Mathematics

 

I. Knowing the Content

 

The professional education program provides evidence that Mathematics certification candidates complete a program of Mathematics studies the same as the academic area content courses and required electives of a major in a bachelors' degree. The program shall require the candidates to demonstrate a knowledge of and competence in teaching students Mathematics concepts and processes necessary for a teacher at the secondary level (7-12) including:

 

I.A. History of mathematics as a tool for life and the workplace, and in contexts as part of a cultural heritage.

 

(All Math courses in a limited way. Statistics 1: Statistical Thinking, Mathematics Special Methods Workshops)

 

 

I.B. Examination of theories, research and practices related to student learning and achievement in mathematics to increase the quality of mathematics teaching.

 

(Mathematics Special Methods Workshops, Ed. 21: Educational Psychology)

 

 

I.C. Use of mathematical communication to:

            • organize and consolidate mathematical thinking,

            • explain mathematical thinking to other,

            • analyze and evaluate strategies of others,

            • express mathematical ideas precisely.

 

(All Math courses, Ed. 21: Educational Psychology, Mathematics Special Methods

Workshops)

 

I.D. Concepts of calculus including:

            • differential and integral calculus (Math 5: Calculus I, 6A: Calculus IIA)

            • sequences and series, (Math 6B: Calculus IIB)

            • methods of integration, (Math 6A: Calculus IIA)

            • transcendental functions, (Math 5: Calculus I, 6A: Calculus IIA)

            • polar coordinates, (Math 6C: Calculus IIC, 18: Several Variable Calculus)

            • analytic geometry, (Math 6C: Calculus IIC, 18: Several Variable Calculus))\

• multivariable derivatives and integrals. (Math 6C: Calculus IIC, 18: Several Variable

Calculus

 

Note: AP credit (scores of 4 or 5) will be granted for Calculus AB or AB/BC, the equivalent of taking Math 5 and 6)

 

I.E. Number theory

 

(Math 37: Number Theory, 48: topics in Algebra, 49: Introduction to Modern Algebra)

 

            • numbers, ways of representing numbers, relationships among numbers and number

systems,

 

• meanings of operations and how they relate to one another

 

I.F. Functions

 

• generalize patterns using explicitly defined and recursively defined functions,

 

(Math 9: Discrete Mathematics or any Computer Science course)

 

• properties of classes of functions; such as polynomial, rational, algebraic, exponential,

logarithmic, and trigonometric functions,

 

(Math 5: Calculus I, 6: Calculus IIA,B,C, l8: Several Variable Calculus)

 

• representing functions numerically, symbolically, graphically, and verbally.

 

(Math 5: Calculus I, 6: Calculus IIA,B,C, l8: Several Variable Calculus)

 

I.G. Geometry

 

(Math 45: Topics in Geometry)

 

            • fundamental ideas of measurement and spatial visualization,

            • nature of axiomatic reasoning,

            • transformations, coordinates and vectors,

            • trigonometry from a geometric perspective,

            • use of technological tools in geometry

            • Euclidean and non-Euclidean geometry

 

I.H. Linear algebra

 

(Math 16: Linear Algebra)

 

            • matrices,

            • systems of linear equations,

            • vector spaces,

            • linear transformations,

            • determinants,

            • eigenvalues.

 

I.I. Abstract algebra

 

(Math 49: Introduction to Modern Algebra)

 

            • structures, properties and examples of groups, rings, and fields,

            • relevance of algebraic properties in the study of number systems

 

 

 

I.J. Probability and statistics

 

(Math 2: Statistical Methods, Statistics 27: Multivariate Statistical Methods, Statistics 41: Probability, 53: Mathematical Statistics I)

 

            • measures of central tendency and variability,

            • axioms of probability,

            • properties of discrete and continuous probability,

            • discrete and continuous probability,

            • discrete and continuous probability distributions,

            • statistical inference.

 

I.K. Discrete mathematics

 

(Math 9: Discrete Mathematics, Computer Science 10: Great Ideas in Computer Science, Computer Science 21: The Imperative Paradigm: Unix and C)

 

            • logic, sets, relations and functions,

            • mathematical induction,

            • elementary graph theory,

            • permutations and combinations.

 

I.L. Mathematical modeling of physical, biological, social, psychological, or conceptual entities.

(Math 5: Calculus I, 6: Calculus II (A,B,C), 18: Several Variable Calculus)

 

I.M. Fundamental concepts and methodologies of analysis, including rigorous definitions and proofs of theorems

 

(Math 9: Discrete Mathematics)

 

            • make and investigate mathematical conjectures,

            • develop and evaluate mathematical arguments.

I.N. Enhancement of the learning of mathematical concepts through instructing students in the effective and appropriate use of technology (graphing calculators, computer software etc.), as well as other computational tools

 

(All Math courses, Education 16: Practice Teaching, Special Methods Workshops in Mathematics)

 

 

II. Performances

 

The professional education program provides evidence of the candidates participation in sequential and developmental field experiences and student teachings, under the supervision of college personnel and cooperating teachers who are well trained in mathematics, have interpersonal skills and demonstrated competence in teaching. The program also provides evidence that the criteria and competencies for exit from the Mathematics certification program are assessed in coursework, field experiences and student teaching and require candidates to demonstrate their knowledge and competence in fostering student learning through:

 

 

II.A. Managing the instructional environment

 

(Education 16: Practice Teaching, Ed. 17: Curriculum and Methods seminar, Ed. 21: Educational Psychology)

 

            • communicate challenging learning expectations to each student

 

            • establish and maintain rapport with students and promote mutual respect among students

              

• instill in all students a belief that they can succeed in mathematics

 

• establish and maintain consistent standards of classroom behavior

 

• make the physical environment safe and conducive to learning

 

• model school to career attributes and behaviors

 

II.B. Long-range and short-range planning of instruction, done independently and in collaboration with other educators

(Education 16: Practice Teaching, Ed. 17: Curriculum and Methods seminar, Ed.21: Educational Psychology, Special Methods Workshops in Mathematics)

 

            • mathematics subject matter,

            • students and the community,

            • Pennsylvania Academic Standards, content analysis with specific objectives,

            • instructional methods, including materials and activities,

            • results of student assessments

 

II.C. Selecting, adapting and implementing a variety of instructional strategies ranging from computational exercises to complex problem solving to "essay-style" homework, class assignments, projects, and utilizing traditional tools as well as modern technologies

 

(Ed. 16: Practice Teaching, Ed. 17: Curriculum and Methods seminar, Special Methods Workshops in Mathematics).

 

II.D. Selecting, analyzing, and modifying instructional materials to meet the needs of diverse learners

 

(Ed. 16: Practice Teaching, 17: Curriculum and Methods seminar, Special Methods Workshop in Mathematics).

 

II.E. Assessing and evaluating student's conceptual understanding of content through a variety of contextual settings, providing formative feedback to align instructional strategies assist to individual student needs

 

(Ed. 16: Practice Teaching, Ed. 17: Curriculum and Methods seminar, Ed 21: Educational Psychology).

 

III. Professionalism

 

The professional education program provides evidence that each teacher certification candidate demonstrate knowledge and competencies that foster professionalism in school and community settings including:

 

 

 

III.A. Professional organizations, journals, and other resources for professional development.

 

Education. 16: Practice Teaching, Ed. 17: Curriculum and Methods seminar, Special Methods Workshops in Mathematics )

 

III.B. Integrity and ethical behavior, professional conduct as stated in Pennsylvania's Code of Professional Practice and Conduct for Educators; and local, state, and federal laws and regulations.

 

            (Education 14: Introduction to Education, Education. 16: Practice Teaching, Ed. 17:

Curriculum and Methods Seminar)

 

III.C. Establish collaborative relationships with colleagues of the elementary, secondary and higher education levels to improve student learning.

 

            (Education. 16: Practice Teaching, Ed. 17: Curriculum and Methods seminar)

 

III.D. Communicate effectively with parents or guardians, other agencies and the co

mmunity at large to support learning by all students.

 

            (Education. 16: Practice Teaching, Ed. 17: Curriculum and Methods seminar)