Mercer University Tift College of Education educ 455: Teaching Math for Middle Grades Education The Transforming Practitioner



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Mercer University

Tift College of Education
EDUC 455: Teaching Math for Middle Grades Education
The Transforming Practitioner

To Know To Do To Be

The Transforming Practitioner,” the living link between the child and learning, is an educator who is changing internally through understanding, practicing, and reflecting such that, individually and collaboratively, he or she implements for all children appropriate and significant life-changing learning experiences that effectively provide for the needs of the whole child, actively engage students in the learning process, and promote life-long learning.


INSTRUCTOR:

Dr. Mary Kay Bacallao

Telephone: 678-547-6531

e-mail: bacallao_mk@mercer.edu


REQUIRED TEXT:

Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. Upper Saddle River, NJ: Merrill Prentice Hall.


A live text account is required. You can purchase your LiveText account at http://www.livetext.com for $89. Your account will be active for the duration of your current program at Mercer and one year beyond your program completion. Additional instructions on creating your LiveText account will be provided. If you have already created a LiveText account for another course in Tift College of Education, you do not need another one; you will use the same account for any classes and assignments that require LiveText.
Professional Education Candidate Demographic Form in LiveText: All Tift students must complete this form in their LiveText accounts. Even if you completed the form last semester, we ask that you check to be sure the information on you is correct. If you had a LiveText account last semester and did NOT complete this form, it is even more important that you check it to be sure any data in it is correct and complete. To complete or check your

information in this form, do the following: Login to your account and click the Forms link in the left menu (Under the Tools section). You should see four or more forms listed there. Ignore all but the one entitled “Professional Education Candidate….” If you have already filled it out or it has been filled out for you, the title of the form will be a link – click the title to see the information that is currently in the form. If it is correct, do nothing. If it is incorrect, click the Go Back button and return to the list of forms, then click the Take Again link; complete the form with the


correct information and Submit. If the title is not a link, that means your form is empty; click Take Form, then complete and submit the form. After you have completed this form correctly, you will not need to do it again unless
you change programs.
Internet Resource:

Georgia Performance Standards: http://www.georgiastandards.org/

CATALOG COURSE DESCRIPTION:

Prerequisites: Must meet Senior Year Progression criteria; C or better in general education mathematics courses.



EDUC 455: An overview of the essential components in middle grades mathematics for all children is the focus of this course. Study includes methods, materials, media, technology, and techniques for diagnosing, correcting, teaching, and evaluating mathematics in grades 4-8.

PURPOSE:

This course relates to each of the three major premises of the Conceptual Framework (CF) of Mercer University’s Tift College of Education: (1) To Know the foundations of the education profession, (2) To Do the work of a professional educator, (3) To Be a 21st Century Educator. In keeping with the CF, this course will be instrumental in helping students to engage in processes, practices, skills and attitudes that will enable them to become transforming practitioners in the teaching of early childhood mathematics. In recognition of the model of "The Transforming Practitioner,” this course will foster students’ pedagogical knowledge (encompassing theory, philosophy, research, and effective mathematics teaching practice), mathematical content knowledge, awareness of how students best learn mathematics, and interpersonal skills. Furthermore, students will participate in a variety of learning experiences that will enhance their abilities to integrate theory and practice, to communicate effectively, to teach accurate and appropriate mathematical knowledge, to organize and manage the mathematics learning environment, to demonstrate a variety of teaching methods that meet the needs of a diverse student population, to encourage active student learning using multiple group structures, and to demonstrate respect for and acceptance of all educational stakeholders.



COURSE OBJECTIVES (Tied to Tift College of Education’s Conceptual Framework):

CFO The student will:

I b Broaden his or her perspectives concerning the nature of

mathematics.



I b, II a Become more confident in his or her abilities "to do" and to

teach mathematics.



I a, b, c, II a, b, c Demonstrate knowledge of concepts and teaching strategies

needed to provide meaningful instruction in the elementary

school.
CFO The student will:

II a, b, c, III b, c Demonstrate effective ways to motivate all early childhood students to engage in mathematics and to realize the importance of mathematics in their lives.

I b Realize the interrelationships among the various areas of

mathematics.



II b, c Become familiar with the technology relative to

mathematics education.



I a, b, c, II a, b, c, III a, b, c Be able to incorporate the NCTM Principles and Standards for School Mathematics into his or her teaching.

I b, III b Become aware of the contributions of various cultures

throughout the development of mathematics.



III a Understand the need for and develop the ability to analyze teaching and learning of mathematics in grades P-5. II a, b, c Be familiar with Georgia’s QCC objectives and use the Georgia Performance Standards appropriately in

planning lessons.



III a Use reflection and research to enhance mathematics teaching performance, revise and refine instruction, make decisions, and grow as a professional.


COURSE REQUIREMENTS AND EVALUATION:
1. Quizzes— The quizzes will be given to assess knowledge of teaching methods and NCTM content and process standards.
2. Problem Solving Presentations–You will be required to perform a section of a lesson plan based on your assigned NCTM content area. Your presentations will be video taped. You will engage in both self and group reflection on your presentations.
3. Content Essays – The content essays are to be completed throughout the course and turned in as each topic is addressed. The final version of you content essay collection will be your livetext artifact.

Middle Grades Education

Math Methods

Content Essays
There are seven content essays that are required for this course as your portfolio artifact. Each essay is to be at least one typed, double-spaced page in length. When you have finished all the essays, put them together in one Word document. The essays are numbered, but you will use the following outline form, based on the NCTM standards, for headings and sub-headings for your content essays. You may number your essays during the course as you complete them and turn them in. But, you should not number your content essays when they are in final form. Instead, use the outline form with the Roman numerals below.
List of Content Essays
1. Number Sense, Meaning, and Basic Facts

2. Algorithms

3. Measurement

4. Geometry

5. Data Analysis and Probability

6. Algebra

7. Problem Solving with Connections

Outline Form for Portfolio
I. Number Sense and Operations
A. Number Sense, Meaning, and Basic Facts
B. Algorithms
II. Measurement
III. Geometry
IV. Data Analysis and Probability
V. Algebra
VI. Problem Solving with Connections
One of your requirements in this class is to submit a Dispositions Assessment Permission in LiveText to me. At the end of the course, I will provide you with formative feedback on your development and demonstration of the professional dispositions that are important for Transforming Practitioners. No grade or score from the dispositions assessment will affect your course grade, but the submission of your permission form is required before your grade will be posted. Instructions on the submission process will be provided and we will discuss in class the specific dispositions that will be assessed.

Categories for Dispositions Ratings

Respect:

Values self and others

Is considerate of others

Values diversity

Exhibits tolerance

Responsibility:

Is reliable and trustworthy

Accepts consequences for personal actions or decisions

Prepares for classes/meetings/group work/ instruction

Demonstrates ethical behavior

Maintains confidentiality of students/colleagues

Flexibility

Adapts to change

Is open to new ideas

Handles less than ideal situations when necessary

Maintains a positive attitude when necessary changes occur

Collaboration

Supports teamwork

Shares knowledge and responsibilities with others

Accepts feedback from others

Reflection

Self-assesses knowledge/performance

Demonstrates accurate self-analysis regarding own strengths and weaknesses

Uses constructive feedback

Assesses situations accurately

Commitment to life-long learning

Engages in professional development activities

Is committed to the profession

Models and promotes life-long learning

Have enthusiasm for the discipline(s) s/he teaches and for the process of learning

Belief in teacher efficacy

Demonstrates a belief that all students can learn and that s/he can influence student learning

Is willing to take risks

Views the work of an educator as meaningful and important

Maintains emotional control and responds to situations professionally

Is committed to the use of democratic values in the classroom


COURSE GRADING SCALE:

A: 90-100 C+: 77-79 F: Below 60


B+: 87-89 C: 70-76

B: 80-86 D: 60-69




Honor Policy:

Academic integrity is maintained through the honor system. The honor system imposes on each student the responsibility for his or her own honest behavior and assumes the responsibility that each student will report any violations of the Honor Code. By the act of entering Mercer University, each student personally consents to Mercer’s Honor System and thereby agrees to be governed by its rules. Furthermore, each student is personally responsible for knowing the rights and obligations as set forth in the Honor System. The student is also expected to cooperate with all proceedings of the Honor System and to participate fully in the Honor System.


Students are expected to abide by the Honor Policy for ALL assignments. The instructor will announce those assignments that are specifically designed for cooperative work.
Disabilities Statement:
Students with a documented disability should inform the instructor at the close of the first class meeting. The instructor will refer you to the Chair’s Office for consultation regarding evaluation, documentation of your disability, and recommendations for accommodation, if needed. To take full advantage of disability services, it is recommended that students make contact immediately. The Chair’s Office is located at the Henry County Regional Academic Center.

METHODS OF INSTRUCTION

The instructional methodology for this course will provide both a theoretical foundation as well as practical application of the learning process as it pertains to the teaching of mathematics in middle grades classrooms. Students will participate in multiple experiences including interactive groups, small group discussions, cooperative learning, independent work, student presentations, and lecture. Technology will also play a role in the learning process. Students’ reflections will help guide their learning as they master the course objectives.


Types of Technology to be used in EDUC 455 include word processing (Microsoft WORD), Internet resources, educational software, calculators, and digital photography.

TENTATIVE COURSE OUTLINE




Session

Concept(s)

Assignment(s) Due

Session 1 Oct. 18


Number Sense, Meaning and Basic Facts




Session 2 Oct. 25


Algorithms

Number Sense, Meaning, and Basic Facts Essay

Session 3 Nov. 1


Measurement

Algorithms Essay

Session 4 Nov. 8


Blackboard Online Class- Open Ended Questions and The Futures Channel

Measurement Essay

Session 5 Nov. 15


Geometry




Session 6 Nov. 29


Algebra

Geometry Essay

Session 7 Dec. 6


Data Analysis and Probability

Algebra Essay

Session 8 Dec. 13


Problem Solving Presentations

Data Analysis and Probability Essay

Student Presentations



Note: This syllabus is subject to change at the discretion of the instructor in order to accommodate instructional and/or student needs.
Content Essays Scoring Rubric
NOTE: The maximum number of points will not be awarded merely because the component is addressed or included. Points will be awarded based on quality of work and professional polish.

Component

Comments

Possible Number of Points

Number of Points Awarded


Number and Operations/

Discrete Mathematics

The content essay addresses

teaching students how to

1. Understand numbers, ways of

representing numbers,

relationships among numbers, and

number systems

2. Understand meanings of operations and how they relate to one another

3. Compute fluently and make reasonable estimates





0-10




Algebra/Pre-Calculus

The content essay addresses teaching students how to

1.Understand patterns, relations, and functions

2. Represent and analyze mathematical situations and structures using algebraic symbols

3. Use mathematical models to represent and understand quantitative relationships

4. Analyze change in various contexts.






0-10




Geometry

The content essay addresses

teaching students how to

1. Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

3. Apply transformations and use symmetry to analyze mathematical situations

4. Use visualization, spatial reasoning, and geometric modeling to solve problems.





0-10




Measurement

The content essay addresses

teaching students how to

1. Understand measurable attributes of objects and the units, systems, and processes of measurement

2. Apply appropriate techniques, tools, and formulas to determine measurements.





0-10



Data Analysis and Probability


The content essay addresses

teaching students how to

1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

2. Select and use appropriate statistical methods to analyze data

3. Develop and evaluate inferences and predictions that are based on data

4. Understand and apply basic concepts of probability.






0-10



Problem Solving


The content essay addresses

teaching students how to

1. Build new mathematical knowledge through problem solving;

2. Solve problems that arise in mathematics and in other contexts

3. Apply and adapt a variety of appropriate strategies to solve problems

4. Monitor and reflect on the process of mathematical problem solving.






0-10



Representation


The content essay addresses

teaching students how to

1. Create and use representations to organize, record, and communicate mathematical ideas

2. Select, apply, and translate among mathematical representations to solve problems

3. Use representations to model and interpret physical, social, and mathematical phenomena.





0-10



Reasoning and Proof


The content essay addresses

teaching students how to

1. Recognize reasoning and proof as fundamental aspects of mathematics

2. Make and investigate mathematical conjectures

3. Develop and evaluate mathematical arguments and proofs

4. Select and use various types of reasoning and methods of proof.






0-10



Connections


The content essay addresses

teaching students how to

1. Recognize and use connections among mathematical ideas

2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

3. Recognize and apply mathematics in contexts outside of mathematics.





0-10



Communication


The content essay addresses

teaching students how to

1. Organize and consolidate their mathematical thinking through communication

2. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others

3. Analyze and evaluate the mathematical thinking and strategies of others

4. Use the language of mathematics to express mathematical ideas precisely.






0-10




Total




0-100


TOTAL

SCORE:



Tift College of Education Conceptual Framework

Within the context of a distinctive Baptist heritage, the inclusion of the Paideia ideal, and the know-how of blending theory and practice, Tift College of Education has chosen for its conceptual framework the theme: "The Transforming Practitioner - To Know, To Do, To Be."


The Transforming Practitioner

I. TO KNOW


To Know the foundations of the education profession, content bases for curricula, and characteristics of diverse learners.

  1. Demonstrates knowledge of the philosophical, historical, sociological, legal, and psychological foundations of education.

  2. Demonstrates expertise in the content bases for curricula, the appropriate uses of technology, good communication skills, and effective pedagogy.

  3. Shows understanding of and respect for the characteristics, cognitive and social developmental stages, emotional and psychological needs, and learning styles of diverse and special needs learners.

II. TO DO


To Do the work of a professional educator in planning and implementing well-integrated curricula using developmentally appropriate and culturally responsive instructional strategies, materials, and technology.

  1. Plans, implements and assesses well-integrated, developmentally appropriate, and culturally responsive lessons which are well grounded in pedagogical and psychological theory.

  2. Individualizes, differentiates, and adapts instruction to meet the needs of diverse and special needs learners.

  3. Uses a wide variety of teaching methods, strategies, technology, and materials.

III. TO BE


To Be a reflective, collaborative, and responsive decision-maker, facilitator, and role model within the classroom, school, community, and global environment.

  1. Uses feedback, reflection, research, and collaboration to enhance teaching performance, revise and refine instruction, make decisions, develop and modify instruction, and grow as a professional.

  2. Models understanding, respect, and appreciation for diverse educational, cultural, and socioeconomic groups; a willingness to consider diverse opinions and perspectives; and concern for community and global awareness.

  3. Models positive and effective interpersonal skills interacting with learners, parents, other educators, and members of the community.

Bibliography of Selected Related Readings
Ashlock, R. B. (1998). Error patterns in computation. Upper Saddle River, NJ: Merrill.
Baroody, A. J., & Coslick, R. T. (1998). Fostering children’s mathematical power. Mahwah, NJ: Lawrence Erlbaum Associates.
Bassarear, T. (1997). Mathematics for elementary school teachers. Boston, MA: Houghton Mifflin Company.
Brumbaugh, D. K., Ashe, D. E., Ashe, J. L., & Rock, D. Teaching secondary mathematics. Mahwah, NJ: Lawrence Erlbaum Associates.
Cangelosi, J. S. (1996). Teaching mathematics in secondary and middle school. Englewood Cliffs, NJ: Prentice Hall.
Carnegie Council on Adolescent Development. (1989). Turning points: Preparing American youth for the 21st century. Washington, DC: CCAD.
Carnegie Council on Adolescent Development. (1996). Great transitions: Preparing adolescents for a new century. New York: CCAD.
Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2000). Learning mathematics in elementary and middle schools. Upper Saddle River, NJ: Merrill.
Chen, A. (1995). Content knowledge transformation: An examination of the relationship between content knowledge and curricula. Teaching and Teacher Education, 11, 389-401.
Glenn, W. H., & Johnson, D. A. (1960). Sets, sentences, and operations. St. Louis: McGraw-Hill.
Glenn, W. H., & Johnson, D. A. (1960). Understanding numeration systems. St. Louis: McGraw-Hill
Gordon, E., & Fillmer, H. (1997). Professional core cases for teacher decision-making. Upper Saddle River, NJ: Prentice-Hall.
Hashisaki, J., & Peterson, J. (1967). Theory of Arithmetic. New York: Wiley.
Hatfield, M., Edwards, N., & Bitter, G. (1997). Mathematics methods for elementary and middle school teachers. Needham Heights, MA: Allyn and Bacon.
Heddens, J. W., & Speer, W. R. (1997). Today's mathematics. Upper Saddle River, NJ: Prentice-Hall.
Henderson, J., & Hawthorne, R. (1995). Transformative curriculum leadership. Upper Saddle River, NJ: Merill.
Huetinck, L., & Munshin, S. N. (2000). Teaching mathematics for the 21st century. Upper Saddle River, NJ: Merrill.
Lamon, S. J. (1999). Teaching fractions and ratios for understanding. Mahwah, NJ: Lawrence Erlbaum Associates.
Long, C. T. (1972). Elementary introduction to number theory.

Lexington, MA: D. C. Heath and Company.


Maletsky, E. M., & Sobel, M. A. (1988). Teaching mathematics: A sourcebook of aids, activities, and strategies. Englewood Cliffs, NJ: Prentice Hall.
Mustain, K., & Spreckelmeyer, R. (1963). The natural numbers. Boston: D. C. Heath and Company.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for teaching mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics. Mathematics teaching in the middle school and Teaching children mathematics. Reston, VA: NCTM.
Niven, I. (1961). Numbers: Rational and irrational. New York: Random House.
Palmer, P. (1998). The courage to teach: Exploring the inner landscape of a teacher’s life. San Francisco: Jossey-Bass.
Post, T., Ellis, A., Humphreys, A., & Buggey, L. (1997). Interdisciplinary approaches to curriculum: Themes for teaching. Upper Saddle River, NJ: Prentice-Hall.
Schifter, D. (Ed.). (1996). What's happening in math class? Newark, DE: International Reading Association.
Souviney, R. J. (1994). Learning to teach mathematics. New York: Merrill Publishing.

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