Teaching multiplication of numbers from 1 to 10 stkip surya students using matematika gasing slide iicma2013.josephine+sulis

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Table of Content

• Background

• Research Questions

• Theoretical Framework

Matematika GASING

Multiplication of Numbers from 1 to 100 using Matematika GASING

• Research Method

Design Research and Participants

An Overview of the Conjectured Local Instructional Theory

1. Concept of Multiplication

2. Multiplication of Number 1

3. Multiplication of Two Same Numbers



• Results and Analysis

Teaching Experiment

Restrospective Analysis

• Conclusion

• Reference

Background

• Multiplication is one of the most important mathematical topics to be learnt due to its many applications in our daily life.

• Students are still having difficulties in learning multiplication and division (Raharjo et al., 2009). They do not remember basic multiplication (multiplication of two numbers where each number is of one digit) which means multiplication of numbers 1 to 10.

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Research Questions

1. What is the learning trajectory of multiplication of numbers from 1 to 10 like using Matematika GASING?

2. How competent are STKIP Surya students in multiplication of numbers from 1 to 10?

3. How capable are they of teaching multiplication of numbers 1 to 10 using Matematika GASING?

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Matematika GASING

• GASING stands for Gampang, ASyIk dan menyenaNGkan, which is translated as easy, fun and enjoyable (Surya, 2012).

• There are three stages in learning mathematics using GASING: concrete, abstract, mental calculation.

Theoretical Framework:Matematika GASING

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Theoretical Framework:Multiplication of Numbers from 1 to 10 in Matematika GASING

• Multiplication is a mathematical operation which involves adding a number to itself a certain number of times.

• The result of adding a to itself b number of times is called the product of a by b. It is written as a × b or a.b or ab. It is also often called as “a times b”.

• The GASING Critical Point for Multiplication

Critical Point in GASING

1 2 3 45

1. Multiplication concept.2. Multiplication of numbers 1, 10, 9, 2 and 5.3. Multiplication of two same numbers.4. Multiplication of numbers 3 and 4.5. Multiplication of numbers 8, 7 and 6.

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Research Method:Design Research and Participants

Design Research

• There are three phases in conducting design research: (1) preliminary design, (2) teaching experiment, (3) retrospective analysis.

• This method allows researchers to analyze the actual process of students’ learning and mental activities performed when participating in the instructional activities in a classroom (Bustang, et al., 2013).

Participants

• 14 first year undergraduate students at the matriculation mathematics class of the academic year 2013 - 2014 at STKIP Surya of the study program of the Computer and Information Technology.

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Activity Main

Goals

Description of Activity Questions to be Asked Conjectures of Students’

Answers

Concept

of

Multipli-

cation.

Students

understand

the concept

of

multiplicati

on.

The teacher introduces

the meaning of

multiplication using

real objects such as

containers and

markers (concrete).

The teacher explains

the mathematical

writings of

multiplication

(abstract).

The teacher points out

the commutative law

for multiplication.

How to explain

multiplication;

what is 1 x 5; how

about 2 x 5?

Explain 6 x 3 and 3

x 6 using real

objects! What can

be deduced from

multiplication 6 x

3 and 3 x 6? Do

they have the same

meaning?

Multiplication is when

you add repeatedly; 1

x 5 means there are 5

number 1’s or 1

number 5; 2 x 5 means

there are 2 number 5’s

or 5 number 2’s.

Same results so same

meaning; same results

but not the same

concretely; same

results but different

calculations.

Research Method: An Overview of the Conjectured Local Instructional Theory

1. Multiplication Concept

Gampang, Asyik, dan Menyenangkan

Multiplication Concept

2 boxes containing 3 bananas written as 2 □3 2 x 3

3 boxes containing 5 pineapples written as 3 □5 3 x 5

Multiplication Concept

6 x 3 6 □3 = 3 + 3 + 3 + 3 + 3 + 3 = 18

3 x 6 3 □6 = 6 + 6 + 6 = 18


Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Multipli-

cation of

Number 1.

Students

understand, able

to compute and

teach

multiplication of

number 1.


multiplication of

number 1 concretely.


the mathematical

writings of

multiplication of

number 1 (abstract).

The teacher

encourages students to

pick up on the pattern

of the results of

multiplication of

number 1; this helps

students to memorize

the multiplication

easily.

Anyone knows how to

explain multiplication

of number 1

concretely?

What is the next stage

after explaining

concretely? How to

teach multiplication of

number 1 at this stage?

What can be deduced

from the results of this

multiplication so that

theycan be memorized

easily?

Yes – one or two

students are

encouraged to come

forward and explain

using concrete objects;

no.

Abstract stage – just

write the numbers and

the multiplication

results; no answers.

The results are the

numbers themselves;

there is a difference by

1; just add 1 to each

result in ascending

order; no answers.

Activity Main Goals Description of Activity Questions to be Asked Conjectures of

Students’ Answers



Concrete1 x 10 = 1 □10 = 10

2 x 10 = 2 □10 = 10 + 10 = 20

3 x 10 = 3 □10 = 10 + 10 + 10 = 30

4 x 10 = 4 □10 = 10 + 10 + 10 + 10 = 40

5 x 10 = 5 □10 = 10 + 10 + 10 + 10 + 10 = 50

6 x 10 = 6 □10 = 10 + 10 + 10 + 10 + 10 + 10 = 60

7 x 10 = 7 □10 = 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70

8 x 10 = 8 □10 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 80

9 x 10 = 9 □10 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 90

10 x 10 = 10 □10 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 100


Multiplication of Number 1

Abstract1 x 10 = 10

2 x 10 = 20

3 x 10 = 30

4 x 10 = 40

5 x 10 = 50

6 x 10 = 60

7 x 10 = 70

8 x 10 = 80

9 x 10 = 90

10 x 10 = 100



Mental Calculation (Seeing the pattern)

1 x 10 = 10

2 x 10 = 20

3 x 10 = 30

4 x 10 = 40

5 x 10 = 50

6 x 10 = 60

7 x 10 = 70

8 x 10 = 80

9 x 10 = 90

10 x 10 = 100



Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference


Students’ Answers

Multipli-

cation of

two same

numbers.

Students

understand,

able to

compute and

teach

multiplication

of two same

numbers.


multiplication of two same

numbers concretely.

The teacher explains the

mathematical writings of

multiplication of two same

numbers (abstract).

The teacher encourages

students to find a way to

memorize the results

easily.

Based on what you

have learnt about

multiplication of

numbers 1, 10, 9, 2

and 5 so far; anyone

knows how to explain

multiplication of two

same numbers?

How about the abstract

stage?

How would you

memorize the results?

Yes – one or two

students are encouraged

to come forward and

explain using concrete

objects; no.

Just write down the

results.

Just memorize the

results; by recognizing

the patterns.




Concrete

1 x 1 = 1 □1 = 1

2 x 2 = 2 □2 = 2 + 2 = 4

3 x 3 = 3 □3 = 3 + 3 + 3 = 9

4 x 4 = 4 □4 = 4 + 4 + 4 + 4 = 16

5 x 5 = 5 □5 = 5 + 5 + 5 + 5 + 5 = 25

6 x 6 = 6 □6 = 6 + 6 + 6 + 6 + 6 + 6 = 36

7 x 7 = 7 □7 = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49

8 x 8 = 8 □8 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 64

9 x 9 = 9 □9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 81

10 x 10 = 10 □10 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 100

Multiplication of Two Same Numbers


Abstract1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100



Mental Calculation

1 x 1 = 1 (multiplication of number 1)


3 x 3 =

4 x 4 =




3 + 3 = 6 6 + 3 = 9

4 + 4 = 8 8 + 8 = 16

9

16



Mental Calculation1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

6 x 6 = 36

7 x 7 = 49

8 x 8 = 64


Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference


Students’ Answers

Multipli-

cation of

number 3.

Students

understand,

able to

compute and

teach

multiplication

of number 3.


multiplication of

number 3

concretely.


the mathematical

writings of

multiplication of


The teacher

encourages students

to find a way to

memorize the

results easily.

How do you

explain

multiplication of

number 3

concretely?

How about the

mathematical

writings?

How would you

memorize the

results?

For examples: 1 x 3

means there is 1 box

containing 3 markers

or 3 stones, 2 x 3

means there are 2

boxes containing 3

markers or 3 stones

each, etc.; no answers.

Just write down the

results.

Just memorize the

results; by

recognizing the

patterns; by using

fingers.




Concrete1 x 3 = 1 □3 = 32 x 3 = 2 □3 = 3 + 3 = 63 x 3 = 3 □3 = 3 + 3 + 3 = 94 x 3 = 4 □3 = 3 + 3 + 3 + 3 = 125 x 3 = 5 □3 = 3 + 3 + 3 + 3 + 3 = 156 x 3 = 6 □3 = 3 + 3 + 3 + 3 + 3 + 3 = 18 7 x 3 = 7 □3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 8 x 3 = 8 □3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 249 x 3 = 9 □3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27

10 x 3 = 10 □3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 30



Abstract1 x 3 = 3

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

6 x 3 = 18

7 x 3 = 21

8 x 3 = 24

9 x 3 = 27

10 x 3 = 30




2 x 3 = 6

3 x 3 = 9

4 x 3 =

5 x 3 = 15

9 x 3 = 27

10 x 3 = 30


3 + 3 = 6 6 + 6 = 12



2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

6 x 3 = 18

7 x 3 = 21

8 x 3 = 24

9 x 3 = 27

10 x 3 = 30



The Song of The Multiplication of Number 3

• Tiga enam sembilan dua belas

• Lima belas delaapan belas

• Dua satu dua puluh empat

• Dua tujuh itu perkalian tiga

(music: Bintang Kecil - the Little Star)



A Card Game

6

18

8

24

7

21


Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference


Students’ Answers

Multipli-

cation of

number

8.

Students

understand,

able to

compute and

teach

multiplication

of number 8.


multiplication of

number 8 concretely.


the mathematical

writings of

multiplication of


The teacher

encourages students

to find a way to

memorize the

results easily.

How do you explain

multiplication of

number 8

concretely?

How about the

mathematical

writings?

How would you

memorize the

results?

For examples: means

there is 1 box

containing 8 apples or

8 bananas, means

there are 2 boxes

containing 8 apples or

8 bananas each, etc.;

no answers.

Just write down the

results.

Just memorize the

results; by recognizing

the patterns; by using

fingers; by using card

games; by singing

songs.




Concrete1 x 8 = 1 □8 = 82 x 8 = 2 □8 = 8 + 8 = 163 x 8 = 3 □8 = 8 + 8 + 8 = 244 x 8 = 4 □8 = 8+ 8 + 8 + 8 = 325 x 8 = 5 □8 = 8 + 8 + 8 + 8 + 8 = 406 x 8 = 6 □8 = 8 + 8 + 8 + 8 + 8 + 8 = 48 7 x 8 = 7 □8 = 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56 8 x 8 = 8 □8 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 649 x 8 = 9 □8 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 7210 x 8 = 10 □8 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 80



Abstract1 x 8 = 8

2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

5 x 8 = 40

6 x 8 = 48

7 x 8 = 56

8 x 8 = 64

9 x 8 = 72

10 x 8 = 80




2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

5 x 8 = 40

6 x 8 = 48

7 x 8 = 56

8 x 8 = 64

9 x 8 = 72

10 x 8 = 80

6 x 8 = 48


Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Result and Analysis: Teaching Experiment

• Conjectured local instructional theory was used as a guidance for the teacher and the researchers to refer to whilst conducting the actual experiment.

• An episode of teaching the concept of multiplication:Teacher : What is multiplication?Raja : Repetitive addition.Every students agreed that multiplication is repetitive addition. The teacher asked the next question.Teacher : What does it mean by 3 x 5 ? Raja & Nyong : Keep adding number 3 for 5 times.Ferry : Add number 5 for 3 times.There are obviously two different understandings.

Continued episode:•The teacher then explained 3 x 5 by showing three cards with

pictures of 5 bananas on each card to illustrate multiplication 3 x 5.

•The teacher also explained using picture cards that 2 x 5 and 5 x 2 had same results but different meanings.

Result and Analysis: Teaching Experiment

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• Reference

Result and Analysis: Analysis RetrospectiveI. Tests to measure computational

competenceTests Results:

• Written Test (100 questions): Average score 94 out of 100 Average time 5 minutes 6

seconds• Oral Test (50 questions)

Average score 42.50 out of 50 Average time 3 minutes 8

seconds

A Few Points of Observations:

•The results in I indicates that students could do multiplication of numbers

from 1 to 10 well both orally and in writings

•The result of written test in II contrasted the result of microteaching test. This

showed that students tended to find it more difficult to write the learning

process materials as opposed to delivering them orally

•There was a student who performed poorly during microteaching test, it was

discovered that she did not even understand addition - a material taught and

supposed to be mastered prior to multiplication. In this case she should go

back and restart from addition.

II. Tests to measure capability of teaching

Tests Results:• Written Test (5 questions, 60

minutes):Average score 43.57 out of 100

• Microteaching Test (20 minutes each)Average score 83.04 out of 100

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• References

Conclusion

1. Matematika GASING helped students to understand the concept of multiplication better.

2. Matematika GASING was able to create a fun and exciting environment when learning multiplication of numbers from 1 to 10; students were enthusiastic in participating in the activities.

3. Students were able to calculate and perform mental calculation of multiplication of numbers from 1 to 10 as well as teaching the materials relatively well.

4. The revised local instructional theory should contain added activities such as drilling at the end of every session as well as activities that focus on the emphasis of the ways of memorizing multiplication of numbers from 1 to 10.

5. Further research can be done to implement and test the revised local instructional theory. Other research can be done to investigate the problems students have with their mathematical writing skills.

Table of Content

• Background



Matematika GASING


• Research Method









Teaching Experiment


• Conclusion

• References

References

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[2] Bustang, Zulkardi, Darmawijoyo, Dolk, M. and van Eerde, D., 2013, Developing a Local Instruction Theory for Learning the Concept of Angle through Visual Field Activities and Spatial Representations, International Education Studies Vol. 6 No. 8, 58-70.

[3] Ibrahim and Suparmi, 2012, Pembelajaran Matematika Teori dan Aplikasinya, SUKA-Press, Yogyakarta.

[4] Gravemeijer, K., 2009, Local Instruction Theories as Means of Supports for Teachers in Reform Mathematics Education, Mathematical Thinking and Learning Journal Vol. 6 No. 2, page 105 – 128.

[5] Gravemeijer, K. and van Eerde, D., 2009, Design Research as a Means for Building a Knowledge Base for Teachers and Teaching in Mathematics Education, The Elementary School Journal Vol. 109 No. 5, 510-524.

[6] Raharjo, M., Waluyati, A., Sutanti, T., 2009, Pembelajaran Operasi Hitung Perkalian dan Pembagian Bilangan Cacah di SD, Depdiknas: Pusat Pengembangan dan Pemberdayaan Pendidikan dan Tenaga Kependidikan (PPPPTK) Matematika.

[7] Reys, B. J., 1985, Mental Computation, The Arithmetic TeacherVol. 32 No. 6 (1985), 43-46.

[8] Surya, Y. and Moss, M., 2012, Mathematics Education in Rural Indonesia, Proceeding in the 12th International Congress on Mathematics Education: Topic Study Group 30, 6223-6229.

[9] Surya, Y., 2013, Modul Pelatihan Matematika GASING SD Bagian 1, PT. Kandel, Tangerang.

[10] Van den Akker, J., Gravemeijer, K., McKenney, S., and Nieveen, N., 2006, Educational Design Research, Routledge, Taylor and Francis Group, Abingdon.

References