Unit TEACHING OF MATHEMATICS
- Course
- Primary teacher education
- Study-unit Code
- A000594
- Curriculum
- In all curricula
- CFU
- 7
- Course Regulation
- Coorte 2020
- Offered
- 2021/22
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
TEACHING OF MATHEMATICS
| Code | A000596 |
|---|---|
| CFU | 6 |
| Teacher | Fabio Pasticci |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Discipline matematiche |
| Academic discipline | MAT/04 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | italian |
| Contents | Methodological indications on particular topics of mathematics. Problem solving. Critical analysis of the main teaching methods developed in research in mathematics education and in the history of mathematics, also with reference to the specific role of the teacher, to the conceptual, epistemological, linguistic and didactic problems of teaching and learning mathematics. |
| Reference texts | Palladino F., Lombardi L., Palladino N., Algoritmi elementari del calcolo aritmetico e algebrico. Tradizione e modernità, Pitagora Editrice, Bologna 2005 D’Amore B., Elementi di didattica della Matematica, Pitagora Editrice, Bologna 1999 |
| Educational objectives | The course aims to provide adequate theoretical tools for the disciplinary content of mathematics education. The aim is to allow students to guide the pupils of preschool and primary school to a vision of mathematic built on the basis of concrete experiences. Moreover students, who will be future teachers, will lead the users of the preschool and primary school through learning paths based on observation and intuition to reach an adequate property of language, useful both in defining the objects and in describing their properties. All this with a view to arouse interest in the discovery of bonds, of common characteristics without losing sight of the reality experienced. |
| Prerequisites | Mastery of the basic tools of logic and mathematics including: - elementary algebraic calculation: powers, absolute value, polynomials, equations and inequalities of 1st and 2nd degree; - basic notions of geometry. |
| Teaching methods | No educational intervention can be independent of the training needs of learners and also of preconceptions, false knowledge, prejudices, shortcomings of the same. If the teacher does not take into account these data, the intervention risks becoming not only ineffective, but perhaps also generative of confusion, disaffection for the discipline, decline in interest and motivation. Moreover, an educational intervention that does not actively involve the learners, making them partners and protagonists of their own training path, could turn into a simple (and quite useless) "transmission of notions". Therefore we believe that it is necessary, where and whenever possible, to set up classroom meetings for interlocutors and workshops (where "laboratory" obviously means an attitude of the mind rather than a physical space). This is because any learning is by its nature a social co-construction, we consider very important the continuous dialogue with and among the students, thus genuine knowledge can emerge from the comparison. This is an important condition to reach competence. Method choices • Use of brainstorming (oral or written) for cognitive purposes • Direct experimentation of the concepts dealt with through graphic representations, games, direct body experiences ... • Constant feedback on requests and learning • Periodic, formal and non-formal tests related to learning, without evaluative purposes but, rather, for students to ascertain and self-evaluate their own path • Periodic comparisons and discussions on the perceived effectiveness of educational intervention and relationship • Writing a diary / lessons-record of the topics explained in each lecture to be shared with the learners to gradually and dialogically build the general framework of the cognitive path • Use of the web page to consult lesson times, reception schedule, program, diary / topic log |
| Other information | Office hours: by appointment (email fabio.pasticci@unipg.it ) |
| Learning verification modality | The verification method consists of an exam (written /oral) with a score of thirty and possible laude. The test allows to ascertain both the ability to know and understand, and the ability to apply the acquired skills. |
| Extended program | General teaching and disciplinary teaching. Misconceptions in arithmetic and geometry: the angle, the heights, the diagonals. Examination of some textbooks of primary schools. The student / teacher interaction: the didactic contract. Problem solving. Cooperative learning. The constructivism. Utility of history in mathematics education. Types of learning obstacles. How to structure a work. Natural numbers; dividers and multiples of a natural number. The prime numbers and methods of use in class from the history of mathematics. The sieve of Eratosthenes. Prime numbers and cryptography: tools for playing in class. Prime factors and the fundamental theorem of arithmetic. Maximum common divisor and least common multiple: definition and algorithms from the history of mathematics (Euclid's algorithms). Multiplication with the "Arabian" grid method. Multiplication with the Egyptian method. The sticks of Nepero. Fibonacci numbers and golden section: art, nature and history. The square root: side and diagonal numbers. Incommensurability and irrational numbers: Pi and Phi. Pythagorean geometric numbers; triangular numbers, square numbers, pentagonal numbers; how to use them in the classroom; how to deduce formulas to generate them. The Pythagorean triads. First degree equations. Problems solvable by first degree equations; alternative methods to equations. The role and importance of logic in teaching; flow charts; an example of activity with "the figurines". The laboratory and the artifacts. The geopiano and the algorithm of the Arabs (of easy realization). Definition of a regular star polygon. The use of star polygons in the learning of elementary plane geometry. The misconceptions highlighted in plane geometry. Presentation of a classroom activity. Misconceptions on the concave polygons. The link between regular star polygons and coprime numbers. Sfard's research on learning mathematics. Presentation of activities in the classroom: from solid geometry to plane geometry (the polyhedra and the Euler formula); the golden section; plane geometry with paint. Critical analysis of the main teaching methods developed in research in mathematics education and in the history of mathematics, also with reference to the specific role of the teacher, to the conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics. |
LABORATORY FOR TEACHING OF MATHEMATICS
| Code | A000595 |
|---|---|
| CFU | 1 |
| Teacher | Nicla Palladino |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Discipline matematiche |
| Academic discipline | MAT/04 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | The aim is to integrate the Mathematics Education course with laboratory activities and software use. The pedagogical methodologies in the Didactics course will be applied |
| Reference texts | Palladino, Palladino, Lombardi; Algoritmi elementari del calcolo aritmetico e algebrico. Tradizione e modernità. Bologna, Pitagora 2005. |
| Educational objectives | analysing and planning teaching sequences relative to the topics of the course |
| Prerequisites | Basic knowledge of sets, operations, algebra, elementary geometry |
| Teaching methods | Individual and group-work activities and exercises on mathematics problems; brain storming, problem solving |
| Other information | Per approfondire: Materiale didattico in rete sul sito del G.R.I.M. (Gruppo di Ricerca insegnamento/Apprendimento delle Matematiche): http://dipmat.math.unipa.it/~grim/matdit.htm e dal sito https://rsddm.dm.unibo.it/ |
| Learning verification modality | Oral examination starting from a work on a topic chosen by the student with the support of the teacher. |
| Extended program | Particular topics of the school curriculum will be chosen to be explored and to develop learning units |