Core Curriculum Review Process
Department of Mathematical Sciences
University of Alaska Fairbanks


Introduction

The Department of Mathematical Sciences has the following core courses: Math 107X, Math 131X, Math 200X, Math 201X, Math 202X, Math 262X, and Math 272X. The Department of Mathematical Sciences has formed a special sub-committee of the Curriculum Committee to consider assessment documents and recommend appropriate changes in curriculum.

The core mathematics curriculum was designed so that students will achieve "advanced literacy in mathematics." According to the Core Curriculum Requirements document, "advanced literacy in mathematics implies a solid grasp of quantitative reasoning and appreciation of mathematical applications. Most important is acquiring the knowledge necessary for informed judgment on the uses of mathematical and statistical interpretations confronting us in everyday life." Our assessment of each of the core mathematics courses will address this goal. Each core class is, of course, unique and will address mathematical literacy in a unique way. Below we list the specific competencies that each class addresses.


Math 131X - Concepts and Contemporary Applications of Mathematics

The content of Math 131 is chosen in an attempt to make a more relevant and meaningful mathematics course for a student majoring in a non-technical field. As a core course, it is expected that the enrollment will include most majors in the liberal arts, the fine arts, and other disciplines where analytical skills such as Calculus have not traditionally played an important part. With emphasis on management science, statistics and data management, social choice and decision-making, the topics covered in Math 131 are a good representation of the logical and computational needs of a modern college graduate.

This course is viewed as a terminal mathematics course. As a result, it is not the aim of the Department of Mathematical Sciences to create a rigidly standardized syllabus. Our current textbook contains more material than can be discussed in one semester and therefore the instructors retain some flexibility in choosing which topics to choose. At present seven chapters from the text are mandatory, leaving several chapters to the discretion of the instructor.

Our main diagnostic tool for this course is the final exam. Typically, several sections of this course are offered each semester. The final examinations contain a core of common questions covering the required material, while the balance of the examination can reflect the special topics covered by each instructor.

Our review of this course shall consist of a review of the final exams by the departmental assessment committee. This committee shall ensure that the core material is being covered to a sufficient degree and, if necessary, make recommendations to alter the core material in order to keep the course topics relevant to the intended audience. In particular, the committee will assess whether the following objectives are being met:

  1. Students master problem solving skills.
  2. Students learn to manipulate abstract symbols.
  3. Students learn and appreciate the rigorous use of deductive arguments in math and science.
  4. Students learn a broad spectrum of mathematical applications, including:
  1. Basic statistics
  2. Graph Theory and its applications
  3. Probability
  4. Social Choice and Voting Systems

Math 107X - Functions for Calculus

The primary goal of this course is to prepare students to take the various Calculus courses. As such it covers a wide range of topics such as algebra, graphing, logarithms, and exponential functions. Because of the large number of topics that must be covered, the syllabus for this course is fairly rigid. This fixed syllabus is our way to ensure that the course meets the spirit of the Core. In addition to this, the departmental assessment committee plans to review the final exams given each year in order to ensure that the students are leaning the appropriate material in sufficient depth.

The final exams will be reviewed to ensure that, in addition to the general mathematical literacy, the following objectives are being met by Math 107:

  1. Students master problem solving skills.
  2. Students learn to manipulate abstract symbols.
  3. Students learn and appreciate the rigorous use of deductive arguments in math and science.
  4. Students gain a broad spectrum of mathematical understanding, including:
  1. understanding the nature of functions
  2. solving equations
  3. graphing polynomial and rational functions
  4. exponential and logarithmic functions
  5. applications of exponential and logarithmic functions

Math 200X, 201X, 202X, 262X, 272X - Calculus

We have a common strategy for these courses. Math 200, 201, and 202 form a three semester sequence intended for majors in the physical sciences, Math 262 is intended for business majors and Math 272 is intended for majors in the life sciences. As usual, each of these courses must cover a lot of ground and our syllabi are fairly rigid. Individual instructors are required to adhere to these syllabi and hence the syllabi are our one tool in assuring that the course meets the spirit of the Core. To further assure this, the departmental committee shall review the final examinations to ensure that the material was covered in sufficient depth and to assure that the students developed competence in the subject matter. In particular, we shall assess whether the following objectives are being met:

  1. Students master problem solving skills.
  2. Students learn to manipulate abstract symbols.
  3. Students learn and appreciate the rigorous use of deductive arguments in math and science.
  4. Students learn a broad spectrum of mathematical applications, including:
  1. limits and continuity
  2. differentiation and integration
  3. maximization/minimization problems
  4. analysis of functions of one variable and their graphs
  5. applications of integrals and derivatives
  6. infinite sequences and series (Math 201X only)
  7. analysis of functions of several variables and their graphs (Math 202X only)
  8. multiple integrals and partial derivatives (Math 202X only)
  9. applications of multiple integrals (Math 202X only)

In addition, each of these courses is reviewed by appropriate accreditation agencies as part of the regular evaluation of various UAF programs. Math 200X, 201X, and 202X are reviewed by the Accreditation Board for Engineering and Technology and by the Computing Sciences Accreditation Board. Math 262 is reviewed by the American Assembly of Collegiate Schools of Business. Math 272 is reviewed by the Society of American Foresters. These reviews by specialized accreditation agencies will supplement our evaluation and serve as assurance that we are in compliance with national outcome standards.


Conclusion

The above plan will allow us to perform a comprehensive review of each of the core classes in our department. We shall be able to identify strengths and weaknesses in our curricula and recommend the appropriate changes.

As of May 1999