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DEVELOPING CONCEPTS IN MATHEMATICSCarlo Magno, PhD
College of Education
De La Salle University, Manila
GET A PARTNER AND ANSWER THE QUESTION (5 MINUTES):
What are the important skills that students need to learn in mathematics?
13 AREAS OF MATHEMATICS THAT IS IMPORTANT
10 BASIC SKILLS IN MATHEMATICS (NCSM)
WHOLE NUMBER CONCEPTS
Skill for K to Year 2 K : Year 1: Year 2:
Topic applicable for levels teaching whole number conceptsBasic skills before computation skills
IN A PIECE OF PAPER..
Write the procedure how you can teach the concept of a number to grade 1 students…
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
STAGE IN LEARNING THE CONCEPT OF WHOLE NUMBERS
Prenumberattribute recognition sorting and classifying patterningcomparison and order
The concept of numbercountingnumerals number principles counting stages
Numeration principleCounting SeparationWholisticstructure
Numeration processnumber recognition place value seriationequivalence comparison and order renaming rounding
Sequencingconcept of number early grouping2 digit numbers3 digit numberslarge numbers
PRENUMBER SKILLS
Attributes Attribute recognition
=
PRENUMBER SKILLS
Attributes Matching objects
=
PRENUMBER SKILLS
Attributes Continuous-discreet
Table Height
Window weight
Lights Speed
chairs distance
PRENUMBER SKILLS
Sorting and classifying
Give me a number…. Label the “yes” and the “no” number…
PRENUMBER SKILLS
Patterning
2 2 4 4 6 6 __ __A B C __ E __
PRENUMBER SKILLS
Comparison and order Comparison (= or =, < or >) Order (2, 4, 6, ___ or skip counting)
THE CONCEPT OF NUMBER
Counting
THE CONCEPT OF NUMBER
Numerals
THE CONCEPT OF NUMBER
Number principle
THE CONCEPT OF NUMBER
Counting stages
NUMERATION PRINCIPLE
Counting
NUMERATION PRINCIPLE
Numerical partitioning and position 384
Base and values
4 ones
8 tens
3 hundreds
NUMERATION PRINCIPLE
Wholistic/Quantity
aggregate
Wholistic
NUMERATION PRINCIPLE
Structure/Multiplicative relationship 111
1 x 1
10 X 1
10 x 10
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?
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
NUMERATION PROCESS
Equivalence and renaming/regrouping 234 = 23 tens and 4 ones 234 = 234 ones 234 = 1 hundred 11 tens and 24 ones
100110
+ 24
NUMERATION PROCESS
Rounding and benchmarking 236 = 240 Show a number line that 236 is very near
240
SEQUENCING
Concept of number – numeral understanding and late operations
Early groupings – counting by 1s, counting by 5s, counting by 10s.
HYPOTHESIS
SET A SET B
1 5 7 11 13 17
2 4 6 9 12
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?
WORKSHOP
Create a math game tapping on the whole number concepts of learners
Prenumberattribute recognition sorting and classifying patterningcomparison and order
The concept of numbercountingnumerals number principles counting stages
Numeration principleCounting SeparationWholisticstructure
Numeration processnumber recognition place value seriationequivalence comparison and order renaming rounding
Sequencingconcept of number early grouping2 digit numbers3 digit numberslarge numbers
YOU CAN DOWNLOAD THIS SLIDE AT:
http://www.slideshare.net/crlmgn/developing-concepts-in-mathematics
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