Department of Mathematics and Statistics’ Mission Statement

Mathematics is one of the great unifying themes in our modern culture. It is a language, a science, an art form, and a tool of tremendous power. The Department of Mathematics and Statistics, in its courses for both majors and nonmajors, seeks to introduce students to this vast area of knowledge and to show them how mathematics can be used to solve problems.

B.S. Mathematics – Matrix Assessment

OVERARCHING GOALS

 

Mathematics instruction should:

(from MAA’s Source Book for College Mathematics Teaching , Schoenfeld, 1990)

·        Provided students with a sense of the discipline of mathematics.

·        Develop student’s understanding of important concepts in core areas of mathematics.

·        Develop student’s ability to explore problem situations in a range of settings, at several levels of difficulty, and with a variety of methods. 

·        Help students to develop a mathematical point of view – perceive and represent structure and structural relationships. 

·        Help student’s to develop the ability to read and use mathematical literature and reference material.

 

LEVEL 16 - MATHEMATICS MAJOR

 

A graduate of a baccalaureate program in mathematics should:

 

1.  Excel in the use of basic quantitative skills

      including:

¨                  Symbolic representation.

¨                  Symbolic manipulation.

¨                  Modeling.

¨                  Pattern recognition.

¨                  Problem solving.

¨                  Quantitative reasoning.

¨                  Estimation.

 

2.  Demonstrate content knowledge of core areas of mathematics

      including:

¨      Algebraic, order, and completeness properties of the real number system.

¨      Analysis of functions from Rⁿ to R^m_.

¨      Algebra of linear functions from Rⁿ to R^m_.

¨      Axiomatic Systems

¨      Additional content areas such as abstract algebra, geometry, probability/statistics, differential equations, graph theory, etc. 

 

3.  Apply analytic, algebraic, and algorithmic techniques to solving applied problems. 

¨      Include techniques from several areas such as differential equations, linear transformations, numerical analysis, series of functions, analysis of algorithms, statistics, operations research, etc. 

¨      Use appropriate technology.

¨      Communicate how the problem is translated into a mathematical formulation, and how to interpret the result of the mathematical analysis. 

 

4.  Read, analyze, and write mathematical proofs.

¨      Analyze logical structure of statements using logical connectives, negation, and quantifiers. 

¨      Use contradictions and counter examples appropriately.

¨      Use mathematical induction.

 

5.      Historical and social development of mathematics.

 

6.      Collaborative Skills

 

7.      Critical Thinking

¨      Develop Research Questions.

¨      Analyze and Interpret Data.

¨      Use results to formulate new questions.

 

 

 

Alignment of First two years of Coursework with Standards/Outcomes

                                                                                                                                                                 

 

 

Alignment of Required Coursework in Mathematics Major with Standards/Outcomes

 

Core Areas of Mathematics									Communication Skills
		Real Numbers System	Analysis of Functions	Algebra of Functions	Statistics			Oral		Written
	3435	x			x					x
	4441									x
	4435	x	x	x	x			x		x
	4751				x					x
	4661	x	x	x						x

 

 

 

 

 

Time line of assessment

 

 

Use Senior Seminar to administer departmental survey (attached). (Secondary School Teaching survey attached).
 

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B.S. in Mathematics Program Survey

 

Program Overview:

Undergraduate programs in mathematics should prepare graduates to understand the field of mathematics, both as an academic discipline and as a profession within the context of a larger society. Thus, graduates should be aware of the history of mathematics, including those major developments and trends – economic, scientific, legal, political, and cultural – that have combined to shape the discipline.

 

SA: Strongly Agree, A: Agree, N: Neutral, D: Disagree, SD: Strongly Disagree

 

	SA	A	N	D	SD
The program exposed you to the history of mathematics.
The program exposed you to the major developments of mathematics
The program exposed you to the trends -economic, scientific, legal, political, and cultural-that have combined to shape the discipline

 

 

 

Program Goals:

The first goal for undergraduate mathematics programs, therefore, is to provide a coherent and broad-based coverage of the discipline of mathematics. Graduates should develop a reasonable level of understanding in each of the subject areas and the processes that define the discipline, as well as an appreciation for the interrelationships that exist among them.

 

Seven broad subject areas have been identified as comprising the subject matter of the discipline. Each of these areas has a significant theoretical base, significant abstractions, and significant design and implementation achievements. While these subject area definitions cover the entire discipline, they each contain certain fundamental subjects that should be required in all undergraduate programs in mathematics.

 

The seven subject areas are:

 

Algebra                                               Linear Algebra                                                Geometry

Analysis                                               Discrete Mathematics and Combinatorics

Probability and Statistics                    Applied Mathematics

 

	SA	A	N	D	SD
The program exposed you to the specified areas.
The program contained to many required classes

 

A second goal for undergraduate programs in mathematics is to function effectively within the wider intellectual framework that exists within the institutions that house the programs. These institutions vary widely in their respective missions. Some of them emphasize breadth of study over depth, while others emphasize the opposite. Some are rigid in the overall balance between requirements and electives, while others are more flexible. As is the case in other disciplines, undergraduate programs in mathematics necessarily reflect institutional differences in their respective degree requirements. It follows that graduates of different programs will have received different levels of coverage in the subject areas of mathematics, as well as a different balance of emphasis among the processes of theory, abstraction, and application.

 

	SA	A	N	D	SD
The program emphasized breadth over depth.
The program contained too much theory.
The program contained too much abstraction.
The program contained too much application.

 

Third, different undergraduate programs place different levels of emphasis upon the objectives of preparing students for entry into a mathematics profession, preparing students for graduate study in the discipline of mathematics, and preparing students for the more general challenges of professional and personal life.  Students enrolled in any undergraduate program in mathematics should be aware of that program’s particular emphasis with regard to these three objectives.

 

	SA	A	N	D	SD
The program adequately prepared me to get a job.
The program adequately prepared me for graduate study.
The program adequately prepared me to do research.

 

Fourth, undergraduate programs should provide an environment in which students are exposed to the ethical and societal issues that are associated with the mathematics and mathematics teaching fields. This includes maintaining currency with recent technological and theoretical developments, upholding general professional standards, and developing an awareness of one’s own strengths and limitations, as well as those of the discipline itself.

 

	SA	A	N	D	SD
The program provided adequate exposure to ethical and societal issues.
The program provided adequate exposure to recent technological and theoretical developments.
The program provided guidance on upholding general professional standards.
The program developed an awareness of my own strengths and limitations
The program exposed me to the strengths and limitations of the discipline itself.

 

 

Fifth, undergraduate programs should prepare students to apply their knowledge to specific, constrained problems and produce solutions. This preparation includes

·        the ability to define a problem clearly;

·        to determine its tractability;

·        to determine when consultation with outside experts is appropriate;

·        to evaluate and choose an appropriate solution strategy; to study, specify, design, implement, test, modify, and document that solution;

·        to evaluate alternatives and perform risk analysis on that design;

·        to integrate alternative technologies into that solution;

·        to communicate that solution to colleagues, professionals in other fields, and the general public. This also includes the ability to work within a team environment throughout the entire problem-solving process.

	SA	A	N	D	SD
The program provided me with the ability to apply my knowledge to specific, constrained problems and produce solutions
The program taught me to define a problem clearly.
The program taught me to determine its tractability.
The program taught me to determine when consultation with outside experts is appropriate.
The program taught me to evaluate and choose an appropriate solution strategy.
The program taught me to study, specify, design, implement, test, modify, and document that solution.
The program taught me to evaluate alternatives and perform risk analysis on that design
The program taught me to integrate alternative technologies into that solution
The program taught me to communicate that solution to colleagues, professionals in other fields, and the general public.
The program taught me to work within a team environment throughout the entire problem-solving process.

 

Finally, undergraduate programs should provide sufficient exposure to the rich body of theory that underlies the field of mathematics, so that students appreciate the intellectual depth and abstract issues that will continue to challenge researchers in the future. In this light, graduates should be aware of the unusually high rate of change in the application of mathematics, the relatively gradual rate of growth in the theory of mathematics, and the delicate interaction that takes place between these two. They should thus have a strong foundation on which to base lifelong learning and development.

 

	SA	A	N	D	SD
The program provided me with sufficient exposure to the theory that underlies the field of mathematics.
The program provided me with an adequate appreciation to the intellectual depth and abstract issues that will continue to challenge researchers in the future.
The program provided me with adequate appreciation to the unusually high rate of change in the applications of mathematics.
The program provided me with an adequate appreciation to the relatively gradual rate of growth in the theory of mathematics.
The program provided me with adequate appreciation to the delicate interaction that takes place between these two.
The program provided me with a strong foundation on which to base lifelong learning and development in the area of mathematics?.

 

 

Science and Technology Literacy:

To support the development of maturity in the technical and scientific aspects of mathematics, an undergraduate curriculum should also include certain computer science and science course material to complement the subject matter in the discipline. Similarly, to support the development of maturity in the scientific and engineering aspects of the discipline, the present guidelines recommend that students regularly engage in laboratory work and other educational experiences.

 

	SA	A	N	D	SD
The program provided me with adequate computer science courses.
The program provided me with an adequate with adequate science courses.
The program provided me with sufficient laboratory work.
The program provided me with adequate with adequate written and oral skills.

 

Please also include any comments, specific or general, concerning your program. What do you consider to have been the strengths and weaknesses of the program?

 

Concentration in Secondary School Teaching Survey

 

 (from http://www.ferris.edu/education/education/Edu.htm)

 

SA: Strongly Agree, A: Agree, N: Neutral, D: Disagree, SD: Strongly Disagree

 

 

1. I have a commitment to student learning and achievement, including the understanding and ability to:	SA	A	N	D	SD
a. Apply knowledge of human growth, development, and learning theory.
b. Expand cognitive, affective, physical, and social capacities of students for the development of the “whole person”.
c. Demonstrate appropriate classroom management and disciplinary techniques to ensure a safe and orderly environment that is conducive to learning.
d. Plan instruction to accommodate diversity, e.g., cultural, racial, and social diversity.
e. Plan instruction to accommodate various backgrounds of students.
f. Use multiple approaches to appropriately assess student abilities and needs to plan instruction.
g. Use various kinds of literacy to promote access to knowledge, e.g., numeracy, graphics, printed text, computers, and other electronic media.

 

2. I have knowledge of subject matter and pedagogy, including the understanding and ability to:	SA	A	N	D	SD
a. Create learning environments that promote critical and higher order thinking.
b. Help students access and use information, technology, and other resources to become independent learners and problem solvers.
c. Integrate and transfer knowledge across subject areas and encourage the same among students.
d. Engage students in practical activities that demonstrate the relevance, purpose, and function of subject matter.

 

3. I have the ability to manage and monitor student learning, including the understanding and ability to:	SA	A	N	D	SD
a. Plan and use different cognitive, affective, and psychomotor strategies to maximize learning and to accommodate differences in the backgrounds, learning styles, aptitudes, interests, levels of maturity and achievement of students.
b. Use a variety of teaching methodologies and techniques, e.g., lectures, demonstrations, group discussion, cooperative learning, small-group activities and how to assess one's effectiveness in utilizing them.
c. Involve and work effectively with parents and/or guardians to maximize opportunities for students' achievement and success.

 

4. I have the ability to systematically organize teaching practices and learn from experiences, including the understanding/ability to:	SA	A	N	D	SD
a. Exercise good judgment in planning and managing time and other resources to attain goals and objectives.
b. Maximize the use of instructional time by engaging students in meaningful learning experiences.
c. Demonstrate an understanding of the economic, social, political, legal, and organization foundations and functions of schools.
d. Accept teaching as a lifelong learning process and continue efforts to develop and improve.
e. Interact successfully with other teachers, parents, students, administrators, counselors, and other support personnel to benefit students and to advance one's own professional development.
f. Engage in meaningful self-evaluation and reflect on the professional practice of colleagues.

 

 

5. I have a commitment and willingness to participate in learning communities, including the understanding and ability to:	SA	A	N	D	SD
a. Use community and home resources to enhance school programs.
b. Interact with parents to maximize the learning of students at school, home, and in the local community.

 

 

6. I have an ability to use information technology to enhance learning and to enhance personal and professional productivity. I …	SA	A	N	D	SD
a. Design, develop, and implement student learning activities that integrate information technology for a variety of student grouping strategies and diverse student populations.
b. Identify and apply resources for staying current in applications of information technology in education.
c. Demonstrate knowledge of uses of multi-media, hyper-media, telecommunications, and distance learning to support teaching/learning.
d. Use information technologies to support problem solving, data collection, information management, communications, presentations, and decision-making including word processing, database management, spreadsheets, and graphic utilities.
e. Use information technology to enhance continuing professional development as an educator.

 

 

Survey information that is specific often reveals how our program is actually performing. Please give detailed information about yourself that would qualify as evidence to the impact of our teacher preparation program (ex. achievements, student assessment levels, research, etc).