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

Voices of the Partner Disciplines:

Mathematical Needs of Other Departments

Starting Points

Crossroads in Mathematics,

AMATYC 1995 CUPM Discussion Papers about

Mathematics and the Mathematical Sciences

in 2010: What Should Students Know?,

MAA 2001 Principles and Standards of School

Mathematics, NCTM

Current Documents

Beyond Crossroads, Draft

Curriculum Guide, MAA 2004

Curriculum Foundations Project, 2004

Current Documents

Crossroads

Intellectual development, Content,

Pedagogy Beyond Crossroads

Learning Environments, Instructional

Strategies, Curriculum Development,

Assessment and Professionalism

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!

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!

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.

Business

Content

Pedagogy

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.


• 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.


• 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.

Computer Science

Content

Pedagogy

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

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.”

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.”

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.

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.”

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.

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.

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.”

Some Major Themes in Technology

1. Math Courses as FiltersWe regret that, in many settings, mathematics courses are intentionally viewed as filters for entry into IT curricula.

Information TechnologyMathematics should not be a filter that causes students to drop out of our programs.

Biotechnology and Environmental TechnologyThese students get discouraged in remedial mathematics, and a refresher class might be more effective.

Mechanical and Manufacturing 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 TechnologyThere 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


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.


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


3. Education of Mathematics FacultyMathematics instructors should be encouraged to attend the technical courses.


Participation in summer internships in industry is an excellent way for teachers to understand the practical aspects of mathematics in the IT field.


Mathematics instructors may need to apprentice in the technology areas to learn the applications and understand which topics are important.



4. Course ContentMastery of the basics is more important than exposure to a lot of mathematics.

Biotechnology and Environmental TechnologySemiconductor technicians need little more than ratios, elementary algebra, and elementary statistics. Electronics and telecommunications technicians need more mathematics.

Electronics and TelecommunicationsPreparation for students pursuing IT careers should not require advanced topics but should instead provide a solid foundation of elementary content.



5. Applications-based coursesCourses 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


6. Technology in the Mathematics ClassroomStudents should develop proficiency with at least one [computation software] program, as well as a working knowledge of spreadsheets.


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


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.


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.



7. Estimation and Approximation[Students] should question their answers, not accept them blindly. Students should use common sense and estimation skills.

Biotechnology and Environmental TechnologyStudents 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 TechnologyApproximation and estimation: having a feel for the right order of magnitude, the right units of measure, and the appropriate precision for an answer.



8. Articulation with Four-Year SchoolsIf mathematics courses were developed for specific applications, they would probably not be transferable towards a baccalaureate degree program.

Biotechnology and Environmental TechnologyWe 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 TechnologyProvide bridge courses for job-oriented students in two-year programs to help them make the jump to a baccalaureate program.



9. The Most Frequently Requested Topics

Basic algebra

Basic statistics

Graphs and graphical representation

Spreadsheets

Software packages


10. The Most Frequently Requested Skills

Problem-solving

Teamwork

Communication

Estimation

Multi-step projects

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.”

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.”

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).

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

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

Documents

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