EDUC 12/MATH 12, Syllabus, Section 2

Mathematics for the Early Childhoodand Intermediate Grades (Fall, 1998)

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I. Textbook: There is no textbook for this section. However, some excellent materials prepared by the North Carolina Department of Public Instruction for Grades 1 through 5 will be available. These are not copyrighted, so you may duplicate any of them which you might find useful. The materials and activities will be useful to you in student teaching and in your teaching later. Other sources for teaching children mathematics are provided at the end of this syllabus, and most of these references are on reserve at the House Undergraduate Library. You will be collecting and designing material and learning activities from these sources as outside assignments. The Arithmetic Teacher, (name recently changed to Teaching Children Mathematics) a monthly journal published by the National Council of Teachers of Mathematics for K-5 teachers, should be a main source for you.

 

II. Teacher: Hunter Ballew, 307B Peabody Hall. Office Hours: Most Mondays and Thursdays, 9:00 - 11:00, or please see me in class for an appointment, or call 962-9198. If I am not there, leave a message and I will return your call. You can also contact me for an appointment at my e-mail address: hballew@email.unc.edu

 

III. Course Objectives: This course is designed specifically for students preparing to teach mathematics in grades K-5. The course is based on the Standards of the National Council of Teachers of Mathematics and the competency guidelines of the state of North Carolina. This course is taken as part of a block during the Senior year by all candidates for the K-5 certificate. The course is crosslisted as a Mathematics and an Education course. Therefore, the course provides instruction both in the mathematical background underlying the K-6 curriculum and the directions students will take in mathematics after they leave the elementary school. The course also addresses the decision-making processes for the selection of curriculum and instruction for the elementary school mathematics program, resources and methods to help teach the selected content, and discussion of issues and trends in teaching children mathematics. The course emphasizes the importance of learning through concrete and manipulative experiences, and on the development of positive attitudes toward mathematics. The course also includes suggestions for the use of calculators and computers in teaching children mathematics. Part of the course will be devoted to the North Carolina Computer Competencies now being required of students and teachers in grades K-12.

To achieve the above general purpose, students completing this course will be able to:

  1. 1. Explain prenumeration and numeration concepts
  2. 2. Explain the concepts of whole numbers, integers, common and decimal fractions, rational numbers, ratio, proportion, and percent
  3. 3. Demonstrate the usual and some alternative algorithms for operations on whole numbers and fractions in common and decimal form
  4. 4. Justify and use estimation procedures
  5. 5. Illustrate the relations of equality and inequality with whole numbers, integers, and rational numbers
  6. 6. Demonstrate measurement in the metric and customary units
  7. 7. Use a variety of manipulatives to develop number and pre-number concepts, geometric concepts, spatial relationships, and probability
  8. 8. Use the hand calculator as an instructional tool
  9. 9. Use the computer, including the LOGO language, as an instructional tool in geometry, arithmetic, and probability
  10. 10. Demonstrate the ability to organize and interpret data
  11. 11. Demonstrate knowledge of the skills required for problem solving, knowledge of how to diagnose the strengths and weaknesses of students in relation to these skills, and knowledge of how to prescribe treatment for the various weaknesses
  12. 12. Serve as a model of a positive attitude toward mathematics for young children
  13. 13. Plan lessons in accordance with Gagne's model of desired learning outcomes., and lessons in accordance with Skemp's model of relational and instrumental understanding.
  14. 14. Understand and use the North Carolina Computer Competencies.

 

A more informal goal statement is that my hope for you is that by the end of this term, no matter where you stand now, you will have

1. a more positive attitude toward mathematics;

2. more confidence in your own ability to do mathematical thinking and that you will find yourself enjoying it!

3. more confidence in your ability to help children develop self-confidence and a positive attitude toward mathematics

4. many ideas and much knowledge of materials that you can use directly in teaching children mathematics

5. many ideas and activities that you can adapt to different grade levels and to different ability levels in teaching children mathematics

IV. Grading

First Test (About the end of September): 20 points

Second Test (About the end of October) 20 points

Final Examination 30 points

Class Attendance and Participation,

and outside assignments 30 points

You cannot get credit for this course solely by writing papers and passing the final examination. According to the Standards of the National Council of Teachers of Mathematics, discourse is of primary importance in learning mathematics. This means I need to hear your opinions, you need to hear my opinions, and you need to hear each other's opinions. This is the way opinions are shared, perhaps changed or refined, and formed into knowledge. This can only happen if you come to class. Your class participation and completion of the outside assignments earn you the 30 points in the above list.

Grading Scale

A : 95-100

A-: 90-94

B+: 88-89

B : 82-87

B-: 80-81

C+: 78-79

C : 72-77

C-: 70-71

D+: 68-69

D : 60-67

F : Below 60

 

*******Final examination: *******

From a memorandum from the Provost, September 4, 1990: "Excuses from final exams: The respective Deans' offices are the only agencies authorized to excuse a student from a scheduled final examination for the purpose of allowing the student to take the examination at a later date. No other agency is authorized to excuse a student from a final examination."

 

V. Topical Outline

A. Mathematical Content of the Elementary School Curriculum

  1. 1. The concept of number
  2. 2. A system of counting
  3. 3. The concept of zero
  4. 4. The place-value system of notation
  5. 5. Mathematical equality and inequality
  6. 6. Operations on whole numbers
  7. 7. The concept of rational numbers, with emphasis on the non-negative
  8. 8. Operations on rational numbers in common fraction form
  9. 9. Operations on rational numbers in decimal fraction form
  10. 10. Ratio and percent
  11. 11. Factors, primes, lowest common multiples, and greatest common factors
  12. 12. Measurement, including the metric system
  13. 13. Word problems--diagnosis of difficulties and treatment of deficiencies
  14. 14. Importance of teaching geometry in the elementary school, and specific geometric concepts, including the use of LOGO in teaching children geometry
  15. 15. The use of the computer in teaching various mathematical concepts
  16. 16. Probability and statistics, including graphing
  17. 17. Negative numbers
  18. 18. Irrational numbers
  19. 19. Computer Competencies

Note: The remainder of this outline is taught, not as separate topics, but as appropriate parts of the topics listed in A above. For example, geoboards and tangrams are used both to increase understanding of geometric concepts by prospective teachers and to illustrate how these manipulatives can be used in teaching children mathematics.

B. Specific materials and ideas for enhancing basic skills, for enrichment of mathematical content, for increasing understanding, and for illustrating the use of these materials with children.

  1. 1. Cuisenaire rods
  2. 2. Unifix cubes
  3. 3. Geoboards
  4. 4. Tangrams
  5. 5. The abacus
  6. 6. Magic squares
  7. 7. Number games
  8. 8. Spatial visualization activities
  9. 9. Creative use of the calculator
  10. 10. The computer as a manipulative

C. Mathematics Instruction

  1. 1. Teaching from the concrete and familiar toward the abstract and unfamiliar
  2. 2. The stages of a good mathematics lesson
  3. 3. Gagne's categories of learning outcomes
  4. 4. Skemp's Relational and Instrumental Understanding
  5. 5. Piaget's stages of intellectual development
  6. 6. Using problem solving and discovery learning as modes of inquiry
  7. 7. Gathering and organizing data, and forming and testing conjectures based on these data
  8. 8. The nature of mathematical proof
  9. 9. Higher order thinking based on understanding
  10. 10. Using manipulatives

D. Issues and Trends

  1. 1. NCTM Standards (1989)
  2. 2. National Assessment of Educational Progress
  3. 3. The use of calculators in the elementary school
  4. 4. The use of computers in teaching mathematics
  5. 5. Mathematics anxiety
  6. 6. Women and minorities in mathematics
  7. 7. Basic skills
  8. 8. Standardized testing

 

The above content will be organized into the following units (not necessarily in this order):

  1. 1. Teaching Geometry to Elementary School Children
  2. 2. Using LOGO and HyperStudio to Help Teach Children Mathematics
  3. 3. The Use of Calculators in Teaching Children Mathematics
  4. 4. Teaching Number and Computation to Elementary School Children
  5. 5. Teaching Problem Solving to Elementary School Children
  6. 6. Teaching Probability and Statistics to Elementary School Children

VI. Selected Bibliography

The Arithmetic Teacher (Renamed Teaching Children Mathematics in 1994) (A monthly publication by the National Council of Teachers of Mathematics for grades K-8. Current copies are kept in the periodicals reading room of Davis Library. This should be your main resource for ideas for teaching children mathematics for this course and for your entire teaching career.)

Ashlock, R.B. (1986) Error Patterns in Computation (4th ed.) Columbus: Charles E. Merrill.

Ballew, H. (1973) Teaching Children Mathematics. Columbus, Ohio: Charles Merrill Company.

Baretta-Lorton, M. (1976) Mathematics Their Way. Menlo Park, Calif.: Addison-Wesley.

Bishop, A.J. (1988) Mathematical Enculturation: A Cultural Perspective on Mathematics Education. London: Kluwer Academic Publishers.

Bitter, C.G. & Mikesell, J.L. (1980) Activities Handbook for Teaching with the Hand-Held Calculator. Boston: Allyn and Bacon, Inc.

Bolt, B. (1985). More Mathematical Activities. Cambridge: Cambridge University Press.

Brownell, G. (2nd ed) (1992) Computers and Teaching . St. Paul: West Publishing Company

Cathcart, W. G. (ed.) (1977). The Mathematics Laboratory: Readings from The Arithmetic Teacher. Reston, Virginia. National Council of Teachers of Mathematics.

Clewell, B. C. Anderson, B.T., & Thorpe, M.E. (1992) Breaking the Barriers: Helping Female and Minority Students Succeed in Mathematics and Science. San Francisco: Jossey-Bass Publishers.

Copeland, R.W. (4th ed.) (1984 How Children_Learn Mathematics: Teaching Implications of Piaget's Research. New York: Macmillan Publishing Company.

Court, N. A. (1958). Mathematics in Fun and in Earnest. New York: Dial Press

Driscoll, M. (1987) Stories of Excellence: Ten Case Studies from a Study of Exemplary Mathematics Programs. Reston, VA: National Council of Teachers of Mathematics.

Hill, J. M. (ed.) (1987). Geometry for Grades K-6: Readings from the Arithmetic Teacher. Reston, Virginia. National Council of Teachers of Mathematics.

Hohmann, C. (1990) Young Children and Computers. Ypsilanti, Michigan: The High/Scope Press.

Jensen, Robert J. (ed) (1993) Research Ideas for the Classroom: Early Childhood Mathematics. New York: Macmillan.

Kamii, C.K. (1985) Young Children Reinvent Arithmetic: Implications of Piaget's Theory. New York: Teachers College Press.

Krause, M. C. (1983). Multicultural Mathematics Materials. Reston, Virginia: National Council of Teachers of Mathematics.

Krulik, S. & Rudnick, J. A. (1980) Problem Solving: A Handbook for Teachers. Boston: Allyn and Bacon, Inc.

Mason, J. H. (1988). Learning and Doing Mathematics. London: Macmillan.

Morris, J. (1981) How to Develop Problem Solving Using a Calculator. Reston, VA: National Council of Teachers of Mathematics.

National Council Of Teachers of Mathematics. (1989) Curriculum and Evaluation Standards for School Mathematics. Reston, VA: The Council

National Council of Teachers of Mathematics. (1991) Professional Standards for Teaching Mathematics. Reston, VA: The Council.

National Council of Teachers of Mathematics. (1995) Assessment Standards for School Mathematics. Reston, VA: The Council.

National Council of Teachers of Mathematics Yearbooks.

National Research Council. (1989) Everybody Counts: A Report to the Nation on the Future of Mathematics Education. Washington, D.C.: National Academy Press.

Niman, J. (1985). A Teacher's Companion to Microcomputers. Lexington, Mass: D. C. Heath.

O'Daffer, O.G. (1988) Problem Solving: Tips for Teachers. Reston, VA: National Council of Teachers of Mathematics.

Owen, L.B. & Lamb, C.E. (1996) Bringing the NCTM Standards to Life. Princeton, N.J.: Eye on Education, Inc.

Owens, Douglas T. (ed) (1993) Research Ideas for the Classroom: Middle School Mathematics. New York: Macmillan.

Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books, Inc.

Phillips, J. (1995) Math Solutions: Problem Solving, Tools, and Applications. Syracuse: New Readers Press

Reesink, C.J. (ed.) (1985) Teacher-Made Aids for Elementary School Mathematics (vol, 2) Reston, VA: National Council of Teachers of Mathematics.

Ross, P. (1985) Logo Programming for the IBM PC. Reading, Mass.: Addison-Wesley Publishing Company.

Sachs, L. (ed.) (1988) Projects to Enrich School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Schwartz, J.E. & Riedesel, AC.A. (1994) Essentials of Classroom Teaching: Elementary Mathematics. Boston: Allyn and Bacon

Sharp, V.F. (2nd ed) (1994) HyperStudio in One Hour. Eugene, Oregon: International Society for Technology in Education.

Sheffield, L.J. & Cruikshank, D.E. (3rd ed) (1996) Teaching and Learning Elementary and Middle School Mathematics. Englewood Cliffs,N.j.: Prentice Hall

Smith, S.E. Jr. & Blackman, C.A. (eds.) (1974) Teacher-Made Aids for Elementary School Mathematics. (vol. 1) Reston, VA: National Council of Teachers of Mathematics.

Sobel, M.A. & Maletsky, E.M. (1988) Teaching Mathematics: A Sourcebook of Aids, Activities, and Strategies. (2nd ed.) Englewood Cliffs, N.J.: Prentice Hall.

State-adopted textbooks for North Carolina. (LT6 .N6 in Davis Library)

Tipps, S., Riordon, T.P., & Bull, G. (1984) Nudges: IBM Logo Projects.

Tobias, S. (1978) Overcoming Math Anxiety. Boston: Houghton Mifflin Co.

Tobias, S. (1987) Succeed with Mathematics. New York: College Entrance Examination Board.

Tobias, S. (1990) They're Not Dumb, They're Different. Tucson, Arizona: Research Corporation.

Troutman, A.P. & Lichtenberg, B. K. (1991) Mathematics, A Good Beginning: Strategies for Teaching Children. (4th ed.) Monterey, California: Brooks/Cole Publishing Company.

University of North Carolina Mathematics and Science Education Network. (1997) Teach-Stat Activities: Statistics Investigations for Grades 1-3. Palo Alto: Dale Seymour Publications.

University of North Carolina Mathematics and Science Education Network. (1997) Teach-Stat for Teachers. Palo Alto: Dale Seymour Publications.

University of North Carolina Mathematics and Science Education Network. (1997) Teach-Stat Activities: Statistics Investigations for Grades 3-6. Palo Alto: Dale Seymour Publications.

Wheeler, E. R. & Barnard, J. T. (1995) Activities Manual for Elementary School Teachers. Pacific Grove: Brooks/Cole.

Willoughby, S.S. (1990) Mathematics for a Changing World. Alexandria, VA: ASCD

 

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