1. DEVELOPING CONCEPTS IN
MATHEMATICS
Carlo Magno, PhD
College of Education
De La Salle University, Manila

2. GET A PARTNER AND ANSWER THE QUESTION
(5 MINUTES):
 What are the important skills that students need to
learn in mathematics?

3. 13 AREAS OF MATHEMATICS THAT IS
IMPORTANT

4. 10 BASIC SKILLS IN MATHEMATICS (NCSM)

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. IN A PIECE OF PAPER..
 Write the procedure how you can teach the concept
of a number to grade 1 students…

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. 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 order
Prenumber renaming
numerals
attribute recognition rounding
number
sorting and classifying
principles
patterning
counting stages
comparison and order

9. PRENUMBER SKILLS
 Attributes
 Attribute recognition
=

10. PRENUMBER SKILLS
 Attributes
 Matching objects
=

11. PRENUMBER SKILLS
 Attributes
 Continuous-discreet
Table Height
Window weight
Lights Speed
chairs distance

12. PRENUMBER SKILLS
 Sorting and classifying
 Give me a number….
 Label the “yes” and the “no” number…

13. PRENUMBER SKILLS
 Patterning
2 2 4 4 6 6 __ __
A B C __ E __

14. PRENUMBER SKILLS
 Comparison and order
 Comparison (= or =, < or >)
 Order (2, 4, 6, ___ or skip counting)

15. THE CONCEPT OF NUMBER
 Counting

16. THE CONCEPT OF NUMBER
 Numerals

17. THE CONCEPT OF NUMBER
 Number principle

18. THE CONCEPT OF NUMBER
 Counting stages

19. NUMERATION PRINCIPLE
 Counting

20. NUMERATION PRINCIPLE
 Numerical partitioning and position
 384
4 ones
8 tens
3 hundreds
 Base and values

21. NUMERATION PRINCIPLE
 Wholistic/Quantity
aggregate
Wholistic

22. NUMERATION PRINCIPLE
 Structure/Multiplicative relationship
 111
1x1
10 X 1
10 x 10

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. 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. 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. NUMERATION PROCESS
 Rounding and benchmarking
 236 = 240
 Show a number line that 236 is very near 240

27. SEQUENCING
 Concept of number – numeral understanding and
late operations
 Early groupings – counting by 1s, counting by 5s,
counting by 10s.

28. HYPOTHESIS
SET A SET B
 1  2
5 4
7 6
 11 9
 13  12
 17

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. 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