Textbooks and resourcesforthe pre-serviceteacher training Salomé Martínez Departamento de Ingeniería Matemática Centro de Modelamiento Matemático Universidad de Chile
FondefReFIP Project • FondefReFIP “Resourcesfortheinitial training of elementaryschoolteachers in mathematics” March 2011-April 2014 • R&D projectfinancedbyConicyt, withpublic and privatepartners (Ministry of Education, ChileanAcademy of Sciences, Fundación Luksic, Ediciones SM) • Thegoalis to developmaterialsforpre serviceelementaryschoolteacher training. • Main “product”: Mathtextbooks (Numbers, Geometry, Algebra, Data and randomness) • Interactives (7) done in collaborationwithLITE, UNAM. Collaborationwith José Luis Abreu, due to ourprevious meeting!! • Teachingresourcesformatheducators, complementingthebooks. • Theprojectgavetheopportunity to do matheducationresearch.
Mathcoursesforelementaryschoolteachers • Teacher training is quite diverse. Eachinstitution has itsownprogram. • In thelastyearstherehavebeenefforts to improveinitial training (standards, new resourcesforuniversities). • Thefocusison general pedagogycourses. • Wehavethefeelingthatnumber of disciplinarycourses has increased in thelastyears. But… • In 2007 aprox. 20% of thecoursesforteachersweredisciplinary (spanish, math, science, social sciences) (withoutspecialization). • Now, is 25% (aprox. 1 more course) • Mathcoursesincreasedfrom 2 to 2 ½. • Institutionsnowofferspecializations, butteachers can teacheverything. There are institutionsthatoffer no mathclassesunlessyour“major” ismath.
Whoteachesmath and mathdidacticscourses to preserviceelementaryschoolteachers? • Itdependsontheinstitutions: matheducators, highschoolteachers, elementaryschoolteachers, mathematicians. • In most cases thereis no appointment of thelecturer in theuniversity (justhiredforthecourse). Mathbooksforteachers in spanish • Booksavailable are mostlymathdidacticsspanishbooks. Mathematics in themis quite abstract. A largedifferencebetweenhowtheconcepts are learnedbyteachers and howthey are taught, forinstance: to define multiplicationfirstthey define thecartesianproductbetweentwo sets, fractions as equivalentclasses, etc… • Wedidn’tfoundreasonablemathbooksbeingused, mostly notes fromlecturer, whichwereusuallycommonmath.
Math and mathdidacticscoursesforteachers • How are thecoursesforteachers? • type of instruction?, type of contentaddressed at mathlessons? • Duringtheprojectwehadtheoportunityto observe math and mathmethodologyclasses (initial training) (Chandía, Reyes, Martínez 2013) • 7 teachereducators of differentprofiles, 3 classes. • Forcodingtheclasswasdivided in 7 moments • Theclasseswerecentered in commonmathcontent, no connectionwithclassroom(89%) • Directinstruction (82%) • Problemsolving (routine) (12%) • Little differencesbetweenmath and mathdidactics, and betweendifferentprofiles.
Opportunitiesforimprovement Thereisageementregardingtheneed of improvement, and manyinstitutions are makingsignificantchange s totheirprograms. Sincethelast 5 yearstherehavebeenseveralinitiatives to improveinitialteacher training • INICIA PROGRAM • Developmentof standardsforinitialteacherpreparation • INICIA DiagnosticEvaluation. Itisnotmandatory! • Beca Vocación de Profesor, a fellowship to attractbetterstudents to theteachingprofession (since 2010) • Convenios de Desempeño en Formación de Profesores, Mineducgranttofinanceuniversitiesthat prepare teachers (through a 3 yeargrant). Thegoalistopromotesignificantstrategicalchanges (7 institutions 2012+4 institutions 2013).
How can wecontribute? Developingresourcesthat can helpimprovethecoursesforfutureteacherswhichshould: • Addresstheneeds of theteachers (MKT), curriculumdemands… • Takeintoconsiderationtheprofessionalsthattrainteachers • Takeintoconsiderationthereality of the country. Forinstance: (lack) knowledgetheyhavefromelementary and highschool, mathanxiety…
Team • Theteamthatproducedthefirstdrafts: 6 matheducators and 8 mathematiciansfrom 7 institutions. • Therewasteamsworking in eachtextbook, butthecontentwasdiscussedbythewholeteam. • Nobodywas a “specialist”. Everybodycouldquestionsomepart of thebook, ormakesuggestions. Thiswascommonpractice in allourpreviouswork. • The final version of thebookswereproducedby a smallerteam of mostlymathematicians.
Mathknowledgeforteaching and thetextbooks • Focusedonthespecializedmathknowledge • Contents are mainlythose of schoolcurriculum • To show thedeepness of schoolmathematics • Topromotemathreasoning • Promotethinkingaboutmathematics, and itsteaching, posingquestions • Use of representations and models, differentways of justifying and proving • Illustrativeexamples • Tostudycertaintopicsseveral times (exampleproperties of theoperations) • Applications of mathematics, contextualizemathconcepts, promoteproblemsolving • Use of manipulatives (concrete-pictorical-symbolical) • To show thatmathematicsiscoherent
Preliminaryversion (pilot) • Thebooksfocused in specializedmathknowledge • Alsoincludedotheraspectssuch as lessonplanning, assessment, curriculum, misconceptions, etc • Included “ready to use” lessonplans (somethingthatwasrequestedbyteachers) • Bymanythiswastheopportunityto “solve” manyproblems at once • Constructedby a largeteam, sum of differentcontributions, lack a thread. Also a lot of repetition (whichwasgoodto use them in courses) • Mathreflection (Para pensar) • Focusoncurriculumcontent, butthereweresomeadvancedmathcontents
Universities • Pontificia Universidad Católica de Chile (sedes Santiago y Villarrica) • Universidad Católica de la Santísima Concepción • Universidad de Concepción (sedes Concepción y Los Ángeles) • Universidad de Magallanes • Universidad de Playa Ancha (sede San Felipe) • Universidad de las Américas (sedes Santiago y Viña del Mar) • Universidad del Bío-Bío • Universidad del Desarrollo • Universidad Diego Portales • Universidad San Sebastián (sedes Santiago, Concepción, Valdivia, Puerto Montt) • Universidad Santo Tomás • Universidad Alberto Hurtado • Universidad de Viña del Mar • Universidad Católica de Temuco • Universidad Arturo Prat • Universidad de los Andes • Good regional coverage • Differenttypes of universities(selective-non selective, traditional-non traditional, public-private) • Differenttypes of teachereducators • Around 4000 studentsparticipated, 20000 total enrollment in Chile.
Userexperiences and evaluations Wereceived a lot of suggestions and opinionsfromabout 15 evaluators and the 50 lecturersthatusedthebookduringthepilotingstage(includingsomeauthors): • Thebookswereusefulbutchaotic • So manydifferentcomponentsmadethem lose focus • Theywereuneven • Manypartswereneverused • Notallbookwereusedwiththesameintensity (Algebra and Datos y Azar)
Final books • Wecutseveralparts • Wedecidednottoincludelessonplanning, assessment. • Wekeptcommonerrors, difficulties, misconceptions. Some of themwereregardingelementaryschoolpupils, someregardingthestudents. • Wealsoinclude use manipulatives • Manyexcercises, of differenttype. • Wealsokeptthemostrelevantmathcontent • In manypartswefocusedonapplications (functions) • Decisionson final contentwasmadeby a smallerteam • The final versionwasproducedconsideringseveralopinions, butitwasnotmerelyananswertothat.
Un niño pregunta: “si 0,4·0,4=0,16 ¿por qué 0,4·0,2 no es 0,8?”. ¿Qué le respondería al niño? ¿Qué ejercicio le sugeriría para que se diera cuenta de su error?
Sesgos en expectativas Mathanxiety and teacherexpectations • No significant effects on the formation of opinion on personal characteristics of students. • There are significant effects of the sex of the student and future teacher math anxiety in the formation of academic expectations. Men received better academic expectations than females, and future teachers with math anxiety have lower academic expectations. • There is a significant effect of math anxiety of the future teacher in the allocation of support measures in special class.
New projectsrelated to preserviceteacher training (elementaryschoolteachers) • FONDEF IT13I10005 “Resources for pre service training of elementary school teachers based on classroom experiences” (2014-2016): • Case development for training of teachers based on classroom math activities, including examples of student work, teacher-student interactions… • Development of a case study based workshop for teacher educators, including different aspects that are relevant for teacher training. • Professional development program (Diploma in math education) for teacher educators (starting January 2014).