To make students aware of the role of mathematics in the evolution of civilization and how mathematics has been used in solving problems associated with that evolution.
To have students develop an appreciation of the nature of mathematical reasoning and how it was used in the creation of mathematical systems.
To enable students to apply mathematical problem solving techniques to both the classic areas of mathematics as well as the newer areas of the mathematical sciences.
To stimulate students to be lifelong learners in the mathematical sciences.
To prepare students for graduate work in the mathematical sciences and mathematics education.
To prepare students for careers using the mathematical sciences as including the teaching profession.
University of Colorado: The undergraduate degree in mathematics emphasizes knowledge and awareness of:
basic real analysis of one variable;
calculus of several variables and vector analysis;
basic linear algebra and theory of vector spaces;
the structure of mathematical proofs and definitions; and
at least one additional specialized area of mathematics.
In addition, students completing a degree in mathematics are expected to acquire the ability and skills to:
use techniques of differentiation and integration of one and several variables;
solve problems using differentiation and integration;
solve systems of linear equations;
give direct proofs, proofs by contradiction, and proofs by induction;
formulate definitions;
read mathematics without supervision; and
utilize mathematics
Central Oregon Community College: Students who successfully complete any mathematics course at Central Oregon Community College will be able to:
Work independently to explore mathematical applications and models, and to develop algebraic/symbolic, graphical, numerical, and narrative skills in solving mathematics problems.
Work as a member of a group/team on projects or activities that are designed to explore mathematical applications and models.
Use both written and oral skills to communicate about mathematical concepts, processes, complete mathematical solutions and their implications.
Use a variety of problem solving tools including symbolic/algebraic notation, graphs, tables, and narratives to identify, analyze, and solve mathematical problems.
Develop mathematical conjectures and use examples and counterexamples to examine the validity and reasonableness of those conjectures.
Create and analyze mathematical models of real world and theoretical situations, including the implications and limitations of those models.
From Central Oregon Community College Assessment Project:
Elementary Algebra I
Students who complete Math 60: Elementary Algebra I will be able to:
Use the arithmetic of real numbers and order of operations:
The department recognizes that success in the other outcomes in Math 060 require mastery of these fundamentals. While many students may have previously encountered these in prior courses, we cannot assume such prior knowledge. Thus, we acknowledge the necessity of spending up to three weeks of the term on this outcome.
Solve Linear Equations:
The importance of this outcome both reinforces the first outcome and previews the following one. Emphasis on the applications here is as important as the manipulative skills being addressed. Thus, we acknowledge the necessity of spending up to three weeks of the term on this outcome.
Graph (with emphasis on straight lines):
Graphs of all sorts will be investigated with the emphasis on the basic connections between numerical, graphical, and algebraic representations of relationships. The concept of a function will be introduced at its most fundamental level, emphasizing the connections between input-output and various representations numerically, graphically, and algebraically. Equations of straight lines and their application will form the basis of the algebraic part of this course. Thus, we acknowledge the necessity of spending up to three weeks of the term on this outcome.
Solve systems of Linear Equations (Introduction; graphical and addition methods):
Emphasis here will focus on the graphical method of solution and understanding and interpreting graphical solutions. Thus, we acknowledge the necessity of spending up to one week of the term on this outcome.
Elementary Algebra II
Students who complete Math 65: Elementary Algebra II will be able to
Use the algebra of exponents and apply to polynomials:
he department recognizes that success in the other outcomes in Math 065 require mastery of these fundamentals. Thus, we acknowledge the necessity of spending up to three weeks of the term on this outcome.
Solve Quadratic Equations:
Emphasis here should focus on the connections among the numerical, algebraic, and graphical methods of solution. Equations of straight lines and their application will be reviewed but quadratic equations will form the basis of the algebraic part of this course. Factoring, the Quadratic Formula, and Graphs of Quadratic Equations will all be emphasized. Thus, we acknowledge the necessity of spending up to three weeks of the term on this outcome.
Graph (with emphasis on quadratic equations):
Graphs of all sorts will be investigated with the emphasis on the basic connections between numerical, graphical, and algebraic representations of relationships. The concept of a function will be further explored, emphasizing quadratic equations and their applications. In addition, graphs of rational and radical equations will be investigated in the context of understanding the unique behavior of these functions. Emphasis will be on connections between the meaning of a solution graphically and algebraically. Thus, we acknowledge the necessity of spending up to three weeks of the term on this outcome.
Further solve systems of equations (e.g., two linear or one linear and one quadratic):
Systems of linear equations will be further investigated, both graphically and algebraically. Algebraic methods of solution of systems including substitution and elimination will be examined. Emphasis will be on connections between the meaning of a solution graphically and algebraically.
The Mathematics Department assesses student outcomes in mathematics courses in a variety of ways. Each instructor decides on a mix of assessment items and publishes those choices in his/her syllabus. Student expectations are clearly defined and resources for success both in and out of the classroom are identified. Assessment is specifically linked to reaching benchmarks for specific competencies. Work on this area has begun by developing competencies for all courses offered in the curriculum.
Homework: traditional assessment tool used in most classes to offer students clear and prompt feedback related to mastery of specific course competencies; focus on skill competencies. Students are encouraged to work together, share ideas, visit the tutoring center, visit instructors during office hours.
Quizzes and Examinations: traditional assessment component, though sometimes group rather than individual effort; used to assess specific competencies at specific junctures during term.
Group activities: can be short, focused on particular competencies or exploratory in nature in which students attempt to define their own understanding of a competency in a variety of ways, including written, oral, symbolic, and visual representations; often requires integration of concepts, transfer of competency to unique context, critical thinking, analysis of real-world data, multiple representations of outcomes, and skill in group processes.
Open-ended projects: formal written presentations incorporating mathematical analysis using skills and competencies developed in the course in a critical analysis of applied, real-world context; typically includes technology component; may be group or individual efforts.
Portfolios: term-long collections of student work used to assess mastery of course-specific competencies, especially emphasizing integration and extension of course objectives.
Journals: regularly submitted and annotated dialog between student and teacher; purpose is less assessment and more Òreality checkÓ focusing on real-time student perceptions of course dynamics, learning activities, and structure; allows instructor access to student feedback which in turn allows for flexibility in course structure.
Teaching Intensive Laboratories: labs allow for student teams to experience and explore specific course competencies in depth through an integration of skills and concepts in open-ended investigations with specific outcomes defined by the instructor; usually includes technology component and writing to assess integration and understanding of related competencies.
