Developing concepts in mathematics

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Developing concepts in mathematics

  1. 1. DEVELOPING CONCEPTS INMATHEMATICSCarlo Magno, PhDCollege of EducationDe 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 ISIMPORTANT
  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. Sequencing concept of number STAGE IN LEARNING THE early grouping 2 digit numbers CONCEPT OF WHOLE NUMBERS 3 digit numbers large numbers Numeration process number Numeration recognition principle place value Counting seriation The concept of Separation equivalence number Wholistic comparison and counting structure orderPrenumber renaming numeralsattribute recognition rounding numbersorting and classifying principlespatterning counting stagescomparison and order
  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 Patterning2 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 4 ones 8 tens 3 hundreds Base and values
  21. 21. NUMERATION PRINCIPLE Wholistic/Quantity aggregate Wholistic
  22. 22. NUMERATION PRINCIPLE Structure/Multiplicative relationship 111 1x1 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. HYPOTHESISSET A SET B 1  25 47 6 11 9 13  12 17
  29. 29. QUESTIONS TO FACILITATE THE CONCEPTATTAINMENT 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 The concept of Numeration Numeration attribute recognition number principle process sorting and classifying counting Counting number patterning numerals Separation recognition comparison and order number Wholistic place value principles structure seriation counting stages equivalence comparison and Sequencing order concept of number renaming early grouping rounding 2 digit numbers 3 digit numbers large numbers

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