This document outlines important concepts and skills in mathematics that students need to learn, according to the National Council of Supervisors of Mathematics (NCSM). It discusses 13 areas of mathematics and 10 basic skills, focusing on whole number concepts. These include prenumber skills like attribute recognition, sorting, patterning and comparison. It also discusses the stages of learning the concept of whole numbers, including counting, numerals, number principles and counting stages. The document provides examples for teaching these concepts to students in grades K-2.

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. 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. 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
 Base and values
4 ones
8 tens
3 hundreds

21. NUMERATION PRINCIPLE
 Wholistic/Quantity
aggregate
Wholistic

22. NUMERATION PRINCIPLE
 Structure/Multiplicative relationship
 111
1 x 1
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
 5
 7
 11
 13
 17
 2
 4
 6
 9
 12

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
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. YOU CAN DOWNLOAD THIS SLIDE AT:
 http://www.slideshare.net/crlmgn/developing-
concepts-in-mathematics