A high school background of 4 years of mathematics, including the equivalent of precalculus, is assumed. The equivalent of a college major in mathematics should provide for the successful completion of the outcomes listed below.
Please list the mathematics requirements, including the course number and title, for prospective teachers preparing to teach mathematics in grades 7–12.
1. Math121(*)
Calculus and Analytic Geometry I
4
2. Math122
Calculus and Analytic Geometry II
4
3. Math221
Calculus and Analytic Geometry III
4
4. Math222
Differential Equations
4
5. Math333
Linear Algebra
4
6. Math423
Advanced Calculus
4
7. Math/CS Electives(**)
12
(*) Math119 - Computer
Algebra System (1 hr), is a pre/corequisite of Math121.
(**) Math/CS Electives:
Math 210 - Probability and Statistics I,
4 hrs, 4 crs.
Math 211 - Probability and Statistics II,
4 hrs, 4 crs.
Math 230 - Theory of Numbers, 4 hrs, 4
crs.
Math 241 - Combinatorial Geometry, 4 hrs,
4 crs.
Math 242 - Geometric Structures, 4 hrs,
4 crs.
Math 310 - Operations Research, 4 hrs,
4 crs.
Math 311 - Mathematical Methods for Physical
Science, 4 hrs, 4 crs.
Math 332 - Modern Algebra, 4 hrs, 4 crs.
Any Math 400 level or above courses.
CS172 - Introduction to Computing, 4 hrs,
4 crs.
Any CS 200 level or above courses.
Please list the mathematics methods requirements, including the course number and title, for teacher candidates preparing to teach mathematics in grades 7–12.
1. Educ 340
Literacy Instruction Inside Middle & Secondary
Classrooms
3
2. Educ 373
Teaching Mathematics in Secondary Schools
3
Mathematics Preparation
The Four Themes: Problem Solving, Reasoning, Communication, and Connections are four overriding themes that should permeate all mathematics programs. Although these four areas are inherently interrelated, for the purpose of this review you are asked to explicate how each of these areas is incorporated into your teacher preparation program.
1.1 Problem Solving: Submit a narrative that describes how the requirements of your program provide opportunities for your candidates to mature in their problem solving ability.
The required mathematics courses provide rich experiences
in problem solving. A central activity of all courses
is problem solving, through applications (which involve modeling too)
and proofs. Student homework regularly
includes such activities.
1.2 Reasoning: Submit a narrative that describes how the requirements of your program provide opportunities for your candidates to make and evaluate mathematical conjectures and arguments, and to validate their own mathematical thinking.
Upper-level mathematics courses are conducted with
an emphasis on mathematical thinking as math majors.
Math 333 and Math 423 in particular, emphasize mathematical proof.
1.3 Communication: Submit a narrative that describes how the requirements of your program provide opportunities for your candidates to use both oral and written discourse between teacher and candidates and among candidates to develop and extend candidates’ mathematical understanding.
Math courses have practice problems and exercises
assigned through-out the semesters. As part of graduation requirements,
all majors are required to take at least one writing-intensive upper
level mathematics course. Junior and seniors are given opportunities in
math tutoring in the labs and monitoring online discussions. Many classes
have students present their solutions to the class, with class discussion
about various solution methods.
1.4 Connections: Submit a narrative that describes how the
requirements of your program provide opportunities for your candidates
to demonstrate an understanding of mathematical relationships across
disciplines and connections within mathematics.
The major's calculus sequence courses, differential
equation , linear algebra, and the required math/cs electives provide
opportunities for majors to have an understanding of mathematical relationships
across disciplines and connections within mathematics. Courses use applications
in the natural and social sciences, finance, and computer science. Upper
level courses tend to be more abstract than lower level courses. Part of
the abstraction involves finding commonality among various application areas
of mathematics.
1.5.1 apply
concepts of number, number theory, and number systems;
Experiences, Courses
1.5 Programs prepare
prospective teachers who can—
Calculus I -
III; In-class discussion, drills, homework, tests, and final exams provide
performance data and experiences.
1.5.2 apply numerical computation and estimation techniques
and extend them to algebraic expressions;
Performance and
experiences evidenced through successfull completion of calculus sequence
courses.
1.5.3 apply the process of measurement to two- and three-dimensional
objects using customary and metric units;
Application examples
and exercises in multivariable calculus (Math 221), and linear algebra
(Math 333).
1.5.4 use geometric concepts and relationships to describe
and model mathematical ideas and real-world constructs;
Application examples
and exercises in Math 221 and Math 333.
1.5.5 understand the major concepts of Euclidean and
other geometries;
Math221, Math333;
In-class discussion, drills, homework, and tests.
1.5.6
use both descriptive and inferential statistics to analyze data, make
predictions, and make decisions;
Real world modeling
examples and exercises in Math 211 provide both descriptive and
inferential statistics for data analysis and decision making.
1.5.7
understand the concepts of random variable, distribution functions,
and theoretical versus simulated probability and apply them to real-world
situations;
Math210 - Probability
and Statistics I introduces basic concepts of probability theory,
random variables, distribution functions, and applications. Class drills,
homework assignments, and tests provide performance data and experiences.
1.5.8
use algebra to describe patterns, relations, and functions, and to
model and solve problems;
The performance
data and experiences are provided through all the math courses required
as well as the electives. Most math courses are conducted with homework assignments
and exercises which demand the use of algebra to describe, model, and solve
problems.
1.5.9 understand the role of axiomatic systems and proofs
in different branches of mathematics, such as algebra and geometry;
The linear algebra
course (Math 333) and advanced calculus course (Math 423) , both
required for the math major, provide examples and homework exercises in
applying axiomatic systems to different branches of mathematics.
1.5.10 have a firm conceptual grasp of limit, continuity,
differentiation and integration, and a thorough background in the techniques
and application of calculus;
The calculus
sequence courses (Math 121, 122, 221), plus differential equations (Math
222) and advanced calculus (Math 423) provide a thorough background in the
technoques and application of calculus. As part of the evidences of
performance and experiences, all majors in the college need a GPA
of at least 2 (out of 4) in the major's required courses for graduation.
1.5.11 have a knowledge of the concepts and applications
of graph theory, recurrence relations, linear programming, difference
equations, matrices, and combinatorics;
Basic concepts
and applications of matrices are covered in the linear algebra course.
Other topics are partly covered in Math 241 and 310 as electives.
1.5.12
use mathematical modeling to solve problems from fields such as natural
sciences, social sciences, business, and engineering;
Mathematical
modeling is an approach used in many of the required mathematics courses.
An elective course for mathematical modeling (Math 410) is usually offered
on a two-year cycle.
1.5.13
understand and apply the concepts of linear algebra;
The linear algebra
course (Math333) provides in-class discussion, drills, writing assignments,
homework exercises, and tests for the assessment of student performance
and learning experiences.
1.5.14 understand and apply the major concepts of abstract
algebra.
The required
linear algebra course (Math333), and the elective course in Modern Algebra
(Math 332).
1.6 Programs prepare
prospective teachers who have a knowledge of historical development
in mathematics that includes the contributions of underrepresented
groups and diverse cultures .
General history of mathematics
as included in many textbooks as an aid in the learning of mathematics is
considered favorably in the selection of mathematics textbook. There
is a shortage of mathematics text that provides handy topics and references
in the contributions of underrepresented groups and diverse cultures. We
will provide such information and access to our students if available. A
course in history is under consideration to meet this need when suitable
textbooks become available.
Teaching Preparation
Integrated Essential Outcomes
Certain essential outcomes within a program preparing teachers of mathematics are integrated throughout the program. Such outcomes include teaching diverse learners, the appropriate use of technology, and the alignment of assessment and instructional practices.
For each of these outcomes, respond in narrative form describing how candidates attain these outcomes in your mathematics education program. For each outcome: include specific experiences that promote the outcome and describe how you measure its attainment; and describe the process that establishes connections among these experiences. Describe how your program, both in mathematical and pedagogical contents, enables your candidates to gain experience that helps them to achieve this outcome.
2.1 Diverse Learners
Teachers of mathematics use their knowledge of student diversity to affirm and support full participation and continued study of mathematics by all students. This diversity includes gender, culture, ethnicity, socioeconomic background, language, special needs, and mathematical learning styles.
2.2 Technology
Teachers of mathematics use appropriate technology to support the learning of mathematics. This technology includes, but is not limited to, computers and computer software, calculators, interactive television, distance learning, electronic information resources, and a variety of relevant multimedia.
Students are required to have some basic skills in a computer algebra
system in order to start their first course in calculus. Majors are
encouraged to take some math courses with online components to experience
the use of a course management system for online teaching and learning.
Most calculus-sequence course sections are technology-enhanced through
the use of a computer algebra system, which in most cases is either Maple
or Mathematica, chosen by the instructor.
2.3 Assessment
Teachers of mathematics use formative and summative methods to determine students' understanding of mathematics and to monitor their own teaching effectiveness. Teachers are careful to align their instructional and assessment practices.
Teachers use formative assessment to monitor student learning and to adjust instructional strategies and activities. Formative assessment includes, but is not limited to, questioning strategies, student writing, student products, and student performance.
Teachers use summative assessment to determine student achievement and to evaluate the mathematics program. Summative assessment includes, but is not limited to, teacher-designed tests, criterion-referenced tests, norm-referenced tests, portfolios, projects, and other open-ended student products.
Assessments are done through question-and-answer strategy; scheduled
short quizzes, tests, midterm, and final exam; homeworks, exercises,
and writing assignments.
Experiences, Courses
2.4 Programs prepare
prospective teachers who can identify, teach, and model problem solving
in grades 7-12.
Lesson plans, student teaching, examinations Courses - Ed 373, 440, 441.
1.
Teacher candidates are exposed to variety of models to solve
problems and apply this knowledge when the student teach and tutor student
in local schools
2.
Class lectures include problem solving strategies
and modeling.
2.5 Programs prepare
prospective teachers who use a variety of physical and visual materials
for exploration and development of mathematical concepts in grades 7-12.
1.
Teacher candidates prepare suitable materials
to teach various mathematical concepts. Ed.373
2.
Teacher candidates utilize teacher made materials
as well as manufacturered materials when they student teach. Teacher made
materials, manufactured materials. Ed 440, 441
2.6 Programs prepare
prospective teachers who use a variety of print and electronic resources.
1.
Teacher candidates are use website for lesson
plans and other assignments
2.
Teach school students to program a scientific
calculator. Website & calculators. Ed 373, 440, 441
2.7 Programs prepare
prospective 7-12 teachers who know when and how to use student groupings
such as collaborative groups, cooperative learning, and peer teaching.
Exam, quizzes & fieldwork
1.
Teacher candidates learn the techniques of
formulating groups. Ed 373
2.
Teacher candidates use different grouping
techniques to group students for instruction.
3.
Teach candidates utilize "cooperative learning"
style when the student teach Ed 440/441
2.8 Programs prepare
prospective teachers who use instructional strategies based on current
research as well as national, state, and local standards relating to
mathematics instruction.
Examinations, lesson plans and fieldwork.
1.
Teacher candidates compare and contrast the
NCTM standards with NYS and NYC standards. Ed 373
2.
Teacher candidates incorporate NCTM standards
when they plan and deliver lesson. Ed 440/441
2.9 Programs prepare
prospective teachers who can work on an interdisciplinary team and in
an interdisciplinary environment.
Ed 373, 440, 441
1.
Teacher candidates prepare and conduct lessons
using interdisciplinary approach.
2.10 Programs introduce
and involve prospective teachers in the professional community of mathematics
educators.
1.
Teacher candidates are encouraged to become
members of NCTM and NYSMA. Ed 373, 440/441
3.0 FIELD-BASED EXPERIENCES
3.1 Programs provide prospective teachers with a sequence
of planned opportunities prior to student teaching to observe and participate
in 7-12 mathematics classrooms with qualified teachers. Experiences include
observing, tutoring, miniteaching, and planning mathematics activities
and lessons for different mathematics courses.
Teacher candidates
spend 28 hours in the field observing experienced Teachers and tutoring students
in the schools they also prepare and conduct lessons in their college classroom.
Ed 373, 440/441.
Portfolio, observation, report and lesson plans.
3.2 Programs provide
prospective teachers with a full-time student teaching experience in
7-12 mathematics that is supervised by a qualified teacher and a university
or college supervisor with a 7-12 mathematics teaching experience.
Teacher candidates
in their final year do supervised student teaching for 250 hours (1 semester)
in 7-12 mathematics classroom and they are observed by the college supervisor
for 6 times during the semester. Ed 440/441.
Lesson plans, supervised observations and post observations.
PROPOSED DESIGN FOR
SECONDARY SCHOOL MATHEMATICS
( Required Courses in Education at York College)
Required Courses (24-27 Credits)
I. Foundation Courses (10-13 Credits) Credits
Education
280 - Childhood Adolescent for Teachers ...............................................................
3
Education 281 - Fieldwork in Education Environments
............................................................. 1
Sociology 202 - Major Ideas and Issues in
Education ..............................................................
3
Education 283 - Effective Teaching and Learning
.....................................................................
3
Academic Computing 101 - Introduction to Microcomputers
I .................................................... 0-1
Academic Computing 210
- Microcomputer Applications in Education .......................................
0-1
Academic Computing 250
- Advanced Microcomputer Applications in Education ........................
0-1
II. Methods Courses (6 Credits)
Education
340 - Literacy Instruction Inside Middle & Secondary Classrooms ..............................
3
Education 373 - Teaching Mathematics in Secondary
Schools .................................................. 3
III. Student Teaching
(8 Credits)
Education
440 - Supervised Teaching of Mathematics in Junior High School ...............................
4
Education 441 - Supervised Teaching of Mathematics
in Senior High School .............................. 4