Voices of the Partner Disciplines: Mathematical Needs of Other Departments

1. Voices of the Partner Disciplines: Mathematical Needs of Other Departments

2. Starting Points • Crossroads in Mathematics, AMATYC 1995 • CUPM Discussion Papers about Mathematics and the Mathematical Sciences in 2010: What Should Students Know?, MAA2001 • Principles and Standards of School Mathematics, NCTM

3. Current Documents • Beyond Crossroads, Draft • Curriculum Guide, MAA 2004 • Curriculum Foundations Project, 2004

4. Current Documents • Crossroads Intellectual development, Content, Pedagogy • Beyond Crossroads Learning Environments, Instructional Strategies, Curriculum Development, Assessment and Professionalism

5. Associates Degrees in Mathematics In 2000, P There were 564,933 associate degrees P Of these, 675 were in mathematics This is one-tenth of one percent!

6. Bachelor’s Degrees in Mathematics In 2000, PThere were 457,056 bachelor’s degrees POf these, 3,412 were in mathematics This is seven-tenths of one percent!

7. Curriculum Foundations Project A series of 11 workshops with leading educators from 17 quantitative disciplines to inform the mathematics community of the current mathematical needs of each discipline. The results are summarized in the MAA Reports volume: A Collective Vision: Voices of the Partner Disciplines, edited by Susan Ganter and Bill Barker.

8. Business • Content • Pedagogy

9. What Business Faculty Said Mathematics is an integral component of the business school curriculum. Mathematics Departments can help by stressing conceptual understanding of quantitative reasoning and enhancing critical thinking skills. Business students must be able not only to apply appropriate abstract models to specific problems but also to become familiar and comfortable with the language of and the application of mathematical reasoning. Business students need to understand that many quantitative problems are more likely to deal with ambiguities than with certainty. In the spirit that less is more, coverage is less critical than comprehension and application.

10. What Business Faculty Said • Courses should stress problem solving, with the incumbent recognition of ambiguities. • Courses should stress conceptual understanding (motivating the math with the “why’s” – not just the “how’s”). • Courses should stress critical thinking. • An important student outcome is their ability to develop appropriate models to solve defined problems.

11. What Business Faculty Said • Courses should use industry standard technology (spreadsheets). • An important student outcome is their ability to become conversant with mathematics as a language. Business faculty would like its students to be comfortable taking a problem and casting it in mathematical terms.

12. Computer Science • Content • Pedagogy

13. CHEMISTRY • Multivariable, multidimensional problems from the outset • “Listen to the equations”…”most specific mathematical expressions can be recovered from a few fundamental relationships in a few steps.” • “Of widespread use in chemistry teaching and research are spreadsheets…graph & stat

14. CHEMICAL ENGINEERING • “A good chemical engineer brings together the fundamentals to build and refine a mathematical model of a process that will help him or her understand and optimize its performance.” • “Alumni surveys typically show that probability and statistics, in addition to the extensive use of spread-sheeting software, is the most common application of mathematics for the practicing chemical engineer with a B. S. degree.”

15. CIVIL ENGINEERING • Modeling the 2nd component in a 5-component problem solving scheme • “…adjust the balance of course material to more applied and numerical solution techniques and less advanced analytical techniques, integrating more technology into the curriculum, and coordinating the mathematics and engineering curricula.” • Introductory mathematics courses to be taken over a 3 or 4 year period rather than 2 years • “Technology must be a major component of mathematics curriculum”. Use Microsoft Excel and MathCad, “technology used in their engineering classes and in their careers.”

16. ELECTRICAL ENGINEERING • “Be able to mathematically model physical reality”-Outcome 6 of 8 for math to EE • “Of critical interest are the logical thinking skills …” “ mathematics required should emphasize concepts and problem-solving skills more than emphasizing repetitive mechanics of solving routine problems. • “Introducing symbolic manipulation programs, e.g. MathCAD, Mathematica, Maple, would be valuable to subsequent EE courses”-pedagogy choices need to be coordinated.

17. MECHANICAL ENGINEER Our “we want” list of 9 math abilities includes: • “Use modeling techniques”. • “Be familiar with software applications for numerical and symbolic computation. They also need to be introduced to spreadsheets.” • “The internet gives access to vast amounts of information, allowing solution of more interesting complex problems.”

18. Health-Related Life Sciences • “Many participants put special emphasis on the use of models.” “Models are a way of organizing information for the purpose of gaining insight and providing intuition into systems that are too complex to understand any other way”. • “Students should master a higher level interface, e.g.: spreadsheet, symbolic/numerical computational packages( e.g. Mathematica, Maple, Matlab), statistical packages. • BE FLEXIBLE: package topics creatively thru long-term interaction between mathematics and the life sciences.

19. PHYSICS • “The panel was unanimous in suggesting that practice in solving problems should be extensively couched in real-world contexts that are meaningful to students.” • “There is general agreement among the panelists that some experience with a symbolic manipulation program like Mathematica or Maple is desirable. • “…a compelling alternative opinion: Spread sheets are by far the best medium (for teaching with technology) since data, text, and graphics are all visible at once, and since the techniques are easily learned and useful for numerical approximations “really try to understand what is in the mind of the student”-best practice in instruction for all partners.

20. Teacher Prep: K-12 Mathematics • “In general, there should be less symbolic manipulation, and more modeling and problem solving from both a discrete and continuous perspective” in algebra • “There was virtually universal agreement among workshop participants that reasoning and proof should be a theme in all college mathematics courses, beginning at least with calculus.” • In introductory courses, ask students to explain their thinking or to justify their responses based on definitions. • “Spread sheets and the graphing and table-generating features of graphing calculators can be effectively used to solve problems about functions and families of functions.”

21. Some Major Themes in Technology 1. Math Courses as Filters We regret that, in many settings, mathematics courses are intentionally viewed as filters for entry into IT curricula. Information Technology Mathematics should not be a filter that causes students to drop out of our programs. Biotechnology and Environmental Technology These students get discouraged in remedial mathematics, and a refresher class might be more effective. Mechanical and Manufacturing Technology

22. Some Major Themes in Technology 2. Who should teach technical math courses? Should mathematics be taught in the technical program itself, or should it be taught by the mathematics department? Should it be taught by “captive” mathematics instructors who work for the technical program? Biotechnology and Environmental Technology There needs to be more cooperation … between faculty members in mathematics and … the technical fields. … Arrange for interdepartmental visits. … [Invite industry representatives to make presentations.] Electronics and Telecommunications

23. Some Major Themes in Technology 2. Who should teach technical math courses (ctd)? Team teaching, with mathematics faculty entering apprenticeships with technology faculty, would improve the teaching of mathematics … required in the content area. Mechanical and Manufacturing Technology One might ask whether some mathematical reasoning skills could be obtained from other disciplines. … we promote the notion of mathematics across the curriculum. Information Technology

24. Some Major Themes in Technology • 3. Education of Mathematics Faculty • Mathematics instructors should be encouraged to attend the technical courses. • Electronics and Telecommunications • Participation in summer internships in industry is an excellent way for teachers to understand the practical aspects of mathematics in the IT field. • Information Technology • Mathematics instructors may need to apprentice in the technology areas to learn the applications and understand which topics are important. • Mechanical and Manufacturing Technology

25. Some Major Themes in Technology 4. Course Content Mastery of the basics is more important than exposure to a lot of mathematics. Biotechnology and Environmental Technology Semiconductor technicians need little more than ratios, elementary algebra, and elementary statistics. Electronics and telecommunications technicians need more mathematics. Electronics and Telecommunications Preparation for students pursuing IT careers should not require advanced topics but should instead provide a solid foundation of elementary content. Information Technology

26. Some Major Themes in Technology 5. Applications-based courses Courses in algebra and statistics should use an applications-based approach instead of the traditional textbook approach, considering real-life problems. Biotechnology and Environmental Technology IT-based applications should drive the development of mathematical theory and its use. … Applications should be considered first, and then theory. Information Technology Avoid teaching mathematics to simply teach mathematics. Move heavily to the application of the concepts within the mathematics classroom. Mechanical and Manufacturing Technology

27. Some Major Themes in Technology 6. Technology in the Mathematics Classroom Students should develop proficiency with at least one [computation software] program, as well as a working knowledge of spreadsheets. Electronics and Telecommunications Students should use a variety of software packages in mathematics classes. … students should be able to use ordinary and statistical calculators and should become comfortable with spreadsheets for calculation and graphing. Biotechnology and Environmental Technology

28. Some Major Themes in Technology 6. Technology in the Math Classroom (ctd) To the extent that mathematics courses teach and reinforce the use of technological tools, IT students are well served. Information Technology Our students should have experience with graphing calculators, word processors, spreadsheets, data base management software, and computer presentation applications … they should also have experience with mathematical and statistical software. Mechanical and Manufacturing Technology

29. Some Major Themes in Technology 7. Estimation and Approximation [Students] should question their answers, not accept them blindly. Students should use common sense and estimation skills. Biotechnology and Environmental Technology Students should learn how to perform an error analysis. They must learn to estimate answers and to obtain approximate solutions. Electronics and Telecommunications [Technological] tools should never replace abilities such as estimating, performing simple mental arithmetic with precision, or evaluating a tool’s accuracy. Information Technology Approximation and estimation: having a feel for the right order of magnitude, the right units of measure, and the appropriate precision for an answer. Mechanical and Manufacturing Technology

30. Some Major Themes in Technology 8. Articulation with Four-Year Schools If mathematics courses were developed for specific applications, they would probably not be transferable towards a baccalaureate degree program. Biotechnology and Environmental Technology We focus on the mathematical skills students should master while completing the associate degree as an entry into the job market. … It may be necessary for students to complete a bridge course in order to enter a baccalaureate program. Information Technology Provide bridge courses for job-oriented students in two-year programs to help them make the jump to a baccalaureate program. Mechanical and Manufacturing Technology

31. Some Major Themes in Technology 9. The Most Frequently Requested Topics Basic algebra Basic statistics Graphs and graphical representation Spreadsheets Software packages

32. Some Major Themes in Technology 10. The Most Frequently Requested Skills Problem-solving Teamwork Communication Estimation Multi-step projects

33. CUPM Curriculum Guide 2004 • “Indeed, the participants in the Curriculum Foundations workshops were so excited by the possibility of increasing the use of real models in mathematics courses that many volunteered to help develop such models” • “…chemistry gave an urgent plea for an earlier introduction to multivariable calculus…Even more colleagues expressed dissatisfaction with the level of student understanding of concepts-geometric and otherwise-in three dimensions.”

34. CUPM CG ‘04 Thinking Theme • “Faculty who participated in the CF workshops commented frequently that all disciplines look to mathematics courses to enhance students’ abilities to reason logically and deductively, but that they want this ability developed in a context that increases understanding of underlying concepts.” • “…the computer scientists specifically requested that lower-division discrete mathematics courses include an introduction to formal proof” • “The correct balance can and should be determined through consultation with colleagues in partner disciplines.”

35. CUPM CG ’04 Technology Use • “Participants in the CF workshops understood the importance of technology, and took for granted that mathematics courses would incorporate technology to some degree”…. “Perhaps more surprising is that spreadsheets are the most utilized technology for a large number of partner disciplines”(p. 36). • Recommendation 5 of 6 says every level of the curriculum should have some courses incorporating technology use. Cross reference with 2001 Guidelines for Programs and Departments (p 7).

36. RESOURCES • Today’s slides at www.piercecollege.edu/faculty/yhoshibw • CG at maa.org/cupm/curr_guide.html • CF at maa.org/cupm/crafty/cf_project.html • Instructor Resources at maa.org/cupm/illres_refs.html Descriptions and web links to examples, experiences, and resources for one to work toward the recommendations of CG • MET at cbmsweb.org • MAA Guide-Prog./ Dept. maa.org/guidelines