Preparing Students for Transfer and a Major.

1. Preparing Students for Transfer and a Major. Martin Flashman IMPAC Lead Faculty for Mathematics Professor of Mathematics Humboldt State University flashman@humboldt.edu

2. IMPAC Project An Intersegmental Approach http://www.cal-impac.org

3. Abstract • As the economics of college education continue to evolve, more students will be planning to transfer from Community Colleges to the CSU and UC systems. • IMPAC is the California intersegmental project that is trying to improve the transfer process by focusing on preparation for a major. • Professor Flashman will discuss some of the recommendations of IMPAC for prospective Mathematics majors and relevant developments at the CSU and UC campuses.

4. What is IMPAC? The Intersegmental Major Preparation Articulated Curriculum (IMPAC) project is a unique intersegmental, faculty-designed and faculty-run project to ensure that students transferring from the community colleges to UC and CSU are prepared for work in their chosen major and can avoid having to repeat coursework.

5. How does IMPAC work? • Regional Meetings attended by many discipline groups. Science I- Mathematics • 2 in 2004-2005 [4 in 2003-2004] • South and Metro RegionsNovember 13, 2004atLAX Sheraton Gateway • UC: Irvine, Los Angeles, Riverside, Santa Barbara, San Diego • CSU: Bakersfield, Channel Islands, Dominguez Hills, Fullerton, Long Beach, Los Angeles, Northridge, Pomona, San Bernardino, San Diego, SLO, San Marcos • CCC: Allan Hancock, Antelope Valley, Bakersfield, Barstow, Canyons, Cerritos, Cerro Coso, Chaffey, Citrus, Coastline, Compton, Copper Mountain, Crafton Hills, Cuesta, Cuyamaca, Cypress, Desert, East Los Angeles, El Camino, Fullerton, Glendale, Golden West, Grossmont, Imperial Valley, Irvine Valley, Long Beach City, Los Angeles City, Los Angeles Harbor, Los Angeles Mission, Los Angeles Pierce, Los Angeles Southwest, Los Angeles Trade Tech, Los Angeles Valley, MiraCosta, Moorpark, Mt. San Antonio, Mt. San Jacinto, North Orange CCCD/Noncredit, Orange Coast, Oxnard, Palo Verde, Palomar, Pasadena City, Porterville, Rio Hondo, Riverside, Saddleback, San Bernardino Valley, San Diego Centers for Ed. & Tech., San Diego City, San Diego Mesa, San Diego Miramar, Santa Ana, Santa Barbara City, Santa Monica, Santiago Canyon, Sequoias, Southwestern, Taft, Ventura, Victor Valley, West Los Angeles • Statewide Meeting • April 29 - 30, 2005Radisson Hotel-LAX,

6. IMPAC on the WWW • Register on-line for meetings at http://www.cal-impac.org/

7. What Are The IMPAC Objectives ? The two specific objectives of IMPAC are: • the creation of a common understanding of the major preparation including key components of the lower division curriculum; and • the establishment of a system of state and regional intersegmental faculty dialogues, by discipline and among related disciplines, to address curriculum issues related to articulation and transfer.

8. What Has IMPAC Done So Far? • Advisory Letters to Mathematics Faculty, Community College Counselors, and Transferring Mathematics Majors. (Approved and Distributed 2004) • Recommendations for 2004-2005 • Communications (WWW and ASSIST) • Community (Regional Intersegmental Math Councils) • Curriculum (CAN)

9. Related Projects • CANCalifornia Articulation Number [CC and CSU] • ASSIST [www.assist.org] • The University of California • http://www.ucop.edu/pathways/ • Dual Admissions Program (DAP) • Guaranteed Transfer Option (GTO) • The California State University • http://www.csumentor.edu/ (GE planning) • California State University Lower Division Major Requirements(Lower Division Transfer Project)

10. CAN: California Articulation Number • The California Articulation Number System (CAN) is a course identification system for common core lower-division transferable, major preparation courses commonly taught on CCC and CSU campuses. • Colleges and universities that demonstrate common acceptance of courses through traditional articulation agreements can qualify courses for CAN designations. • Courses with CAN designators are accepted by any other CAN participating institutions as being comparable to their local courses with the same CAN designators to meet local requirements, even if the receiving university has not established an explicit traditional articulation agreement with a particular California Community College.

11. ASSIST [www.assist.org]Articulation System Stimulating Interinstitutional TransferProject • ASSIST is a computerized student-transfer information system that can be accessed over the World Wide Web. • It displays reports of how course credits earned at one California college or university can be applied when transferred to another. • ASSIST is the official repository of articulation for California’s colleges and universities and therefore provides the most accurate and up-to-date information available about student transfer in California.

12. To: Humboldt State |From: Los Angeles Pierce College Semester| Semester Articulation Agreement by Major Effective during the 04-05 Academic Year ====Mathematics==== The following are the LOWER DIVISION REQUIREMENTS for this major. MATH 109 Calculus I (4)|MATH 261 Calculus I (5) (CAN MATH 18) | (CAN MATH 18) (§ CAN MATH SEQ B) | (§ CAN MATH SEQ B) (§ CAN MATH SEQ C) | (§ CAN MATH SEQ C) -------------------------------------------------------------------------------- MATH 110 Calculus II (4)|MATH 262 Calculus II (5) (CAN MATH 20) | (CAN MATH 20) (§ CAN MATH SEQ B) | (§ CAN MATH SEQ B) (§ CAN MATH SEQ C) | (§ CAN MATH SEQ C) -------------------------------------------------------------------------------- MATH 210 Calculus III (4)|MATH 263 Calculus III (5) (CAN MATH 22) | (CAN MATH 22) (§ CAN MATH SEQ C) | (§ CAN MATH SEQ C) -------------------------------------------------------------------------------- MATH 240 Introduction to (3)|No Course Articulated Mathematical Thought | -------------------------------------------------------------------------------- MATH 241 Elements of Linear (3)|MATH 270 Linear Algebra (3) Algebra | (CAN MATH 26) -------------------------------------------------------------------------------- Choose one of the following: CIS 130 Introduction to (3)|No Course Articulated Programming | CIS 230 C++ Programming (3)|No Course Articulated CIS 235 Java Programming (3)|No Course Articulated Same as: CS 235 | CIS 240 Visual Basic Programming (3)|No Course Articulated Same as: CS 240 | Same lower division requirements for Applied Mathematics Option. Students must earn a minimum grade of C- in all courses for the major (all options). END OF MAJOR §Humboldt State University MATH 109 + MATH 110 qualified as CAN MATH SEQ B Humboldt State University MATH 109 + MATH 110 + MATH 210 qualified as CAN MATH SEQ C Los Angeles Pierce College MATH 261 + MATH 262 qualified as CAN MATH SEQ B Los Angeles Pierce College MATH 261 + MATH 262 + MATH 263 qualified as CAN MATH SEQ C THE ABOVE ARTICULATION AGREEMENT IS SUBJECT TO PERIODIC REVISION. PLEASE CONSULT A COUNSELOR EVERY SEMESTER TO OBTAIN CURRENT INFORMATION ABOUT POSSIBLE CHANGES IN THE AGREEMENT.

13. Mathematics LettersAdvisory Memorandum to Prospective Mathematics Majors March 1, 2004 To: Students at community colleges considering a major in mathematics. From: The Intersegmental Major Preparation Articulated Curriculum (IMPAC) Mathematics Advisory Committee Re: Advice in preparing for a major in mathematics. As a result of consultations with mathematics departments of the University of California, The California State University, and the California Community Colleges, the Mathematics Advisory Committee of IMPAC provides the following recommendations to assist community college students preparing for transfer as mathematics majors.

14. SUMMARY OF ADVICE: • Work closely with the mathematics and counseling faculty of your college as soon as possible to design a program of courses in preparation for transfer to a university. • Take as many lower division mathematics courses required for a major in Mathematics as possible. • Work to develop familiarity with proofs. • Be familiar with geometric concepts including proofs at least at the level usually treated in high school geometry courses.

15. Complete the full calculus sequence (including infinite series and an introduction to the calculus of several variables) or at least one full year (2 semesters or 3 quarters) of a scientific / engineering style calculus course at the same institution. • Take a linear algebra course. (Encouraged) • Take a differential equations course. (Encouraged) • Consider taking a computer course that develops competency in a computer programming language including the construction of algorithms. • Consider taking a course in statistics. • Try to take full year applications courses for science majors. • Consider deferring a calculus-based physics course until you have completed at least one year of calculus.

16. General Recommendations • Since you are considering a major in mathematics, you should work closely with the mathematics and counseling faculty of your college as soon as possible to design a program of courses in preparation for transfer to a university. • Initially you should become familiar with requirements for majoring in mathematics at universities to which you may transfer. It is important to note that the requirements for a mathematics major may differ significantly among the universities you are considering. Use current catalogs, mathematics department web sites, and other resources such as the ASSIST web site [http://www.assist.org] to learn more about transfer requirements for a mathematics major. Discuss your choices with your counselors and mathematics instructors. Contact a university’s mathematics faculty or program advisors to discuss any potential problems with transferring courses there. • You should take as many lower division mathematics courses required for a major in Mathematics as possible before you transfer.

17. General Education: In order to complete lower division requirements in mathematics, take only the minimum number of lower division General Education requirements needed for transfer.

18. Mathematical Maturity: Junior‑level university mathematics majors are expected to read and write proofs of various types and levels of sophistication. This is referred to frequently as mathematical maturity. There are many levels of mathematical maturity, but junior‑level mathematics majors are expected to perform at a level of maturity distinctly above that of lower division students. • Some university mathematics programs develop and certify mathematical maturity through a specific lower or upper division course with an emphasis on proof writing. Other programs provide the opportunity to develop mathematical maturity in the context of lower‑division courses such as discrete mathematics or linear algebra. • In any case, prior to transfer, you should work to develop familiarity with proofs. How this work will be received at a university varies from school to school. You should consult with a transfer university's faculty or program advisor as early as possible for specific information and recommendations regarding mathematical maturity.

19. Specific Recommendations • Geometry:You should be familiar with geometric proofs and concepts, at least at the level usually treated in high school geometry courses. This familiarity might be developed through a single geometry course or as part of other courses such as analytic geometry, calculus, or linear algebra courses.

20. Calculus: There are often different approaches taken during the first year calculus course. Ideally, you should have completed the full calculus sequence (including infinite series and an introduction to the calculus of several variables) prior to transfer. This generally should take 3 semesters (4‑5 quarters). • When you cannot take the full calculus sequence prior to transfer, you should take at least one full year (2 semesters or 3 quarters) of a scientific / engineering style calculus course at the same institution. • Splitting the first year of calculus between courses at different colleges can result in missing concepts and may make articulation more difficult.

21. Non-Calculus Courses • Linear Algebra: You should take some course that covers linear algebra at least at the level of matrix algebra. At the university level this course is often a prerequisite for advanced courses. Some universities make linear algebra a key part of sophomore level course work while others have no formal course in linear algebra in the lower division. Depending on the university, the process and result for transferring a linear algebra course taken at a community college may differ substantially. Nonetheless, you are encouraged to take a course studying linear algebra before transfer. You should consult with your chosen transfer university’s mathematics faculty or program advisor as early as possible for more advice on linear algebra courses.

22. Differential Equations: A differential equations course is required lower division course work at some universities, while at others a more sophisticated first course in differential equations is required at the junior level. However, the mathematics major option for prospective high school mathematics teachers often does not require a course in differential equations. Depending on the university and the mathematics program, the process and result for transferring a differential equations course taken at a community college may differ substantially. Despite these considerations, you are encouraged to take a course in differential equations before you transfer. You should consult with your chosen transfer university’s mathematics faculty or program advisor as early as possible for more advice on differential equations courses.

23. Computer Programming: Knowledge of computers is required at varying levels for a university mathematics major. Therefore, you should consider taking a computer course that develops competency in a computer programming language as well as the construction of algorithms before you transfer.

24. Statistics: A statistics course is a lower division requirement for a mathematics major at some universities. However at others, statistics is not required at all or is required as a more sophisticated upper division course. Depending on the university and the mathematics program you choose, the process and result for transferring a statistics course taken at a community college may differ substantially. Thus, when you consider taking a course in statistics you should be aware of the different levels of acceptance it may receive. You should consult as early as possible with your chosen transfer university’s mathematics faculty or program advisor for more advice on statistics courses.

25. Courses That Use Mathematics: At some universities, the mathematics major requires course work in a separate discipline that uses mathematics, such as physics, chemistry, or economics. These courses may also fulfill parts of general education requirements. To avoid a possible mismatch in course work between two schools, you should try to take full year applications courses for science majors before you transfer. However, you should also consider, with advice from your counselors and instructors, deferring a calculus-based physics course until you have completed at least one year of calculus.

26. The University of California • Dual Admissions Program (DAP) honored but no longer being offered. • Transfer Admission Guaranteed (TAG) programs: Davis, Merced, Riverside, San Diego, Santa Cruz, Santa Barbara • Transfer Opportunity Program (Davis) • Transfer Provisional Admissions (Irvine)

27. University of California MajorsThe following majors are available at university campuses for the selected discipline. The campuses that offer the major are identified next to each major name. Click a campus abbreviation next to a major to see more information about that major. • Computational Applied Science, B.S. (UCD)Creative Studies: Mathematics Emphasis B.A./B.S. (UCSB)Economics and Mathematics (joint major) B.A. (UCSD)Economics/Mathematics B.A. (UCSB)Engineering Mathematics and Statistics B.S. (UCB)Financial Mathematics & Statistics B.S. (UCSB)Mathematical and Scientific Computation, B.S. (UCD)Mathematical Sciences B.S. (UCSB)Mathematics - Computational B.A. (UCSC)Mathematics - Computer Science B.A. (UCSD)Mathematics - Mathematics Education B.A. (UCSC)Mathematics - Pure B.A. (UCSC) • Mathematics - Secondary Education B.A. (UCSD)Mathematics A.B./B.S. (UCD)Mathematics and Economics (joint major) B.A. (UCSD)Mathematics B.A. (UCB, UCSB, UCSC, UCSD)Mathematics B.A./B.S. (UCR)Mathematics B.S. (UCI, UCLA, UCSB)Mathematics of Computation B.S. (UCLA)Mathematics, Applied Science B.A. (UCSD)Mathematics, General B.S. (UCLA)Mathematics, Scientific Computation, B.S. (UCSD)

28. California State University Lower Division Major Requirements(Lower Division Transfer Project) • Initiated by the Academic Senate of the CSU in collaboration with the Academic Affairs Division of the Chancellor’s Office. • To create transfer program agreements to facilitate student transfer to the CSU. • Identify a set of courses and/or competencies that will satisfy the lower-division expectations for a particular major at all or most CSU campuses, so that a student can complete those expectations at a community college and know that they will be appropriate regardless of the specific CSU campus to which the student transfers. • This set of courses and/or competencies is referred to as a “common Core.” • The project does not, in fact, require all CSU departments offering a major to agree upon the same specific courses as lower-division requirements. • The goal is to provide students with the information they need to plan their community-college course work to expedite the timely completion of their baccalaureate major degree program after they transfer to a CSU campus.

29. CSU Lower Division Transfer Project Mathematics (pending 2005?) • Statewide: All areas of General education except the area of the Physical Science. [The Area of General Education Physical Science is required for all campuses, but is subject to some restrictions under local control.] • • Three semesters or four quarters of calculus. Students who take the sequence of courses in CAN MATH SEQ C (Calculus I - III (semester) or Calculus I-IV (quarter) will have these courses accepted by all CSU campuses as satisfying the lower division requirements in calculus. • Local: Mathematics programs also expect transfer students to have completed one or more additional courses besides calculus as well as the area of Physical Science for General Education. • These courses and possible restrictions on what courses may be taken to satisfy the General Education area of Physical Science are determined by the local campuses. • Locally determined courses examples: Linear Algebra, Differential Equations, A Computer Programming Course, Lower Division GE “Physical Universe”.

30. Mathematics Recommendations Statewide IMPAC Meeting 2004 • I. Course Related Recommendations. These relate to the nature of and CAN description of the lower division Linear Algebra Course and the development of a description and proposals for a variety ways to provide a "bridge" course, i.e., a transitional course for Mathematics majors. • II. Improving communications within the Mathematics Community regionally and/or statewide for mathematics transfer students.

31. Course Related Recommendations. A. Linear Algebra • Recommendation 1. The lower division linear algebra course should include in its presentation some structural aspects of linear algebra. These include, but are not limited to, the statement of axioms and structural definitions for real vector spaces, linear transformations, and linear operators. Use of these structures should be demonstrated with some proofs- though only a reading level of literacy is supposed. Limited writing literacy may be required in verifying structural properties with examples and applying structural results in specific contexts.

32. Recommendation 2. The CAN description for Linear Algebra should be modified to reflect a limited treatment of the structural aspects of linear algebra. Current: CAN: MATH 26 Title: Linear Algebra Description: Matrices and linear transformations; vector spaces; determinants; eigenvalues and eigenvectors. Prerequisite: CAN MATH 17/18. 3 semester units or 4 quarter units. • Recommended modification: CAN: MATH 26 Title: Linear Algebra Description: An introduction to computation and algebraic structures for real vector spaces, matrices and linear transformations; determinants; eigenvalues and eigenvectors. Prerequisite: CAN MATH 17/18. 3 semester units or 4 quarter units.

33. B. Lower Division Bridge or Transition Courses • Preface. Many CSU and UC Mathematics programs have a lower division required course that provides a transition from the computational and algorithmic nature of lower division courses such as calculus to the more structural and proof oriented organization of upper division mathematics courses. [9 CSU and 3 UC recommended or required in the lower division.] • Other programs make this kind of course a initial part of upper division course work or have no such course.

34. Recommendation 1. When possible the student should be encouraged to cross-register in a bridge course at a local university. • Recommendation 2. Universities that offer these bridge courses should coordinate their summer course offerings. • Recommendation 3. A consortium of colleges and universities should organize a special summer program (funded by the NSF, a state agency, or some private philanthropy) that would provide the kind of experience in working with proofs found in these bridge courses along with beginning work in mathematical research. • Recommendation 4. A new CAN Number and descriptor should be developed for this bridge course.

35. II. Improving Communications within the Mathematics Community • Preface: Better communication could provide information about transfer courses, the nature of mathematical studies in upper division courses, and key people to contact and places to obtain information with regard to the specifics of transfer. • The recommendations are divided into two categories: • A. University and College Recommendations and • B. Organizational Recommendations.

36. A. University and College Recommendations. • Recommendation 1 Each University department should designate one or more faculty or advising staff members as transfer advisor(s). The advisor(s) will be responsible for matters related to transferring students –such as transfer course approval and program planning . • Recommendation 2 Each College department should develop a structure (using resources such as MESA, matriculation funds, and other grants) to assist students planning to transfer.

37. Recommendation 3. Each University department should designate one or more faculty members responsible for articulation agreements . University departments should keep recognized feeder colleges informed on relevant changes to requirements and courses. • Recommendation 4. Each University department should maintain a web page to advise prospective transfer students on relevant requirements and advice for transferring as a mathematics major. This page should be linked clearly from the department home page and should address at least the main issues from the IMPAC letters of advice for transfers while indicating how to obtain details on articulation agreements through ASSIST or otherwise. It should give the name and other relevant information of the department’s designated transfer advisor(s).

38. Recommendation 5. Each College and University department should work with their campus articulation officer to maintain current articulation and contact information with ASSIST. • Recommendation 6. When possible University departments will provide information through the web describing required courses for the major including course outlines.

39. B. Organizational Recommendations • Recommendation 1. A web page should be developed containing information and links for all university mathematics departments. This web page will be developed in cooperation with ASSIST and placed in an easily found location on the ASSIST web site and possibly mirrored elsewhere at the CSU and UC system transfer information web sites. The web page will include the following information for each University Campus: • A Contact Person / Advisor with E-mail Address and Phone. • A link to the Mathematics Department Web Page and a Recommended Phone Contact Number. • A link to Any Mathematics Department Transfer Information Web Page

41. Intersegmental Mathematics Councils. • Recommendation 2. Regional cooperation should be developed between individual campuses and where possible by the formation of intersegmental mathematics councils. These councils would meet at least once annually to develop programs and disseminate information. Some areas for possible cooperation include: • College Math club guest speakers from the university. • College faculty taking courses or participating in university seminars. Sabbatical leave positions being fostered for College faculty at Universities. • Math contests at the university that the local college students are invited to enter.

42. Math Transfer Day • Math Transfer Day: Math departments at the university campuses could sponsor jointly a regional math transfer day where advising would be available and faculty from feeder colleges and students could come together to participate in joint mathematical activities: poster sessions/ lectures/ demonstrations- a REGIONAL MATH EXPO.

43. Participate in IMPAC related Projects • Meeting at LAX, November 13. • Planning for Spring, 2005 events. • CAN • Mathematics • Mathematics Education • Business Mathematics • Get involved in planning Math Days • Get involved in regional inter-segmental math community.

44. Any Questions? The End! 