Approved by Faculty Senate April 14, 2003.

** **

**Writing
Flag**

The Department of Mathematics and Statistics proposes the following course for inclusion in the University Studies, Writing Flag at Winona State University. The full department at the Thursday, January 18, 2001 department meeting approved this action.

Course: Teaching Mathematics in the Secondary School I (MTED 320), 3 SH

Catalog Description: Organization and methods of teaching mathematics grades 5-12. The course includes a Teaching Assistantship experience. This is a University Studies course satisfying requirements for the Writing Flag. Prerequisites: MATH 165, MATH 210 and EDUC 306. Offered spring semester only.

This is an existing course, which was previously approved by A2C2.

Department Contact Person for this course:

Terry M. Price, Assistant Professor, Mathematics and Statistics Department

Email: tprice@winona.edu

General Discussion of University Studies – Writing Flag with respect to MTED 320:

**University Studies: Writing
Flag**

The purpose of the Writing Flag requirement is to reinforce the outcomes specified for the basic skills area of writing. These courses are intended to provide contexts, opportunities, and feedback for students writing with discipline-specific texts, tools, and strategies. These courses should emphasize writing as essential to academic learning and intellectual development.

Courses can merit the Writing Flag by demonstrating that section enrollment will allow for clear guidance, criteria, and feedback for the writing assignments; that the course will require a significant amount of writing to be distributed throughout the semester; that writing will comprise a significant portion of the students’ final course grade; and that students will have opportunities to incorporate readers’ critiques of their writing.

These courses must include requirements and learning activities that promote students’ abilities to…

**a. practice
the processes and procedures for creating and completing successful writing in their
fields**

Course Objective 2 (Use a variety of manipulative and visual materials for exploration and development of mathematical concepts in grades 5-12) provides the opportunity for students meet this requirement. Specifically they will meet the following Standards of Effective Practice:

· Design lessons and activities that operate at multiple levels to meet the developmental and individual needs of diverse learners and help each progress (7F)

Activity 1, a major component of the course, provides the opportunity for students to “develop a variety of clear, accurate presentations and representations of concepts” by requiring students to “spot-journal” mathematical topics of the day with respect to a variety of pedagogical considerations. These considerations shall include, but are not limited to, appropriate teaching strategies and materials to support student learning, prior knowledge, strategies to meet different developmental needs as well as the types of questions to be used in the teaching-learning process. Students will also have the opportunity for peer- and self-assessments exercises.

**b. understand
the main features and uses of writing in their fields**

Course Objective 4 requires that the mathematics preservice teacher “select appropriate mathematical tasks that will stimulate students’ development of mathematical concepts and skills”. As future teachers of mathematics this requires they “understand learning theory, subject matter, curriculum development, and student development and know how to use this knowledge in planning instruction to meet curriculum goals” (7A of Standards for Effective Practice).

Students are assigned readings from a variety of education, mathematics and mathematics education journals. The assigned readings will range in complexity from formal research in the areas listed to practitioner and inservice teacher publications. Students will be required to write a formal paper to demonstrate attainment of this requirement.

The research paper assignment will be grounded in learning theory. The work of individuals in the fields of educational psychology, mathematics education, or educational research will form the basis of this assignment. Each student will be assigned a different contributor to one of the fields listed above. Multiple assessment and feedback points, including two peer reviews, will be built into the learning theory assignment.

**c. adapt
their writing to the general expectations of readers in their field**

The inservice teacher must demonstrate the ability to effectively communicate with respect to a variety of audiences. In addition to generating clear, concise lesson plans and student tasks, they must be able to effectively communicate with administrators and peers within the field. Course Objective 5 is designed to provide our students with the opportunity to meet this requirement by examining patterns of communication “between teacher and student, among students, between the teacher and the community as they develop and extend their students’ mathematical understanding. Assigned readings and whole-class discussion help the student to “understand theory behind and role of language in learning” (6A of Standards for Effective Practice), while course requirements provide the application of knowledge.

For example, the required Teaching Assistantship allows the students to participate in actual inservice-teacher/5-12-student experiences. Students record field notes of the interactions and submit reflections on those episodes. Students are also given the opportunity to communicate via email with 5-12 students as they solve problems written by the students in our methods courses.

In addition to real-life, hands-on activities, general classroom tasks also provide the student with the opportunity to become effective writers in the field of mathematics. For example, students constructed Origami cubes, without access to written instructions, during the exploration of the development of geometric language and concepts. Students are required to produce a set of written instructions, without the presence of diagrams, which would allow someone not familiar with the task to complete the cube.

**d. make
use of the technologies commonly used for research and writing in their fields**

Course Objective 3 provides the future teacher of 5-12 mathematics with the opportunity to “use a variety of resource materials such as software, print materials, technology, etc. to enhance the learning of mathematics”. As future teachers of mathematics they should be able to “enhance learning by using a wide variety of materials” as well as “support and expand learner expression in speaking, writing, other media” (4D and 6I, respectively, Standards for Effective Practice).

Assigned readings and classroom activities are designed to help students become familiar with the technologies commonly used in the teaching of mathematics. Although MTED 320 is not technically a research course, students are required to use the technologies commonly used in mathematics as they prepare lessons for presentation. Teacher, peer and self-assessments of activities provide additional opportunities to practice effective writing in mathematics.

**e. learn
the conventions of evidence, format, usage, and documentation in their fields**

To document teaching effectiveness, the beginning teacher must not only understand and be able to incorporate state and national standards into their teaching; they must be able to provide evidence of learning. Activity 1 provides students with the opportunity to learn and apply the mathematics portion of the MN Graduation Standards (Grades 5-12).

In particular, students complete a Task Analysis assignment similar to the documentation required by the state of Minnesota during the implementation of a performance package. Students choose lessons from current middle and high school level textbooks and align the lesson(s) with the appropriate Minnesota Graduation Standard(s). The activity requires that students generate both the student activity and assessment necessary to meet the objective of that particular lesson. The standards utilized in this assignment may be revised based upon the recommendations of the Governor’s Task Force. In particular the National Council of Teachers of Mathematics (NCTM) Principles and Standards (2000) will be used in addition to the state standards for completion of this assignment.

A Curriculum Concept
Mapping (CCM) project has been integrated into the course requirements. The purpose of the project is to provide a broader
perspective as students analyze and evaluate K-12 Curriculum in the preparation and
implementation of target lesson plans. This
project is a FULL SEMESTER assignment and there will be multiple components as well as the
opportunity for feedback throughout the semester in preparation of the final submission. This particular project will constitute
approximately one-fifth of the course grade. The
major components of the project are: 1) concept mapping as a process, 2) identification
and incorporation of appropriate NCTM and MN Mathematics Standards, 3) Construction and
Incorporation of Appropriate Bloom’s objectives and supporting questions, 4)
construction of methods of assessment to document achievement of objective, and 5) peer
and instructor evaluation and feedback.

WINONA
STATE UNIVERSITY

COLLEGE
OF SCIENCE AND ENGINEERING

DEPARTMENT
OF MATHEMATICS AND STATISTICS

Course
Title: Teaching Mathematics in the Secondary School I

Frequency
of Offering: Yearly, Spring Semester

Prerequisites:
MATH 165, 210; ENG 111; EDUC 306

Grading:
Secondary major and minor Grade Only basis; Graduate credit P/NC or Grade

Course
Applicable: MTED Secondary Major and Minor, required.
Graduate credit is available for inservice teachers.

Catalog
Description: Organization and methods of teaching mathematics grades 5-12. The course
includes a Teaching Assistantship experience. This
is a University Studies course satisfying requirements for the Writing Flag. Prerequisites:
MATH 165, MATH 210 and EDUC 306. Offered
spring semester only.

Number
of Credits: 3 Semester Hours

__Required Textbooks__: 1) Teaching Secondary School
Mathematics: Techniques and Enrichment Units (A. S. Posamentier & J. Stepelman, 1999),
Fifth Edition, Prentice-Hall, Inc.

2)
Principles and Standards for School Mathematics (NCTM, 2000).

3)
Every Minute Counts (D. Johnson, 1982), Palo Alto, CA: Dale Seymour Publications.

__Additional
Readings__: In addition to the readings from the required texts, student will be
assigned additional readings during the course of the semester. Although these readings may vary based on the
current issues surrounding the field of Mathematics Education, they will always include
learning theory and discourse in the classroom.

__Standards Included__: Minnesota law requires that
Secondary programs include topics appropriate to issues encountered in grades 5-12. This course is designed to help students develop
competencies outlined in the Minnesota Standards of Effective Practice for Beginning
Teachers. In particular, this course will
address the following standards:

Standard
2 - Student Learning (A, D, E, F)

Standard
4 - Instructional Strategies (A, D, E, G, J, K)

Standard
5 - Learning Environment (C, D, M, O, P, Q, R)

Standard
6 – Communication (A, C, F, H, I, J)

Standard
8 – Assessment (A, B, I)

Standard 9 - Reflection and Professional Development (E, G)

__Additional
Requirements__:
Students will be required to complete a 30-hour Teaching Assistantship in which they
observe and participate in 5-12 mathematics classrooms with qualified teachers. Fifteen of the hours will be at middle school
level and fifteen hours at 9-12 grade level. This
experience may include observing, tutoring, mini-teaching, and planning lessons and/or
students' tasks. The middle school experience
will involve 5 hours of video observation of middle school activity and 10 contact hours
with middle school students.

__Course
Description__:
This course will focus on four major areas of importance to the prospective 5-12
mathematics teacher.

1) In general, the first area addresses the secondary mathematics curriculum with major emphasis on current trends and issues as specified by the National Council for Teachers of Mathematics, with emphasis on new curricular directions for 5-12 mathematics in terms of content, organization and priorities.

2) The
second area of focus is classroom instruction of mathematics, including modes of
instruction, incorporation of manipulatives, models, and cooperative learning in teaching
mathematics.

3) The
third area of focus is classroom management, which includes lesson planning, questioning
techniques, tests, evaluation of student performance, techniques of motivation, homework,
remediation with special attention to individual differences of students, problem solving,
and enriching mathematics through the selection and utilization of a variety of
instructional media.

4) The
fourth area of focus is professional growth with emphasis on professional organizations in
mathematics education, their journals and contributions to the profession.

__University Studies: Writing
Flag__

The purpose of the Writing Flag requirement is to reinforce the outcomes specified for the basic skills area of writing. These courses are intended to provide contexts, opportunities, and feedback for students writing with discipline-specific texts, tools, and strategies. These courses should emphasize writing as essential to academic learning and intellectual development.

Courses can merit the Writing Flag by demonstrating that section enrollment will allow for clear guidance, criteria, and feedback for the writing assignments; that the course will require a significant amount of writing to be distributed throughout the semester; that writing will comprise a significant portion of the students’ final course grade; and that students will have opportunities to incorporate readers’ critiques of their writing.

These courses must include requirements and learning activities that promote students’ abilities to…

a. practice the processes and procedures for creating and completing successful writing in their fields

b. understand the main features and uses of writing in their fields

c. adapt their writing to the general expectations of readers in their field

d. make use of the technologies commonly used for research and writing in their fields

e. learn the conventions of evidence, format, usage, and documentation in their fields

The
Course Objectives were designed in such a way as to combine several of the Course Outline
of Major Topics and Subtopics. Therefore the
University Studies Writing Flag requirements are indicated on the course objectives and
identified as **(a-e)**.

__Course Objectives__: The future teacher should be able to:

1) identify and model
strategies used for problem solving in grades 5-12,

2) use a variety of
manipulative and visual materials for exploration and development of mathematical concepts
in grades 5-12, **(a)**

3) use a variety of
resource materials such as software, print materials, technology, and activity files to
enhance the learning of mathematics, **(d)**

4) select appropriate
mathematical tasks that will stimulate students' development of mathematical concepts and
skills, **(b)**

5) use oral and written
discourse between the teacher and students, among students, between the teacher and the
community in an effort to develop and extend students' mathematical understanding, **(c)**

6) create a learning
environment in which students feel free to take risks,

7) use instructional
strategies in mathematics that include group work, accommodation of different learning
styles, application of knowledge of current national and state guidelines relating to
mathematics instruction, **(e)**

8) Use assessment in the
classroom to make instructional decisions.

__Course
Outline of the Major Topics and Subtopics__:

I. Secondary Mathematics Curriculum: The mathematics curriculum (5-12) with focus on new directions (NCTM Standards) and the scope and sequence.

A. Content, Scope, Sequence for
Middle School (Grades 5-8), High School (Grades 9-12)

B. Modes of Instruction

C. Current Trends and Issues

II. Classroom Instruction: Classroom instruction to include lesson planning, unit planning, questioning techniques, techniques of motivation, homework strategies, remediation, problem solving, mathematics enrichment, discipline, mathematics anxiety, and textbook selection.

A. Lesson Plans

B. The “Art” of
questioning and responding

C. Motivation

D. Using manipulatives and
models

E. Cooperative Learning

F. Homework

G. Enrichment and Extra
curricular activities

H. Remediation

1. What
is it?

2. Strategies

3. Evaluation

IV.
Learning Theory: Learning models and their impact on the teaching and learning of
mathematics

A. Constructivism

B. Behaviorism

C. Cognitively
Guided Instruction

A. Professional Organizations in
Mathematics Education

B. Home/school/community
communications

Method
of Instruction: The method of instruction for this class will vary and may include,
lecture, whole-class discussion, small-group work, individual and/or group presentations,
hands-on activities, demonstrations, written assignments, independent learning,
whole-class viewing of videotapes, panel discussions by area teachers and student
teachers.

General
Expectations: All students are expected to communicate their ideas and demonstrate their
level of understanding in both verbal and written forms; therefore, ACTIVE student
involvement in discussions and activities is expected.

REGULAR
ATTENDANCE IS EXPECTED. In addition, students
are expected to attend the Minnesota Council of Teachers of Mathematics annual spring
meeting as part of their professional development.

Method of Assessment: Assessments will occur often and will vary in style, including: 1) successful completion of the Teaching Assistantship; 2) oral presentations and/or interviews; 3) written assignments (lesson plans, article reviews, etc); 4) projects; and 5) in-class examinations. Since this course is designated as a University Studies Writing Flag written work will account for approximately 30% of the grade in this course.

Grading Scale: A (100%-90%), B (89%-80%), C (79%-70%), D (69%-60%), F (59%-0%).

Additional
References:

Ameis,
J. A., & Ebenezer, J. V. (Eds.). (2000). *Mathematics
on the internet: A resource for K-12 teachers*. Upper Saddle River, NJ: Prentice-Hall,
Inc.

Emmer,
E. T., Evertson, C. M., Clements, B. S., & Worsham, M. E. (Eds.). (1997). *Classroom Management for secondary teachers*, 4^{th}
Edition. Needham Heights, MA: Allyn & Bacon.

Fosnot,
C. T. (Ed.). (1996). *Constructivism: Theory,
perspectives, and practice*. New York, NY: Teachers College Press.

Leinhardt,
G., Putnam, R., & Hattrup, R. A. (Eds.). (1992). *Analysis of arithmetic for mathematics teaching*.
Hillsdale, NJ: Lawrence Erlbaum Associates.

Sowder,
J. T. & Schappelle, B. P. (Eds.). (1995). *Providing
a foundation for teaching mathematics in the middle grades*. Albany: State University
of New York Press.

Secada,
W. G., Fennema, E., & Adajian, L. B. (1995). *New
directions for equity in mathematics education*. New York, NY: Cambridge University
Press.

Research
Ideas for the Classroom High School Mathematics, NCTM, 1993.

Research
Ideas for the Classroom Middle School Mathematics, NCTM, 1993.

Making
Minutes Count Even More, Johnson, 1986.

Curriculum
and Evaluation Standards for School Mathematics Addanda Series, NCTM, 1990's.

Current
mathematics textbooks for grades 5-12.

NCTM
Yearbooks 1985-1995.