Unit GEOMETRY
- Course
- Primary teacher education
- Study-unit Code
- A000641
- Curriculum
- In all curricula
- CFU
- 7
- Course Regulation
- Coorte 2017
- Offered
- 2020/21
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
GEOMETRY
| Code | A000643 |
|---|---|
| CFU | 6 |
| Teacher | Fabio Pasticci |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Discipline matematiche |
| Academic discipline | MAT/03 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Plane euclidean geometry: euclid's postulates polygon(generalities, convexity,concavity, angles) triangles and Pythagoras' Theorem, Euclid theorems quadrilateral and their properties, regular polygons circumference and circle Space euclidean geometry: polyhedra, pyramids, prisms regular polyhedra solido f devolution Analytic geometry Use of cartesian coordinates in the line, in the plane, in the three-dimensional space The cartesian plane: equation of straight lines Graphs, Cartesian coordinate system for a three-dimensional space |
| Reference texts | Idà M., Note di Geometria, Pitagora Editrice, Bologna 2001 Montagnoli L., Appunti di geometria elementare, EDUCatt, Milano 2015 |
| Educational objectives | The course aims to provide adequate theoretical tools for the disciplinary content of geometry and also to integrate them with educational ideas. The aim is to allow students to guide the pupils of preschool and primary school to a vision of geometry 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 analytical geometry: line, circumference, parabola, ellipse and hyperbola. |
| 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 | Euclidean geometry in the plane. - Cognitive Brainstorming (What geometry is // What is it for, what rational and practical needs do I meet // What geometrical concepts do you think to know // What geometrical concepts do you think you should ignore) on the students' previous knowledge and training needs. Introduction to National Guidelines in relation to the "geometry" discipline. - Deepening on National Indications in relation to geometry. Spatial orientation, fundamental geometric entities. - Basic geometric entities (point, straight line, plane), straight line parts and plane parts, measurement (quantities and measurement, international system, length measurements, derived quantities, extent measurement). - Polygons, vertices and diagonals, convexities, internal and external angles, the perimeter, the triangles. - The quadrilaterals, the regular polygons, the heights, the area. - A measure linked to polygons: the area, the equispectable polygons, the formulas. The circumference and the circle, the first definitions, the irrational number pi, the transcendence of pi, the measure of the circumference and the area of the circle, the inscribed polygons and the circumscribed polygons. The area of circumscribed polygons, the area of regular polygons. - The transformations of the plan. The isometries: the translation, the axial symmetry, the central symmetry, the rotation. - The translation, the axial symmetry, the central symmetry, the rotation. The homotheties, the similarities. Problems. - Problems, the geometry of space. The axioms and the first properties, the solid figures and their representation. The polyhedra, Euler's formula, the regular polyhedra, the prisms, the pyramids, the rotation solids, the cylinder, the cone, the sphere, other rotation solids. Regular solids - Volumes of solids, logic of the propositions vel and et, injective, surjective, bijective functions. - The theorem of Pythagoras with proof, Euclid's first theorem with proof, according to Euclid's theorem with proof. Solid geometry. General notions, the axioms and the first properties, perpendicularity straight-plane, theorem of the three perpendiculars, angle dihedral, angle, polyhedra and regular polyhedra, prisms, pyramids, surfaces and rotation solids, volume of a solid. Regular solids. Solid geometry. Analytic geometry: - Cartesian plane, bijective functions, straight line through two points, straight lines parallel to the axes, equation of a straight line through two points, equations of lines parallel to the axes, angular coefficient, systems, coordinates in space. - The volume of the sphere, the principle of Cavalieri and its application to the calculation of volumes, the volume of the sphere, exercises on calculation of volumes of rotation solids, specific gravity, density, areas of surfaces of solids of rotation. - Height of a regular tetrahedron with proof, equation of the straight line by two points, distance between two points in the three-dimensional space, exercise on the equation of the circumference known the center and the radius, equation of the line parallel to a given line and passing through a point. Distance between two points in three-dimensional space. Sphere of center (a, b, c) and radius r. |
GEOMETRY LAB
| Code | A000642 |
|---|---|
| CFU | 1 |
| Teacher | Emanuela Ughi |
| Teachers |
|
| Hours |
|
| Learning activities | Caratterizzante |
| Area | Discipline matematiche |
| Academic discipline | MAT/03 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Mathematical Laboratory: from the theory to teaching activities |
| Reference texts | www.emanuelaughi.com http://www.mathematicsinthemaking.eu/ |
| Educational objectives | The student will experience many examples of innovative teaching proposals, all belonging to a laboratory approach. He/she will learn how apply this methodology, using concrete or visual artifacts in planning teaching activities for the mathematics. |
| Prerequisites | No |
| Teaching methods | The students will be engaged in Mathematical Laboratory activities, as described in the document Matematica2003 )Unione Matematica Italiana). They will use mathematical exhibits, and their meaning and possible teaching uses. Moreover, the students will be guided to realize some copies of the mathematical object themselves. |
| Learning verification modality | The exam is intended to assess the student's ability to apply the laboratory modality for mathematics teaching illustrated during the course. Therefore the student, after having agreed on a theme with the teacher, will develop an educational proposal on this topic. The exam will therefore consist of the presentation and discussion of this proposal. The exam can also be taken in English, upon request by the student. |
| Extended program | Workshop experiences on vision. Workshop on construction and study on the theme ofn polyhedra. From the cube to the cells of the bees. How a soccer ball is made. The cubosoma. Napier bones, binary notation, Chinese Remainder theorem. Mathematics laboratory in case of difficulty or handicap: Bhaskara cards, exhibits for the blind. Early deaf activities. |