Mercer University Tift College of Education educ 454: Teaching Math for Early Childhood Education

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Mercer University

Tift College of Education
EDUC 454: Teaching Math for Early Childhood 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.

Dr. Mary Kay Bacallao

Telephone: 678-547-6531



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 may be required. You can purchase your LiveText account at 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.
Internet Resource:

Georgia Performance Standards:


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

Study includes developmentally appropriate methods, materials, media, technology, and techniques for diagnosing, correcting, teaching, and evaluating mathematics in grades P-5.


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):

ESE Objectives The students will learn how to use algorithms that are designed for special education students such as Hutchings Low Stress Addition and Subtraction and Lattice Multiplication.

CFO The student will:

I b Broaden his or her perspectives concerning the nature of


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


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. GACE ECE 0013

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. GACE ECE 0013, GACE ECE 0014, GACE ECE 0015, GACE ECE 0016, GACE ECE 0017

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.

1. Midterm (25% of final grade) — The midterm will be given to assess knowledge of computation, problem solving, and mathematics teaching methods.
2. Mathematics Content Essays (25% of final grade) — There are seven content essays that are required for this course as your portfolio artifact. You will write a content essay for each topic discussed in class and turn it in during the next class session. Each essay is to include information on the topic as well as strategies for teaching the given topic in a classroom setting. There is a detailed description of the assignment below. After submitting the content essays, you will write a reflection on how your essays have demonstrated that you have met the mathematics content and process standards.
3. Problem Solving/Technology Lesson Plan/Bulletin Board Presentation (25% of final grade)–You will be expected to write a lesson plan that could be used to teach a concept from the middle grades mathematics curriculum. You will select and use a Georgia Performance Standard that will assist you in writing your lesson plan. The lesson plan must be written according to the Mercer University lesson plan format. Your lesson plan must incorporate meaningful opportunities for problem solving and the meaningful use of some sort of technology (calculators, computer software, Internet sites, etc.). You will also be expected to design a bulletin board that could enhance your lesson. (Please use a piece of poster board to create a “mini” version of your bulletin board.) You will be required to give a presentation in which you summarize your lesson plan and show your bulletin board design. Your presentation should last approximately 3 minutes.

4. Final Examination (25% of final grade)–The final examination will include questions related to mathematics teaching methods as well as a mathematics content skills check encompassing the NCTM Content and Process Standards.

Early Childhood 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 and Counting

2. Meaning and Basic Facts

3. Algorithms

4. Measurement

5. Geometry

6. Data Analysis and Probability

7. Algebra
Outline Form for Portfolio
I. Number Sense and Operations
A. Number Sense and Counting
B. Meaning and Basic Facts
C. Algorithms
II. Measurement
III. Geometry
IV. Data Analysis and Probability
V. Algebra
Dispositions Assessment

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.

Assessment Descriptors for Dispositions


Values self and others

Is considerate of others

Values diversity

Exhibits tolerance


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


Adapts to change

Is open to new ideas

Handles less than ideal situations when necessary

Maintains a positive attitude when necessary changes occur


Supports teamwork

Shares knowledge and responsibilities with others

Accepts feedback from others


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
Professional Candidate Demographics Form

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.


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.


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 454 include word processing (Microsoft WORD), Internet resources, educational software, calculators, and digital photography.




Assignment(s) Due

Session 1

August 25, 2005

Course Introduction

Developing Concepts of Number and Developing Understanding of Numeration

Read Chapters 5 and 6

Session 2

September 1, 2005


Read Chapters 7 and 8

Session 3

September 8, 2005

Developing Measurement Concepts and Skills

Read Chapter 15

Session 4

September 15, 2005

Collecting, Analyzing and Interpreting Data

Fractions and Decimal Concepts

Read Chapters 10, 11, 12 and 16

Problem Solving/Technology Lesson Plans and Presentations

Session 5

September 22, 2005

Midterm Exam

Session 6

September 29, 2005

Developing Geometric Thinking and Spatial Sense

Read Chapter 14

Hot Topics” Presentations/Brochures Due

Session 7

October 6, 2005

Developing Algebraic Thinking

Read Chapter 17

Session 8

October 13, 2005

Final Exam

Journals Due

Note: This syllabus is subject to change at the discretion of the instructor in order to accommodate instructional and/or student needs.

Problem Solving/Technology Lesson Plan and Presentation 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.



Possible Number of Points

Number of Points Awarded

Lesson Plan

--Written according to the

Mercer University Lesson

Plan Format

--Includes all required


--Is appropriate for intended

grade level



--Lesson plan integrates meaningful use of technology (calculators, computer software, Internet sites, or some other form of technology)

--Type of technology to be used is well explained


Problem Solving

--Provides for authentic problem solving opportunities.

--Includes a real world situation for solving problems.


Bulletin Board Idea

--Is presented neatly and professionally

--Is designed to enhance the presented lesson plan in a meaningful way



--Is presented professionally

--Reflects stated objective(s) for the lesson

--Summarizes key points of the lesson plan

--Includes explanation of how technology is integrated into lesson plan

--Includes explanation of how problem solving is integrated into lesson plan


Overall Presentation




“Hot Topics” Brochures

Scoring Information

A brochure that earns a grade of “A” will have (minimally) the following characteristics:

--adheres to the selected topic

--carefully discusses the selected topic as it relates to mathematics education

--documents references according to APA style

--integrates references, as appropriate, throughout the brochure

--is free or virtually free of grammatical and spelling errors

--is neat, polished, and professional in style

--is accompanied by a brief verbal presentation

--is distributed at the time of the presentation to all members of the class, including the instructor

Sample Topics:

Computations vs. Applications

Problem Solving

Group Work in Mathematics

Math Journals

Master Learning vs. the Spiral Curriculum

Gender and Mathematics

Integrating Mathematics with Content Areas

The Use of Manipulatives

Understanding Meaning over Memorization for the Basic Facts

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


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.


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.


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.

ECE 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.



Possible Number of Points

Number of Points Awarded

Number and Operations

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



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.



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.



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.


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.


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.



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.


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.



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.



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.






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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