Developing Mathematical Problem Solving to Prepare theImplementation of Lesson Study of Mathematics Teachingin Indonesian Schools of Disaster Area
To be presented atAPEC- Tsukuba International Conference VI:
Innovation of Mathematics Education through Lesson Study
Challenges to Emergency Preparedness for Mathematics
February, 14-18, 2012
Tsukuba-Tokyo, Japan
By

Marsigit, Djamilah B.W., R. Rosnawati
Department of Mathematics Education, Faculty of Mathematics and Science, Yogyakarta State
University Indonesia

Data of Earthquake in Indonesia at the Last Century(Source: YMBI, 2011)

Data of Casualties in Bantul’s Earthquake 2006
(Source: IRP, 2009)

Damage and Impact of Yogyakarta and Central Java
Earthquake (Bantul) 2006
(Source: Bappenas in Yoyok Wahyu Subroto, 2006)

Damage and Impact of Yogyakarta and Central Java
Earthquake (Bantul) 2006

Source: Yuwono Sri Suwito in Yoyok Wahyu
Subroto, 2009

Source: Yuwono Sri Suwito in Yoyok Wahyu
Subroto, 2009

Source: Fenty Yusdayanti in Yoyok Wahyu
Subroto, 2009

Source: Fenty Yusdayanti in Yoyok Wahyu
Subroto, 2009

Priority areas for disaster risk
reduction that must be addressed:• Ensure that disaster risk reduction is a national and alocal priority with a strong institutional basis forimplementation• Identify, assess and monitor disaster risks and enhanceearly warning• Use knowledge, innovation and education to build aculture of safety and resilience at all level• Reduce underlying risk factors• Strengthen disaster preparedness for effective
response at all levels(T. Yoyok Wahyu Subroto, 2009)

Various Related Lesson Study Activities in
Schools of Disaster Area
IMSTEP – before the 2006’s earthquake(1999-2004)

In Bantul District, before the 2006’s earthquake disaster, it wasimplemented the Lesson Study activities under IMSTEP_JICA project.
This project was supported by three universities UPI Bandung, UNY
Yogyakarta, and UM Malang. The implementation of lesson study hassome impacts as follows:• (1) collaboration, collegiality, and communication among teachers
and lecturers are formed,• (2) Implementation of research lesson is opened to be observed byothers,• (3) Mathematics lecturers directly involved in mathematics
instruction in school,• (4) Mathematics teachers association is more empowered

Various Related Lesson StudyActivities in Schools of Disaster AreaSISTTEMS – after the 2006’s earthquake• JICA has supported to implement Program forStrengthening In-service Teacher Training for Science andMathematics (SISTTEMS, 2006-2008), in the disaster area ofBantul.
• It targeted all junior secondary science and mathematics
teachers in three districts and restructured the district levelin-service teacher training by introducing Lesson Study(LS).
• This program takes advantage of results and experiences ofthe previous projects and programs, and aims todisseminate Lesson Study models extensively in the nation.

Various Related Lesson Study
Activities in Schools of Disaster Area
SBLS (School Based Lesson Study) – after the 2006’searthquake• Lesson Study activities have been diffused in Bantul district
after the event of 2006 earthquake disaster. It wasconducted by PELITA in collaboration with JICA.
• Resource Persons are from among the principals, teachers,
officials from Dinas P&K, and lecturers from resource
universities from three districts who have an eye to observe
lessons, who can make good comments on the essence ofstudents’ learning in reflection, and who have experience inimplementing LSBS activities in their own schools.

Indonesian Competencies onMathematics
In Indonesia, the curriculum outlines the aims of teaching learning ofmathematics are as follows:(1) to understand the concepts of mathematics, to explain therelationships among them and to apply them to solve theproblems accurately and efficiently,(2) to develop thinking skills to learn patterns and characteristics ofmathematics, to manipulate them in order to generalize, to proof
and to explain ideas and mathematics propositions,(3) to develop problems solving skills which covers understanding theproblems, outlining mathmatical models, solving them andestimating the outcomes,(4) to communicate mathematics ideas using symbols, tables,
diagrams and other media, and(5) to develop appreciations of the uses of mathematics in daily lifes,
curiosity, consideration, and willingness to learn mathematics aswell as tough and self-confidence.

Developing Problem Solving Based Teaching
Learning Processes for Schools in Disaster Area
To promote problem solving based mathematics teachinglearning processes in the schools of disaster area, weneed:
1. to make good atmosphere for teaching and learning,
2. to promote to implement various teaching methods andteaching learning resources,
3. to give the chances for their students to perform theirinitiatives,
4. to promote cooperative learning, and5. to support the students to be the active learner.
6. to improve awareness of problem solving approach.

Strategies for Problem Solving
Activities
The strategies for problem solving activities in mathematics
consist of:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

Trial and Error,
Making diagram,
Trying the simple problem,
Making Table,
Finding the pattern,
Breaking down the goal,
Considering the possibilities,Thinking Logically ,Reversing the Order, andIdentifying the impossibility.

Polya and Pasmep (in Fajar Shadiq:2004:13)

The Criteria for the Problem Solving
based Mathematics Textbook
Problem solving based mathematics textbook should meet the following
criteria:• It should motivate the students to learn mathematics• It should develop students’ oriented teaching learning of mathematics• It should support of achieving learning objective• It should employ flexible teaching learning method• It should facilitate students’ need to learn mathematics• It should facilitate the students to do exercise mathematics• It should dealing with the students’ difficulties in learning mathematics• It should consist of summary• It should as a communicative writing• It should develop the cognitive schema of learning mathematics• It should be as a students’ learning oriented• It encourage the students to solve mathematics problems
Marsigit, 2010

Prospective Teachers are to Identify theMathematical Problems Arising from the Area ofDisaster
Prospective Teachers:
1. They are undergraduate students of Mathematics
Education Department, Faculty of Mathematics andScience, Yogyakarta State University
2. They are the inhabitant of disaster area ofearthquake
3. They had various experiences of life as the impactof earthquake disaster in Bantul district.

The Prospective Teachers Were Preparing to Develop
Mathematical Problems Reflecting their Own
Experiences of Earthquake DisasterSamples of Developed Disaster Related
Mathematics Problems and Its Solution
Problem 1:
The goverment has calculate the budget about Rp 11
billions for two village which be the victim of earthquake.
The budget for the first village Rp 4,5 billions, and for thesecond village Rp 6,5 billions. The first village consist of295 broken houses in easy category and 162 broken
houses in serious category. The second village consist of518 broken houses in easy category and 192 broken
houses in serious category. So, how much the number ofhelp which will be received for every broken houses ineasy and serious category.

Samples of Developed Disaster Related
Mathematics Problems and Its Solution•••••••••••••••••

Solution of Problem 1:For example the broken houses in easy category is x and the broken houses in serious category is y. Therefore themathematical models are
295x + 162y = 4500000000
518x + 192y = 6500000000
Then, the ellimination method
295 x + 162y = 4500000000 × 192
518 x + 192y = 6500000000 × 162
56640 x + 31104y = 864000000000
83916 x + 31104y = 1053000000000 (-)-27276x = - 189000000000
x = 6929168,5
x = 6929168,5
To find the value of y, we can use the substitution method. Sustitute value of x in first equation.

•295 x + 162 y= 4500000000
295(6929168,5) + 162 y = 4500000000
204410478 + 162 y= 4500000000
162 y = 4500000000 - 204410478
162 y = 2455895293
y= 2455895293 : 162y= 15159847,48•Therefore, every broken house in easy category gets about Rp 7 billions and every broken house in serious category gets
about Rp 15 billions.

Samples of Developed Disaster Related
Mathematics Problems and Its Solution
Problem 2:
The earthquake which happened in Yogyakarta about
five years ago made a lot of victims. More than one
hundred thousand people were dead, and more than
one thousand houses were broken. Goverment help
the victim of Earthquake in Yogyakarta by a lot of way.
One of them is give the victims money to build up
again their home. If a home can finished about sixty
days with twelve bricklayers. Because something
reason, a home have to finish for 40 days. How many
bricklayers have to seek to make a home? how to solve
this problem?

Samples of Developed Disaster Related
Mathematics Problems and Its Solution•••

Solution of Problem 2:
To solve this problem, we need mathematics. We knoew that a home can be finishabout sixty days with twelve bricklayers. But, we must finish a home for fourty
days. To solve this problem, we use the way:DaysBricklayers

601240x

the multiplisation days (1) equals to days (2)so 60 . 12 = 40 . X
x = 60.12/40
by cancel out sixty and fourty, we find that x equals to one point five times twelve
So, x =1,5 . 12
x = 18that is the last of equality (x =18). So, a home have to finish for 40 days with 18
bricklayers. We have twelve bricklayers. So, we must find six bricklayers again to
help twelve bricklayers the other. That us all, so simple and interesting. It isbecause mathematics.

Samples of Developed Disaster Related
Mathematics Problems and Its Solution
Problem 3:
In 2006 an earthquake occurred quite terrible
in Yogyakarta are children / toddlers. Many
refugees everywhere, covering an area ofrefuge is an area of 350 m2 only inhabited by5600 people. 15% resi% of them are parents /seniors. What is the density of the inhabitantsof refugee camps and how many people
whether refugees are teenagers and adults?

Samples of Developed Disaster Related
Mathematics Problems and Its Solution• Solution for Problem 3:
Broad camps: 350
Number of refugees: 5600
Percentage of children under five: 15%
Percentage of seniors: 20%
Question:
The density of refugees in the refugee camps and how many of areteenagers and adult ?
Answer:Density = the number of refugees displaced / refugee area
Displacement density = 5600 / 35 = 16 people per square meter
Percentage of refugee teens: 100% - (15% + 20%) = 100% - 35% =65%
The number of displaced adolescents and adults
65% × 5600 = 3640 peopleSamples of Developed Disaster Related
Mathematics Problems and Its Solution
Problem 5:
In a natural disaster victims will inevitably arise thatneed help, either in money or materials. In anearthquake there were approximately 300 victims who
have not had time to save their possessions and forced
to flee to a place of refuge. Of course the government
should participate in funding assistance to the victims.
In terms of food, the government should provide
adequate funding so that all victims can eat 3 times aday. If the government has 135 million rupiahs to funds
the foods for the victims in a month, then what price amaximum of 1 pack of rice so that each victim can eat
3 times a day in a month?

Samples of Developed Disaster Related
Mathematics Problems and Its Solution
Solution for Problem 5:
Number of victims = 300
Eat frequency = 3 times
Number of funds = 135000000
The length of victims displaced = 30 days
To be asked:
Maximum price of rice packets to every victim can eat three times a day?
Solution:
Will look for the maximum price of rice packs that every victim can eat three times a day.
Maximum price of rice packets is directly proportional to the available funds and inversely
proportional to the number of victims, frequency of meals, and duration of displaced victims.
In mathematics can be formulated as follows:
Take any variable to represent the maximum price of rice packs, eg "A". then:
A= Number of funds divide by (number of victims times eat frequency times the length ofvictims displaced)A = 135000000 : (300 x 3 x 30)
A = 135000000
27000
A = 5000
So, the maximum price of rice packets is 5000 rupiahs.

Samples of Developed Disaster Related
Mathematics Problems and Its Solution
Problem 6:
In the little region had been happen earthquake. The
houses of the people in there break down. Then theybuild evacuation tents. The total of the tents is three.
In the first tent dwelt by five person, the second tent
dwelt by seven person, and the third tent dwelt by
eight person. In the next day, a donor bring 40 piecesof noodles, 100 kg of rice, and 80 eggs. Then he wants
to apportion his contribution and he calculates it. Howmany the donor give his contribution to each tent?

Samples of Developed Disaster Related
Mathematics Problems and Its Solution
Solution for Problem 6:

First, the total of the contribution for the first tent as follows:- noodles: (5/(5+7+8)) x 40 pieces = (5/20) x 40 pieces = 10 pieces- rice : (5/(5+7+8)) x 100 kg = (5/20) x 100 kg = 25 kg- eggs : (5/(5+7+8)) x 80 eggs = (5/20) x 80 eggs = 20 eggs
Second, the total of the contribution for the second tent as follows:- noodles: (7/(5+7+8)) x 40 pieces = (7/20) x 40 pieces = 14 pieces- rice : (7/(5+7+8)) x 100 kg = (7/20) x 100 kg = 35 kg- eggs : (7/(5+7+8)) x 80 eggs = (7/20) x 80 eggs = 28 eggs
Third, the total of the contribution for the third tent as follows:- noodles: (8/(5+7+8)) x 40 pieces = (8/20) x 40 pieces = 16 pieces- rice : (8/(5+7+8)) x 100 kg = (8/20) x 100 kg = 40 kg- eggs : (8/(5+7+8)) x 80 eggs = (8/20) x 80 eggs = 32 eggs
So, the first tent gets 10 pieces of noodles, 25 kg of rice, and 20 eggs. The second tent gets 14 pieces of noodles, 35 kg of rice,and 28 eggs. And the third tent gets 16 pieces of noodles, 40 kg of rice, and 32 eggs.

Proposed Lesson Study for Developing Problem
Solving Based Mathematics Textbook
Aim of Lesson Study
To develop mathematical problem solving based
textbook that suitable to be used for the schoolsof disaster area

Proposed Lesson Study for Developing Problem
Solving Based Mathematics Textbook
The steps of proposed Lesson Study activities:
1. to plan the steps of teaching learning processes,
2. to carry out teaching learning processes and to use
3. the developed draft of problem solving based
4. mathematical textbook,
5. to reflect the teaching learning processes,
6. to improve the initial plan,
7. to re-implement teaching learning processes,
8. to reflect the teaching learning processes,
9. to share the experiences to other teachers

Proposed Lesson Study for Developing Problem
Solving Based Mathematics Textbook
Formulated Problem• How to develop primary problem solving based
mathematical textbook for the schools area ofdisaster.
• How to develop Junior Secondary problem
solving based mathematical textbook for theschools area of disaster.
• How to develop Senior Secondary problem
solving based mathematical textbook for theschool are of disaster.

Proposed Lesson Study for Developing Problem
Solving Based Mathematics Textbook
Year 2012
StepActivity
Feb

Plan

Establish team work●

Share the ideas●

Develop Lesson Plan, Student Work●

Mar April May June July

Sheet, Draft of TextBook
Develop instrument for observation,●questionnaire, interview, etc
Implemen-tation

Collect data in the Open Class in the●

●

●

●

●

●

●

●

scheme of Plan-Do See
Analyses the dataReport

Publish and present the results●END