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