d Japan
Author(s) NATAN, Alfredo, Jr.; ISHII, Hiroshi
Citation 北海道教育大学紀要. 教育科学編, 72(2): 173‑187
Issue Date 2022‑02
URL http://s‑ir.sap.hokkyodai.ac.jp/dspace/handle/123456789/12412
Rights
ComparativeStudyofMathematicsEducationinthePhilippinesandJapan
NATANAlfredo,Jr.andISHIIHiroshi
DepartmentofMathematicsEducation,HakodateCampus,HokkaidoUniversityofEducation
フィリピンと日本の数学教育に関する比較研究
ナタン アルフレッド・石井 洋
北海道教育大学函館校数学教育研究室
ABSTRACT
MathematicseducationinJapanandthePhilippineshasundergonevariousdevelopments.
MathematicseducationinJapanwasrootedinChineseinfluenceuntiltheemergenceof Westernarithmetic-Yosan.InthePhilippines,SpaniardsandAmericanscontributedgreatly tomathematicseducationuntilthecommencementoftheK-12curriculumin2013.This studycomparesmathematicseducationinbothcountriesbyexaminingtheireducation systems,issuesineducation,mathcurricula,textbooks,andlessons.Writtenmaterialsfrom differentprimarysourcesweregathered,andlessonobservationsandseminarsonmath educationwereconductedtoachievethesegoals.Thesignificantfindingsofthisstudy suggestnewperspectivesforeducators,policymakers,andfutureteachersinbothcountries.
Moreover,thesefindingswillhopefullycontributetotheimprovementofmathematics educationinbothcountries.
1．Introduction
1．1．Background
Mathematicsisoneoftheessentialareasof learning that one must acquire for many practicalreasonsanduses.
Just like any othersubject,mathematicsis important to the extent to which it supports and contributes to the purposes of general education.Childrenaresenttoschoolinorder
that they become useful members of the community and contribute to the welfare of society［1］.Furthermore,mathematicalliteracy helps individuals to understand the role that mathematics can play in the real world and makesoundjudgmentsanddecisionsneededby constructive, engaged, and reflective 21st- centurycitizens［2］.
Meanwhile, the status of mathematical literacyinthePhilippinesandJapanisdifferent.
Although mathematical skills are seen as fundamentalallovertheworld,andmathematics isconsideredanessentialsubjecttaughtona dailybasis,mathematicalliteracyinJapanand thePhilippinesisstillanissue.Thiscanbeseen fromtheresultsofthe2018OECD’sProgramme forInternationalStudentAssessment（PISA）
formathematicalliteracywhereJapan’slearners were placed 6th out of 79 nations while the Philippines’learnerswereplaced78th［3］.
WhileJapan’srankingisalreadyhigh,many Japanese educators still aim to find ways to improvetheirinstruction.Thisisinspiteofthe factthatJapanisacountrythathasanefficient educationalsystem.Thisisalsoonereasonwhy manyforeigncountriessendtheireducatorsto observeclassesinJapanandlearnfromtheir educationalsystem.Inaddition,theMinistryof Education,Culture,Sports,ScienceandTechnology
（MEXT）ofJapanprovidesprograms/scholarships toforeigneducatorsforthemtobetrainedand informed about their educational system and teaching practices. As the Philippines have a goodrelationship withJapanandanevolving educationalsystem,thecountrybenefitsgreatly fromsuchopportunities.
Thisresearchstudiesmathematicseducation inJapanandthePhilippinesandaimstoprovide insightsforeducatorsandpolicymakersinboth countries.Itishopedthattheseinsightswillbe beneficial and can provide a tool to improve mathematicseducationinbothcountries.
1．2 ．History of Mathematics Education in the Philippines and Japan
Japan and the Philippines have some commonalities in terms of their historical events-both were subject to some Chinese culturalinfluencesandbothhavebeenruledby theAmericans.Thesefactorshavecontributed
to their education systems and to their mathematics education. Even though their mathematicseducationhascertainChineseand Westerninfluences,instructionsandmethodologies in the current time stilldiffer as it has been throughseveralstagesofdevelopment.
1．2．1 ．History of Mathematics Education in the Philippines
The Philippines has been colonized by different nations, mainly Spaniards, Japanese, andAmericans.However,evenbeforecolonization, earlyFilipinoswerealreadytradinggoodswith Chinese,Malay,Hindu,andIslamicsocieties［4］.
Thishasledtogreatimpactsontheeducational system and mathematics learning in the Philippines.
The economic situation during pre-colonial timeswasagreatcontributorandmajorfactor in the educational system in the Philippines.
ThetypesofsocietypresentbeforetheSpanish colonizationwerePrimitiveCommunalSystem and Asiatic Feudalism. With their practical mode of production, they had to provide an education that was plain and simple［5］. In addition, it has long been believed that mathematicsinthePhilippinesoriginatedwith Chinese traders during prehistoric times.
However,recentdiscoverieshaverevealedthat ancient Filipinos did possess some system of counting and mathematics, including simple additionandsubtractionusingstonesortwigs, timekeeping and geometry as part of star- gazing activities, building houses （i.e., knowledgeofrightangles）,andsoon［6］.
During the Spanish time （1521-1898）, the systemevolvedintoamoreformalstructure.
During the early years, the establishment of schoolsfromprimaryleveltotertiarylevelof education came about because of religious
congregations. Christian doctrines were the main focus in these schools［5］. Spanish education for the Filipinos was designed to convertthemtoCatholicism.Ideally,instruction wasalsogiveninSpanish,arithmetic,various handcrafts,togetherwithalittlereadingand writing［7］. Although many universities and educationalinstitutionswereestablished,science andmathematicswerehardlytaughttostudents.
SimilartotheSpaniards,theAmericanera
（1898-1942） brought many cultural and educational influences to the Philippines.
EducationbecameveryimportantfortheUS colonialgovernment.Everychildfrom7years of age was required to attend the nearest school.UnlikeintheSpanishperiod,religiondid not form part of the school curriculum.
American teachers （Thomasites） arrived in 1901andprovidedtheFilipinoswithaformal education［5］.Thecourseworkforeachlevel placedaheavyemphasisonEnglishgrammar, writing,reading,andarithmetic.Between50%- 70%ofthetotalnumberofhourschildrenspent every day in school was devoted to these courses［8］.
WiththeAmericansoutofthepicture,the Japaneseoccupationstartedin1941.Embodied intheMilitaryOrderNo.2in1942,theyspelled out the basic principles and guidelines of educationwhenre-openingschools.Someofthe guidelinesweretoforgetandtostopusingthe Englishlanguageandinsteadlearnandadopt Nihongo.Otherguidelinessuggestedaneedto growprimaryandvocationaleducation,andto fosteraloveofwork.
Among the colonizers of the country, the Americans dominated. With English as the mediumofinstruction,theeducationalsystem inthePhilippinesisaprototypeoftheAmerican system. New subjects were introduced and
amongthemwasarithmetic［5］.
1．2．2 ．History of Mathematics Education in Japan
ItiscertainthatJapanesemathematicshad itsoriginsinChinesemathematics.Beginningin the Nara period （8th century）, the Japanese introducednumerousaspectsofChineseculture, includingmathematics,intotheirownculture
［9］.BeforetheEdoperiod,itwasknownthat peopleperformeddailycalculationtechniques（the fourarithmeticaloperations）withcomputingrods, whichcomprisedthemaincomputingtoolused beforetheSoroban（Abacus）wasintroducedto Japan.TheintroductionoftheSorobantoJapan marked the beginning of the history of mathematicsintheEdoperiodinJapan［10］.
IntheEdoperiod,inparticular,mathematics developedthroughtheassimilationofChinese mathematicaltextbooks.Therefore,tounderstand Japanesemathematics,itiscriticaltobefamiliar withChinesemathematics.Ontheotherhand, JapanesemathematiciansintheEdoperiodset original problems, developed new methods of solving them, and obtained advanced results.
JapanesemathematiciansmainlyusedAbacifor numerical computations. Abaci were tools importedfromChinathatbecamewidespread throughout the country. The Japanese used them for calculations in both private and businesssettings［9］.
During the late Edo period, the master institutionswereorganizedacrossmanyfields ofhobbies.Inadditiontotraditionalarts,master institutionsthatcontrolledagroupofenthusiasts inotherfields,suchasHaikuandWasan,were established. In the case of Wasan, a huge numberofschoolswithdifferentmasterswere establishedacrossJapan.Juku（privateschool）, wherediscipleswouldcongregatefromacross
Japan,wereformed.Jukuschoolsoperatedin many ways, for example, there was a Juku schoolwherestudentsfirststudiedintroductory arithmetic, and after that they proceeded to solve mathematical problems that were presented to them. Through such practical exercises, they improved their mathematical knowledge.
Ontheotherhand,masterinstitutesalwaystried toactivelysendmessagesbeyondtheconfinesof theirschools.Anexampleofsuchactivitywasthe dedicationofSangaku（mathematicaltablets）to shrinesandtemples.Sangakureferstoatabletin whichamathematicalproblemanditsanswer weredescribed.
WhentheEdoperiodendedandtheMeijiera began,Japanstartedtopromotemodernization inallpossiblefields,inimitationoftheWest.As to arithmetic education within the overall elementarysystem,theMinistryofEducation proposedapolicyemployingacurriculumnot basedonconventionalWasanbutonWestern arithmeticorYosan［10］.
2．Purpose of the Study
Thisstudyaimstocompareandanalyzethe similarities and differences in mathematics education between the Philippines and Japan
（Fig. 1）. This is done by describing the followingareas:
3．Methodology
3．1．Material
Thematerialsusedinthisstudyarewritten materialsfromprimarysourcesorfromexisting data such as journals, books, official records, lessonvideos,andotherliterature.
3．2．Lesson Observations
Mathematics lesson observations were conducted from April-July 2021 at Fuzoku Elementary School, an affiliated school to Hokkaido University of Education. Observers recordedandanalyzedtheteacher-studentand student-studentinteractions,thelessonflow,as wellastheassessmentoflearning.Strongpoints of the lesson were also identified during the observations.
3．3．Seminars
The gathered data and observations about mathematicseducationinthePhilippinesand Japanwerepresentedthroughseminarsessions from April-July 2021. A peer discussion was also conducted to evaluate the data being presented.
4．Results and Discussion
4．1．National Education System 4．1．1．The Philippines
The1987PhilippineConstitutiondeclaresthat education,particularlybasiceducation,isaright of every Filipino. According to Article XIV, Section 2 of the Constitution, the state shall establishandmaintainasystemoffreepublic
Fig. 1 ScopeofStudy
educationatelementaryandhighschoollevels.
Withoutlimitingthenaturalrightsofparentsto rear their children, elementary education （7 yearsincludingkinderlevel）iscompulsoryfor allchildrenofschoolage［11］.
ThePhilippines’educationsystemadopteda trifocalized structure in 1994/1995 having a three-layered system composed of basic education, vocational education, and higher education with three government agencies beingresponsibleforeachlayer（Fig.2）.The Department of Education （DepEd） sets the overalleducationalstandardsandmandatesfor kindertoGrade12（elementarytohighschool）.
TheTechnicalEducationandSkillsDevelopment Authority is responsible for technical and vocationaleducation,whiletheCommissionon Higher Education covers both public and privatehighereducationinstitutions,aswellas degree-granting secondary educational institutionsinthecountry.
Fig. 2 PhilippineTrifocalizationofEducation
From this structure, the education system follows the 7-4-2-4 system of education in general: pre-primary level （nursery and kindergarten）wherekindergarteniscompulsory, 6yearsofprimaryorelementaryeducation,4 yearsofjuniorhighschool,andthen2yearsof senior high school. College education usually takes4,sometimes5,andinsomecases,asin medical and law schools, as long as 8 years.
Graduateschoolingisanadditional2ormore years［12］.
TheeducationalsysteminthePhilippineshas undergonedifferentchangesanddevelopments.
A recently implemented development is the K-12programoftheDepartmentofEducation throughtheRepublicAct10533of2013.This programcoverskindergartenand12yearsof basiceducationtoprovidesufficienttimeforthe mastery of concepts and skills, to develop lifelonglearners,andtopreparegraduatesfor tertiaryeducation,middle-levelskillsdevelopment, employment,andentrepreneurship.Someofthe featuresofthisprogramareasfollows:
a. Universal Kindergarten-at 5 years old, childrenstartschoolandaregiventhemeans to slowly adjust to formal education. In kindergarten, students learn the alphabet, numbers,shapes,andcolorsthroughgames, songs,anddancesintheirmothertongue.
b.Makingthecurriculumrelevanttolearners.
c.Mothertongue-basedmultilingualeducation- aside from mother tongue, English and FilipinoaretaughtassubjectsstartingGrade 1,withafocusonoralfluency.
d.Spiralprogressionofconceptsinallsubjects.
e. Establishment of senior high school where studentsmaychooseaspecializationbasedon aptitude,interest,andschoolcapacity［13］.
4．1．2．Japan
TheJapaneseConstitution（Article26）sets forththebasicnationaleducationalpolicy,which states that all people shall have the right to receiveanequaleducationtothebestoftheir ability,asstatedbylaw.Thereisanobligation forallchildrentoreceiveordinaryeducationas providedforbylaw.Suchcompulsoryeducation shallbefree.
The Basic Act on Education, which was
Fig. 3 SchoolSysteminthePhilippines
Fig. 4 SchoolSysteminJapan
promulgatedandputintoeffectinMarch1947, providesbasicaimsandprinciples,andother educational laws and regulations have been madeinaccordancewiththeaimsandprinciples ofthislaw.Cabinetordershavebeenmadeto enforcethelaws,andtheMinistryofEducation, Science,Sports,andCulture（MEXT）publishes ministerial ordinances andnotices concerning the standards for establishing schools, curriculum standards such as the Courses of Study,andsoon［14］.
TheJapaneseschoolsystemfollowsa6-3-3- 4-yearsystem,whichprimarilyconsistsofsix- yearelementaryschools,three-yearjuniorhigh schools, and three-year senior high schools, followedbytwo-orthree-yearjuniorcolleges orfour-yearcolleges［15］.
Beforebeginningtheirelementaryeducation attheageof6years,childrenhavetheoption toattendkindergartenbetweentheagesof3 and5years.Compulsoryeducationbeginswith 6yearsofelementaryschoolandendswith3 yearsoflowersecondaryschoolforatotalof9 years. Students then proceed to upper secondaryschool,whichcaterstochildrenwho havefinishedtheircompulsoryeducation,and thisiscompletedover3years.Highereducation inJapanisdividedintocollegesoftechnology, junior colleges, and universities. Colleges of technology provide vocational education to studentswhohavecompletedtheircompulsory education,andgrantstudentsassociatedegrees after5yearsofstudy.Juniorcollegesoffer2-to 3-yearassociatedegreeprogramstostudents who have completed their upper secondary education.Universitiesoffer4-yearbachelor’s degrees,2-yearmaster’s,and3-yeardoctoral degrees［16］.
4．2．Issues in Education
Philippineeducationhasundergonedifferent changesanddevelopmentsinresponsetothe issuesandproblemsinthecountry.Japan,in spiteofbeingacountrywithaveryefficient educational system, has its own issues and challenges,aswell.
4．2．1．The Philippines
AlthoughthePhilippineeducationalsystem has been an extensive model for Southeast Asiancountries,inrecentyears,thishasnot beentrue,andthesystemhasdeteriorated.This isoneofthereasonswhytheK-12programwas implementedin2013.Nationwide,thePhilippines faces several issues when it comes to its educationalsystem.
a. Quality of Education
One of the indicators of the quality of educationinthePhilippinesistheresultsofthe NationalAchievementTest（NAT）forgrades 6-10. The most recent results were the 2017 and 2018 NAT scores for grades 6-10 which werethelowesteverscoresinthehistoryof Grade6whileforGrade10,the2017scorewas the lowest ever and the 2018 score was the thirdlowest［17］.
Anotherindicatorthatshowstheproblemsin the Philippine education system is the 2018 PISAresults.Thetablebelowshowstheresults and ranking of the Philippines out of 79 countries［3］.
Theresultsoftheseassessmentsclearlyshow
Table 1 2018PISAResults
Subject Points Rank
Reading 340pts 79th
Math 353pts 78th
Science 336pts 78th
an issue in the quality of education in the Philippines.
b. Budget for Education and Lack of Facilities and Teachers
The Philippines still has one of the lowest budgetallocationsforeducationamongASEAN countries. The provisions of the Constitution statethattheeducationsectorshallcontinueto receive the largest portion of the national budget.However,thebudgetforeducationin 2020remainedat751.7billionpesos（1.6trillion yen）foraround27millionlearners［18］.
Inaddition,therearelarge-scaleshortagesof facilities across Philippine public schools, includingclassrooms,teachers,desksandchairs, textbooks,andaudio-videomaterials.Basedon reportsoftheAllianceofConcernedTeachers
（ACT）,atotalof15regionshavereporteda lackofadequateclassrooms,withmostschools stilloperatingonshiftingschedulesandclass sizesof50to70（Fig.5）［19］.
c. Affordability of Education and Drop-out Rate ThePhilippineshas1.4millionchildrenoverall whoareoutofschool,accordingtoUNESCO’s data.Additionally,itistheonlyASEANcountry thatisinthetopfivecountrieswiththehighest numberofyoungpeopleoutofschool.Poverty isaleadingcauseoftheincreasingnumberof out-of-school children. Price increases in oil, electricity,rice,water,andotherbasiccommodities arepushingthepoorintodirepoverty［20］.
4．2．2．Japan
ThelevelofeducationinJapanishigh,even byworldstandards.Infact,intheOECD’sPISA results,Japanesestudentshaverecordedhigh levelsofachievement［15］.Despitehighresults in almost all education rankings, Japanese educatorsandpolicymakersstillidentifysome issuesinJapan’seducationalsystem.
a. Issues Regarding English Education
Despite the standard 12 years of English- languageeducationfromelementaryschoolto university, many Japanese people find themselvesstrugglingtospeakEnglish.
WhenitcomestoEnglisheducation,Japanese schools mostly focus on reading and writing.
Theseskillsarehonedmainlyinordertopass exams,andverylittletimeisspentondrilling practicalskillssuchasspeakingandlistening
［21］.
OnesolutionwastostartEnglisheducationin elementarylevelratherthanjuniorhighschools fromtheacademicyear2020.Thisisbecause Japanranksclosetothebottomamong29Asian countriesinEnglish-languageproficiency［22］.
b. Increasing Absenteeism and Bullying
A 2019 survey by MEXT found that there were more than 540,000 reported cases of bullyinginschools,ayear-on-yearriseof31%.
Absenteeism, violent incidents, and suicides havealsobeenontheincrease.Amajorcause is the excessive emphasis on rules and conformity,whichcreatesastiflingatmosphere
［23］.
c. The Negative Effects of an Over-Emphasis on University Entrance Examinations
Thereishugecompetitiontoenterprestigious universitiesandthishasmanynegativeeffects onJapanesehighschoolstudents.Studentsare lackingincreativity,freedom,andfuturevision.
Theyareverybusylearningspecifictechniques Fig. 5 ClassroomsinthePhilippinesandJapan
（PublicSchools）
in order to perform well in the entrance examinations,sotheydonotspendmuchtime on other activities such as class discussions, presentations,orexperiments,whicharealso supposedtoformpartoftheireducation［24］.
4．3．Mathematics Curriculum 4．3．1．The Philippines
ThePhilippinemathematicscurriculum（Kto 10）hastwogoals:todevelopstudents’critical thinkingskillsandtoenhancetheirproblem- solvingabilities.Thesetwogoalsareachieved throughanorganizedandrigorouscurriculum, adefinedsetofhigh-levelskillsandprocesses, desirablevaluesandattitudes,andappropriate math tools, taking into account the different contextsofFilipinolearners（Fig.6）.
Fig. 6 ConceptualFrameworkofMathEducation
Mathistaughtfromthesimplestconceptsto morecomplicatednotionsthroughthelevelsin a spiral progression. The following time allocations are given at each level for math lessons:
Therearefivecontentareasinthecurriculum:
• NumbersandNumberSense
• Measurement
• Geometry
• PatternsandAlgebra
• StatisticsandProbability［25］
ThedomainofNumbersandNumberSense includes concepts, operations, and the applicationofnumbers.Measurementfocuseson measures and applications of length, mass, weight, capacity, time, money, temperature, angles, perimeter, area, surface area, and volume.Geometryfocusesontwo-andthree- dimensional figures.Algebrastudiespatterns, relationships,andchangesamongshapesand quantities.StatisticsandProbabilityfocuseson skills in data collection, organization, and interpretation, including making predictions aboutoutcomes［26］.
TheKto10mathematicscurriculumprovides asolidfoundationformathematicsatgrades11- 12. More importantly, it provides the skills neededbyFilipinolearnersastheyproceedto thenextstageoftheirlifeaslearnersandas citizensofthePhilippines［25］.
4．3．2．Japan
MEXT determines the courses of study in terms of the broad standards for all schools, fromkindergartenthroughtosecondaryschools, toorganizetheirprogramsinordertoensurea fixed standard of education throughout the country［14］.
Mathematicsisarequiredsubjectinprimary, lower secondary, and the first year of upper secondaryschool.Themathematicscurriculum consistsofthreeparts:overallobjectivesforthe level,objectivesandcontentforeachgrade,and
Table 2 TimeAllotmentforPHMathClass
Grade/Level Time
Elementary 250mins/week JuniorHighSchool 240mins/week SeniorHighSchool 80hrs/sem
syllabusdesign.
The2008revisionofthecurriculumorganized mathematics content in grades 1-6 into four contentareas:
• NumbersandCalculations
• QuantitiesandMeasurements
• GeometricFigures
• MathematicalRelations
At lower secondary level, the mathematics contentisorganizedintofourareas:
• NumbersandAlgebraicExpressions
• GeometricFigures
• Functions
• MakingUseofData［27］
Mathistaughtthroughaspiralprogression andhasatimeallotmentasinthetablebelow.
Table 3 TimeAllotmentforJPMathClass
Grade/Level Time
Elementary 250mins/week JuniorHighSchool 240mins/week SeniorHighSchool 4–5hrs/week
Themaingoalofmathematicseducationisto developactivelearningthroughthesystematic abstractionofmathematicalconceptsfollowing thethreepillarsforachievingtargetsinmath
（Fig.7）.
4．4．Mathematics Textbooks 4．4．1．The Philippines
Allmatterspertainingtotextbookplanning, content review and evaluation, technical standard setting, and procurement and allocationarecoordinatedbytheInstructional MaterialsCouncilSecretariatoftheDepartment ofEducation.Text-basedandnon-text-based learning resources suitable to the needs of learners are aligned with the curriculum, addressingthelearningcompetenciesfoundin thecurriculumguides［28］.
Ontheotherhand,allprivateschoolshave theprerogativetochooseandprescribetheir owntextbookonconditionthatthesearelocally authored,published,andfitintotheguidelines asprescribedbylaw［29］.
Generally, mathematics textbooks in the Philippines provide detailed explanations for eachlessoninastraightforwardandinteresting approachthroughrelevantlifesituations.Also, creative and critical thinking, as well as understandingproblem-solvingstrategies,are developed through worked examples in each lesson［30］.
Sincealllearningmaterialsshouldbealigned withthecurriculumguide,allthecontentand standards of the curriculum guide should be foundinamathtextbook,fromNumbersand NumberSensetoStatisticsandProbability.
The math textbook provided by the DepartmentofEducationusuallyhasfourparts for each lesson. It usually starts with a （1）
Chapter Introduction describing the general objectives and integration of the lesson in a real-lifesituation.
Then,itproceedstothe（2）Introductionof theLessonthroughwordproblemsorsituations based on the different contexts of Filipino learners.Thisisfollowedbythediscussionof Fig. 7 3PillarsforAchievingTargetsinMath
the （3） Solution and Concepts and other examples. Examples and explanations are enhancedthroughillustrationsandpictures.
Afterprovidingcertainexamples,fourtypes of（4）Activitiesthatdependontheassessment of knowledge, processes, understanding, and productsaresupplied（Fig.8）.
Some of the textbooks in the Philippines provideproject-typeactivitiesineverychapter, as well as a chapter review with additional questionsandactivities［31］.
4．4．2．Japan
Bookscreatedbypublishersdonotqualifyto be used as textbooks in schools unless authorizationisobtainedfromMEXT.Basedon the numbers of textbooks reported, MEXT issues instructions concerning the types and numbers of textbooks to be published to respectivepublishers［14］.
Problem-solvinghasbeenamajorthemein Japanesemathematicscurriculafornearly50 years. Japanese textbooks include ideas from the study of teaching problem-solving. For example, textbooks include open-ended questionstoguidestudentsindevelopingtheir
understanding, instead of explanations of conceptsandprocedures.Theseriescontains alternative approaches to solving a problem, provides diagrams to help students solve problemsindependently,andincludesseparate pages that teach students how to take notes effectively.
Inaddition,theopeningproblemsintheunits appear on the right-hand page of the book.
Onlytheproblemisontheinitialpage,andthe followingpageincludesmultipleapproachesto the solution to support the discussion of a varietyofapproachestothesolution.Also,there aremoreopen-endedquestionsandsuggestions presented by cartoonlike characters. This representsamoveawayfromprovidingclear explanations of concepts and procedures to expectingstudentstoinvestigatemathematics usingtheirownreasoningbasedontheirprior learning.Anotherspecialfeatureistheinclusion of specific pages to support students in developing note-taking skills throughout the grades. Starting in Grade 2, each textbook includessomeexamplesofhowtotakenotesto foster students’ mathematical thinking and problem-solvingskills［32］.
Fig. 8 PartsofaMathTextbookinthePhilippinesandJapan.Mathematics 4 Learner’s Material (left, retrieved from www.slideshare.net) and Mathematics International Grade 6 （right, retrieved from www.
globalresources.com）.
Moreover,otherspecialfeaturesofJapanese math textbooks include “How to Use the Textbook,” which explains the parts of each lesson and their uses; “Study Steps,” which explainsthedifferentstrategiesusedinmath lessons; “Warm-Up Activity,” which connects activitiesfrompreviouslessons;“Practiceand Review,”whichprovidesmoreapplications,and wordproblemsthatthestudentscananswer;
and “Put Your Knowledge to Work,” which providesrecreationalandproject-typeactivities asadditionalpractice.
4．5．Mathematics Lessons 4．5．1．The Philippines
In general, a mathematics class in the Philippines employs a question-and-answer type of exposition, where the teacher starts withdefinitionsandrulesandstudentsarequiet most of the time and simply listen to the teacher.Tobeginatopic,theteacherfirstasks studentswhattheyknowaboutitthenexplains the definition and rules. The most common strategies in teaching mathematics are exposition, practice and consolidation, and discussion.Theteachingstrategiesperceivedto bemosteffectivebyscienceandmathematics teachersinschoolsidentifiedashavingcertain benchmarksinteachingandlearningwereas follows: hands-on experience that allows students to develop to their fullest learning capacitybecausetheydependonthemselves, cooperative learning because they can share knowledgebetterwheningroupsratherthan whenworkingalone,andself-discoverybecause itenhancestheirlearningcapabilities［33］.
InthenewK-12curriculum,thelearnerisat thecenteroftheteachingandlearningprocess.
Thus, the curriculum uses pedagogical approaches that are constructivist, inquiry-
based, reflective, collaborative, differentiated, appropriate,relevant,andintegrative［28］.
Inaddition,differentstrategiesandactivities areusedeverydaydependingontheneedsof the students. The following figure shows a commonprocedureinamathematicsclass.
Fig. 9 CommonMathLessonFlowinthePhilippines
4．5．2．Japan
InJapan,themajorreformsinteachingand learningmathematicsoccurredduringthe1970s and1980s.Amajoraspectofthesereformswas the shift from a traditional classroom that focusesonteachers’instructionstoastudent- centered classroom that focuses on students’
engagementinmathematicalactivities.Japanese mathematics lessons include the following characteristics:
• student-centeredinstructionusingproblem- solvingasafoundation
• structuredproblem-solving
• carefullyselectedwordproblemsandactivities, andtheircohesiveness
• extensivediscussion（Neriage）
• emphasisonblackboardpractice（Bansho）.
The instructional approach, known as structured problem-solving, is designed to create interest in mathematics and stimulate creativemathematicalactivityintheclassroom throughstudents’collaborativework.Thelesson u s u a l l y s t a r t s w i t h s t u d e n t s w o r k i n g individuallytosolveaproblemusingtheirown mathematical knowledge. After working with problems, students bring various approaches and solutions to classroom discussions. The teacher then leads students in a whole-class discussion in order to compare individual approachestosolutions.Thisdiscussionisoften called Neriage in Japanese, which implies polishing ideas. This whole-class activity providesstudentswithopportunitiestodevelop theirmathematicalabilities,includingconceptual andproceduralunderstanding.
Moreover,Japaneseclassroomsareequipped with a large blackboard at the front for the following purposes: to keep a record of the lesson; to help the students remember what theyneedtodoandthinkabout;tocompare, contrast, and discuss ideas that students present;tofosterorganizedstudentnote-taking
skills;andtohelpstudentsseetheconnection betweendifferentpartsofthelesson.
Towardtheendofalesson,ateacheroften takes the lead to pull all the different approaches and ideas together to see the connections. Then, he/she summarizes the lessontohelpthestudentsachievethelesson objectives.Theteacheroftenasksstudentsto reflectonwhattheyhavelearnedduringthe lesson［34］.
5．Conclusion
Mathematicseducationinbothcountrieshas somesimilaritiesanddifferencesandbothare stillaimingforqualitymathematicseducation through curriculum development, changes in the system, and improvements in facilitating learning.
InthePhilippines,therearenumerousissues andflawsintheeducationalsystem,including thequalityofeducation.Manysuggestionsand changeshavebeenprovidedandconductedto fixtheseproblems.Recently,abigcurriculum shift has been carried out through its K-12 curriculum which was implemented in 2013
（following on from its former 10-year basic education system）. In this new curriculum, certainchangeswereimplementedintermsof theeducationsystem,thecurriculum,learning materials,lessonflow,andfacilitationoflearning.
This is in response to the country’s goal of upgradingthequalityofeducation,addressing thepoorperformanceofstudentsinmathematics, science,andreading,andpreparinglearnersfor 21st-centuryskills.Withthisnewcurriculum,it is hoped that the quality of education will improveforyearstocome.
Japan,despitebeingacountrywithavery efficienteducationsystemwhichisalwayson Fig. 10 CommonMathLessonFlowinJapan
topintermsofmath,science,andreading,also hassomechallengesandissuesinitseducational system. Educators and policymakers are still findingwaystoimprovetheirinstructionand the quality of education, especially in mathematicseducation.“LessonStudy”isoneof the greatest contributions to the field of educationinJapanasitimprovesinstructionin mathematicsteaching.Mathematicstextbooks, materials, curricula, and the facilitation of learning are all considered as part of this process.
In terms of the education system and curriculum,thereisnotmuchdifferencebetween thetwocountries.Whenitcomestoissuesof education, math textbooks, and facilitation of learning,thereare,however,greatdifferences.
References
［1］E.Breslich,“ImportanceofMathematicsinGeneral Education,”TheMathematicsTeacher,vol.59,no.5,pp.
pp.464-469,1966.
［2］O.f.E.E.C.-o. （OECD）, “PISA 2021: Mathematics Framework,” 2021.［Online］.Available: https://pisa 2021-maths.oecd.org.
［3］“FactsMaps,” 2018.［Online］. Available: https://
factsmaps.com/pisa-2018-worldwide-ranking-average- score-of-mathematics-science-reading/.
［4］O.B.Group,“ThePhilippines’historyoftradeand migration has created a diverse, globally minded society,”2021.［Online］.Available:https://oxfordbusi nessgroup.com/overview/evolving-nation-history- trade-and-migration-has-created-diverse-globally- minded-society.
［5］M.a.R.Z.Sajid,“FeaturesandHistoricalAspectsof thePhilippinesEducationalSystem,”EuropeanJournal ofContemporaryEducation,pp.160-165,2012.
［6］Q.N.Lee-Chua,“MathematicsTeacher,”Mathematics inTribalPhilippinesandOtherSocietiesintheSouth Pacific,pp.50-55,2001.
［7］K. Schwartz, “Comparative Education Review,”
FilipinoEducationandSpanishColonialism:Toward anAutonomousPerspective,pp.202-218,1971.
［8］C.I.Sobritchea,“AmercianColonialEducationandIts ImpactontheStatusofFilipinoWomen,”American ColonialEducation,pp.70-91,1990.
［9］T.Ogawa,“AReviewoftheHistoryofJapanese Mathematics,”Revued’histoiredesMathematiques, pp.137-155,2001.
［10］S. Ken’ichi, “Japanese Mathematics in the Edo Period,”2011.［Online］.Available:https://www.ndl.
go.jp/math/e/s1/1.html.
［11］M.A.Llego,“TeacherPH,”2021.［Online］.Available:
https://www.teacherph.com/legal-bases-of-philippine- educational-system/.
［12］K.C.AbajaandM.K.S.Lavadia,“Educationinthis Country is Trifocalized, Should We Continue Implementing This or Should We Only Have One DepartmentofEducation,” PolytecnicUniversityof thePhilippines,Sta.Mesa,Manila,2018.
［13］O.G.o.t.R.o.t.Philippines,“OfficialGazette,”［Online］.
Available:https://www.officialgazette.g.,ov.ph/k-12/.
［14］MEXT,“Ministryof Education,Culture,Sports, ScienceandTechnology,”［Online］.Available:https://
www.mext.go.jp/en/policy/education/overview/index.
htm.
［15］JNTO, “Japan Educational Travel,”［Online］.
Available: https://education.jnto.go.jp/en/school- exchanges/japanese-education-system/.
［16］E.o.J.i. USA, “Embassy of Japan in the United StatesofAmerica,”［Online］.Available:https://www.
us.emb-japan.go.jp/itpr_en/education-system-in- japan.html.
［17］E.J.Albano,“SeniorHighStudentsScoreLowestin NationalAssessmentHistory,”TheManilaTImes,6 November2020.
［18］DBM,“DepartmentofBudgetandManagement,”
2020.［Online］.Available:https://dbm.gov.ph/index.
php/secretary-s-corner/press-releases/list-of-press- releases/1778-prrd-signs-the-p4-506-trillion-natio nal-budget-for-fy-2021.
［19］D.Nazario,D.JeffreyandR.Panaligan,“‘Sameold problems’towelcome27.2millionlearnerstoschool thisyear,”ManilaBulletin,2June2019.
［20］K.Academics,“K12Academics,”［Online］.Available:
https://www.k12academics.com/Education%20World wide/Education%20in%20the%20Philippines/issues- regarding-educational-system.
［21］K.Tsunekawa,“tsunaguJapan,”2020October2020.
［Online］.Available:https://www.tsunagujapan.com/
6-real-reasons-why-japanese-cannot-speak-english/.
［22］T.Sawa,“JapangoingthewrongwayinEnglish-
educationreform,”TheJapanTimes,21January2020.
［23］I. Tomano, “Transforming Japan’s Conformist Education System,” Nippon.com, 26 May 2020.
［Online］. Available: https://www.nippon.com/en/
japan-topics/g00831/.
［24］I.Yasko,“JapaneseEduationalSystemProblems,”
［Online］.Available:http://jhu.sites.tru.ca/files/2019/
03/Japanese-Educational-System-Problems.pdf.
［AccessedJuly2021］.
［25］DepEd,“Kto12CurriculumGuide-Mathematics,”
DepartmentofEducation,Pasig,2016.
［26］M.U. Balagtas, D.C.B. Garcia and D.C. Ngo,
“Looking through Philippine’s K to 12 Curriculum Mathematics and Science vis-a-vis TIMSS 2015 Assessment Framework,” EURASIA Journal of Mathematics,ScienceandTechnologyEducation,p.3, 2019.
［27］T.&.P.I.S.Center,“TheMathematicsCurriculum in Primary and Lower Secondary Grades-Japan,”
Boston College, 2019.［Online］. Available: http://
timssandpirls.bc.edu/timss2015/encyclopedia/count ries/japan/the-mathematics-curriculum-in-primary- and-lower-secondary-grades/.
［28］DepEd,“DepEdOrderNo.21s.2019,”Department ofEducation,2019.
［29］DepEd,“DepEdOrderNo.36s.1990,”Department ofEducation,1990.
［30］P.P.House,“PhoenixPublishingHouse,”［Online］.
Available: https://h.phoenix.com.ph/wp-content/
uploads/2018/06/grade-school-and-pre-school- ilovepdf-compressed.pdf.［Accessed2021］.
［31］A.R.Tabilangandet.al.,Mathematics4-Learner’s Material,PasigCity:DepartmentofEducation,2015.
［32］A. Takahashi, “Recent Trends in Japanese Mathematics Textbooks for Elementary Grades:
SupportingTeacherstoTeachMathematicsthrough ProblemSolving,”UniversalJournalofEducational Research,vol.4,no.2,pp.313-319,2016.
［33］S.A.Ulep,“GoodMathematicsTeachingPractices -InTheMaking:APhilippineExperience,”Tsukuba JournalofEducationStudyinMathematics,vol.25, 2006.
［34］A.Takahashi,“CharacteristicsofJapaneseMathematics Lesson,”DePaulUniversity.
（ナタン アルフレッド 教員研修留学生）
（石井 洋 函館校准教授）
