MATHEMATICS EDUCATION

Cristina COPPOLA MATHEMATICS EDUCATION

0522200036
DIPARTIMENTO DI MATEMATICA
EQF7
MATHEMATICS
2022/2023



YEAR OF COURSE 1
YEAR OF DIDACTIC SYSTEM 2018
SPRING SEMESTER
CFUHOURSACTIVITY
648LESSONS
Objectives
THE AIM OF THE COURSE IS TO PROVIDE KNOWLEDGE OF MATHEMATICS EDUCATION IN A HISTORICAL CONTEXT AND SUPPORT THE DEVELOPMENT OF CRITICAL REFLECTION ABOUT THE MAIN EPISTEMOLOGICAL ISSUES REGARDING MATHEMATICS TEACHING AND LEARNING.

KNOWLEDGE AND UNDERSTANDING: THE COURSE AIMS AT SUPPLYING STUDENTS WITH THE MAIN THEORETICAL FRAMEWORKS IN MATHEMATICS EDUCATION AND THE MAIN METHODOLOGIES, BY SETTING IT IN THE HISTORICAL CONTEXT AND IN THE NATIONAL AND INTERNATIONAL RESEARCHES AND BY DEALING THE CONCEPTUAL QUESTIONS BY AN EPISTEMOLOGICAL POINT OF VIEW.

APPLYING KNOWLEDGE AND UNDERSTANDING: THE COURSE AIMS AT STIMULATE A CRITICAL ANALYSIS OF THE MAIN TEACHING METHODOLOGIES, ALSO REFERRING TO THE SPECIFIC ROLE OF THE TEACHER, TO THE CONCEPTUAL, EPISTEMOLOGICAL, LINGUISTIC AND DIDACTIC POINTS FOR THE MATHEMATICS TEACHING AND LEARNING.

MAKING JUDGEMENTS: THE COURSE, STARTING FROM THE ANALYISIS OF THE MAIN THEORETICAL FRAMEWORKS IN MATHEMATICS EDUCATION, INTENDS TO MAKE STUDENTS BECOME INDEPENDENT IN REFLECTION ABOUT THE PROJECT OF DIDACTICAL ACTIVITIES AND OF A MATHEMATICAL CURRICULUM COHERENT WITH THE AIMS OF THE NATIONAL INDICATION FOR EDUCATION.

COMMUNICATION SKILLS: THE COURSE AIMS AT STRENGTHEN MATHEMATICAL TOOLS AND LINGUISTIC COMPETENCIES ALSO FROM A METACOGNITIVE POINT OF VIEW, USEFUL TO MAKE STUDENTS ABLE TO COMMUNICATE, PROBLEMS, IDEAS AND SOLUTIONS REGARDING MATHEMATICS AND MATHEMATICS EDUCATION AND ABLE TO CLEARLY AND RIGOROUSLY EXPLAIN THE ACQUIRED KNOWLEDGE.

LEARNING SKILLS: DURING THE COURSE, AN AIM IS TO FOSTER STUDENTS’ DEVELOPMENT OF A FLEXIBLE AND ANALYTICAL MINDSET ALLOWING THEM TO IDENTIFY AUTONOMOUSLY WHICH KIND OF KNOWLEDGE HAS TO BE EXAMINED IN DEPTH IN ORDER TO ANALYSE DIDACTICAL PRACTICES FOR THE LEARNING OF MATHEMATICS AND, MORE IN GENERAL, FOR PROBLEMS MANAGEMENT BOTH IN A MATHEMATICAL CONTEXT AND IN OTHER CONTEXTS SUCH AS THE BUSINESS ONES.
Prerequisites
BASIC MATHEMATICAL KNOWLEDGE
Contents
WHAT MATHEMATICS EDUCATION IS, THE ORIGINS OF THE RESEARCH. THE SO CALLED JUSTIFICATION PROBLEM. THE FORMATIVE VALUE OF MATHEMATICS EDUCATION. GENERAL DIDACTICS AND DISCIPLINARY DIDACTICS. DIFFERENT POINT OF VIEWS ABOUT MATHEMATICS EDUCATION, EVOLUTION OF RESEARCH OVER THE YEARS. DIDACTICS OF TYPE A AND ITS LIMITS. DIDACTICS OF TYPE B, EPISTEMOLOGY OF LEARNING. DIDACTICS OF TYPE C.
THE DIDACTIC SYSTEM (ACCORDING TO CHEVALLARD). THE THREE POLES: TEACHER, STUDENT, KNOWLEDGE AND THE RELATIONSHIPS BETWEEN THEM. THE DIDACTIC TRANSPOSITION. DEVOLUTION AND INSTITUTIONALIZATION PROCESSES. THE NOOSPHERE.
DIFFICULTIES IN MATHEMATICS, ERROR AND EVALUATION.
CAUSES AND INDICATORS OF DIFFICULTIES IN MATHEMATICS. CRITICALITY OF THE TRADITIONAL INTERVENTION, ON THE TEACHER SIDE AND ON THE STUDENT SIDE. THE MYTH OF COMMITMENT. ERRORS AND FAILURES. PERCEIVED CAUSES OF FAILURE. MOTIVATION AND VOLITION. THE IMPORTANCE OF THE METHODOLOGY: PROBLEM SOLVING AND LABORATORY. THE EXPRESSION: “TO BE GIFTED AT MATH”: STUDIES AND RESEARCHES. SELF-ASSESSMENT. REFLECTIONS ON ASSESSMENT IN MATHEMATICS.
THE EPISTEMOLOGY OF ERROR IN MATHEMATICS. ERRORS AND DIFFICULTIES. THE ERROR IN HISTORY. THE "COMPROMISE OF CORRECT ANSWERS". SUCCESS THEORIES AND FAILURE IN MATHEMATICS. THE TIME VARIABLE. EVOLUTION OF THE APPROACH TO ERROR. THE METAPHOR OF GETTING LOST BY RAFFAELLA BORASI. REFLECTIONS ON THE OBJECTIVITY OF THE ASSESSMENT PROCESSES AND ON THE RECOVERY INTERVENTIONS. DIFFERENCES BETWEEN OBSERVATION AND INTERPRETATION.
SPECIALIZED KNOWLEDGE OF MATHEMATICS TEACHERS. PEDAGOGICAL CONTENT KNOWLEDGE. MATHEMATICAL KNOWLEDGE FOR TEACHING. INTERPRETATIVE KNOWLEDGE AND RELATED RESEARCH.
LEARNING THEORIES: FROM BEHAVIORISM TO CONSTRUCTIVIS.
BEHAVIORISM. THE OBJECT OF STUDY AND THE LEARNING MODELS. EXPERIMENTS AND RESEARCH: WATSON, PAVLOV, THORNDIKE (LEARNING LAWS), SKINNER. LINK BETWEEN STIMULUS AND RESPONSE AND LEARNING PROCESSES. THE INFLUENCE OF BEHAVIORISM ON TEACHING. THE TRANSMISSION MODEL IN MATHEMATICS EDUCATION. THE CRITICISMS OF THE TEACHING MODEL BASED ON TRANSMISSION. OVERCOMING THE BEHAVIORIST VIEW. ERLWANGER'S STUDY.
COGNITIVISM: SIMILARITIES AND DIFFERENCES BETWEEN COGNITIVISM AND BEHAVIORISM. RADICAL CONSTRUCTIVISM. VON GLASERSFELD. PIAGET: THE PROCESSES OF ASSIMILATION AND ACCOMMODATION; THE FOUR FUNDAMENTAL STAGES OF THE INDIVIDUAL'S COGNITIVE DEVELOPMENT. CRITICISMS OF PIAGET (DONALDSON). SOCIAL CONSTRUCTIVISM. VYGOTSKY. THE IMPORTANCE OF THE CONTEXT. THE ROLE OF CULTURE AND LANGUAGE. THE ZONE OF PROXIMAL DEVELOPMENT. LEARNING AS A CONSTRUCTIVE ACTIVITY. ANALYSIS OF RESEARCHES ON THE IMPORTANCE OF THE CONTEXT: KAHNEMAN AND TVERSKY EXPERIMENT; MCCLOSKEY AND SCHOENFELD EXPERIMENT; WASON TEST.
COLLABORATIVE LEARNING AND PEER TUTORING. COLLABORATIVE GROUPS AND ROLE ASSIGNMENT. THE ROLE OF THE TEACHER. THE ASSESSMENT. PEER-REVIEW METHODOLOGY.
THE DIDACTIC CONTRACT. HISTORY OF THE CONCEPT OF DIDACTIC CONTRACT. THE RESEARCH "THE AGE OF THE CAPTAIN". INTERPRETATIONS OF STUDENT RESPONSES AND POSSIBLE CAUSES. DIDACTIC CONTRACT CLAUSES. IMPLICATIONS IN THE TEACHING-LEARNING PROCESSES OF MATHEMATICS. JOURDAIN EFFECT AND TOPAZE EFFECT. BREAKDOWN OF THE DIDACTIC CONTRACT AS A STRATEGY.
VIEWS OF MATHEMATICS: INSTRUMENTAL APPROACH TO MATHEMATICS (AND INSTRUMENTAL UNDERSTANDING) AND RELATIONAL APPROACH TO MATHEMATICS (AND RELATIONAL UNDERSTANDING).
Teaching Methods
LABORATORY INDIVIDUAL AND GROUP ACTIVITIES BOTH IN PRESENCE AND IN BLENDED E-LEARNING MODALITIES, MATHEMATICAL DISCUSSION, FRONT LECTURES BY THE USE OF MULTIMEDIA TOOLS, DISCUSSION OF RESEARCH PAPERS.
DURING THE LESSONS, WE TRY TO COLLECTIVELY CONSTRUCT THE SPEECH BY ALTERNATING SHORT EXPLANATIONS FROM THE TEACHER TO MOMENTS OF DISCUSSION DURING WHICH STUDENTS WILL BE ACTIVELY INVOLVED IN ASKING QUESTIONS, IN EXPOSING IDEAS, IN PROBLEMATIZING, IN REFLECTING CRITICALLY. THE LABORATORY MOMENTS INCLUDE BOTH INDIVIDUAL AND IN COLLABORATIVE GROUP WORK ON SUITABLE ACTIVITIES, USING MATERIAL OR SYMBOLIC ARTIFACTS WITH THE AIM OF REFLECTING AND INTERNALIZING THE TOPICS, ASKING STUDENTS TO PLAY THE DUAL ROLE OF STUDENTS AND FUTURE TEACHERS. ALL TOPICS ARE TREATED WITH AN ALTERNATION OF THE DESCRIBED METHODOLOGIES.
Verification of learning
THE FINAL EXAMINATION IS AIMED TO ASSESS KNOWLEDGE AND UNDERSTANDING CAPABILITIES OF THE CONTENT PRESENTED DURING THE COURSE, AS WEL AS THE ACQUIRED COMPETENCES.
THE ASSESSMENT WILL BE CARRIED OUT BY MEANS OF AN ORAL EXAMINATION, STRUCTURED IN A SEMINAR AND AND AN ORAL EXAM WHICH WILL ALSO INCLUDE THE DISCUSSION OF THE PLANNING OF AN EDUCATIONAL PATH.
IN THE SEMINAR THE CAPABILITY OF EXAMINING IN DEPTH A TOPIC AND OF PRESENTING IT WILL BE EVALUATED. IN THE ORAL EXAM WILL BE ASSESSED THE KNOWLEDGE OF THE CONTENT OF THE SUBJECTS EXPOSED, THE ABILITY TO EXPOSE THEM CRITICALLY AND TO CONTEXTUALIZE THEM WITHIN THE FRAMEWORK OF MATHEMATICAL EDUCATION AND TO APPLY THEM CRITICALLY IN THE DESIGN OF EDUCATIONAL PATHS.
IN BOTH THE MOMENTS THE ACQUIRED GENERAL CROSS COMPETENCIES WILL BE EVALUATED.
THE FINAL EVALUATION WILL BE EXPRESSED IN THIRTY-FIVE. LODE MAY BE ATTRIBUTED TO STUDENTS SHOWING TO BE ABLE TO TO APPLY THE ACQUIRED KNOWLEDGE AND COMPETENCIES IN CONTEXT DIFFERENT FROM THOSE PROPOSED IN THE LESSONS.
Texts
ANNA BACCAGLINI FRANK, PIETRO DI MARTINO, ROBERTO NATALINI, GIUSEPPE ROSOLINI, 2017. DIDATTICA DELLA MATEMATICA. MONDADORI UNIVERSITÀ.
RECOMMENDED TEXTS:
ROSETTA ZAN, 2007. DIFFICOLTÀ IN MATEMATICA. OSSERVARE, INTERPRETARE, INTERVENIRE. SPRINGER

PIER LUIGI FERRARI (2021). EDUCAZIONE MATEMATICA, LINGUA, LINGUAGGI. UTET UNIVERSITÀ.

ROSETTA ZAN, ANNA BACCAGLINI-FRANK, 2017, AVERE SUCCESSO IN MATEMATICA. STRATEGIE PER L’INCLUSIONE E IL RECUPERO. UTET UNIVERSITÀ.

BRUNO D’AMORE, 1999, ELEMENTI DI DIDATTICA DELLA MATEMATICA. PITAGORA EDITRICE BOLOGNA.
More Information
THE UNIVERSITY’S MOODLE PLATFORM WILL BE USED FOR THE COURSE MATERIAL AND FOR CARRYING OUT THE PROPOSED ACTIVITIES.
FOR FURTHER INFORMATION, PLEASE CONTACT THE TEACHER (email: ccoppola@unisa.it).
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