LABORATORY FOR MATHEMATICS TEACHING

Annamaria MIRANDA LABORATORY FOR MATHEMATICS TEACHING

0522200048
DIPARTIMENTO DI MATEMATICA
EQF7
MATHEMATICS
2020/2021



YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2018
SECONDO SEMESTRE
CFUHOURSACTIVITY
648LESSONS
Objectives
KNOWLEDGE AND UNDERSTANDING: THE COURSE AIMS AT FOSTERING STUDENTS’ CAPABILITIES IN APPLYING THE ACQUIRED KNOWLEDGE FOR THE ELABORATION OF DIDACTICAL PATHS AIMED TO PROMOTE MATHEMATICS LEARNING, THROUGH THE STUDY OF THE MAIN METHODOLOGIES IN MATHEMATICS EDUCATION, FRAMED IN THE NATIONAL AND INTERNATIONAL RESEARCHES, WITH PARTICULAR ATTENTION TO THE USE OF ARTIFACTS.
APPLYING KNOWLEDGE AND UNDERSTANDING: THROUGH THE REFLECTION ON LABORATORY ACTIVITIES, ANCHORED TO THE RESEARCHES IN MATHEMATICS EDUCATION, STUDENTS WILL BE ABLE TO USE IN A CRITICAL WAY THE ACQUIRED KNOWLEDGE TO REALIZE EFFICIENT DIDACTICAL PRACTICES.
MAKING JUDGEMENTS: THE COURSE AIMS AT STIMULATE THE CRITICAL ANALYSIS OF THE MAIN METHODOLOGIES IN MATHEMATICAL EDUCATION AND INTENDS TO MAKE STUDENTS BECOME INDEPENDENT IN PROJECTING DIDACTICAL ACTIVITIES, IN PARTICULAR FOCUSED ON THE LABORATORY AS METHODOLOGY AND ON THE USE OF ARTIFACTS.
COMMUNICATION SKILLS: THE COURSE AIMS AT STRENGTHEN MATHEMATICAL AND LINGUISTIC TOOLS USEFUL TO MAKE THEM 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 ANALYZE 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, IN PARTICULAR IN THE TEACHING.
Prerequisites
BASIC MATHEMATICAL KNOWLEDGE
Contents
THE DIDACTIC SYSTEM; THE DIDACTIC TRIANGLE; THE DIDACTIC TRANSPOSITION. THE CULTURAL VALUE, THE INSTRUMENTAL VALUE, THE EDUCATIONAL VALUE OF MATHEMATICS. EXTENSION OF THE DIDACTIC TRIANGLE TO THE MODEL OF TETRAHEDRON IN DIGITAL ENVIRONMENTS.
INSTRUMENTAL VISION AND RELATIONAL VISION OF MATHEMATICS: INFLUENCE ON EDUCATIONAL CHOICES. ATTITUDE TOWARDS MATHEMATICS, THE THREE-DIMENSIONAL MODEL BY DI MARTINO AND ZAN.
THE IMPORTANCE OF METHODOLOGIES. THE MATHEMATICS LABORATORY AS A METHODOLOGY. MULTIMODALITY.
SEMIOTIC MEDIATION THEORY. DIDACTICAL CYCLES WITH ARTIFACTS. MATHEMATICAL DISCUSSION.
MISCONCEPTIONS IN LEARNING MATHEMATICS. INTUITIVE MODELS, PARASITE MODELS.
LANGUAGE IN MATHEMATICS. LABORATORY ON LANGUAGE AS ARTIFACT. RELATIONSHIP BETWEEN LANGUAGE AND THE DEVELOPMENT OF MATHEMATICAL THOUGHT. PIAGET AND VYGOTSKIJ. ANNA SFARD'S DISCURSIVE APPROACH. THE LANGUAGE OF MATHEMATICS IN THE CLASSROOM: COMPARISON AND INFLUENCES BETWEEN EVERYDAY LANGUAGE AND MATHEMATICAL LANGUAGE. THE PARADOX OF SPECIFIC LANGUAGE (D’AMORE). CHARACTERISTICS OF THE MATHEMATICAL LANGUAGE: PRECISION. CONCISENESS. UNIVERSALITY. DENOTATIONAL HYPOTHESIS, INSTRUMENTAL HYPOTHESIS. SOCIO-CULTURAL APPROACH. LABORATORY ON LANGUAGE AND COMMUNICATION.
SEMIOTIC REPRESENTATION SYSTEMS. DUVAL'S STUDIES: A COGNITIVE APPROACH. CHARACTERIZATION OF MATHEMATICAL ACTIVITY FROM A COGNITIVE POINT OF VIEW. SEMIOTIC REPRESENTATIONS IN MATHEMATICAL ACTIVITY. RELATIONSHIP BETWEEN KNOWLEDGE PROCESSES AND REPRESENTATION PROCESSES, NOESIS AND SEMIOSIS. TREATMENT AND CONVERSION. ANALYSIS OF POSSIBLE STUDENTS’ DIFFICULTIES. COORDINATION AMONG SEMIOTIC SYSTEMS AND DIDACTIC FALLOUT. LABORATORY ACTIVITIES.
PRAGMATIC INTERPRETATION OF THE MATHEMATICAL LANGUAGE. COMPARISON BETWEEN MATHEMATICAL LANGUAGE AND EVERYDAY LANGUAGE FROM THE POINT OF VIEW OF THE CONTEXT. PRAGMATICS. GRICE COOPERATION PRINCIPLE. CONVERSATIONAL IMPLICATIONS. COOPERATION IN THE MATHEMATICAL CONTEXT. THEORETICAL IMPLICATIONS AND DIDACTIC CONSEQUENCES. A FUNCTIONAL PERSPECTIVE: FUNCTIONAL LINGUISTICS. THE REGISTERS: COLLOQUIAL AND LITERATE ONES. IMPORTANCE FROM DIDACTIC AND METHODOLOGICAL POINT OF VIEW.
ARGUMENTATION AND PROOF IN MATHEMATICS. PROOF IN TEACHING PRACTICE. RESEARCH ON ARGUMENTATION AND PROOF. PROOF AS AN OBJECT AND AS A PROCESS. AIMS AND FUNCTIONS OF THE PROOF. THE SOCIAL DIMENSION. RELATIONSHIP BETWEEN PROOF AND THEORETICAL REFERENCE SYSTEM. LABORATORY ON PROOF. HEALY AND HOYLES' STUDY. THE DIDACTIC TRANSPOSITION OF THE PROOF: TEACHING THE PROOF AT SCHOOL, RELATED RESEARCHES. THEORY OF DIDACTIC SITUATIONS. THE ACQUISITION OF SOCIAL AND SOCIO-MATHEMATICAL RULES. SEMINAL THEORIES. THE CONSTRUCT OF "COGNITIVE UNITY". INFERENCES CHARACTERIZING THE ARGUMENTATION ON A STRUCTURAL LEVEL: DEDUCTION, INDUCTION, ABDUCTION.
THE RELATIONSHIP BETWEEN THEOREMS, DEFINITION AND MATHEMATICAL OBJECTS. THE CONSTRUCTION OF EXAMPLES AND COUNTEREXAMPLES: DIDACTIC STUDIES. ANALYSIS AND EVALUATION OF ARGUMENTATION.
PROOF AND DEFINITIONS IN GEOMETRY. THE MANIPULATION OF OBJECTS. LEARNING GEOMETRY IN THE VARIOUS SCHOOL PHASES. THE PROBLEM OF THE TRANSITION FROM THE CONCRETE GEOMETRY OF THE FIRST SCHOOL LEVELS TO THE HYPOTHETICAL DEDUCTIVE METHOD OF HIGH SCHOOL. REFLECTIONS ON THE AXIOMATIC APPROACH TO GEOMETRY. MOVING INTO A THEORY. AN ALTERNATIVE PROPOSAL: THE POINT-FREE APPROACH.
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 COLLABORATIVE GROUP WORK ON ARTIFACTS AND SUITABLE ACTIVITIES 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 WELL AS THE ACQUIRED COMPETENCES.
THE ASSESSMENT WILL BE CARRIED OUT BY MEANS OF THE DISCUSSION OF A WRITTEN COMPOSITION AND AN ORAL EXAMINATION, STRUCTURED IN A SEMINAR AND AN ORAL EXAM.
IN THE WRITTEN COMPOSITION AND IN THE SEMINAR THE CAPABILITY OF EXAMINING IN DEPTH A TOPIC AND OF PRESENTING IT WILL BE EVALUATED. IN THE ORAL EXAM KNOWLEDGE OF THE CONTENT OF THE ARGUMENTS, CAPABILITY TO EXPOSE THEM IN A CRITICAL MANNER AND TO CONTEXTUALIZE THEM IN THE FIELD OF MATHEMATICS EDUCATION WILL BE EVALUATED.
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 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
ANNA BACCAGLINI FRANK, ROSETTA ZAN. AVERE SUCCESSO IN MATEMATICA. UN NUOVO LIBRO SULLE STRATEGIE PER L’INCLUSIONE E IL RECUPERO. DEA LIVE - DEA SCUOLA
ROSETTA ZAN. DIFFICOLTÀ IN MATEMATICA. OSSERVARE, INTERPRETARE, INTERVENIRE. SPRINGER
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