success in recruiting and retaining mathematics majors. The primary philosophy at Potsdam that governs this mathematics major program quite possibly has something for OSU to consider relative to its entry-level mathematics courses and the students that take these courses. The Potsdam philosophy is summed up as "Teach the students you have, not the ones you wish you had" (attributed to Clarence Stephens of SUNY Potsdam in [Spencer, 1995, p. 862]). As a result, the highly successful Potsdam program for mathematics majors is based "on the premise that the study of pure mathematics can be undertaken successfully by a large number of students if they are provided with a supportive environment including: careful and considerate teaching by a well-trained and dedicated faculty, continual encouragement, successful (student) role models, enough success to develop self-esteem, enough time to develop intellectually, recognition of their achievement, and the belief that the study is a worthwhile endeavor. [Spencer, 1995, p. 860]. Are Students "Ready" for College-level Study of Mathematics? The dominant college-level pedagogy is situated in the traditional lecture. The pedagogy of the lecture can be effective, especially in the hands of an educator who takes pains to organize the content, elucidate the underlying "big ideas," illustrate these important ideas with well-chosen examples, and connect these ideas to previous content, while setting the stage for future content. While the lecture pedagogy can be helpful in guiding learning, the way that students truly learn mathematics is by doing mathematics.

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George Polya, an internationally acclaimed 20th century mathematician, captured well what is gained by "doing mathematics" when he wrote:

Solving problems which are not too easy for [the student], the student learns to persevere through unsuccess, to appreciate small advances, to wait for the essential idea, to concentrate with all his might when it appears. If the student had no opportunity in school to familiarize himself with the varying emotions of the struggle for the solution his mathematics education failed in the most vital point [Polya, How to Solve It, 1973].

College-level mathematics instructors assume that students "know" mathematics, when, in most cases, all they know is a collection of facts or procedures, many of which are remembered imperfectly. Students need to learn how to learn and how to do mathematics the "right" way. Another factor that supports the need to address how to learn and how to do mathematics the "right" way within the instructional delivery of calculus is a recent study that shows "a dramatic decline in study time occurred for students from all demographic subgroups, for students who worked and those who did not, within every major, and at four-year colleges of every type, degree structure, and level of selectivity" [Babcock and Marks, Leisure College, USA: The Decline in Student Study Time , American Enterprise Institute for Public Policy Research, No. 7, August 2010]. As just one example, we consider data from a recent study conducted by Duke University. Duke University is a highly selective university with an average SAT score for entering freshmen of 1435 (equivalent to an ACT score of 32). For comparison, the average ACT score for entering freshmen at Oklahoma State University is 25. In 2007, a Duke University "Campus Life and Learning Project" [The Campus Life and Learning Project, Duke University, June 2007] study found, from student interviews, that the average student-reported academic time per week (academic time is defined to be class time plus study time) was 24.4 hours per week. In 1961, a similar survey of Duke students found that the average student-reported academic time per week was 48.6 hour per week. One way of dramatically interpreting these data is that, in 1961, going to college was equivalent to a full-time job, while for today's students going to college is equivalent to a part-time job. A Fundamental Premise Students are placing themselves at risk for success in college-level mathematics, not just calculus, because they are not prepared with the skills for learning and for doing mathematics nor are they prepared for recognizing, through meta-cognitive learning feedback, what is an appropriate time-on-task needed for success in mathematics. If colleges and universities desire to address the issue of increasing student success in college entry-level mathematics courses, colleges and universities must address the problem of readiness for the study of college mathematics. To address the problem of student "readiness" for college-level study of mathematics, we recommend that, instead of thinking only in terms of "remediation," college and university intervention strategies should think in terms of addressing, not only areas of content weakness, but also "how

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to learn mathematics and how to do mathematics." More specifically, the committee has determined that there are at least two basic conditions that are related to the student readiness issue and that contribute to lack of success in entry-level mathematics courses. These are:

• Improper placement: Mathematics courses are cumulative in building content and understanding, unlike some areas of study. Students who enroll in a mathematics course, even those with a transcript certification of an appropriate prerequisite course, may still have little chance of success, especially if their previous knowledge is memorized facts or solution procedures based on imitating worked-out examples. It is crucial, in addition to avoiding the enormous waste of time and resources, that students be placed in courses that are commensurate with their level of mathematical skill.

We note that finding the proper math placement for entering students was a major component in the implementation strategies for increasing the success of students at the University of Illinois and the University of Texas. Proper math placement was also a chief recommendation at the two Arizona universities.

• Lack of effective participation in the learning process: Many students begin

college level mathematics courses with the proper prerequisites, but quickly become discouraged with some even giving up entirely. Students who make no effort are certain to fail. But the Committee believes that many unsuccessful students do try, at least until they give up. The issue with these students is that they simply do not know how to effectively learn and do mathematics. The Committee believes that these are the students who can, and should, be helped.

The University of Texas has instituted a Mentor Academy as another intervention strategy, in addition to the ALEKS placement and remediation system, to shore up entering students' transition to effective participation in a college level mathematics course. The University of Texas implicitly recognizes the fact that many of their entering students are not "ready" for college level courses; in spite of the transcript evidence that says that they are ready. The OSU Committee to Explore Enhancements to the Mathematics Education Curriculum notes that University of Texas entering freshmen are much better prepared for college than are OSU students (Average UT ACT = 27 compared to Average OSU ACT = 25). The OSU Committee believes that OSU students' lack of effective participation in mathematics is critically related to student skill in learning and doing mathematics.

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A General Strategy for Solving the Problem Entry mathematics courses at OSU should be designed to focus on: (1) the content of mathematics: moving students forward in content; (2) learning mathematics: addressing, within the course, the right way to learn mathematics; and (3) doing mathematics: also, within the course, helping students to become "familiar with the varying emotions of the struggle for a mathematical solution." With regard to the learning of mathematics the "right" way, recent research in how people learn, examining learning in general and mathematics in particular, has enlightened the process of learning, reinforcing elements that common sense suggested were important to learning, while also bringing to light other principles that are important to learning, but were hidden from view. Current research on learning identifies seven principles that are at the heart of quality learning. These are: The Learning Research Principles 1. Conceptual understanding facilitates learning, i.e., “big ideas” help to organize

learning. 2. “New” knowledge is constructed from “old” knowledge. 3. Metacognitive strategies are critical to learning, i.e., talking to yourself as a means

of monitoring your learning helps learning. 4. Learners have different strategies and learning styles. 5. Learning is situated in activity, i.e., learning is acquired by doing and by thinking

Socrates once said: “I cannot teach anybody anything; the best that I can do is to make them think.”

6. Motivation and self-confidence are important. 7. Learning is a human and social endeavor. [Gollub, J. P., Bertenthal, M. W., Labov, J. B., & Curtis, P. C. (Eds.). (2002). Learning and Understanding: Improving advanced study of mathematics and science in U. S. high schools. Washington, D.C.: National Academy Press.] Entry-level mathematics courses should leverage these research findings in how people learn by incorporating them into the instructional process for mathematics.

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Committee Recommendations MLRC – Mathematics Learning Resource Center The Committee recommends funding for the renovation, furnishing, and continuance and enhancement of the MLRC as well as increased funding for MLRC staff. The MLRC is critical for providing support services to OSU students in their quest for success in entry-level mathematics courses. It is also crucial for continuation and expansion of computer-assisted courses such as college algebra.

Background: The MLRC was established in 1984 as a computer laboratory and student assistance and support center in mathematics. When the MLRC was opened in 1984, it was the first of its kind to offer a range of services integrated with the mathematics instructional program to support students taking entry-level mathematics courses. Since 1984 many mathematics departments across the country have followed the OSU lead by establishing centers modeled after the MLRC. Today the MLRC serves as a meeting place for computer assisted courses in College Algebra and provides over 50 hours per week of free tutoring on a walk-in basis for all lower division mathematics students. It is an integral part of our undergraduate mathematics instructional program, and it plays a central role in current and future computer-assisted courses. The center is currently housed on the 4th floor of the Classroom building. Permanent space for the MLRC has been allocated in the basement of the Classroom building, but significant refurbishing is required. Additional funding for staff will be necessary to accommodate the growing role of the MLRC in mathematics instruction. Funding Alert: The implementation of this recommendation will require a commitment of funding from University Central Administration.

Placement Exam The Committee recommends a mandatory mathematics placement exam for all students who are planning on their first mathematics course enrollment at OSU modeled after the University of Illinois program.

Background: A strong placement component is an important strategy in the successful programs at the University of Illinois and the University of Texas. Funding Alert: The implementation of this recommendation may require a commitment of funding from University Central Administration.

Placement Based on Exam Results The Committee recommends that the University institute a university-wide policy requiring mathematics course advisement for any student failing to make a placement cut-score. For MATH 1715 (Precalculus) and MATH 2144 (Calculus I) students failing to make the required cut-score should be denied enrollment regardless of their previous mathematics record.

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Background: Students, who fail to make a cut-score on an OSU placement exam, even though they may have transcript evidence that says they are prepared for the given course, should have the opportunity to discuss their situation with an adviser who is knowledgeable about the high school courses and the entry-level mathematics courses at OSU. The successful programs at both Illinois and Texas depend on mandatory placement for Precalculus and Calculus . Funding Alert: The implementation of this recommendation may or may not require a commitment of funding from University Central Administration.

Advising Recommendation The Committee recommends that the Mathematics Department provide enhanced support to advisers who advise incoming freshmen. This should include workshops that offer training on the various entry-level OSU mathematics courses, high school mathematics courses, at-risk variables to watch for, and other questions that advisers may have. Background: Advising plays a key role in student placement, and it is crucial that advisors be properly informed about course content and the indicators of student success. Funding Alert: The implementation of this recommendation may require a commitment of funding from University Central Administration.

The ALEKS Web-Based Placement and Learning System The Committee recommends the implementation of the ALEKS system to replace the existing placement process in mathematics and for mathematics support for students prior to matriculating at OSU.

Background: The ALEKS system is used in the successful programs at the University of Illinois and the University of Texas. Funding Alert: The implementation of this recommendation will require a commitment of funding from University Central Administration.

The Calculus Sequence The Committee recommends that the Calculus sequence, which currently is formatted as a three semester 4-3-3 sequence, be changed back to its original two semester 5-5 sequence.

Background: The current three semester 4-3-3 sequence was implemented in Fall 2002 at the request of the College of Engineering. The DWF rate in the first course of this sequence, MATH 2144, is 47.4% (see Table 4.). Data for the

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original calculus sequence from Fall 1999 to Spring 2002 shows that the DWF rate for MATH 2145, the first course of this original sequence was 34.7%. This is a significant difference between the two Calculus I courses. There is also an improved success rate for the original sequence when the Calculus II courses are compared, a DWF rate for MATH 2155 of 33.9% compared to a DWF rate for MATH 2153 of 39.5%. These differences, in favor of the original sequence, are attributed to calculus meeting every weekday in the original sequence as compared to meeting 4 days per week, a 5-credit course carries significant GPA consequences compared to a 4-crdit course, and greater face-time with students and instructor giving the instructor and the student more opportunities to head off problems. The table below displays the DWF rates for these two OSU calculus sequences. Table 4.

Comparison of DWF Rates for Two Calculus Sequences

Course Percent

of DWFs in Fall

Percent of

DWFs in

Spring

Percent of

DWFs in

Acad. Yr.

Original sequence MATH 2145 34.3 35.0 34.7

MATH 2155 39.5 26.3 33.9

Current sequence MATH 2144 43.3 52.0 47.4

MATH 2153 40.4 38.6 39.5

MATH 2163 28.1 28.0 28.1

Funding Alert: The implementation of this recommendation may require a commitment of funding from University Central Administration.

A Pedagogical Model to Teach the Learning and the Doing of Mathematics within the Mathematics Course The Committee recommends that a new course format be designed, developed, and piloted for OSU entry-level courses that not only teaches students content, but also

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teaches students the right way to learn mathematics and how to do mathematics. Additional faculty development is needed to support this new format.

Background: Each of the universities that were featured in this report implicitly or explicitly agree: students have transcript verification that they are ready for a given college entry-level course, but the DWF rates indicate otherwise for more than 40% of these students. In fact, even placing these students in courses that they already have had does not solve the problem for many of them. This evidence suggests that the problem is that student knowledge of mathematics is short-term knowledge. Put another way, students not only need content knowledge of mathematics, but they also need knowledge and skill at how to learn mathematics for long-term use and how to do mathematics. The proposal, tied to this recommendation, is to implement a new section of Calculus that emphasizes the content and the learning of mathematics. To accomplish this, the section will differ from the regular section by replacing one 50-minute class meeting with a lab section running 110 minutes, or two class periods long. The lab sections would be limited to 25 students. Curriculum and pedagogical materials will need to be designed and developed for this lab section to support a student-centered and inquiry-oriented pedagogy that emphasizes the learning and doing of mathematics by students. The curriculum and pedagogical materials will also need to support faculty in delivering effective inquiry-oriented and formative assessment-based pedagogy in this lab section. Because the pedagogy for this section is a radical departure from the traditional lecture style that most faculty use in teaching mathematics, the design and development of this new section of Calculus will require a design and development phase and a pilot phase. Once this content and learning approach to the study of calculus is available, it will be implemented for all Calculus sections. It is expected that as the content and learning section confirms that it increases student success in Calculus at OSU, this content and learning approach will be considered for design and development for other entry-level mathematics courses at OSU. Funding Alert: The implementation of this recommendation will require a commitment of funding from University Central Administration.

Faculty Oversight Position The Committee recommends that a new tenure-track faculty position be created within the Mathematics Department primarily responsible for accomplishing an integrated approach to increasing OSU student success rates in the entry-level mathematics courses. The faculty position would have a research focus on the pedagogy and

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content of college-level mathematics. This faculty member would be expected to teach, conduct research, and, most importantly, provide leadership for coordinating the MLRC, the placement system, the advisement of mathematics, the ALEKS system, the computer-assisted learning courses, and other new innovations in mathematics content and pedagogy related to keeping OSU student success in the mathematics entry-level courses high.

Background: The Committee recommendations given prior to the current recommendation can be viewed as separate and independent recommendations. However, an integrated strategy for improving the OSU DWF rates in the entry-level mathematics courses is one that adopts all of these recommendations, and does so utilizing a coordinating approach that maximizes the benefits of each of these strategies. Funding Alert: The implementation of this recommendation will require a commitment of funding from University Central Administration.

Increased Mathematics Staffing The Committee recommends increased staffing for the mathematics department so that section sizes can be reduced. Few of the recommendations offered here can be implemented with current staffing.

Background: The Department of Mathematics teaches more semester credit hours than any other department on the OSU campus. The Academic Ledger credits Mathematics with 15,913 undergraduate semester credit hours in 2010 with an instructional staff of 38.88 full time equivalents. Mathematics taught 104 sections with an average size of 46.4 students. By way of comparison, English teaches the second largest number of semester credit hours on campus. In 2010 it is credited with 13,710 undergraduate semester credit hours, 15% fewer than mathematics, with an instructional staff of 100.58 full time equivalents, two and a half times the mathematics staff. The average section size for undergraduate English classes was 19.5 students – less than half that of mathematics sections. The comparative allotment of resources is striking in view of expressed concern regarding student success in lower division mathematics. Educational literature indicates that smaller section sizes alone do not guarantee greater student success. But innovative instructional techniques such as those offered in this document are impossible in large sections. Increased mathematics staffing is essential.

Funding Alert: The implementation of this recommendation will require a commitment of funding from University Central Administration.

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Outreach Program to High Schools The Committee recommends a university outreach program to cooperate with state high schools to prepare students for college level mathematics.

Background: Preparation is the key to success in college. High school teachers are the people who make it all possible. It is essential both that high school teachers be kept abreast of requirements for college-bound students and that universities be aware of issues in secondary education. Strengthening the relationship of OSU to high schools across the state will be beneficial to all involved. Further information on this issue is in Appendix C. Funding Alert: The implementation of this recommendation may require a commitment of funding from the University Central Administration.

Additional Considerations The Committee considered two other issues without making any specific recommendations: the effectiveness of MATH 1715, Precalculus and the concept of a mandatory attendance policy as employed by the English Department.

MATH 1715, Precalculus. There is concern about the effectiveness of MATH 1715 (precalculus) as a preparation for calculus. Many students currently taking this course do not continue into calculus. The Mathematics Department might investigate if changes in both content and delivery of this course are appropriate.

Mandatory Attendance Policy The idea of a mandatory attendance policy such as English employs for its beginning courses was discussed. Pros and cons were offered, but no consensus was reached on this issue. The Mathematics Department should consider if such policies are appropriate.

OSU Data and Attributes of At-Risk Students The Committee to Explore Enhancements to the Mathematics Education Curriculum spent several meetings examining DWF rate data for the OSU entry-level courses in an attempt to familiarize ourselves with the scope of the problem of student unsuccess in these courses, and to identify, if possible, any potential at-risk factors among a number of various student attributes. Below we present four tables that show DWF rates for the OSU Calculus sequence broken down by ACT Composite Score (Table 5.), ACT Math Score (Table 6.), HS GPA (table 7.), and Gender (Table 8.).

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Table 5.

DWF Rates for MATH 2144 Broken Down by ACT Composite Score Current Calculus Sequence Previous Calculus Sequence

ACT Score MATH 2144 MATH 2153 MATH 2145 MATH 2155 < 19 74.3 64.1 53.3 38.8

19 – 23 60.3 51.0 50.7 46.0 24 – 27 44.5 41.1 30.3 35.8

> 27 29.9 29.3 21.3 26.8 Table 6.

DWF Rates for MATH 2144 Broken Down by ACT Math Score Current Calculus Sequence Previous Calculus Sequence

ACT Score MATH 2144 MATH 2153 MATH 2145 MATH 2155 < 19 78.5 64.5 67.0 50.0

19 – 23 65.0 54.3 51.0 46.8 24 – 27 48.6 45.6 34.7 40.0

> 27 26.0 29.0 18.3 26.0 Table 7.

DWF Rates for MATH 2144 Broken Down by HS GPA Current Calculus Sequence Previous Calculus Sequence

HS GPA MATH 2144 MATH 2153 MATH 2145 MATH 2155 < 2.00 94.4 93.4 73.3 50.0

2.00 – 2.49 78.6 73.0 85.0 93.3 2.50 – 2.99 69.6 60.3 53.7 56.8 3.00 – 3.49 58.8 50.4 42.7 43.8

> 3.50 31.6 30.1 19.7 24.8 Table 8.

DWF Rates for MATH 2144 Broken Down by Gender Current Calculus Sequence Previous Calculus Sequence

Gender MATH 2144 MATH 2153 MATH 2145 MATH 2155 Female 39.9 34.3 27.0 22.8

Male 48.3 40.1 37.7 38.0 The result of this examination of DWF rate data by student attributes did not provide any clear evidence of telltale at-risk factors, except possibly at the highest level of ACT score and HS GPA. By looking at the data in the charts above, it appears that ACT

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Math score seems to give the best indicator of success in Calculus, and this is for scores above 27. ACT Math scores from 24 – 27 seem to generate DWF rates that are roughly equivalent for the overall DWF rate in Calculus. Also, we note that female students out-perform male students in Calculus at OSU by a significant margin. One reason for this, based on anecdotal observations of female students versus male students in the classroom, could be that female students are far more diligent in meeting the responsibilities of course assignments than are males. Another way to put this is that the study skills and the diligence of female students are stronger than the male students. This would add support for implementing the Committee recommendation for developing a "Content and Learning" section for Calculus. Implications from a Statistical Analysis of the Data The DFW rates in lower division mathematics courses are higher on average than is desirable, but the rate differs dramatically across various student subpopulations. What are the student characteristics that lead to higher probability of failing to succeed in these courses? To provide additional assistance to students who might struggle in lower division mathematics courses the characteristics that lead to higher probability of a student making a D, F, or W need to be identified. The Committee to Explore Enhancements to the Mathematics Curriculum reviewed D, F, W data for all lower division math courses and analyzed those data for student attributes that lead to greater risk of poor grades in those courses. The data that were considered are the D, F, W rates for all lower division mathematics courses from fall 1999 through fall 2010, which is the time period covered by the current student data system, SIS. The D, F, W rates were compared across categories of the following student attributes. High School Core GPA * High School Graduating Class Size ACT Composite Score * ACT Math Score * Classification in College, slight* Graduation/Retention GPA ** College Gender * Ethnicity Attempted Hours during that semester Total DFW Rates * where * indicates slight pattern of correlation and ** indicates strong pattern of correlation. For the attributes that seem to have some correlation to D, F, W status the following general ideas were gathered from two dimensional data graphs:

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• HS Core GPA – as HS Core GPA goes up, the DFW rate goes down. This relationship is not as strong in MATH1493, but overall this holds true.

• ACT Composite and ACT Math Score – except for the remedial courses, UNIV0023 and UNIV0123, both of these variables have a definite pattern of DFW rates decreasing as ACT composite and/or math score went up.

• Classification – In general, older students seem to have higher DFW rates. This may be attributed to smaller numbers of older students in these courses. But also, waiting to take college algebra, for example, until one is a junior or senior may also indicate anxiety over taking math courses and feeling uncertain as to how one might perform in a college math class.

• Gender – Female students consistently had lower DFW rates than males in all courses in almost all time periods covered by the data.

• Attempted hours – The relationship is not strong between attempted hours and DFW rate, but there was a slight curvilinear relationship that indicated that the DFW rate went down as attempted hours went up, to a point, and then as hours increased past 15, the DFW started to go back up. This perhaps is attributable to students initially enrolling in more hours than they can successfully negotiate.

• Total DFW Hours during a single semester – as total DFW hours goes up, the DFW rate in math courses goes up, which would be an expected relationship. But more importantly, if a student has D, F, or W in one class there is a high probability that it is the math course in which they have that grade.

Appendix D contains a detailed report on the statistical analysis of the data, including various logistic single- and multivariate-models for predicting the probability of DFW rate in two important entry-level mathematics courses, MATH 1513, College Algebra; and MATH 2144, Calculus I.

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References Ahlgren, Allison and Harper, Marc. Assessment and Placement through Calculus I at the University of Illinois. An unpublished article. AP Report to the Nation, 2005 – 2011, The College Board, New York, NY. Babcock and Marks, Leisure College, USA: The Decline in Student Study Time, American Enterprise Institute for Public Policy Research, No. 7, August 2010. Bransford, John D., Brown, Ann L. and Cocking, Rodney R. editors. How People Learn: Brain, Mind, Experience, and School. Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice: Donovan, M. Suzanne, Bransford, John D. and Pellegrino, James W. editors. Commission on Behavioral and Social Sciences and Education, National Research Council, NATIONAL ACADEMY PRESS, Washington, D.C. (2005) The Campus Life and Learning Project, Duke University, June 2007. Donovan, M. Suzanne and Bransford, John D., editors. How Students Learn: Mathematics in the Classroom. Committee on How People Learn: A Targeted Report for Teachers, National Research Council, 2005, 272 pp. Failing the Future: Problems of Persistence and Retention in Science, Technology, Engineering, and Mathematics (STEM) Majors at Arizona State University. A report of the ASU Freshman STEM Improvement Committee, submitted to Executive VP and University Provost Elizabeth Capaldi, July 2, 2007. Gollub, J. P., Bertenthal, M. W., Labov, J. B., & Curtis, P. C. (Eds.). (2002). Learning and Understanding: Improving advanced study of mathematics and science in U. S. high schools. Washington, D.C.: National Academy Press Polya, G. How To Solve It: A New Aspect of Mathematical Method. Princeton, NJ: Princeton University Press, 1973. Spencer, A. (1995, August). On attracting and retaining mathematics majors – Don't cancel the human factor. Notices of American Mathematical Society, 42(8), 859-862. (This article is available at the following URL: http://www.math.buffalo.edu/mad/special/potsdammath.pdf)

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Appendices

Appendix A Descriptions of OSU MATH Courses

The courses that were the subject of this study (as described in the current OSU Catalog) and the associated history, pedagogy and technology, and enrollment are described below. MATH 1483 (A) Mathematical Functions and Their Uses. Prerequisite(s): Intermediate algebra or placement into 1513. Analysis of functions and their graphs from the viewpoint of rates of change. Linear, exponential, logarithmic and other functions. Applications to the natural sciences, agriculture, business and the social sciences.

History. This course was developed in the early1990's as an alternative to college algebra. The course was designed to meet the needs of client disciplines that have only a basic mathematics requirement. Pedagogy and Technology. Traditional lecture format. Limited written homework graded. Requires a graphing calculator which is used to supplant non-linear algebraic manipulations. A graphing calculator is required of all students and used by the instructor. Calculators are available free to students for checkout during the semester. Enrollment. Fall 2010: 12 sections of 40 each Spring 2011: 8 sections of 35 each MATH 1493 (A) Applications of Modern Mathematics. Prerequisite(s): Intermediate algebra or placement into 1513. Introduction to contemporary applications of discrete mathematics. Topics from management science, statistics, coding and information theory, social choice and decision making, geometry and growth. History. This course was developed in the early 1990’s as an alternative to college algebra. It was designed to meet the needs of client disciplines that require a mathematics course for breadth of knowledge and not as a calculation tool. Pedagogy and Technology. Traditional lecture format. Limited written homework graded. Does not require a graphing calculator.

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Enrollment. Fall 2010: 1 section of 97 Spring 2011: 1 section of 94 MATH 1513 (A) College Algebra. Prerequisite(s): Two years of high school algebra or intermediate algebra. Quadratic equations, functions and graphs, inequalities, systems of equations, exponential and logarithmic functions, theory of equations, sequences, permutations and combinations. No credit for those with prior credit in 1715 or any mathematics course for which 1513 is a prerequisite. History. This college algebra course serves as pre-requisite for trigonometry, business calculus, geometric structures, mathematical structures, and along with trigonometry for calculus I and technical calculus. The department has a long history of redesign of this course involving various delivery models utilizing various evolving forms of technology. Providing students with opportunities to choose from among various delivery options that best meets their learning styles has always been a fundamental belief of the department. For example, currently students choose from sections that are delivered according to a traditional lecture format, a blended format (traditional and computer-aided), or a strictly online format. Pedagogy and technology. About half the sections are taught in a traditional lecture format with limited written graded homework. The remainder of the sections are taught according to a blended computer-aided format that was first implemented in Fall 2007. All homework and quizzes are graded using the computer software program MyMathLab (MML). We plan to migrate more toward the blended format as soon as facilities allow. The strictly online format will be offered using MML commencing in Fall 2011. Regardless, of the delivery format, requires a graphing calculator which is used throughout. A graphing calculator is required of all students and used by the instructor. Calculators are available free to students for checkout during the semester. Enrollment. Fall 2010 blended computer-aided: 16 sections of 35 each Fall 2010 traditional lecture: 13 sections of 50 each Spring 2011 blended computer-aided: 16 sections of 35 each Spring 2011 traditional lecture: 3 sections of 50 each MATH 1613 (A) Trigonometry. Prerequisite(s): 1513 or equivalent, or concurrent enrollment. Trigonometric functions, logarithms, solution of triangles and applications to physical sciences. No credit for those with prior credit in 1715 or any course for which 1613 is a prerequisite.

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History. This course is essential for students who will be entering Calculus I or Technical Calculus. A strictly online format using MML was developed in Spring 2010 and has been offered since then. Pedagogy and Technology. Traditional lecture format. Limited written homework graded. Requires a scientific calculator. Enrollment. Fall 2010: 8 sections of 50 each Fall 2010: 1 online section of 20 using MML Spring 2011: 6 sections of 50 each Spring 2011: 1 online section of 30 using MML MATH 1715 (A) Precalculus. Prerequisite(s): One unit of high school plane geometry, and intermediate algebra or high school equivalent. Preparation for Calculus. Includes an integrated treatment of topics from College Algebra and Trigonometry. Combined credit for 1513, 1613, and 1715 limited to six hours. No credit for those with prior credit in any course for which 1613 is a prerequisite. Satisfies the six hour general education Analytical and Quantitative Thought requirement. History. In the Fall semesters, students attend a large lecture session 3 days each week followed by break out recitations of 50 each twice each week. This delivery format was dictated by the large number of students desiring the needed precalculus prerequisite for Calculus I. In the Spring semesters, this course is taught in a single section that meets 5 days each week. A strictly online format using MML was developed in Fall 2010 and has been offered since then. Pedagogy and Technology. Traditional lecture format (with breakout recitation section only in Fall semesters). Homework graded using the computer software package WebAssign. Requires a scientific calculator. Enrollment. Fall 2010: Large Lecture section of 275 breaking into recitation sections of 45 each. Fall 2010: 1 traditional lecture section of 47 (due to large enrollment) Spring 2011: 1 sections of 46 each. Spring 2011: 1 online section of 9. MATH 2103 (A) Elementary Calculus. Prerequisite(s): 1513. An introduction to differential and integral calculus. For students of business and social sciences.

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History. This is “business calculus”. Students attend a large lecture session 2 days each week followed by break out recitations of 50 each once each week. A strictly online course is planned. Pedagogy and Technology. Traditional lecture format. Limited grading for homework and quizzes done by the recitation assistants. A graphing calculator is required of all students and used by the instructor. Calculators are available free to students for checkout during the semester Enrollment. Fall 2010 Two large lectures (of 6 sections each) of about 250 students each. Spring 2011 Two large lectures (of 8 sections each) of about 290 students each. MATH 2123 (A) Calculus for Technology Programs I. Prerequisite(s): 1715 or 1513 and 1613. First semester of a terminal sequence in calculus for students in the School of Technology. Functions and graphs, differentiation and integration with applications. History. The first course of a two-semester sequence of courses in calculus for students pursuing majors in such areas as construction management, fire protection, and programs in engineering technology. Pedagogy and Technology. Traditional lecture format. Limited written homework graded. Enrollment. Fall 2010: 2 sections of 45 each. Spring 2011: 2 sections of 45 each. MATH 2133 (A) Calculus for Technology Programs II. Prerequisite(s): 2123. Second semester of a terminal sequence in calculus for students in the School of Technology. Calculus of trigonometric, exponential and logarithmic functions and applications to physical problems. History. The second course of a two-semester sequence of courses in calculus for students pursuing majors in such areas as construction management, fire protection, and programs in engineering technology. Pedagogy and Technology. Traditional lecture format. Limited written homework graded. Requires a scientific calculator

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Enrollment. Fall 2010: 2 sections of 45 each Spring 2010: 3 sections of 40 each. MATH 2144 (A) Calculus I. Prerequisite(s): 1715, or 1513 and 1613. An introduction to derivatives, integrals and their applications. History. The first course of a three-semester sequence of courses in calculus for students pursuing majors in engineering, mathematics, and related sciences. Pedagogy and Technology. Traditional lecture format. Homework graded using the software package WebAssign. Enrollment. Fall 2010 : 13 sections of 50 each and 3 honors sections of 22 each. Spring 2011: 10 sections of 50 each. MATH 2153 (A) Calculus II. Prerequisite(s): 2144. A continuation of 2144, including series and their applications, elementary geometry of three dimensions and introductory calculus of vector functions. History. The second course of a three-semester sequence of courses in calculus for students pursuing majors in engineering, mathematics, and related sciences. Pedagogy and Technology. Traditional lecture format. Homework graded using the software package WebAssign. Enrollment. Fall 2010: 6 sections of 50 each Spring 2011: 8 sections of 50 each and 2 honors sections of 22 each. MATH 2163 Calculus III. Prerequisite(s): 2153. A continuation of 2153, including differential and integral calculus of functions of several variables and an introduction to vector analysis. History. The third course of a three-semester sequence of courses in calculus for students pursuing majors in engineering, mathematics, and related sciences. Pedagogy and Technology. Traditional lecture format. Homework graded using the software package WebAssign.

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Enrollment. Fall 2010: 6 sections of 50 each Spring 2011: 5 sections of 50 each Math 2233 Differential Equations. Prerequisite(s): 2153. Methods of solution of ordinary differential equations with applications. First order equations, linear equations of higher order, series solutions and Laplace transforms. Pedagogy and Technology. Traditional lecture format. Limited written homework grading. Enrollment. Fall 2010: 4 sections of 45 each Spring 2010: 5 sections of 45 each.

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Appendix B

Assessment and Placement through Calculus I at the University of Illinois

Alison Ahlgren1 and Marc Harper2

September 16, 2010 University students come from many geographic locations and types of secondary and

post-secondary schools (including public, private, and preparatory) with very different mathematical backgrounds. The diversity of mathematical knowledge is augmented by the fact that what constitutes precalculus at feeding institutions varies, as do grading procedures used by different schools and instructors. These variations confound indicators of student knowledge and maturity such as high school grades. Additionally, students and institutions have disparate expectations of preparation for higher educational institutions.

The University of Illinois at Urbana-Champaign draws primarily from Chicago and Illinois communities, both urban and rural, and there are enrolled students from the majority of states in the US and from many foreign countries. In addition to the near-universally applicable variations above, many students in Illinois do not take a mathematics course in the final year of high school because it is not required by the educational standards of the state of Illinois. This further limits the utility of existing standardized exam scores for placement as the exams are typically taken more than a year before the student begins a university course. Students may have forgotten significant amounts of material or learned more depending on if they took additional mathematics courses in their final year of high school. In this article, we discuss how the University of Illinois mathematics department has used an online testing tool called ALEKS to place students in appropriate mathematics courses.

Previous research showed that the ACT Math was a poor measure of preparedness and demonstrated that ALEKS1, an assessment and learning mechanism based on the theory of knowledge spaces,[5] can serve as a preparedness measure for calculus as higher initial ALEKS scores correlated with higher final grades.[2] Earlier research indicated that the SAT, a standardized exam similar to the ACT, is a relatively poor predictor of student performance.[1] Mathematics placement at the University of Illinois prior to 2007 was a recommendation based on ACT Math scores. Because of undesirably high proportions of students failing to successfully complete Calculus I, the mathematics department began searching for a more effective placement program. Although such proportions are often in excess of 40% at similar institutions, the high cost and negative consequences to students and the university of such proportions were the impetus for improvement.

In 2007 the Mathematics department at the University of Illinois began a new placement

1 University of Illinois, aahlgren@illinois.edu 2 University of California, Los Angeles, marcharper@ucla.edu

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program using ALEKS3, which was chosen because of its quick turnaround (scores are instantly available), the ability of students to be assessed remotely via the internet, and the ability of ALEKS to provide personalized remediation. The initial assessment primes the learning module within ALEKS and the organization of items within the knowledge space allows ALEKS to present to the student items that a particular student is ready to learn or review. Students are automatically re-assessed as they progress. The remediation component of ALEKS complements the use of an assessment as a placement exam by allowing students to self-remediate before courses begin. At Illinois, the students must achieve the minimum measure of readiness within four months preceding the course. This approach allows the absolute enforcement of the placement policy, avoiding the difficulties with static and not easily-repeatable placement exams. Moreover, the responsibility for review of prerequisite material is shifted from the instructors and course to the students. The learning mechanism allows students to refresh forgotten knowledge and distinguish themselves from students who are in a novel learning situation.

The placement exam is an ALEKS assessment, an adaptive series of questions that determines the knowledge state of a student, which is a set of items such as the ability to plot an exponential function or to solve an equation involving rational expressions that reduces to a quadratic expression. A particular knowledge state is a subset of the total set of items, the collection of which is called knowledge space.[3]4 ALEKS has knowledge spaces appropriate for many courses and grade levels. For the placement program, the Preparation for Calculus5 knowledge space was chosen because of the high degree of overlap between the assessment items and the syllabi of the courses and prerequisites that the placement program governs. The placement score is the cardinality of the knowledge state, used simply as a percentage of total items demonstrated by the student. Note that this is a substantial reduction of the total information provided by a knowledge state since there are many combinations of items that yield the same cardinality.

Along with the changes in the placement policy, the syllabi of the placement courses leading up to but not including Calculus were examined and modified to emphasize their preparatory role with a view towards readiness for Calculus. In particular, precalculus was redesigned from a five credit course to a three credit course with a college algebra prerequisite (as determined by the placement exam) and includes topics that lead into Calculus, such as areas under simple curves (computable with basic geometric formulas), limits and continuity of piecewise functions, and basic derivatives. While precalculus has historically been a terminal mathematics course, our redesign instead emphasizes the role of precalculus as a preparatory course for calculus.

The placement program and policy were specifically designed to be independent of uncontrollable variables, such as instructor variation and textbook selection. The placement exam and syllabi can be modified to respond to variations in the student population over time and course goals while maintaining an objective standard of readiness.

The placement courses at Illinois are College Algebra, Precalculus, Business Calculus, and Calculus I, which has two versions, one for students with Calculus experience and another for students without. Students are initially tested during the summer be- fore enrollment in Fall

3 See http://www.aleks.com 4 A well-graded knowledge space is an anti-matriod. 5 Items and the groupings of items into categories (such as ’exponentials and logarithms’) are given at http://www.aleks.com/about_aleks/course_products.

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courses. All students complete an ALEKS assessment and are offered the opportunity to use the mechanisms within ALEKS (the learning module) to remediate if they do not place into the course they wish to take. Approximately 4,000 students take an assessment in the summer preceding their freshmen year, in addition to all continuing students who wish to enroll in courses which the placement program governs. Roughly 20% of the students being assessed independently use the learning module or take another assessment to improve their placement. ALEKS is also used in on campus summer programs that reach out to certain subsets of the student population to help prepare for college level studies. A sufficient ALEKS score is the only access point to enrollment – grades from any prerequisite courses do not allow or deny access to enrollment under the placement policy. The placement score is the highest cardinality achieved on an assessment within four months of the start of the course.

The underlying hypothesis of the placement program at the University of Illinois is that ALEKS effectively measures the current knowledge of students before beginning a course and that the initial knowledge should be indicative of student performance. Three years of data (over 20,000 assessments) support this hypothesis. In many of the courses and semesters examined, the correlation between ALEKS assessment cardinality and mean grade exceeds r = 0.90. This greatly outperforms the former placement policy, which relied on ACT Math scores taken by the students during high school. In multiple cases, mean ACT Math score correlated negatively with mean final grade. (A similar result for the SAT and class rank was found in previous work by Baron and Norman.[1])

Data analysis indicates that ALEKS scores and some subscores correlate well with final grades and that the ALEKS-based placement program lowered failure and with- draw rates in nearly all the placement classes in each semester. The subscores used in the analysis are derived from the assessment used for placement and are simply intersection cardinalities for particular subsets of the knowledge space. Subscores for the categories linear and quadratic functions and geometry and trigonometry correlate most strongly with final grade, and the categories for rational expressions, radical expressions, and equations and inequalities all correlate well. The remaining two categories real numbers and exponentials and logarithms had relatively weak correlations as most students either demonstrated knowledge of all of the items in the former and few of the items in the latter. The placement exam does not require mastery of every subcategory; nevertheless, a sufficient score for Calculus indicates broad mathematical knowledge and maturity, and near-mastery or mastery of some subcategories. For placement only the total score was used; the subscore correlations are an interesting consequence of the data provided by an ALEKS assessment.

Using the subscore data in aggregate, Illinois is able to compare the knowledge states of students completing Precalculus to those entering directly into Calculus. This allows an objective measurement of the effectiveness of Precalculus, as taught by the university, as preparation for Calculus. If students want to take one of the placement courses in a future semester at Illinois, they must take another assessment so that the knowledge state is current. This incidentally allows tracking of some students as they progress through the courses, enabling the measure of specific knowledge gains and aggregate knowledge gain in several subcategories. Some of these aggregate comparisons will appear in a contributed chapter of [4].

Using these before and after snapshots, it is also possible to determine which items correlate most significantly with student performance in Calculus and to see if these items are being adequately absorbed by students in Precalculus. For example, items regarding absolute value and exponential functions (plotting, solving equations involving, etc) correlate highly with

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performance in Calculus, and these are topics that students struggle with, anecdotally. The Precalculus curriculum can be modified in accordance with the importance of particular topics as dictated by the data, in addition to what instructors and authors believe to be the most important items for future courses.

Departmental changes due to the use of ALEKS also include a reduction in advising staff in the mathematics department and increases in enrollment (perhaps because of the limited temporal validity of the assessments). Lower withdraw percentages yield more stable rosters, which may allow for more effective course planning and management of instructional resources. The success of the placement program at the University of Illinois has lead to several other institutions adopting similar mechanisms, including the University of Texas at Austin, the University of Arizona, Arizona State, and others, in addition to several institutions that are currently implementing ALEKS-based placement programs.

The authors believe that the success of the placement program is based largely on the accountability of a knowledge-based placement exam that is independent of grades in previous coursework and the active assumption of responsibility of preparation by students. The link between the placement exam and the personalized remediation mechanism strengthens the effectiveness of the placement program, allowing students to demonstrate preparation in a low-risk and high-reward setting. Finally, we believe the success of any placement program hinges on strict enforcement, which is university policy at Illinois. These properties and policies support a successful program that serves the student body and university well.

References [1] Jonathan Baron and Frank Norman. SATs, achievement tests, and high-school class rank

as predictors of college performance. Educational and Psychological Measurement, 52:1047–1055, 1992.

[2] J. Carpenter and R. Hanna. Predicting student preparedness in calculus. Pro- ceedings of

the 2006 Annual Conference of the American Society for Engineering Education, 2006.

[3] E. Cosyn, C.W. Doble, J.-Cl. Falmagne, A. Lenoble, N. Thiery, and H. Uzun. Assessing mathematical knowledge in a learning space. In D. Albert, C.W. Doble, D. Eppstein, J.-Cl. Falmagne, and X. Hu, editors, Knowledge Spaces: Applications in Education. 2010. In preparation.

[4] Jean Paul Doignon and Jean Claude Falmagne. Learning Spaces: Interdisciplinary

Applied Mathematics. Springer, 2010. (in press).

[5] J.-Cl. Falmagne, E. Cosyn, J.-P. Doignon, and N. Thi ́ery. The assessment of knowledge, in theory and in practice. In B. Ganter and L. Kwuida, editors, Formal Concept Analysis, 4th International Conference, ICFCA 2006, Dresden, Germany, February 13–17, 2006, Lecture Notes in Artificial Intelligence, pages 61–79. Springer-Verlag, Berlin, Heidelberg, and New York, 2006a.

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Appendix C

PREPARATION for COLLEGE READINESS: A PreK–16 APPROACH

The 2010 Education Survey by Deloitte found that 92% of high school teachers say that receiving data on students’ academic performance in college is critical to evaluate high school effectiveness, yet only 13% receive information on how they perform after high school, and the vast majority receive that information from former students or their parents. If they had such data, 78% would plan coursework based on it and 83% would use the data to improve subject matter. Common ed teachers are ready and willing to receive feedback from higher ed sources to inform their own practice and to help prepare their students to be college and career ready. Research on college persistence has consistently demonstrated that students with better academic preparation in high school are more likely to complete college. According to a recent report by ACT, “…..this is a systems issue that must be addressed by all levels (P-16) of our education systems. Improving college and career readiness is crucial to the development of a diverse and talented labor force that can maintain and increase U.S. economic competitiveness throughout the world.” By creating a vertical alignment between Oklahoma State University and common ed, P-12 students, parents, and teachers can benefit from OSU’s expertise and the school’s college-ready expectations in mathematics. Oklahoma is one of 42 states who have currently adopted the Common Core State Standards (CCSS) for K-12 mathematics. It is a rigorous set of standards for all grade levels with conceptual understanding, creative problem solving, and communicating at its core. Tests will be developed and administered 4 times during a year for most grade levels, and at this time over 1000 institutions of higher education will help design the last high school test that will gauge college readiness in mathematics. A new partnership between the American Association of State Colleges and Universities (AASCU) and the Council of Chief State School Officers (CCSSO) and the State Higher Education Executive Officers (SHEEO) has recently been formed to promote the implementation of Common Core State Standards in mathematics and English language arts. Their focus will be in four areas: 1) Leadership - build relationships between key officials, 2) College Readiness – bring higher ed and P-12 administrators and instructors together to craft strategies for improving readiness and aligning standards with college placement, 3) In-Service Professional Development – work with existing high school teachers to address problem areas in preparing high school students for college-level work, and 4) Pre-Service Teacher Training Programs – improve teacher preparation programs based on the new Common Core State Standards. Many institutions have seen the value of collaborating with common education during the past several years and already have a vehicle in place to continue this focus of college readiness. The following is a sample of some of the current programs:

     

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  California  State  University  System  

This  system  has  developed  a  program  named  the  Early  Assessment  Program  (EAP),  which  is  being  considered  as  a  model  in  several  other  states.  It  has  three  components:  1)  Provide  11th  grade  voluntary  tests  to  identify  students  before  their  senior  year  who  need  additional  coursework  in  English  or  mathematics  to  be  college-­‐ready,  2)  Provide  students  with  supplemental  preparation  including  an  online  interactive  program,  and    3)  Provide  professional  development  to  aid  high  school  teachers  with  a  focus  of  improving  college  readiness  among  their  students.      (http://www.calstate.edu/eap/)  

  Rice  University  Educational  Outreach  

Rice's  Vision  for  the  Second  Century  calls  for  the  university  to  “recognize  our  responsibility  as  an  educational  institution  to  create  opportunity  and  equality  by  opening  our  doors  to  our  community.”    Educational  outreach  has  evolved  as  a  natural  outgrowth  of  the  research,  teaching,  and  service  of  the  faculty.  Its  programs  include  K-­‐12  Teacher  Professional  Development  including  a  Center  for  College  Readiness  and  the  School  Mathematics  Project,  K-­‐12  Student-­‐Focused  Programs,  Community  Outreach,  and  Higher  Education  Outreach.      Rice  University's  outreach  efforts  directly  or  indirectly  affect  approximately  7,000  K-­‐12  teachers  and  100,000  students,  throughout  Houston  and  across  the  state.  (http://professor.rice.edu/Template_EducationalOutreach.aspx?id=1363)  

  Purdue  University  

The  Mathematics  K-­‐12  Outreach  program  at  Purdue  has  objectives  which  include:  1)  Promote  involvement  in  mathematics  and  science  among  Indiana  high  school  students,  2)  Collaborate  with  Indiana's  teachers  to  improve  the  teaching  and  learning  of  K-­‐12  mathematics  and  science,  and    3)  Increase  the  recruitment  and  retention  rates  of  all  students  in  the  Department  of  Mathematics  and  the  College  of  Science  at  Purdue.    In  reaching  these  goals,  the  Mathematics  K-­‐12  Outreach  program  offers  professional  development  to  math  teachers  and  provides  and  scores  math  and  physics  tests  in  the  High  School  Testing  program.      (http://www.math.purdue.edu/outreach/)                  

35

University  of  Texas                                                                                                                                                                                                                                                                           The  Dana  Center  located  at  UT  in  Austin  collaborates  with  local  and  national  entities  to  improve  education  systems  so  that  it  fosters  opportunity  for  all  students,  particularly  in  mathematics  and  science.  It  is  dedicated  to  nurturing  students'  intellectual  passions  and  ensuring  that  every  student  leaves  school  prepared  for  success  in  postsecondary  education  and  the  contemporary  workplace.    It  began  as  a  workshop  program  designed  to  increase  the  number  of  college  freshmen  excelling  in  calculus  who  came  from  groups  underrepresented  in  mathematics-­‐based  disciplines.    It  is  now  a  large  and  influential  presence  in  the  world  of  mathematics  education  through  professional  development  for  teachers,  curriculum  creation,  assessment  for  K-­‐12  students,  technology  courses,  and  leadership  in  research  and  educational  programming.      The  Dana  Center  is  now  developing  tools  and  strategies  to  enable  educators  to  work  in  districts  and  states  to  ensure  coherent  implementation  of  the  CCSS.    (http://www.utdanacenter.org/index.php)  

Connecticut  State  University  System                

Building  A  Bridge  to  Student  Success  is  a  new  initiative  in  Connecticut    

that  was  started  2  years  ago  at  Western  Connecticut  State  University  and  is  seeing  success  in  its  early  stages.      The  program  has  been  expanded  to  the  other  state  schools.  It  started  as  an  innovative  collaboration  between  university  faculty  and  teachers  at  Danbury  and  Bethel  High  Schools  to  improve  core  subject  college  readiness  and  has  produced  dramatic  reductions  in  the  number  of  students  needing  remediation  in  mathematics  and  writing.    It  has  also  improved  retention  levels  from  freshman  to  sophomore  year  among  college  students  who  participated  in  Bridges  while  in  high  school.    Successful  students  in  the  program  are  more  likely  to  continue  on  to  higher  education,  less  likely  to  need  remedial  classes  when  they  get  there,  and  more  likely  to  stay  in  school  after  their  freshmen  year.    Another  important  benefit  has  been  the  establishment  of  a  collaborative  working  relationship  between  the  university  and  high  school  faculties  and  the  impact  it  has  had  on  both  curriculum  and  student  achievement. Bridges was formed  after  the  Board  approved  a  policy  requiring  all  full-­‐time,  first-­‐time-­‐in-­‐college  freshmen  to  successfully  complete  any  necessary  remedial  courses  within  their  first  24  

36

academic  credits.  Any  student  failing  to  complete  remediation  prior  to  the  sophomore  year  would  not  be  allowed  to  register  for  credit  courses  in  any  of  the  

four  system  universities  until  the  remedial  courses  were  completed  successfully.  

(http://www.ctstateu.edu/initiatives/readiness/#bridges)      

A recent report “Beyond the Rhetoric” was written by the National Center for Public Policy and Higher Education and the Southern Regional Education Board. It states, “Increasingly, it appears that states or postsecondary institutions may be enrolling students under false pretenses. Even those students who have done everything they were told to do to prepare for college find, often after they arrive, that their new institution has deemed them unprepared. Their high school diploma, college-preparatory curriculum, and high school exit examination scores did not ensure college readiness.” This ‘college readiness gap’ is costly in terms of money and time for the students and their families and our state; it is also responsible for low graduation rates as the majority of students who begin with remedial courses never complete their degree. Common education and higher education are both stakeholders in this dilemma and need to share responsibility in creating successful remedies. The current implementation of the Common Core State Standards in mathematics makes this an ideal time for OSU and common education to form a P-16 partnership with a shared focus and a vision for college preparation.

37

Appendix D

Attributes of At-­‐risk Students

Logistic Regression to Predict Probability of DFW To study the variables more completely that seem to have the most effect on the DFW rate in two important courses, MATH 1513, College Algebra; and MATH 2144, Calculus One, logistic regression was used to model the DFW rate based on various sets of contributing variables. A logistic regression model can be used to estimate the probability on the values of a binomial response or dependent variable based on a set of explanatory or independent variables. For example, a logistic regression model can be used to estimate the probability of a student being in the DFW category of a specific course based on the student's core high school grade point, or some other critical variable, or set of variables. The data used to estimate the logistic regression models were drawn from the Student Information System, SIS, from 2003 to the present. It did not extend back to 1999 as the SIS system does, since the variable grade in prior mathematics courses was used as one of the predictor variables in some of the models. The process to estimate the probability that a student’s grade will result in a D, F, or W with a logistic model involves two steps. First, least squares estimation is used to fit a univariate or multivariate linear model with DFW status as the dependent variable and a set of predictor variables as the independent variables, shown below as f(x). Secondly, the result of the estimated model equation is scaled or adjusted to generate values within the interval of 0 to 1 to be valid for probability, shown below as P(DFW).

P(DWF) = ef (x)

ef (x) +1 , where f(x)= β0 + β1(x1) + β2(x2) + β3(x3) + … + βk(xk), -∞< f(x) <∞.

In the above representation, f(x) designates the estimate from the regression equation and the xi indicate the predictor variables for DFW status. Multivariate data are used to estimate the beta values in the above equation, and then the estimated f(x) value is scaled through the fuction P(DFW), which is the predicted probability of of a student making D, F, or W in a course with specific values for the predictor variables.

The Logistic Regression Models The first model on the following pages estimates the probability of a student making a D, F, or W based on the ACT composte score, ACTCOMP, for each of the two classes, college algebra and calculus one. Following this first model on Composite ACT, two

38

sets of models are described. The first set of models predicts the DFW rate for Math 1513, College Algebra, and the second set of models described are assoicated with Math 2144, Calculus One. For each model the variables contained in the model are stated, a column of estimated probability of DFW is given for a range of values for the variables in the model, and graphs of the estimated probability of DFW are provided.

General Conclusions from the models: • Higher ACT Math score is associated with reduced probability of DFW • Higher Core GPA is associated reduced probability of DFW • Higher score on a prerequisite math class is associated with reduced probability of DFW • Holding all other factors constant, first-year students have lower probability of DFW • Higher Grad-Retention GPA is associated with lower probability of DFW • Especially for Math 1513 female students have a lower DFW rate than male students.

Models provided in Appendix D: 1. Model 1: MATH1513: DFW = f(ACTCOMP) 2. Model 2: MATH2144: DFW = f(ACTCOMP) 3. Model 3: Math 1513: DFW = f(COREGPA) 4. Model 4: Math 1513: DFW = f(Core HS GPA, GENDER, SO, JR, SE) 5. Model 5: Math 1513: DFW = f(COREGPA, SO, JR, SE, GRADGPA) 6. Model 6: Math 1513: DFW=F(COREGPA, SO, JR, SE, GRADGPA)

Students without ACT scores 7. Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA,

ACTMATH ) 8. Model 8: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, ACTMATH )

Students without OSU graduation GPA Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH )

9. Model 9: MATH 2144: DFW=F(GENDER, COREGPA, ACTMATH) Students who do have an OSU Graduation GPA, implying they are past their first OSU semester

10. Model 10: MATH 2144: DFW=F(GENDER, COREGPA, ACTMATH) Students who do not have an OSU Graduation GPA, implying they are in their first OSU semester

A Related Excel File, A supplement to this report: Included with this report is an Excel file, which contains a sheet for each of the above models. It can be used to calculate the predicted probability of DFW for a specific student with set variable values. The risk of making a D, F, or W can then be assessed and the student could be advised based on that information. If the risk of DFW is deemed high and the student is going to proceed with enrollment in the course then directed actions should be in place to assist the student to be successful in the course.

39 Model 1: MATH1513: DFW = f(ACTCOMP)

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard

Error

Wald Chi-

Square Pr > ChiSq Intercept 1 2.3458 0.1259 346.9453 <.0001 ACTCOMP 1 -0.1246 0.00560 494.5917 <.0001

Model 2: MATH2144: DFW = f(ACTCOMP) Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard

Error

Wald Chi-

Square Pr > ChiSq Intercept 1 3.6785 0.1840 399.8376 <.0001 ACTCOMP 1 -0.1528 0.00717 453.8255 <.0001

As an example of how the models provide an estimate for the probability of a student making a DFW consider the following: If a student has a Composite ACT score of 29 then the estimated probability that the student would make a D, F, or W in Calculus One, Math 2144, first calcuate f(x) = 3.6785 – 0.1528(29) = -0.7527, then scale that value by e-0.7527/( e-0.7527 + 1) = 0.3202, as shown in the 2144 column of the table above in the Composite ACT of 29 row.

ACT COMP

P(DFW ) 1513

P(DFW) 2144

10 0.7502 11 0.7262 0.8806 12 0.7007 0.8635 13 0.6739 0.8445 14 0.6460 0.8234 15 0.6170 0.8000 16 0.5872 0.7745 17 0.5567 0.7467 18 0.5257 0.7167 19 0.4946 0.6847 20 0.4635 0.6508 21 0.4327 0.6153 22 0.4024 0.5786 23 0.3729 0.5409 24 0.3442 0.5028 25 0.3167 0.4647 26 0.2903 0.4270 27 0.2653 0.3901 28 0.2418 0.3544 29 0.2197 0.3202 30 0.1991 0.2879 31 0.1799 0.2576 32 0.1623 0.2295 33 0.1460 0.2036 34 0.1312 0.1799 35 0.1176 0.1585 36 0.1392

40

Model 3: Math 1513: DFW = f(COREGPA)

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard

Error

Wald Chi-

Square Pr > ChiSq Intercept 1 4.9433 0.1327 1387.1967 <.0001 COREGPA 1 -1.6714 0.0410 1665.6947 <.0001

Error! Not a valid link. CORE GPA

P(DFW)

1.25 0.9455 1.51 0.9183 1.75 0.8827 2.01 0.8297 2.25 0.7654 2.51 0.6788 2.75 0.5859 3.01 0.4781 3.25 0.3802 3.51 0.2843 3.75 0.2101 4.01 0.1469 4.25 0.1034 4.51 0.0695

41

Model 4: Math 1513: DFW = f(Core HS GPA, GENDER, SO, JR, SE) DFW = β0 + β1(Core HS GPA) + β2(Gender) + β3(Sophomore) + β4(Junior) + β5(Senior) + Ɛ, where 1 is placed into the model if the student is sophomore and 0 otherwise, similarly for the other levels.

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard

Error

Wald Chi-

Square Pr > ChiSq Intercept 1 4.5274 0.1427 1006.4435 <.0 01 COREGPA 1 -1.5877 0.0422 1415.2567 <.0001 GENDER 1 0.1917 0.0390 24.1664 <.0001 SO 1 0.3044 0.0578 27.6919 <.0001 JR 1 0.5068 0.1182 18.3824 <.0001 SE 1 0.6328 0.1720 13.5397 0.0002

CORE HS GPA

PFFR PFSO PFJR PFSE CORE HS GPA

PMFR PMSO PMJR PMSE

1.25 0.9271 0.9452 0.9548 0.9599 1.25 0.9390 0.9543 0.9624 0.9667 1.51 0.8938 0.9194 0.9332 0.9406 1.51 0.9107 0.9325 0.9442 0.9505 1.75 0.8518 0.8863 0.9051 0.9154 1.75 0.8744 0.9042 0.9204 0.9291 2.01 0.7919 0.8376 0.8633 0.8775 2.01 0.8217 0.8620 0.8844 0.8967 2.25 0.7221 0.7789 0.8118 0.8303 2.25 0.7589 0.8102 0.8394 0.8556 2.51 0.6323 0.6999 0.7406 0.7641 2.51 0.6757 0.7385 0.7757 0.7969 2.75 0.5402 0.6143 0.6611 0.6887 2.75 0.5873 0.6587 0.7026 0.7282 3.01 0.4374 0.5132 0.5635 0.5942 3.01 0.4850 0.5608 0.6099 0.6394 3.25 0.3469 0.4187 0.4686 0.5000 3.25 0.3915 0.4659 0.5165 0.5478 3.51 0.2601 0.3228 0.3685 0.3983 3.51 0.2987 0.3660 0.4141 0.4450 3.75 0.1936 0.2456 0.2850 0.3114 3.75 0.2253 0.2828 0.3256 0.3539 4.01 0.1371 0.1773 0.2087 0.2303 4.01 0.1614 0.2070 0.2422 0.2660 4.25 0.0979 0.1283 0.1527 0.1697 4.25 0.1162 0.1513 0.1792 0.1985 4.51 0.0670 0.0888 0.1066 0.1192 4.51 0.0801 0.1055 0.1262 0.1408

42

GRAPHS for Model 4: Math 1513: DFW=f(COREGPA, GENDER, SO, JR, SE)

43

Model 5: Math 1513: DFW = f(COREGPA, SO, JR, SE, GRADGPA) DFW = β0 + β1(Core HS GPA) + β2(Sophomore) + β3(Junior) + β4(Senior) + β5(OSU Graduation GPA) + Ɛ

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard

Error Wald

Chi-Square Pr > ChiSq Intercept 1 5.4484 0.1972 763.3901 <.0001 COREGPA 1 -0.9765 0.0601 264.1712 <.0001 SO 1 0.2413 0.0653 13.6505 0.0002 JR 1 0.3820 0.1223 9.7512 0.0018 SE 1 0.6482 0.1773 13.3653 0.0003 GRADGPA 1 -1.0115 0.0402 632.8443 <.0001 Variable Mean Minimum Maximum COREGPA 3.27 1.25 4.53

GRADGPA 2.69 0 4

Table of Predicted Probability of DFW for Model 5: Math 1513: DFW = f(COREGPA, SO, JR, SE, GRADGPA) GRADGPA PFR PSO PJR PSE

0.00 0.9051 0.9239 0.9332 0.9480 0.26 0.8800 0.9033 0.9149 0.9334 0.50 0.8519 0.8799 0.8940 0.9167 0.76 0.8156 0.8492 0.8663 0.8943 1.00 0.7763 0.8154 0.8356 0.8690 1.26 0.7273 0.7725 0.7963 0.8361 1.50 0.6767 0.7271 0.7541 0.8001 1.76 0.6167 0.6719 0.7021 0.7547 2.00 0.5579 0.6163 0.6490 0.7070 2.26 0.4924 0.5526 0.5870 0.6497 2.50 0.4322 0.4921 0.5272 0.5927 2.76 0.3691 0.4268 0.4616 0.5280 3.00 0.3146 0.3688 0.4021 0.4674 3.26 0.2608 0.3099 0.3408 0.4028 3.50 0.2168 0.2605 0.2885 0.3461 3.76 0.1754 0.2131 0.2377 0.2892 4.00 0.1430 0.1752 0.1965 0.2419

44

Graph for Model 5: Math 1513: DFW = f(COREGPA, SO, JR, SE, GRADGPA) DFW = β0 + β1(Core HS GPA) + β2(Sophomore) + β3(Junior) + β4(Senior) + β5(OSU Graduation GPA) + Ɛ

Notice in the graph above the relative increase in the probability of DFW if the student takes College Algebra later in college rather than as a freshman. There are probably at least two effects that contribute to this increase. Perhaps students wait to the enroll in the course if they think that it will be challenging for them, but also the longer they wait to take algebra the further they are from the foundation math courses that they had in high school.

45 Model 6: Math 1513: DFW=F(COREGPA, SO, JR, SE, GRADGPA) Students without ACT scores DFW = β0 + β1(Core HS GPA) + β2(Sophomore) + β3(Junior) + β4(Senior) + β5(OSU Graduation GPA) + Ɛ In the previous models all students who were enrolled in Math 1513 from 1999 through fall 2010 were included in the estimation of the model parameters. In this model, only students who do not have ACT scores in the SIS system were included in the estimation of the model parameters.

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard

Error Wald

Chi-Square Pr > ChiSq Intercept 1 5.4101 0.2084 673.9717 <.0001 COREGPA 1 -0.9576 0.0640 224.0480 <.0001 SO 1 0.2457 0.0680 13.0419 0.0003 JR 1 0.3474 0.1272 7.4652 0.0063 SE 1 0.6111 0.1820 11.2737 0.0008 GRADGPA 1 -1.0187 0.0420 587.6116 <.0001

Variable Mean Minimum Maximum COREGPA 3.289193 1.25 4.53

GRADGPA 2.699187 0 4

GRADGPA PFR PSO PJR PSE

0.00 0.9055 0.9246 0.9314 0.9464 0.26 0.8803 0.9039 0.9124 0.9313 0.50 0.8521 0.8805 0.8907 0.9139 0.76 0.8155 0.8496 0.8622 0.8906 1.00 0.7759 0.8157 0.8305 0.8645 1.26 0.7265 0.7725 0.7899 0.8303 1.50 0.6753 0.7267 0.7464 0.7931 1.76 0.6148 0.6711 0.6931 0.7462 2.00 0.5555 0.6151 0.6388 0.6972 2.26 0.4895 0.5508 0.5758 0.6386 2.50 0.4289 0.4898 0.5152 0.5805 2.76 0.3656 0.4242 0.4492 0.5150 3.00 0.3109 0.3659 0.3898 0.4540 3.26 0.2572 0.3068 0.3289 0.3895 3.50 0.2133 0.2574 0.2773 0.3331 3.76 0.1722 0.2101 0.2275 0.2771 4.00 0.1401 0.1724 0.1874 0.2309

To interpret the values in the above table consider a freshman student with an OSU Graduation GPA of 2.50, then the estimated probability of DFW in Math 1513 would be .4289, given that the student had a Core high school GPA of the average value of 3.3.

46 The graph below indicates the estimated probability of DFW in Math 1513 for a student at different levels in college across varying values of OSU Graduation GPA, assuming that the student has a Core high school GPA at the mean value of 3.3. For example, a sophomore student who has an OSU Graduation GPA of 3.00 and an average Core High School GPA of 3.3 has an estimated probability of .37 of making D, F, or W in Math 1513.

Graph for Model 6: Math 1513: DFW=F(COREGPA, SO, JR, SE, GRADGPA) Students without ACT scores DFW = β0 + β1(Core HS GPA) + β2(Sophomore) + β3(Junior) + β4(Senior) + β5(OSU Graduation GPA) + Ɛ

47 Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH ) This is the last model to predict the probability of DFW for Math 1513 that considers the variation between males and females. Parameter DF Estimate Intercept 1 6.6459

COREGPA 1 -0.6953

GENDER 1 0.2232

SO 1 0.1703

JR 1 0.2348

SE 1 0.5615

GRADGPA 1 -1.0075

ACTMATH 1 -0.1057

Variable Mean Minimum Maximum COREGPA 3.27 1.25 4.53

GRADGPA 2.69 0 4

ACTMATH 21.56 9 36

This model is a multivariate model with three numerical variables, Core HS GPA, OSU Graduation GPA, and ACT Math score. The estimated probability values stated in the tables and the associated graphs are interpreted while holding the other variables constant at their mean values stated in the above table. For example, the estimated probability values stated on the next page are based on varying values of Core HS GPA for females and males at various college levels, while holding OSU Graduation GPA and ACT Math score constant at their mean values stated in the above table. The following pages have estimated probability of DFW and associated graphs for Core HS GPA, OSU Graduation GPA, and ACT Math, in that order. In each case the estimates should be considered for a variable while holding the other two variables constant at the means stated above. In the Excel file associated with this report the actual values for the variables listed for a specific student can be placed into the file and the estimated probability of DFW is calculated. To illustrate this process, consider the following. Assume a specific male student who is a junior and has a Core High School GPA of 3.2, an OSU Graduation GPA of 2.9, and a Math ACT score of 23 is considering taking Math 1513. What is the estimated probability based on the above model that this student will make a D, F, or W in the course? First calculate, f(x)=6.6459+(-.6953)*(COREGPA=3.2)+(0.2232)*(male=1)+

(0.1703)*(sophomore=0)+(0.2348)*(junior=1)+(0.5615)*(senior=0)+ (-1.0075)*(OSUGRADGPA=2.9)+(-0.1057)*(MATHACT=23)=-0.47391.

Second scale that value to be between 0 and 1 by calculating, e-0.47391/( e-0.47391+1)=.38. The estimated probability based on the above model that a student with these specific characteristics will make D, F, or W in Math 1513 is .38. This is the calculation that the associated Excel file provides from Sheet 7 if the values are inserted for a student who is a male, junior with Core High School GPA=3.2, OSU GPA=2.9, and a Math ACT score=23.

48

Table of Estimated Probability of DFW for Core HS GPA based on Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH ) COREGPA PFFR PFSO PFJR PFSE COREGPA PMFR PMSO PMJR PMSE

1.25 0.6866 0.7221 0.7348 0.7935 1.25 0.7326 0.7646 0.7760 0.8277 1.35 0.6715 0.7079 0.7211 0.7818 1.35 0.7187 0.7518 0.7637 0.8175 1.45 0.6560 0.6933 0.7069 0.7697 1.45 0.7044 0.7386 0.7509 0.8069 1.55 0.6401 0.6783 0.6922 0.7572 1.55 0.6898 0.7250 0.7377 0.7958 1.65 0.6239 0.6630 0.6772 0.7442 1.65 0.6747 0.7109 0.7240 0.7843 1.75 0.6075 0.6473 0.6619 0.7307 1.75 0.6593 0.6964 0.7099 0.7723 1.85 0.5908 0.6312 0.6461 0.7168 1.85 0.6435 0.6815 0.6953 0.7599 1.95 0.5739 0.6149 0.6301 0.7025 1.95 0.6274 0.6662 0.6804 0.7469 2.05 0.5568 0.5983 0.6137 0.6878 2.05 0.6110 0.6506 0.6651 0.7336 2.15 0.5396 0.5815 0.5971 0.6726 2.15 0.5943 0.6346 0.6495 0.7198 2.25 0.5223 0.5645 0.5803 0.6571 2.25 0.5774 0.6184 0.6335 0.7055 2.35 0.5049 0.5473 0.5633 0.6413 2.35 0.5604 0.6018 0.6172 0.6909 2.45 0.4875 0.5301 0.5461 0.6252 2.45 0.5432 0.5851 0.6006 0.6758 2.55 0.4702 0.5127 0.5288 0.6087 2.55 0.5259 0.5681 0.5838 0.6604 2.65 0.4529 0.4953 0.5114 0.5921 2.65 0.5085 0.5509 0.5668 0.6447 2.75 0.4357 0.4780 0.4941 0.5752 2.75 0.4912 0.5337 0.5497 0.6286 2.85 0.4187 0.4606 0.4767 0.5581 2.85 0.4738 0.5164 0.5324 0.6122 2.95 0.4019 0.4434 0.4594 0.5409 2.95 0.4565 0.4990 0.5151 0.5956 3.05 0.3853 0.4263 0.4422 0.5236 3.05 0.4393 0.4816 0.4977 0.5787 3.15 0.3690 0.4094 0.4251 0.5062 3.15 0.4223 0.4643 0.4803 0.5617 3.25 0.3529 0.3927 0.4082 0.4888 3.25 0.4054 0.4470 0.4630 0.5445 3.35 0.3372 0.3763 0.3915 0.4715 3.35 0.3888 0.4299 0.4458 0.5272 3.45 0.3219 0.3601 0.3751 0.4542 3.45 0.3724 0.4130 0.4287 0.5099 3.55 0.3069 0.3442 0.3589 0.4370 3.55 0.3563 0.3962 0.4117 0.4925 3.65 0.2923 0.3287 0.3431 0.4200 3.65 0.3405 0.3797 0.3950 0.4751 3.75 0.2781 0.3136 0.3276 0.4032 3.75 0.3251 0.3635 0.3785 0.4578 3.85 0.2644 0.2988 0.3125 0.3865 3.85 0.3100 0.3475 0.3623 0.4406 3.95 0.2511 0.2844 0.2977 0.3702 3.95 0.2953 0.3319 0.3464 0.4236 4.05 0.2382 0.2705 0.2834 0.3541 4.05 0.2811 0.3167 0.3308 0.4067 4.15 0.2258 0.2570 0.2695 0.3384 4.15 0.2672 0.3019 0.3156 0.3900 4.25 0.2139 0.2439 0.2560 0.3230 4.25 0.2538 0.2874 0.3008 0.3736 4.35 0.2025 0.2313 0.2430 0.3080 4.35 0.2409 0.2734 0.2864 0.3575 4.45 0.1915 0.2192 0.2305 0.2934 4.45 0.2284 0.2598 0.2724 0.3417 4.53 0.1830 0.2098 0.2207 0.2820 4.53 0.2187 0.2492 0.2615 0.3293

49

Graph for Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH )

50

Table of Estimated Probability of DFW for OSU Graduation GPA based on Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH ) GRADGPA PFFR PFSO PFJR PFSE GRADGPA PMFR PMSO PMJR PMSE 0.0 0.8903 0.9058 0.9112 0.9343 0.0 0.9102 0.9232 0.9277 0.9468 0.1 0.8800 0.8969 0.9027 0.9279 0.1 0.9017 0.9158 0.9206 0.9414 0.2 0.8690 0.8872 0.8935 0.9208 0.2 0.8924 0.9077 0.9129 0.9356 0.3 0.8571 0.8767 0.8835 0.9131 0.3 0.8823 0.8989 0.9046 0.9293 0.4 0.8443 0.8654 0.8727 0.9048 0.4 0.8714 0.8893 0.8955 0.9224 0.5 0.8306 0.8532 0.8611 0.8958 0.5 0.8597 0.8790 0.8857 0.9149 0.6 0.8159 0.8401 0.8486 0.8860 0.6 0.8471 0.8679 0.8751 0.9067 0.7 0.8003 0.8261 0.8352 0.8754 0.7 0.8336 0.8559 0.8637 0.8978 0.8 0.7837 0.8112 0.8209 0.8640 0.8 0.8192 0.8430 0.8514 0.8882 0.9 0.7661 0.7953 0.8056 0.8517 0.9 0.8037 0.8292 0.8382 0.8778 1.0 0.7476 0.7784 0.7893 0.8385 1.0 0.7874 0.8145 0.8240 0.8665 1.1 0.7281 0.7605 0.7721 0.8244 1.1 0.7700 0.7988 0.8089 0.8544 1.2 0.7077 0.7417 0.7538 0.8094 1.2 0.7517 0.7821 0.7929 0.8415 1.3 0.6865 0.7219 0.7347 0.7933 1.3 0.7324 0.7644 0.7759 0.8276 1.4 0.6644 0.7012 0.7146 0.7763 1.4 0.7122 0.7458 0.7579 0.8127 1.5 0.6416 0.6797 0.6936 0.7584 1.5 0.6911 0.7263 0.7389 0.7969 1.6 0.6181 0.6574 0.6718 0.7394 1.6 0.6692 0.7058 0.7190 0.7801 1.7 0.5940 0.6344 0.6492 0.7195 1.7 0.6465 0.6844 0.6982 0.7623 1.8 0.5695 0.6107 0.6259 0.6988 1.8 0.6232 0.6623 0.6765 0.7436 1.9 0.5447 0.5865 0.6020 0.6771 1.9 0.5993 0.6394 0.6541 0.7239 2.0 0.5196 0.5619 0.5777 0.6547 2.0 0.5748 0.6158 0.6310 0.7033 2.1 0.4944 0.5369 0.5529 0.6316 2.1 0.5501 0.5917 0.6072 0.6819 2.2 0.4693 0.5118 0.5279 0.6079 2.2 0.5250 0.5672 0.5830 0.6596 2.3 0.4443 0.4866 0.5027 0.5836 2.3 0.4998 0.5423 0.5583 0.6367 2.4 0.4196 0.4615 0.4776 0.5590 2.4 0.4747 0.5172 0.5333 0.6130 2.5 0.3952 0.4366 0.4525 0.5340 2.5 0.4496 0.4920 0.5082 0.5889 2.6 0.3714 0.4120 0.4277 0.5089 2.6 0.4249 0.4669 0.4830 0.5643 2.7 0.3482 0.3878 0.4032 0.4837 2.7 0.4004 0.4419 0.4579 0.5394 2.8 0.3257 0.3642 0.3792 0.4586 2.8 0.3765 0.4173 0.4330 0.5143 2.9 0.3040 0.3412 0.3558 0.4337 2.9 0.3532 0.3930 0.4085 0.4891 3.0 0.2831 0.3189 0.3331 0.4091 3.0 0.3305 0.3692 0.3844 0.4640 3.1 0.2631 0.2974 0.3111 0.3850 3.1 0.3086 0.3461 0.3608 0.4390 3.2 0.2441 0.2768 0.2899 0.3615 3.2 0.2875 0.3236 0.3379 0.4144 3.3 0.2260 0.2571 0.2696 0.3385 3.3 0.2673 0.3020 0.3158 0.3902 3.4 0.2088 0.2383 0.2503 0.3164 3.4 0.2481 0.2812 0.2944 0.3665 3.5 0.1927 0.2205 0.2318 0.2950 3.5 0.2298 0.2613 0.2739 0.3434 3.6 0.1775 0.2037 0.2144 0.2745 3.6 0.2124 0.2423 0.2543 0.3211 3.7 0.1632 0.1879 0.1979 0.2549 3.7 0.1961 0.2243 0.2357 0.2995 3.8 0.1499 0.1730 0.1824 0.2362 3.8 0.1807 0.2073 0.2180 0.2788 3.9 0.1375 0.1590 0.1678 0.2185 3.9 0.1662 0.1912 0.2014 0.2590 4.0 0.1260 0.1460 0.1542 0.2018 4.0 0.1527 0.1761 0.1856 0.2401

51

Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH )

52

Table of Estimated Probability of DFW for Math ACT score based on Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH ) ACTMATH PFFR PFSO PFJR PFSE ACTMATH PMFR PMSO PMJR PMSE 9 0.6700 0.7065 0.7197 0.7807 9 0.7173 0.7506 0.7624 0.8165 10 0.6462 0.6841 0.6979 0.7620 10 0.6954 0.7302 0.7428 0.8001 11 0.6217 0.6608 0.6751 0.7423 11 0.6726 0.7089 0.7221 0.7827 12 0.5965 0.6367 0.6515 0.7216 12 0.6489 0.6866 0.7003 0.7642 13 0.5708 0.6120 0.6272 0.6999 13 0.6244 0.6635 0.6777 0.7446 14 0.5448 0.5866 0.6021 0.6772 14 0.5993 0.6395 0.6542 0.7240 15 0.5185 0.5607 0.5766 0.6537 15 0.5737 0.6148 0.6299 0.7024 16 0.4920 0.5346 0.5506 0.6294 16 0.5477 0.5894 0.6050 0.6798 17 0.4657 0.5082 0.5243 0.6044 17 0.5214 0.5636 0.5794 0.6564 18 0.4395 0.4818 0.4979 0.5789 18 0.4950 0.5375 0.5535 0.6322 19 0.4136 0.4555 0.4715 0.5529 19 0.4686 0.5111 0.5272 0.6072 20 0.3883 0.4294 0.4453 0.5267 20 0.4424 0.4847 0.5008 0.5818 21 0.3635 0.4037 0.4193 0.5003 21 0.4165 0.4584 0.4744 0.5559 22 0.3394 0.3785 0.3938 0.4739 22 0.3911 0.4323 0.4482 0.5296 23 0.3161 0.3540 0.3689 0.4476 23 0.3662 0.4065 0.4222 0.5032 24 0.2937 0.3302 0.3446 0.4217 24 0.3420 0.3813 0.3966 0.4768 25 0.2723 0.3073 0.3212 0.3961 25 0.3187 0.3567 0.3716 0.4506 26 0.2518 0.2853 0.2986 0.3711 26 0.2962 0.3328 0.3473 0.4245 27 0.2324 0.2642 0.2769 0.3468 27 0.2746 0.3098 0.3238 0.3989 28 0.2141 0.2442 0.2563 0.3233 28 0.2541 0.2877 0.3011 0.3739 29 0.1969 0.2252 0.2366 0.3006 29 0.2346 0.2665 0.2793 0.3495 30 0.1807 0.2073 0.2181 0.2789 30 0.2161 0.2464 0.2585 0.3259 31 0.1656 0.1905 0.2006 0.2581 31 0.1987 0.2273 0.2388 0.3031 32 0.1515 0.1747 0.1842 0.2384 32 0.1824 0.2092 0.2201 0.2812 33 0.1384 0.1600 0.1688 0.2197 33 0.1672 0.1923 0.2025 0.2604 34 0.1263 0.1463 0.1545 0.2021 34 0.1530 0.1764 0.1860 0.2405 35 0.1151 0.1336 0.1412 0.1856 35 0.1398 0.1616 0.1705 0.2218 36 0.1047 0.1218 0.1289 0.1702 36 0.1276 0.1478 0.1561 0.2041

53

Model 7: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, GRADGPA, ACTMATH )

54

Model 8: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, ACTMATH ) Students without OSU graduation GPA For this model, only students who do not have an OSU Graduation GPA in the data were included in the estimation of the model parameters. These are students who were in their first semester at OSU when they enrolled in Math 1513. This model has the same variables as the last model, except for the OSU Graduation GPA.

Parameter DF Estimate Intercept 1 5.6855

COREGPA 1 -1.2297

GENDER 1 0.3427

SO 1 0.1239

JR 1 0.2349

SE 1 0.4212

ACTMATH 1 -0.1063

Variable Mean Minimum Maximum COREGPA 3.21 1.25 4.43

ACTMATH 20.83 9 36

The table below indicates the estimated probability of DFW in Math 1513 for female and male students at different levels in college varying across values of Math ACT, but assuming a constant value of 3.21 for Core High School GPA.

Table of Estimated Probability of DFW for Math ACT score based on Model 8 ACTMATH PFFR PFSO PFJR PFSE ACTMATH PMFR PMSO PMJR PMSE 9 0.6850 0.7111 0.7334 0.7682 9 0.7539 0.7762 0.7949 0.8236 10 0.6617 0.6888 0.7121 0.7487 10 0.7337 0.7572 0.7770 0.8076 11 0.6375 0.6656 0.6898 0.7282 11 0.7124 0.7371 0.7581 0.7906 12 0.6126 0.6415 0.6666 0.7067 12 0.6902 0.7160 0.7380 0.7724 13 0.5871 0.6167 0.6426 0.6842 13 0.6670 0.6939 0.7170 0.7532 14 0.5611 0.5913 0.6178 0.6608 14 0.6430 0.6709 0.6949 0.7329 15 0.5348 0.5654 0.5925 0.6366 15 0.6182 0.6470 0.6719 0.7116 16 0.5082 0.5391 0.5666 0.6116 16 0.5928 0.6223 0.6481 0.6893 17 0.4817 0.5126 0.5403 0.5861 17 0.5669 0.5971 0.6235 0.6661 18 0.4552 0.4861 0.5138 0.5601 18 0.5407 0.5712 0.5982 0.6420 19 0.4290 0.4596 0.4872 0.5338 19 0.5142 0.5450 0.5724 0.6173 20 0.4032 0.4333 0.4607 0.5072 20 0.4876 0.5186 0.5462 0.5919 21 0.3779 0.4074 0.4345 0.4807 21 0.4611 0.4920 0.5197 0.5659 22 0.3532 0.3820 0.4085 0.4542 22 0.4348 0.4655 0.4932 0.5397 23 0.3293 0.3573 0.3831 0.4280 23 0.4089 0.4392 0.4667 0.5132 24 0.3063 0.3332 0.3583 0.4022 24 0.3835 0.4132 0.4403 0.4866 25 0.2842 0.3101 0.3343 0.3769 25 0.3587 0.3877 0.4143 0.4601 26 0.2631 0.2878 0.3111 0.3523 26 0.3346 0.3627 0.3888 0.4338 27 0.2430 0.2665 0.2887 0.3285 27 0.3114 0.3385 0.3638 0.4079 28 0.2240 0.2462 0.2674 0.3055 28 0.2891 0.3152 0.3396 0.3825 29 0.2060 0.2270 0.2471 0.2834 29 0.2677 0.2927 0.3162 0.3578 30 0.1892 0.2089 0.2279 0.2623 30 0.2474 0.2712 0.2937 0.3337 31 0.1734 0.1919 0.2097 0.2423 31 0.2281 0.2507 0.2721 0.3105 32 0.1587 0.1760 0.1926 0.2233 32 0.2100 0.2312 0.2516 0.2882 33 0.1450 0.1611 0.1766 0.2054 33 0.1929 0.2129 0.2321 0.2669 34 0.1323 0.1472 0.1617 0.1886 34 0.1769 0.1956 0.2137 0.2466 35 0.1206 0.1344 0.1478 0.1728 35 0.1619 0.1794 0.1964 0.2274 36 0.1098 0.1225 0.1349 0.1582 36 0.1480 0.1643 0.1801 0.2093

55

Graph for Model 8: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, ACTMATH ) Students without OSU graduation GPA Math 1513

56

Table of Estimated Probability of DFW for Core HS GPA based on Model 8: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, ACTMATH ) Students without OSU graduation GPA Math 1513 The table below indicates the estimated probability of DFW in Math 1513 for female and male students at different levels in college varying across values of Core High School GPA, but assuming a constant mean value of 20.83 for Math ACT. COREGPA PFFR PFSO PFJR PFSE COREGPA PMFR PMSO PMJR PMSE 1.25 0.8737 0.8868 0.8974 0.9134 1.25 0.9069 0.9169 0.9250 0.9369 1.35 0.8595 0.8738 0.8855 0.9031 1.35 0.8960 0.9070 0.9160 0.9292 1.45 0.8440 0.8596 0.8725 0.8918 1.45 0.8840 0.8961 0.9060 0.9207 1.55 0.8271 0.8441 0.8582 0.8794 1.55 0.8708 0.8841 0.8950 0.9113 1.65 0.8088 0.8272 0.8425 0.8657 1.65 0.8563 0.8709 0.8829 0.9008 1.75 0.7891 0.8089 0.8255 0.8507 1.75 0.8405 0.8564 0.8695 0.8893 1.85 0.7679 0.7892 0.8071 0.8344 1.85 0.8233 0.8406 0.8549 0.8765 1.95 0.7452 0.7680 0.7872 0.8168 1.95 0.8047 0.8234 0.8390 0.8626 2.05 0.7212 0.7454 0.7659 0.7976 2.05 0.7847 0.8049 0.8217 0.8474 2.15 0.6958 0.7214 0.7431 0.7770 2.15 0.7632 0.7848 0.8030 0.8308 2.25 0.6692 0.6960 0.7190 0.7550 2.25 0.7402 0.7633 0.7828 0.8128 2.35 0.6414 0.6694 0.6935 0.7316 2.35 0.7159 0.7404 0.7612 0.7934 2.45 0.6126 0.6416 0.6667 0.7067 2.45 0.6902 0.7161 0.7381 0.7725 2.55 0.5831 0.6129 0.6388 0.6806 2.55 0.6633 0.6904 0.7136 0.7501 2.65 0.5529 0.5833 0.6100 0.6533 2.65 0.6353 0.6635 0.6879 0.7264 2.75 0.5224 0.5532 0.5804 0.6250 2.75 0.6064 0.6356 0.6609 0.7013 2.85 0.4916 0.5226 0.5502 0.5957 2.85 0.5767 0.6066 0.6328 0.6749 2.95 0.4610 0.4919 0.5196 0.5658 2.95 0.5464 0.5769 0.6038 0.6474 3.05 0.4306 0.4612 0.4889 0.5354 3.05 0.5158 0.5467 0.5740 0.6188 3.15 0.4007 0.4308 0.4582 0.5047 3.15 0.4851 0.5161 0.5437 0.5894 3.25 0.3716 0.4010 0.4279 0.4740 3.25 0.4545 0.4853 0.5131 0.5594 3.35 0.3434 0.3718 0.3981 0.4435 3.35 0.4242 0.4547 0.4823 0.5289 3.45 0.3162 0.3436 0.3690 0.4134 3.45 0.3945 0.4244 0.4517 0.4982 3.55 0.2902 0.3164 0.3409 0.3839 3.55 0.3655 0.3947 0.4215 0.4675 3.65 0.2656 0.2904 0.3138 0.3553 3.65 0.3375 0.3657 0.3918 0.4370 3.75 0.2423 0.2658 0.2880 0.3276 3.75 0.3106 0.3377 0.3630 0.4070 3.85 0.2204 0.2425 0.2634 0.3011 3.85 0.2849 0.3108 0.3350 0.3777 3.95 0.2000 0.2206 0.2403 0.2759 3.95 0.2605 0.2851 0.3082 0.3493 4.05 0.1811 0.2002 0.2185 0.2520 4.05 0.2375 0.2607 0.2826 0.3219 4.15 0.1635 0.1812 0.1983 0.2295 4.15 0.2160 0.2377 0.2584 0.2956 4.25 0.1474 0.1637 0.1794 0.2085 4.25 0.1959 0.2161 0.2355 0.2707 4.35 0.1326 0.1475 0.1620 0.1890 4.35 0.1772 0.1960 0.2141 0.2471 4.45 0.1191 0.1327 0.1460 0.1708 4.45 0.1600 0.1774 0.1941 0.2249 4.53 0.1092 0.1218 0.1342 0.1573 4.53 0.1472 0.1635 0.1792 0.2083

57

Graph for Model 8: MATH 1513: DFW=F(COREGPA, GENDER, SO, JR, SE, ACTMATH ) Students without OSU graduation GPA

58

Model 9: MATH 2144: DFW=F(GENDER, COREGPA, ACTMATH) Students who do have an OSU Graduation GPA This model is associated with students who have an OSU graduation GPA, which implies that they have been at OSU longer than one semester when they took Math 2144. Parameter DF Estimate Intercept 1 7.9667

GENDER 1 0.2846

COREGPA 1 -1.3243

ACTMATH 1 -0.1454

Variable Mean Minimum Maximum COREGPA 3.57 1.58 4.61

ACTMATH 26.87 11 36

The table below states the estimated probability of DFW in Math 2144 for female and male students across varying values of Core High School GPA assuming Math ACT at the mean of 26.87. It also states the estimated probability across varying values of Math ACT assuming Core High School GPA of 3.57.

Table of Estimated Probability of DFW for Model 9: MATH 2144: DFW=F(GENDER, COREGPA, ACTMATH) COREGPA PF PM ACTMATH PFMATH PMMATH 1.58 0.8773 0.9048 11 0.8373 0.8725 1.6 0.8744 0.9025 12 0.8165 0.8554 1.7 0.8591 0.8902 13 0.7937 0.8365 1.8 0.8423 0.8766 14 0.7689 0.8156 1.9 0.8239 0.8615 15 0.7421 0.7927 2.0 0.8039 0.8449 16 0.7133 0.7678 2.1 0.7822 0.8268 17 0.6826 0.7409 2.2 0.7588 0.8070 18 0.6503 0.7120 2.3 0.7337 0.7855 19 0.6166 0.6813 2.4 0.7071 0.7624 20 0.5817 0.6489 2.5 0.6789 0.7376 21 0.5459 0.6151 2.6 0.6494 0.7111 22 0.5097 0.5802 2.7 0.6186 0.6832 23 0.4734 0.5444 2.8 0.5870 0.6538 24 0.4373 0.5082 2.9 0.5545 0.6233 25 0.4020 0.4718 3.0 0.5216 0.5917 26 0.3676 0.4358 3.1 0.4885 0.5594 27 0.3344 0.4005 3.2 0.4555 0.5265 28 0.3029 0.3661 3.3 0.4229 0.4935 29 0.2731 0.3331 3.4 0.3910 0.4604 30 0.2452 0.3016 3.5 0.3599 0.4278 31 0.2193 0.2719 3.6 0.3300 0.3957 32 0.1954 0.2441 3.7 0.3014 0.3645 33 0.1736 0.2182 3.8 0.2743 0.3344 34 0.1537 0.1945 3.9 0.2487 0.3056 35 0.1357 0.1727 4.0 0.2248 0.2782 36 0.1195 0.1529 4.1 0.2026 0.2524 4.2 0.1820 0.2283 4.3 0.1631 0.2058 4.4 0.1459 0.1850 4.5 0.1301 0.1659 4.6 0.1158 0.1483

59

Graph for Model 9: MATH 2144: DFW=F(GENDER, COREGPA, ACTMATH)

60

Model 10: MATH 2144: DFW=F(GENDER, COREGPA, ACTMATH) Students who do not have an OSU Graduation GPA This model contains exactly the same variables as the last model, but the data used to estimate the parameters were from students who did not have an OSU Graduation GPA in the SIS system at the semester in which they enrolled in Math 2144, which indicates that this model is related to students who are in the their first semester of coursework at OSU.

Summary of Forward Selection

Step Effect Entered DF

Number In

Score Chi-Square Pr > ChiSq

Variable Label

1 COREGPA 1 1 221.2380 <.0001 COREGPA 2 ACTMATH 1 2 103.3650 <.0001 ACTMATH 3 GENDER 1 3 7.7586 0.0053 GENDER

Analysis of Maximum Likelihood Estimates

Parameter DF Estimate Standard

Error Wald

Chi-Square Pr > ChiSq Intercept 1 8.3692 0.5776 209.9200 <.0001 COREGPA 1 -1.2824 0.1238 107.3160 <.0001 GENDER 1 0.3298 0.1186 7.7291 0.0054 ACTMATH 1 -0.1664 0.0164 103.2440 <.0001

Variable Mean Minimum Maximum COREGPA 3.63 1.95 4.61

ACTMATH 27.88 15 36

Table of Estimated Probability of DFW for Model 10 COREGPA P(DFWF) P(DFWM) ACTMATH P(DFWF) P(DFWM) 1.95 0.7737 0.8262 15 0.7726 0.8253 2.05 0.7504 0.8070 16 0.7420 0.8000 2.15 0.7256 0.7862 17 0.7089 0.7721 2.25 0.6994 0.7639 18 0.6735 0.7415 2.35 0.6717 0.7400 19 0.6359 0.7083 2.45 0.6429 0.7146 20 0.5965 0.6728 2.55 0.6129 0.6877 21 0.5559 0.6352 2.65 0.5821 0.6595 22 0.5146 0.5958 2.75 0.5506 0.6302 23 0.4730 0.5552 2.85 0.5187 0.5998 24 0.4318 0.5138 2.95 0.4867 0.5687 25 0.3915 0.4722 3.05 0.4547 0.5370 26 0.3527 0.4311 3.15 0.4232 0.5050 27 0.3157 0.3908 3.25 0.3922 0.4730 28 0.2809 0.3520 3.35 0.3621 0.4411 29 0.2485 0.3150 3.45 0.3330 0.4098 30 0.2187 0.2803 3.55 0.3052 0.3792 31 0.1916 0.2480 3.65 0.2787 0.3495 32 0.1672 0.2182 3.75 0.2536 0.3209 33 0.1453 0.1912 3.85 0.2301 0.2937 34 0.1258 0.1668 3.95 0.2082 0.2678 35 0.1086 0.1449 4.05 0.1879 0.2434 36 0.0935 0.1255 4.15 0.1691 0.2206 4.25 0.1518 0.1993 4.35 0.1360 0.1796 4.45 0.1216 0.1615 4.55 0.1086 0.1449 4.61 0.1014 0.1356

61

Graphs for Model 10: MATH 2144: DFW=F(GENDER, COREGPA, ACTMATH) Students who do not have an OSU Graduation GPA