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The Department of Mathematics and Statistics proposes the following course for inclusion in the University Studies Mathematics/Statistics Flag courses at Winona State University. The full department at the Thursday, February 1, 2001 department meeting approved this action.

Course: Mathematics for Elementary Teachers (MTED 125), 4 s.h.

Catalog Description: The study of concepts and properties of operations essential to mathematics in the elementary and middle school grades. This is a university studies course satisfying requirements for the Mathematics/Statistics Flag. Prerequisite: Completion of basic skills mathematics (MATH) requirement. Offered each semester.

This is an existing course, previously approved by A2C2.

Department Contact Person for this course:

Jeffrey R. Anderson, Mathematics and Statistics Department Chair

Email: janderson@winona.edu

Document Prepared By:

George Gross, Mathematics and Statistics Department

Email: wngros144@winona.edu

The purpose of the Mathematics/Statistics flag course requirement is to reinforce the outcomes specified for the basic skills area of mathematics/statistics. These courses are intended to provide students with significant practice in applying prerequisite mathematical or statistical knowledge.

Courses can merit the Mathematics/Statistics Flag if students will be required to make essential use throughout the semester of mathematical or statistical models appropriate to their prerequisite knowledge of those areas, and if the correct use of techniques based on such models will comprise a significant portion of a student’s final grade. It is understood that mere rote computations, algebraic manipulations, or graphical design without inferential content would not merit a Mathematics/Statistics Flag.

This course includes requirements and learning activities that promote students’ abilities to...

Generally, included with all the concepts covered in the course are learning activities and assignments that require the students to apply appropriate related mathematical models correctly.

For instance in dealing with numeration systems, the students do an activity that uses concrete objects to represent the place values of a different base number system. These objects are then used to enhance the learning of counting and performing operations in this different system. Written assignments are then made with problems that involve the abstraction of these concepts.

Generally, built within the discussion of many of the concepts and activities used in the development of the activity, references are made to, and use of the technology associated with a calculator is required.

For example in working with the concept and use of divisibility, the calculator is used to enhance the application of this concept. The student is then able to use the calculator in the assigned homework problems.

Course Title: Mathematics for Elementary Teachers

Frequency of Offering: Each Semester

Prerequisite(s): Completion of basic skills mathematics (MATH) requirement.

Grading: For elementary education majors and minors, offered on a "Grade Only" basis.

P/NC is available to others.

Course Applicable: Elementary Education major, required.

Catalog Description: The study of concepts and properties of operations essential to mathematics in the elementary and middle school grades. This is a university studies course satisfying requirements for the Mathematics/Statistics Flag. Prerequisite: Completion of basic skills mathematics (MATH) requirement. Offered each semester.

Number of Credits: 4 Semester Hours

Required Textbook(s): Billstein, et al, 2001, A Problem Solving Approach to Mathematic for Elementary School Teachers, Addison Wesley Longman.

Principles and Standards for School Mathematics, NCTM 2000.

Additional Readings: None

Standards Included: Minnesota law requires that Elementary Education program include topics appropriate to issues encountered in grades K-8. This course is designed to help students develop competencies outlined in the Minnesota Standards for Effective Practice for Beginning Teachers. In particular this course will address the following Standards: Standard 1- Subject Matter 1) Subpart 3C (1,2,3,7,8) and 2) Subpart 4b ( 1a-d, 2,3).

Additional Requirements: None

Course Description: The major focus of this course is to provide students with

1. foundation knowledge and skills in mathematics content not covered in MTED 201,
2. foundation knowledge in developing, investigating, exploring, discussing, using, illustrating, and explaining mathematics.
3. exposure to and modeling of the NCTM Principles and Standards for School Mathematics.

Course Objectives: The objectives of the course include the following. The future teacher should be able to:

1. use a problem-solving approach to investigate and understand mathematical content,
2. formulate and solve problems from both mathematical and everyday situations,
3. communicate mathematical ideas orally and in writing using everyday and mathematical language and symbols,
4. use models, properties, relationships and patterns to explain their mathematical reasoning,
5. show an understanding of the interrelationships within mathematics,
6. connect mathematics to other disciplines and real-world situations,
7. demonstrate knowledge of the development of numbers and number systems,
8. model, explain and develop computational algorithms,
9. use a variety of mental computation and estimation techniques,
10. understand the meaning of the four basic operations and use them to solve problems,
11. understand and apply the process of measurement,
12. use algebra to describe patterns, relations and functions, and to model and solve problems,
13. use estimation in working with quantities, computation, and problem solving,
14. use calculators in computational and problem-solving situations,
15. show knowledge of the historical development in mathematics,
16. use a variety of manipulative and visual materials for exploration and development of numbers and their relationships, four basic operations with positive and negative rational numbers, geometric concepts and spatial visualization, measurement concepts and procedures, algebraic concepts, logical conjectures and conclusions using words such as all, some and none,
17. select appropriate mathematical tasks that will stimulate students’ development of mathematical concepts and skills,
18. use written and oral discourse between teacher and student and among students to develop and extend their future students’ mathematical understanding,
19. create a learning environment in which students feel to take risks,
20. use instructional strategies in mathematics that include the use of various student groupings, application of knowledge of current research and national, state and local guidelines relating to mathematics instruction.

The purpose of the Mathematics/Statistics flag course requirement is to reinforce the outcomes specified for the basic skills area of mathematics/statistics. These courses are intended to provide students with significant practice in applying prerequisite mathematical or statistical knowledge.

Courses can merit the Mathematics/Statistics Flag if students will be required to make essential use throughout the semester of mathematical or statistical models appropriate to their prerequisite knowledge of those areas, and if the correct use of techniques based on such models will comprise a significant portion of a student’s final grade. It is understood that mere rote computations, algebraic manipulations, or graphical design without inferential content would not merit a Mathematics/Statistics Flag.

This course includes requirements and learning activities that promote students’ abilities to...

a) practice the correct application of mathematical or statistical models that are appropriate to their prerequisite knowledge of those areas; and

b) make proper use of modern mathematical or statistical methods appropriate to their level of prerequisite knowledge, to include, if statistics is used in a substantive way, the use of a statistical package with graphics capability when appropriate.

I. Problem Solving

A. Exploring with Patterns a), b)

B. Using the Problem-Solving Process a), b)

C. Algebraic Thinking a), b)

II. Sets, Whole Numbers, and Functions

A. Describing Sets a)

B. Set Operations & Their Properties a)

C. Addition & Subtraction of Whole Numbers a)

D. Multiplication & Division of Whole Numbers a), b)

E. Functions a), b)

III. Whole Number Computation

A. Numeration Systems a)

B. Algorithms for Whole Number Addition and Subtraction a)

C. Algorithms for Whole-Number Multiplication and Division of Whole Numbers a), b)

D. Mental Mathematics and Estimation for Whole-Number Operations a)

IV. Integers and Number Theory

A. Integers and the Operation of Addition & Subtraction a)

B. Multiplication and Division of Integers a), b)

C. Divisibility a), b)

D. Prime and Composite Numbers a)

E. Greatest Common Divisor and Least Common Multiple a)

F. Clock and Modular Arithmetic a)

1. Rational Numbers and Fractions

A. The Set of Rational Numbers a)

B. Addition and Subtraction of Rational Numbers a)

C. Multiplication and Division of Rational Numbers a), b)

D. Proportional Reasoning a), b)

VI. Decimals, Percents, and Real Numbers

1. Introduction to Decimals a), b)
2. Operations on Decimals a), b)
3. Non-terminating Decimals a), b)
4. Percents a), b)
5. Computing Interest a), b)
6. Real Numbers a), b)

Method of Instruction: The pedagogy employed is left to the discretion of the individual teacher. Instruction may model a variety of methods and strategies including lecture, discovery, group activities, writing, reports, student explanations and/or presentations, teacher lecture, and teacher and/or student guided discussion.

General Expectations: All students are expected to attend class on a regular basis, to be active participants in class and to be readers of the texts and related writings. Students will be expected to demonstrate their knowledge of the subject through writing, problem solving, presentations, peer teaching, projects and at least three examinations.

Method of Assessment: Assessments will vary in style, and may include teacher evaluation of written exams, written homework individual and/or group problems, written reaction papers, and in-class group and individual problems

Problem Solving Strategies, Herr & Johnson, Key Curriculum Press, 1994.

A Survey of Mathematics with Applications (5th edition), Angel & Porter, Addison-

Wesley, 1997.

Curriculum and Evaluation Standards for School Mathematics Addenda Series,

grades 5-8, 3 booklets, grades 9-12, 4 booklets from NCTM.