Sir Victor Raymundo-9b-The-Concept-of-Number_Operations-on-Whole-Number.pptx

ppt

1. How Children Learn Math: The Concept of Number (Operations) Community of Learners Foundation

2. Is Arithmetic = Mathematics ? Community of Learners Foundation Arithmetic is the study of numbers. Mathematics is a way of thinking in logical or organized way. *Math is not a subject or a set of facts that needs to be memorized for a test. Math involves solving problems.

3. THE FOUNDATION: COUNTING Understanding of arithmetic evolves from children’s early counting experiences. Informal concept of addition (adding more) and subtraction (taking away something) guide children’s efforts to construct informal arithmetic procedures. Community of Learners Foundation

4. When knowing ‘facts’ is the objective, children are taught techniques to get ‘facts’ and are drilled to internalize them. (traditional addition) When a child learns to add quantities by using his own logic, repeats the same action every day in interaction with other people (e.g. while at play), he will inevitably remember the result, without adult pressure. Community of Learners Foundation ADDITION as an OBJECTIVE

5. The objective in subtraction, as in addition, should be to encourage children to think and to remember results of their own thinking. Once children have constructed sums and have committed them to memory, they are able to express this knowledge in subtraction. Community of Learners Foundation SUBTRACTION as an OBJECTIVE

6. THE LOGIC OF ADDITION & SUBTRACTION Community of Learners Foundation The understanding of addition and subtraction involves: the logic of inclusion reversibility of thought

7. The Concept of Three (Concept Level) “Ilang kulisap ang nasa kaliwang kamay? Ilang kulisap ang nasa kanang kamay? Ilan lahat ng kulisap?” Hand Game Community of Learners Foundation

8. The Concept of Three (Concept Level) “Ilang kulisap ang nasa ibabaw ng mangkok? Ilang kulisap ang nasa ilalim ng mangkok? Ilan lahat ng kulisap?” Lift the Bowl Community of Learners Foundation

9. The Concept of Three (Concept Level) “Ilang kulisap ang nasa labas ng bahay? Ilang kulisap ang nasa loob ng bahay? Ilan lahat ng kulisap?” Peek Thru The Wall Community of Learners Foundation

10. Stages of Concept Development Community of Learners Foundation Level Teacher … Children … Concept Level ... tells number stories or gives verbal instructions (in the mother tongue) ... manipulate concrete materials

11. Stages of Concept Development Community of Learners Foundation Level Teacher … Children … Connecting Level ... continues to give verbal instructions or tell number stories ... introduces writes mathematical symbols (e.g. numerals) ... introduces mathematical language (e.g. number words in English) ... continue to manipulate concrete materials ... read mathematical symbols

12. The Concept of Three (Connecting Level) “Anong numero ang ilalagay mo sa kaliwang kamay? Anong numero ang ilalagay mo sa kanang kamay? Basahin natin ang nakasulat sa counting mat.” Hand Game Community of Learners Foundation

13. The Concept of Three (Connecting Level) “Anong numero ang ilalagay sa ibabaw ng mangkok? Anong numero ang ilalagay sa ilalim ng mangkok? Basahin natin ang nakasulat sa counting mat.” Lift the Bowl Community of Learners Foundation

14. The Concept of Three (Connecting Level) “Anong numero ang ilalagay sa labas? Anong numero ang ilalagay loob? Basahin natin ang nakasulat sa counting mat.” Peek Thru The Wall Community of Learners Foundation

15. Stages of Concept Development Community of Learners Foundation Level Teacher … Children … Symbolic Level ... continues to give verbal instructions or tell number stories … introduces and writes more mathematical symbols (e.g. + − =) … introduces more mathematical language (e.g. plus, minus, equals) ... continue to manipulate concrete materials ... continue to read symbols ... begin to record or write symbols

16. Hand Game worksheet Community of Learners Foundation

17. Lift the Bowl worksheet Community of Learners Foundation

18. Peek Thru the Wall worksheet Community of Learners Foundation

19. More Counting: Counting Groups “May 2 lababo sa kusina. Sa bawa’t lababo ay maroong tig-4 na maruruming plato. Ilang plato lahat ang kailangang hugasan?” Beginning Multiplication (Concept Level) Community of Learners Foundation

20. BEGINNING MULTIPLICATION Community of Learners Foundation The process of multiplication requires children to think about and count groups of objects rather than single objects. Terms such as stacks of, rows of, groups of, and NOT ‘times’, help children think and visualize problems

21. More Counting: Counting Groups “Mayroong 10 upuan at 2 mesa sa hardin. Ilang upuan ang maaring ilagay sa bawa’t mesa?” Beginning Division (Concept Level) Community of Learners Foundation

22. BEGINNING DIVISION Community of Learners Foundation Two situations that call for division: The grouping process is the dividing of a quantity of objects into smaller groups of a particular size to determines the number of groups that can be made. The sharing process is the dividing of a quantity of objects into a particular number of groups to determine the number of objects in each group.

23. The Logic of Multiplication and Division Community of Learners Foundation The understanding of multiplication (and division) involves: an understanding of the one-to-one correspondence or equivalence of two or more sets (multiplicative equivalence) reversibility of thought

24. More Number Concepts (Multiplication- Connecting Level) Community of Learners Foundation Sinks Plates in each sink All plates 2 3 2 2 2 4 2 1 2 5

25. More Number Concepts (Division - Connecting Level) Community of Learners Foundation Chairs Tables Chairs in each table Remainder 8 2 7 2 4 2 6 2 9 2

26. COORDINATED ACTION ON OBJECTS SERIAL ORDER ORDINAL NUMBER NUMBER ONE-to-ONE CORRESPONDENCE CLASS INCLUSION CONSERVATION CARDINAL NUMBER MULTIPLICATION DIVISION ADDITION SUBTRACTION Community of Learners Foundation

27. QUESTIONS Community of Learners Foundation Why is it important to teach mathematics for children in a logical way rather than teaching a series of rules to memorize? How do children learn the operation of number using his own logic without adult pressure?

28. ARITHMETIC ≠ RULES Arithmetic should not be taught as a series of rules because: Rules are easy to forget Rules minimize thinking. Rules prevent visualizing relationships. Rules do not work well for problem-solving 2 nd grade students selling potato balls at the curriculum fair Community of Learners Foundation

29. REFLECTIONS Community of Learners Foundation What developmentally appropriate activities have you provided your learners in the past months? What gains might learners acquire if we provide more hands-on/concrete activities? What possible difficulties might be encountered when providing more hands-on activities? What classroom management skills would a teacher need to have in order to manage a class that is involved in more hands-on activities?

30. Develop a solid base (informal understanding) before introducing written symbolism. Structure informal calculational experiences to promote discovery. Help children see that formal symbolism is an explicit expression of their informal knowledge. Sequence formal mathematics to exploit children’s informal knowledge. Community of Learners Foundation EDUCATIONAL IMPLICATIONS

31. THERE ARE NO SHORT CUTS TO LEARNING MATH Community of Learners Foundation

32. References: Community of Learners Foundation Association for Supervision and Curriculum Development. The Brain and Mathematics. Association for Supervision and Curriculum Development Press, Alexandria, Virginia, 2001. Baratta-Lorton, Mary. Mathematics Their Way. Addison-Wesley Publishing Company, Menlo Park, California, 1976. Baratta-Lorton, Robert. Mathematics a Way of Thinking. Addison-Wesley Publishing Company, Menlo Park, California, 1977. Baroody, Arthur. Children’s Mathematical Thinking. A Developmental Framework for Preschool, Primary and Special Education Teachers. Teachers College Press, New York, 1987. Burns, Marilyn. About Teaching Mathematics, a K-8 Resource, 2 nd edition. Math Solutions Publications, Sausalito, California, 2000. Copeland, Richard. How Children Learn Mathematics . Teaching Implications of Piaget’s Research. MacMillan Publishing Co., Inc. 1979 Hohmann, Mary and David P. Weikart. Educationg Young Children. Activve Learning Practices for Preschool and Child Care Programs. High Scope Press, Ypsilanti, Michigan, 1995. Kamii, Constance Kazuko. Young Children Reinvent Arithmetic. Implication of Piaget’s Theory. Teachers College Press, New York, New York, 1984. Moomaw, Sally and Brenda Hieronymus. More Than Counting, Whole Math Activities for Preschool and Kindergarten . Redleaf Press, St.Paul, MN. 1995. Sousa, David. How the Brain Learns Mathematics . Corwin Press, California. 2008 Stenmark, Jean Kerr, Virginia Thompson and Ruth Cassey. Family Math . Regents, University of California, 1986. • • • • •