Developing concepts in mathematics

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Developing concepts in mathematics

  1. 1. DEVELOPING CONCEPTS IN MATHEMATICS Carlo Magno, PhD College of Education De La Salle University, Manila
  2. 2. GET A PARTNER AND ANSWER THE QUESTION (5 MINUTES):  What are the important skills that students need to learn in mathematics?
  3. 3. 13 AREAS OF MATHEMATICS THAT IS IMPORTANT
  4. 4. 10 BASIC SKILLS IN MATHEMATICS (NCSM)
  5. 5. WHOLE NUMBER CONCEPTS  Skill for K to Year 2  K :  Year 1:  Year 2: Topic applicable for levels teaching whole number concepts Basic skills before computation skills
  6. 6. IN A PIECE OF PAPER..  Write the procedure how you can teach the concept of a number to grade 1 students…
  7. 7. TEACHING WHOLE NUMBER CONCEPTS  Payne and Rathmell Triangle  Relates the model (representation of the object) with language (name), and symbols in 6 relationships.  model --> language  language --> model  model --> symbol  symbol --> model  language --> symbol  symbol --> language
  8. 8. STAGE IN LEARNING THE CONCEPT OF WHOLE NUMBERS Prenumber attribute recognition sorting and classifying patterning comparison and order The concept of number counting numerals number principles counting stages Numeration principle Counting Separation Wholistic structure Numeration process number recognition place value seriation equivalence comparison and order renaming rounding Sequencing concept of number early grouping 2 digit numbers 3 digit numbers large numbers
  9. 9. PRENUMBER SKILLS  Attributes  Attribute recognition =
  10. 10. PRENUMBER SKILLS  Attributes  Matching objects =
  11. 11. PRENUMBER SKILLS  Attributes  Continuous-discreet Table Height Window weight Lights Speed chairs distance
  12. 12. PRENUMBER SKILLS  Sorting and classifying  Give me a number….  Label the “yes” and the “no” number…
  13. 13. PRENUMBER SKILLS  Patterning 2 2 4 4 6 6 __ __ A B C __ E __
  14. 14. PRENUMBER SKILLS  Comparison and order  Comparison (= or =, < or >)  Order (2, 4, 6, ___ or skip counting)
  15. 15. THE CONCEPT OF NUMBER  Counting
  16. 16. THE CONCEPT OF NUMBER  Numerals
  17. 17. THE CONCEPT OF NUMBER  Number principle
  18. 18. THE CONCEPT OF NUMBER  Counting stages
  19. 19. NUMERATION PRINCIPLE  Counting
  20. 20. NUMERATION PRINCIPLE  Numerical partitioning and position  384  Base and values 4 ones 8 tens 3 hundreds
  21. 21. NUMERATION PRINCIPLE  Wholistic/Quantity aggregate Wholistic
  22. 22. NUMERATION PRINCIPLE  Structure/Multiplicative relationship  111 1 x 1 10 X 1 10 x 10
  23. 23. NUMERATION PROCESS  Number recognition and place value  Reading and writing numbers  1,238 (read or vice versa)  3 ones, 8 hundreds, 2 tens, what is the value?
  24. 24. NUMERATION PROCESS  Seriation – determine the number that is one before or after  comparison – working the larger or saller (<, >)  Order – putting three or more numbers in sequence
  25. 25. NUMERATION PROCESS  Equivalence and renaming/regrouping  234 = 23 tens and 4 ones  234 = 234 ones  234 = 1 hundred 11 tens and 24 ones 100 110 + 24
  26. 26. NUMERATION PROCESS  Rounding and benchmarking  236 = 240  Show a number line that 236 is very near 240
  27. 27. SEQUENCING  Concept of number – numeral understanding and late operations  Early groupings – counting by 1s, counting by 5s, counting by 10s.
  28. 28. HYPOTHESIS SET A SET B  1  5  7  11  13  17  2  4  6  9  12
  29. 29. QUESTIONS TO FACILITATE THE CONCEPT ATTAINMENT  After observing the numbers, what is the difference of the two sets?  What are the characteristics of the first set? How about the second set?  Given the characteristics, how would you now define each set of numbers?  Give other examples of numbers for the first set, for the second set.  How did you arrive with the examples?  What guided you in coming up with the additional examples?
  30. 30. WORKSHOP  Create a math game tapping on the whole number concepts of learners Prenumber attribute recognition sorting and classifying patterning comparison and order The concept of number counting numerals number principles counting stages Numeration principle Counting Separation Wholistic structure Numeration process number recognition place value seriation equivalence comparison and order renaming rounding Sequencing concept of number early grouping 2 digit numbers 3 digit numbers large numbers
  31. 31. YOU CAN DOWNLOAD THIS SLIDE AT:  http://www.slideshare.net/crlmgn/developing- concepts-in-mathematics

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