The Department of Mathematics

Transcription

1 Union University Department of Mathematics Program Review 2006

2 ACADEMIC PROGRAM REVIEW DEPARTMENTAL QUESTIONNAIRE Department: Department of Mathematics Respondent: Troy Riggs 1. How does your department carry out the mission of Union University? The Department of Mathematics at Union University provides Christ-centered mathematics education that promotes excellence and character development in service to Church and society. Christ-centered mathematics education begins with the faculty. All seven mathematicians in the department are deeply committed to Jesus Christ and to the historic Christian faith. Evidence is seen through the love, care, and concern shown by each member of the department toward other members of the department and their families, staff and administrators, and Union students. Department meetings begin with prayer for one another and for God s direction as the faculty carry out the mission of the department. Furthermore, all faculty members are actively engaged in a local Christian church. Christ-centered mathematics education extends to Union students in mathematics classes. To this end, in Spring 2003 the faculty drafted the following departmental mission statement: Union s mathematics program seeks to further students in their quest for increased understanding of Creation and the created order and to equip students to serve God, church, and society through excellence in thinking and the use of mathematics. We do this through a curriculum that develops the student s ability to think logically, analytically, and abstractly; to pursue a body of knowledge whose basis is independent of both empirical observation and culture; and to learn humility and a sense of wonder at the complexity, beauty, and applicability of mathematics. The Department of Mathematics promotes academic excellence and character development in Union students. The department offers entry-level mathematics courses for non-majors that are content, rather than awareness, driven (e.g. Math for Liberal Arts, College Algebra, Introduction to Probability and Statistics, and Precalculus). The department actively supports a local chapter of the national mathematics honor society Kappa Mu Epsilon. Eligible students are inducted into the chapter each academic year. Mathematics majors, in addition to a rigorous undergraduate curriculum, are required to take Senior Seminar, a capstone course that synthesizes the content of the undergraduate major and requires an undergraduate research project supervised by a faculty mentor. The fulfillment of the research project ensures that the student can think independently and can communicate mathematics effectively through oral and written presentations. Each fall semester on the annual Day of Remembrance holiday, the department offers a discipline-specific service learning opportunity to its majors and minors. In recent years, students have used their mathematical knowledge to aid an at-risk elementary school program housed at a local church and the local Boys and Girls Clubs of America. Finally, academic excellence and character development are evidenced by the quality of the mathematics majors and minors the department produces. Recent graduates are pursuing doctoral degrees in mathematics or related fields at major research universities, teaching mathematics at public or 1

3 Christian high schools or at the college level, and working in the private sector for software or statistical research companies. Six recent graduates have seen the results of their undergraduate research endeavors published in The Pentagon and Proceedings of the National Conference on Undergraduate Research. In addition to these vocational successes, there are numerous stories of these students acting as faithful witnesses and ministers of the gospel of Christ. The Department of Mathematics serves Church and society by successfully implementing and executing its departmental mission statement. Foremost, the department provides for the development of analytical skills and quantitative literacy for all Union students through the general core mathematics requirement. The department s curriculum develops logical, analytical, and abstract thinking skills, uses technology (e.g. graphing calculators, computer algebra systems, geometry software programs) to enhance student learning, provides undergraduate research opportunities for majors, offers peer tutoring that benefits both the gifted mathematics tutor and the student in need of assistance, exposes students to the applicability of the discipline of mathematics, supports other disciplines that depend upon mathematical skills and content (e.g. business, nursing, teacher education, engineering, natural and life sciences, social sciences, and computer science), and enriches the student s understanding of the Creation and the created order. 2. How well has your department achieved your Student and Program Expected Outcomes? During the Vision & Values 2005 departmental self-evaluation we were the Department of Mathematics and Computer Science. In Fall 2005 the joint department separated into two administrative units. The goals and responses from the self-evaluation for the mathematics program are easily distinguished from those for the computer science program. The goals and assessment findings for the mathematics program are presented on the next two pages. Observe that most of the goals have been achieved. We did anticipate a growing need for additional student travel funds. This has indeed been the case. We also noted that despite excellent improvements in student performance on the Major Field Achievement Test scores, students still struggle with proofs in the senior-level courses (MAT 411, 413, 415), and often don t appear to understand the goals of those courses. We noted that we had not yet provided a course (or other means) to help bridge the gap from the computationally focused courses into the more theory intensive courses. In the Section 3 we will discuss how we have used these results to continue improving our program. 2

4 Vision & Values 2005 SUMMATIVE EVALUATION Math (with CSC specific omitted) EXPECTED PROGRAM OUTCOMES Goal Assessment Findings Accomplished for full professors (02-03), associate profs (03-04) and assistant profs (04-05). Occasionally faculty are 1 hour under/over because of 2 & 4hr courses. 1. Reduce full-time faculty to a 24-hour workload while maintaining current programming. 2. Academic Preparation a. The department will graduate well-qualified teachers of mathematics at the middle and secondary levels. b. The department will graduate students who are wellprepared for graduate school. c. The department will graduate students who are wellprepared for the job market. 3. Academic Resources a. Provide the faculty and students with appropriate and sufficient resources related to the field of mathematics, i.e. journals, up-to-date software equipment, and funds for professional development, travel, and speakers. b. Provide the department with appropriate and sufficient physical resources as needed for the discipline. 4. The department will provide the engineering students with service courses which conform to ABET 2000 guidelines. All Math majors seeking teaching endorsement are required to pass the PRAXIS before graduation. All Math majors are now required to take either MAT411 or MAT415. Most Math majors seeking employment found a job within a few months of graduation, though not all in the discipline. Equipment line-item was increased with $400 set aside for Mathematica software. Line item for Student Travel and Professional Membership has been helpful, however needs to be increased. $400 for Mathematica Developer s Conference was added to professional development line item. Mathematical journal resources for students are sufficient The department also has a mobile data projector with laptop. The demand for the use of technology in the classroom is still increasing, so the need for additional IT equipped classrooms is ongoing. Master Plan now calls for Science Building ongoing. Engineering curriculum was adopted Fall

5 EXPECTED STUDENT OUTCOMES Goal 1. Communicate unifying mathematical ideas, both orally and in written form in an organized fashion. 2. Demonstrate understanding with respect to the theory and applications of Calculus and Discrete Mathematics. 3. Show an awareness of the abstract nature of mathematics and formulate a correct mathematical proof at the undergraduate level. Assessment Findings Fall 2000 MFAT Institutional score was highest ever (87 th percentile). Fall 2001 scores returned to their previous levels. Recent MFAT Institutional scores have varied greatly from year to year. Non-routine score on MFAT was greatly improved Calculus scores on the MFAT have also risen. Several students have won regional or national paper competitions with their Senior Seminar projects. Many students continue to struggle with idea of proofs in 400-level classes. Use of Findings to Improve Your Program Mathematics Line item for Student Travel and Professional Membership needs to be increased. The CS discipline has supplemented the former through a 2-year renewable grant from Prentice Hall. Updates in the Calculus curriculum have improved student performance. Curriculum changes may be needed to improve the transition to proof courses. 3. How have you used assessment results to improve your program? As observed in Section 2, despite excellent improvements in student performance on exam scores, students still struggle with proofs in the senior-level courses (MAT 411, 413, 415), and often don t appear to understand the goals of these courses. We noted that we had not yet provided a course (or other means) to help bridge the gap from the computationally focused courses into the more theory intensive courses. In an attempt to address this problem, this spring (Spring 2006) we offered Transition Math as a special topics course (MAT 295). The main objectives of this sophomore-level course are: 1) to teach students how to read and write proofs, 2) to sharpen critical thinking skills, 3) to develop mathematical maturity, 4) to introduce the student to some interesting mathematics not usually taught in undergraduate calculus or linear algebra courses, and 5) to demonstrate to undergraduates the beauty of mathematics. The department will continue to monitor the effectiveness of this course at meeting these goals. We will run the course again next spring and anticipate adding it into the catalog. We also noted in the Summative Evaluation that recruiting and retention of mathematics majors and minors should be priority objectives. We have implemented several initiatives in support of these goals. 4

6 In January 2006 the department completed major upgrades to the departmental website ( Faculty pictures and personal information are included, as well as course syllabi and assignments. The site includes information on tutoring opportunities, careers in the mathematical sciences, specific resources to support women in mathematics, a direct link to the departmental pages in the university catalog, recent student presentations and publications, student honor society, professional organizations, and available scholarships and awards. The Department of Mathematics Hospitality Program is designed to meet any prospective student inquiry with a welcoming, enthusiastic and informative response. Anyone submitting inquiries about the department or its programs to the university receives a letter from the chair. This letter thanks them for their inquiry, offers to respond to questions through phone or , directs them to the abundant information available on the departmental website, and invites them to schedule a personal visit with a professor and a current math major. We have been able to meet every prospective student who has arrived on a campus visit Preview Day. Both a professor and a current math major meet with the students and parents. The faculty member and student each briefly express the value that they see in a Union University education and our department s role in it, reserving the majority of the time to respond to questions from the visitors. Students and faculty in the department have taken steps to encourage communication and establish a greater sense of community among math students. The student honor society, Kappa Mu Epsilon (KME), has established an associate membership for freshman (who would not yet qualify for full membership) to encourage them to attend meetings and activities. Additionally, there is a pizza party scheduled early each fall to which calculus students are invited. As discussed later in this document, the addition of common spaces to the department could be used to support our efforts at building community and a sense of identity for mathematics majors and minors. The department is working to support recruiting and retention of majors and minors by advertising career opportunities for mathematics students. This includes steps as simple as advertising in the department spaces with posters that use stunning visuals presenting information on interesting applications of mathematics in science and industry. Our website includes several valuable links to information on careers in the mathematical sciences. More significantly, in 2003 the department received approval for a minor in actuarial science. This field applies the mathematics of financial risk to problems in insurance and finance and is an excellent career opportunity that has consistently been listed as a top career by the Jobs Rated Almanac. This spring (Spring 2006) we ran the first course in this program. Next year we anticipate two students completing the courses in this program (one graduating, the other anticipating graduating the following year). The department is currently seeking an official preactuarial program designation from the Society of Actuaries. The chair has begun discussions with financial firms in the Memphis area about summer student internship opportunities. One student has applied for a summer internship. 5

7 4. What are the post-graduate experiences of your department? Being a relatively small department we are able to follow our graduates fairly well. Our graduates have been very successful in either finding mathematics related jobs or furthering their education at graduate school. By gathering information about our graduates since May 2000 we have determined we have graduates who have completed or are currently enrolled in graduate programs at the University of Texas M. D. Anderson Cancer Center, Colorado State University (Atmospheric Science), University of Georgia (Mathematics), Emory (Mathematics Education), Union (Education) and Memphis (Education). In addition, we have graduates using their mathematics degrees in areas such as electrical engineering and software engineering. Although the trend appears to be changing, the majority of our graduates have acquired a secondary teaching endorsement while at Union. As a result we have many graduates currently teaching mathematics in middle schools and high schools throughout the state and across the country. 5. Describe the current societal demand for your majors. The reasoning and problem solving skills developed in mathematics courses are invaluable for the job market. The U.S. Department of Labor recognizes this and states that, more workers with knowledge of mathematics will be required in the future ( It follows, therefore, that a degree in mathematics qualifies graduates for a variety of occupations. The following are just a sample of such jobs: actuarial scientist, financial planner, computer-systems analyst, mathematician, software engineer, research analyst, computer programmer, space technology, manufacturing, aeronautics, and statistician. In fact, a recent Jobs Related Almanac gave the following job rankings: (2) actuary, (3) financial planner, (4) computer-systems analyst, (6) software engineer and (9) statistician. Many of our majors pursue a secondary education track. It is widely known that there is great demand for qualified mathematics teachers across the country. A 2002 National Center for Education Statistics (NCES) report revealed that 37% of high school mathematics teachers lack a major or certification in their field ( becometeacher/121_teachershort.htm). Additionally, according to the Recruiting New Teachers 2000 study of the largest urban school districts, 95% reported an immediate demand for mathematics teachers. Shortage of qualified mathematics and science teachers comes just when the expectations for the content that students should know in these subjects are rising. The U.S. Department of Labor echoes this concern in the following statement, Currently, many school districts have difficulty hiring qualified teachers in some subject areas most often mathematics, science (especially chemistry and physics), bilingual education, and foreign languages. ( Because of these opportunities and societal demands, we expect our graduates to be very successful in finding jobs in their field of interest. 6

8 6. Describe departmental initiatives to ensure effective student learning. The department coordinates with the Office of the Dean of Students to staff and promote the Math Study Lab. An upper-level mathematics major or minor is available in the lab to provide homework assistance to students enrolled in lower-level mathematics courses (8 hrs/wk for Spring 2006). This is in addition to the traditional tutoring services that are available to students through the Hundley Center for Academic Enrichment. The department has implemented new technology in various ways that support and enhance student learning. In addition to the use of teaching aids such as graphing calculators with projectors in many of our courses, some sections of the introductory probability and statistics course (MAT 114) incorporate on-line resources that give students immediate feedback on their mastery of basic skills. Student and faculty evaluations show that this appears to be especially beneficial with nontraditional students who have limited access to campus resources (instructor, tutors and peers). In the calculus sequence and above, the computer algebra system Mathematica is used as a tool to solve more complex problems. Students have incorporated this tool into their own scholarly projects. We are proud of the resources mentioned above that are intended to assist students with the course content; but these resources are far more effective if the student is placed in a course that is well-matched with his or her abilities. The department is currently working to implement an on-line nationally standardized mathematics placement exam for incoming freshmen. Our Mathematics Seminar (MAT 498) course for seniors has been very successful at achieving its goals of reviewing critical content from the curriculum, unifying principles and reflecting upon the history and nature of the discipline through discussion, individual investigation, and oral and written presentations. Student seminar projects have resulted in papers presented at regional and national meetings, as well as student publications. (See Student Presentations and Student Publications on the Fall 2005 Mathematics Academic Update.) In Vision and Values 2005, the department identified a need to assist students with the transition to senior-level proof courses. In our Summative Evaluation we determined that we had not yet met that goal. As discussed in Section 3, this year we have addressed this need by offering Transition Mathematics. This sophomore-level course is designed to develop an awareness of the abstract nature of mathematics and develop skill at reading and writing mathematical arguments. While this was taught as a special topics course, we anticipate adding the course to the catalog. 7. What resources are needed to ensure effective student learning? The University has identified five areas of active learning (undergraduate research, service learning, technology, active learning strategies in the classroom, and intercultural/study abroad opportunities). Our department needs (1) more space (faculty offices, student work areas) for conducting student research, (2) increased funding for student expenses and travel involved in 7

9 undergraduate research, (3) increased funding for service learning opportunities such as tutoring (both on-campus and in the community) and discipline-specific internship/service projects, (4) the latest in educational technology available to department faculty in our offices and in the mathematics classrooms, including hardware and software support, (5) faculty development opportunities and funding to investigate varied teaching methods for mathematics faculty, and (6) seed incentive money to begin study abroad experiences for majors and minors and faculty. Mathematics courses are currently taught in the Penick Academic Complex (PAC). A much higher percentage of classrooms in PAC need to be enhanced with technology. Technology would include at minimum a computer workstation (with appropriate software), a projection system, document camera and corner mounted screen. We recommend hiring a consultant to examine the classroom environment (including lighting and noise pollution) in every classroom in PAC. Student success in mathematics courses depends upon placing students in courses that are appropriate to their current abilities. The department has identified the need for a placement exam to ensure that this is done more effectively. Hence, resources are needed to implement a placement exam to all incoming freshman. We would like for students to feel comfortable in our departmental spaces. We would especially like to develop a sense of community and identity for our majors. Thus, communal areas that facilitate discussion and collaborative work among students and faculty are highly desirable. These would ideally include a lounge area, work tables, whiteboards, shelves for books and periodicals, and a quiet reading/study area. This could best be implemented by a new mathematics facility, perhaps a new wing on White Hall. Until such resources are available for that wing, these needs can be met by renovating vacated spaces adjoining our department in PAC. Other departments on campus have been well-served by such facilities. 8. Statistical data analysis We next present a comprehensive comparison of Union s mathematics program to other colleges and universities in issues of productivity and curriculum. Sources include Union s IRO; the Delaware Study; CBMS 2000: Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States, published by the American Mathematical Society (published 2002, data from 2000, latest available, CBMS 2005 not yet published); and Science and Engineering Indicators 2006 (see Overall mathematics and statistics enrollment. Overall mathematics and statistics enrollments, as a percentage of total enrollment, is given below. math stat total Coll/Univ Union All four-year colleges and universities, including those that offer graduate degrees in mathematics. Source: CBMS 2 Fall 2005, based on total undergraduate enrollment of 2,022, will be adjusted when correct value is supplied 8

10 As can be seen, Union s mathematics enrollment is significantly lower, as a percentage of total enrollments, than that of the average college or university. As shall be shown later, a significant portion of that difference is a result of Union not needing to offer remedial courses. On the other hand, Union s statistics enrollment is nearly twice that of the average college; this also is a drain from mathematics enrollments. Half of the deficit in the total math/stat enrollment is the result of no remedial enrollment. Course enrollments by type and level. Mathematics course enrollments by type and level are given in the next table. Union s courses fit into these categories as follows: remedial, none; introductory, MAT 101, 107, 111, 112, 116; calculus-level MAT 201, 211, 212, 213, 205, 314, 315; advanced level MAT 310, 320, 360, 411, 413, 415, 498. Notice, in particular, that discrete mathematics, linear algebra, and differential equations are all considered calculus-level courses for the purposes of the CBMS survey. The fact that each of those courses is required for some Union degree other than mathematics tends to lend credence to that selection. Coll 3 Union 4 number pct. number pct Math remedial 101,000 20% 0 0% Intro 236,000 46% % calc.level 137,000 27% 69 32% advanced 35,000 7% 6 3% Total 509, The next table gives the same information for mathematics and statistics combined. Statistics courses are assigned as follows: elementary, MAT 114, 208; upper-level, MAT 305, 400, 401, 402, and 405. (The categories for statistics are a little less well-defined than for mathematics; MAT 208 could almost be placed in the advanced category.) Coll 3 Union 4 number pct number pct math Remedial 101,000 17% 0 0% Intro 236,000 41% % calc. level 137,000 24% 69 20% Advanced 35,000 6% 6 2% Stat Elementary 62,000 11% % upper-level 11,000 2% 0 0% Total Three items stand out in the above tables. One is that our advanced enrollment is lower than that of other colleges. This could partly be due to the even/odd year phenomenon; a larger advanced course enrollment is expected in Fall Also, upper-level statistics courses are offered exclusively in the spring. The second is the absence of remedial courses, due to the nature of Union s student clientele. The third is Union s much greater statistics enrollment. Statistics is required by many of Union s professional programs, and it is an option for meeting the general 3 Four-year colleges and universities that do not offer graduate degrees in mathematics. Source: CBMS 4 Fall

11 core requirement. Since most of our students have had the equivalent of college algebra in high school but have not had statistics, we often advise our students to go that route. We see this difference from other colleges as a positive, as representative of Union s core value of being future-directed. Overall, the total enrollment in courses at or above calculus for four-year colleges is 32% of the total, while at Union it stands at 22%. We believe that a major portion of that difference is accounted for by many Union students taking an introductory-level class rather than calculus for their required mathematics course. A large number of students with high mathematics ACT scores and a strong background in high school mathematics take the easy route for their mathematics requirement, opting to take, for example, college algebra rather than calculus. This is unfortunate, and it contradicts our core value of being excellence-driven. We continue to work with faculty advisors, and hope that the implementation of a placement exam will help correct this situation. Class size. Average section sizes for various level courses in mathematics and statistics are given below. Class Size Coll 3 Union 4 Math remedial 23 NA introductory calc-level advanced Stat elementary upper-level 15 NA Union s class sizes are significantly smaller than average. The small introductory/elementary class sizes are partly due to the effects of teaching smaller-than-average classes in the evening and on the Germantown campus due to requests from non-traditional programs. Small class sizes and instruction by tenure-track faculty are benefits that we should market to students and parents. Faculty. Several items from the Delaware Study point to major differences between Union and similar colleges. We shall begin with the prevalence of teaching done by tenured/tenure-track faculty. Percentage of Lower-Division Student Credit Hours Taught tenuretrack other regular supplemental Comprehensive 55% 20% 0% Baccalaureate 65% 9% 25% CCCU/ASBCS 75% 5% 19% Union 94% 0% 6% 10

12 Percentage of Upper-Division Student Credit Hours Taught tenuretrack other regular supplemental Comprehensive 93% 3% 2% Baccalaureate 90% 1% 7% CCCU/ASBCS 85% 1% 4% Union 100% 0% 0% Not all rows add to 100%, but the values are as reported in the Delaware study. These tables show that Union relies on adjunct and part-time faculty to teach mathematics much less than other colleges do. The fact that Union s enrollments are relatively heavier in lower-level courses than are other colleges and that we also rely less upon non-tenure-track faculty makes the following comparison inevitable: What Faculty Teach Student Credit Hours Lecture sections lower division upper division lower division upper division Comprehensive 87% 12% 68% 23% Baccalaureate 85% 14% 70% 28% CCCU/ASBCS 90% 10% 71% 23% Union 95% 5% 79% 21% Faculty in our department not only do more lower-level teaching than tenure-track faculty in other colleges, but also more than any other department on our campus (when measured by SCH), according to the productivity study provided by the IRO. The small class sizes listed above are consistent with the following data from the Delaware Study: Student Credit Hours per Full-Time Equivalent SCH/FTE 5 Sections/FTE 6 Comprehensive Baccalaureate CCCU/ASBCS Union Union is within the range of other colleges on number of sections taught. This number may be more dependent upon the number of credit hours given to such courses as calculus, and the prevalence of calculus sections, than on anything else. 5 Student credit hours per full-time equivalent faculty 6 Sections taught per full-time equivalent faculty 11

13 Major schedule changes were implemented for the academic year. Our department eliminated all adjunct teaching on the Jackson campus and also placed some regular contract teaching load in the winter term. These and other changes (possibly including changes in the method of counting load credit for undersized classes) contributed to a decrease in FTE equivalent for fall and spring semesters combined from 7.2 during to 5.5 during Therefore the SCH/FTE comparison for , which appears in the table above, is outdated. Using the values provided by the IRO s productivity study, the SCH/FTE for our department 7 is 193, which is in line with other institutions. Smaller class sizes, heavier use of tenure-track faculty for lower-level courses and very little reliance on adjunct faculty, along with the facts that even the younger members of the department are now full professors 8 and that members of the department receive release time for duties benefiting the entire campus 9, all lead to higher average costs per student credit hour. Total costs in the IRO productivity study are combined with computer science, with whom our department officially split for the academic year. It is possible that this may also have inflated some of the figures for mathematics. Personnel Costs Personnel cost as a Total $/SCH percentage of total Comprehensive $121 97% Baccalaureate $138 97% CCCU/ASBCS $158 97% Union $242 97% Freshman majors. According to Science and Engineering Indicators 2006, about 0.7% of all entering college freshmen intend to be mathematics majors. If Union had an entering freshmen class of 430 students, that would give just three entering mathematics majors. Union generally meets or exceeds this value. Graduates. According to Science and Engineering Indicators 2006, nationally there is less than 1 bachelor s degree awarded in mathematics or statistics for every 1,000 students enrolled in college. 10 Our department easily meets this ratio, but we do not go significantly above it. SEI data shows that the number of graduates in mathematics/statistics has declined slightly over the last 20 years, even though total enrollment and degrees awarded have increased. One trend over the last 20 years that has contributed to a national decline in the percentage of students majoring in mathematics and taking upper-level courses is the rise of computer science. In fact, over the last 20 years computer science bachelor degrees granted have doubled, while as noted mathematics degrees awarded have slightly declined. Students who traditionally were attracted to mathematics now have another choice available, and some make that other choice. 7 Calculated by halving the fall 2004/spring 2005 total of 386; actual fall 2004 value is likely a little larger 8 Two were not yet promoted for the timeframe of this data 9 c.f. Undergraduate Research leadership 10 12,273 bachelor s degrees in mathematics or statistics awarded in 2002 (latest data available), while over 15 million were enrolled in 2001 (latest data available) 12

14 Curriculum. The CBMS study reported the availability of courses during an academic year. The table below gives the percentage of four-year college departments without graduate programs offering particular courses during the academic year. Course titles are abbreviations of those given in the CBMS report, not Union s course titles. NL means not listed in the report. That is compared in the table to Union s frequency of offering (courses that actually ran), per academic year, for the period fall 2002 through spring For example, a value of 25 for Union (%) indicates that this course runs every 4 years. Course Offerings Course Coll (%) Union (%) math modern algebra real analysis geometry senior seminar math/secondary teach complex analysis NL 25 history of math NL 50 numerical analysis NL 25 number theory topology 13 0 applied math/modeling 13 0 foundations/logic 12 0 combinatorics 11 0 operations research 10 0 stat actuarial science NL 25 math stats 47 0 Probability 31 0 experimental design 5 0 biostatistics 5 0 applied stat analysis Regression & correlation 3 0 Union compares well with other bachelors-degree granting mathematics departments in the area of course offerings. Every mathematics course offered by at least 15% of colleges in any particular year was offered at Union within the last four years. We also have approximately the same level of variety of course offerings as the average bachelors-degree-granting mathematics department. Another way of trying to determine the same information is by looking at course enrollments in advanced-level courses. That appears in the next table, along with a column marking those courses offered by Union. 13

15 Course Enrollment Advanced Courses Course Coll enrol. (1000s) Union offers math modern algebra 6 X intro to proofs 5 Y real analysis 3 X discrete structures 3 X math/secondary teach. 2 X geometry 2 X number theory 2 Y senior seminar 2 X history of math 1 X complex var 1 X numerical analysis 1 X topology 1 advanced diff eq 1 partial diff eq 1 adv math eng & phys 1 Z logic/foundations 1 actuarial math 0 X applied math/modeling 0 advanced linear alg 0 vector analysis 0 combinatorics 0 other 2 stat math stats 4 W probability 4 applied stat anal 1 X design & anal of exper 1 Key: X = catalog course regularly or recently offered, W = catalog course not yet offered, Y = special topics course recently offered, Z = offered by the physics department. Again, this analysis shows that Union has developed appropriate course offerings for its type of school. Miscellaneous curricular matters. The CBMS study, although now 6 years old, is the latest data available on a wide range of mathematics curricular topics. What follows is a list of much of that miscellanea and how our department compares. Colleges shall refer to four-year colleges and universities that do not offer graduate degrees in mathematics. Colleges/universities shall refer to all four-year colleges and universities. K-8 teacher education programs. Percentage of colleges with a K-8 teacher certification program: 85%; Union does. Percentage of those that have a mathematics department member on the certification program control committee: 68%; Union does. Percentage that offer a special course or course sequence for K-8 teachers: 73%; Union does. Percentage that designate special sections of regular courses for K-8 teachers: 4%; Union does not. Average number of mathematics courses required for early grades (K-3) certification: 2.3. Average number of mathematics courses required for later grades certification (through 8 th ): 2.8. Union requires two for each. 14

16 Placement tests. 66% of colleges offer mathematics placement tests; Union does not. It is interesting that over 80% of those with graduate programs, and 98% of community colleges, offer placement tests. Tutoring center. 88% of colleges offer a mathematics tutoring center; Union does. Percentage of those offering tutoring by students: 100%; Union does. Among other services offered, in order of prevalence, were computer software, 60% (Union, yes); computer-aided instruction, 39% (no); tutoring by para-professional staff, 36% (no). Math or stat club. 51% of colleges offer a math or stat club; Union does. Math or stat contests. 55% of colleges offer math or stat contests. Union does not. Colloquia. 46% offer special math or stat colloquia for undergraduates. Some of Union s Mathematics and Computer Science Colloquium Series presentations are designed for students, and some are not. Mathematics outreach opportunities. 46% of colleges offer mathematics outreach opportunities to local K-12 schools. Our department has sometimes offered such opportunities. Undergraduate research opportunities. 52% of colleges offer undergraduate research opportunities in mathematics. Union requires it in MAT 498. Independent Study Opportunities. 79% of colleges offer independent study opportunities. Union does, but students rarely take advantage of the opportunity. Advisors in department. 78% of colleges offer advisors within the mathematics department. Union does. Distance learning. Mathematics departments in colleges are almost not involved in distance learning at all. Just 1.7% of math for liberal arts sections are taught via distance learning; for Union, that corresponds to one section every 14.7 years. For both college algebra and elementary statistics, it was 0.5% of sections. That also works out to about one section of each every 15 years. Reform methods in statistics teaching. Percentages of colleges and universities that use various methods in elementary statistics courses taught by mathematics departments in regularsized sections (<36) (corresponding to our MAT 114, and somewhat to our MAT 208) are as follows: graphing calculators, 48% (all Union instructors require a calculator with two-variable statistics capabilities and some require graphing calculators); writing assignments, 42% (MAT 305); computer assignments, 54% (in MAT 208, yes; in MAT 114, no); group projects, 25% (unknown percentage at Union); weekly computer lab, 20% (no). Reform methods in calculus teaching. Percentages of colleges and universities that use various methods in instruction for mainstream Calculus I, taught in regular-sized sections are as 15

17 follows: graphing calculators, 50% (nearly universal at Union); writing assignments, 31% (minimal at Union); computer assignments, 46% (required at Union); group projects 24% (Union percentage unknown); weekly computer lab, 13% (required at Union). 9. Project your needs to 2010 from the data provided by the IRO. As discussed in Section 8, the data suggest that typically the department is currently teaching at an under-load. This will not be the case next year, as one of the department members will be out on research leave. Another member also plans to take such a leave in the near future. Also, we anticipate that with accreditation the needs of the Engineering program for mathematics course offerings will increase over the next several years. Thus, we do not plan to actively address course load in the near future. The department anticipates that we will need an office secretary that is no longer shared with the Department of Engineering. Over the last two years, we have seen that the secretary that is shared with the Departments of Computer Science, Engineering and Physics is spending the bulk of her time (approximately 40-45%) on work for the Department of Engineering. The work load has been heavy at times, and we would anticipate that the administrative demands of the Engineering Program are likely to increase in the future. While we have met the majority of our program outcomes stated in Vision and Values 2005, we have not been able to provide the department with appropriate and sufficient physical resources as needed for the discipline (Program Outcome 3b). We have implemented technology into the classroom as facilities have been available, and the university has continued to increase the number of classrooms equipped with appropriate technology. However, the supply has not kept up with the growing demand. For example, facilities that we originally shared with the Department of Nursing (e.g. C-24) are now almost exclusively used by Nursing. Moving, setting up and taking down portable laptops and projectors often expends valuable classroom time. Additionally, we have a growing need for spaces for faculty/student and student/student collaboration. There is increasing departmental involvement in student scholarship and faculty/student research, but we do not have the facilities to encourage this activity. (See Student Presentations and Student Publications on the Fall 2005 Mathematics Academic Update.) Ideally, there would be space in the department for student study carrels, whiteboards, and a small lounge area for building a stronger sense of community. For the departments on campus that enjoy such facilities, these have proven to be helpful in recruiting and retaining students in their programs. As our students are increasingly involved in scholarship, the department needs to be able to support student travel. Several students have presented at regional and national meetings. We have had recent graduates who have gone on to graduate work in mathematics who would have benefited from attending the Joint Mathematics Meetings. Our student travel funds need to increase to meet these needs. 16

18 Finally, as discussed earlier, there is an increasing societal demand for mathematical understanding and quantitative skills. At the same time there are problems across the nation with recruiting and retaining students in the mathematical sciences. Additionally, nationwide student success rates in required mathematics courses are not improving. We believe that we can address all of these problems on our campus to some degree by ensuring that students are placed into courses that are appropriate for their skill level. An efficient and widely accepted tool for accomplishing this task is the mathematics placement exam. In the past, administering paper and pencil placement exams has proven to be a logistical challenge. However, there are now inexpensive exams available that take less than half an hour to complete. These can be taken, graded and results instantly posted on-line from any computer with internet access. We believe that Union University should require such an exam from all incoming freshman. 10. What would you like your department to look like in 2010? By 2010, the Department of Mathematics hopes to see many of the following goals implemented so that the department can continue to be an integral part of a vibrant undergraduate liberal arts program and can fulfill both its own mission statement and the mission statement of Union University. Physical Resources: The Department seeks to create a sense of community among the faculty and students. The current structure of physical space assigned to the department (Penick Academic Complex horseshoe area) does not provide sufficient space for building community. The department needs a designated non-office area where mathematics students and mathematics faculty can interact outside the classroom and can work together on collaborative projects. Furthermore, the current size of faculty offices hampers the mentoring of student researchers and severely limits faculty interaction with students on other non-routine assignments. Two possible scenarios for addressing these pressing space problems are either adding space to the department from adjacent areas in Penick Academic Complex or possibly relocating the department to another building. More classrooms that are fully equipped with technology are needed. At a minimum, more workstations and projector systems are needed. Projector systems that will interface with laptop computers, and the installation of document cameras would be ideal. Faculty and Faculty Resources: The department wishes to see all of its faculty members embracing one or more of the active learning strategies in each of their courses and pursuing scholarly activity in their chosen area of scholarship (discovery, integration, application, or teaching). Faculty members who explore new ways to enhance student learning and contribute new ideas in their discipline will certainly be attractive to prospective and current students. To achieve this, the faculty must have the latest technology available both in their offices and in their classrooms. The option of a laptop computer (rather than the desktop) for each faculty member is desirable. The department also hopes for more departmental professional development funds to cover inflating travel expenses, so that its faculty members can gain 17

19 knowledge of active learning strategies and can share the results of their scholarly activities in more venues. Students and Student Resources: The department would like to have more undergraduate majors and minors in mathematics and graduate more students pursuing a career in mathematics (e.g. academician, actuarial scientist, government or private researcher, statistician) or mathematics education. Designated scholarships would contribute to increasing the number of gifted mathematics students who chose to come to Union University. Currently, the department supports the Joe Tucker Scholarship Fund, which assists juniors and seniors in mathematics or computer science. By 2010, the department desires to have designated scholarship money from both the University and from outside donors that will directly support the financial costs of students studying mathematics. Furthermore, the department believes that targeted recruiting of high school and home school students who excel in mathematics and science coupled with attractive financial aid packages will greatly increase the pool of potential mathematics majors and minors on this campus. The department also seeks to develop students who have confidence and creativity when using discipline-specific technology to communicate mathematics. Obviously, students must have access to the latest discipline-specific software, appropriate hardware, and technology compatible rooms on this campus. A substantial increase in student travel funds will allow Union students to learn from mathematics students at other universities and to disseminate their own mathematical ideas in appropriate venues. 11a. In what ways should we be advancing the department s service mission to the other departments on campus? As discussed earlier in this document, there is an increasing societal need for graduates who have a solid mathematics background. At the same time, the undergraduate curriculum is undergoing radical revision for several key programs. These programs include business, computer science, education, engineering, pre-professional programs, and many others. Hence, it becomes critical that our department regularly review the content of our service courses. This includes reviewing the contents of MAT 101 and 107 so that they satisfy the criteria that the School of Education must meet. Similarly MAT 111, 112,114, 116, and 201 are essentially service courses for other programs. These programs need to be included in the process of reviewing these courses. We have done this reasonably well, as the department has recently changed course content and offerings to meet the needs of other departments. In addition to content and offerings, the department should coordinate delivery methods with the programs that are served. We will continue to explore the feasibility of new times, places and methods for offering service courses. We will continue to explore new possibilities, based upon faculty release time and other resources to develop and deliver these courses and on solid enrollment projections showing sufficient demand for non-traditional offerings. Again, since it is especially appropriate to this mission, we mention that a placement exam will help insure that incoming freshmen are placed in a mathematics class that they are prepared for 18

20 and that they will derive a maximum benefit from. Beginning at the appropriate level should help all students progressively increase in mathematical ability. Professors will continually strive to become more effective teachers. We will incorporate new teaching methods in the classroom as those prove to be effective in improving student skill and knowledge. Finally, in an effort to promote student success in mathematics classes, the department initiated a mathematics study lab where students can come to receive assistance with homework from upper-level mathematics students. This lab is funded and managed through the Office of Student Services. The Union University Math Study Lab has provided services for two years and continues to coordinate with the department in selecting assistants, times and locations to best meet student needs. The above service ideas are offered to help all programs produce well-qualified graduates and enhance the academic integrity of Union University. 11b. How should we be using technology in placing, supporting, and assessing students? One of the most recent proposals that received the unanimous approval of the department was to investigate mathematics placement software that is currently available. We have begun discussions with faculty and staff on its implementation. The School of Business Administration has expressed support of this proposal. A technology-based placement system would be of assistance to faculty advisors in identifying the specific mathematical strengths and weaknesses of their majors. Students taking precalculus courses primarily use graphing calculators, Geometers Sketchpad and Microsoft Excel. The department faculty members provide demonstrations using a calculator interfaced with an overhead viewer in appropriate courses. Several instructors have incorporated PowerPoint presentations into their lectures. Calculus students and upper-level mathematics students use the computer algebra system Mathematica in the computer labs, library and dormitory workrooms. The department is interested in providing additional on-line resources for students taking precalculus courses. Tables wired for laptop computers should be purchased for the classrooms that we use in PAC to support student learning. The majority of our classes are currently taught in classrooms that have very small desktops built into plastic chairs. Informal discussions have begun on ways to improve and assess our students competence in the use of technology used in the mathematics courses, including student facility with Mathematica. This assessment may require modification of the curriculum and/or the addition of technology support staff. Our goal is for upper-level majors to be able to demonstrate their ability to make effective use of this technology. 19