B024358 - MATHEMATICS FOR BASIC EDUCATION & MATHEMATICS WORKSHOP

Italian

Basic facts on elementary logic. Elementary probability theory and mathematical statistics.
Topics of plane and solid geometry.
Geometric transformations.
Mandatory activities in didactic laboratory for analyzing, designing and simulating didactic contexts.

Alessandro GIMIGLIANO, Leonardo PEGGION, Elementi di matematica, UTET – De Agostini, Novara, 2018.
Notes provided by the teachers.
A complete and updated bibliography will be indicated at the beginning of the course.
A complete and updated bibliography will be indicated at the beginning of the course and of the activities in laboratory.

About the mathematical subjects addressed in the course, students must show:
- to possess basic knowledge and understanding of mathematical concepts and to know how to use and apply them to solve exercises and to propose simple mathematical models in problematic context of various levels of complexity;
- to be able to organize knowledge in a hypothetical-deductive set, in particular to be able to place hierarchically definitions, sufficient conditions, necessary conditions, characterizations, properties and to draw simple conclusions by discussing the assumed hypotheses;
- to possess communicative skills, by using correctly mathematical language, both in peer-to-peer relationships and in simulating teaching-learning sets also in didactic laboratory;
- to show good skills to learn autonomously and personally and to deepen the subjects, developed in the course;
- to be able to analyze, design and simulate teaching activities in teaching-learning contexts on topics dealt with in both mathematical courses of the first two years.

Fundamental prerequisites are both basic knowledge and algorithmic skills, useful to understand the arguments developed in the course, which are developed in any pre-academic teaching, which is supposed to be followed with dealt with seriousness and commitment.
The subjects and the skills, learned in first year course Matematica per la formazione di base (I), are supposed to be well-known.
Strong motivations towards the teaching, a positive attitude toward mathematics and awareness of the importance of mathematical education in training to a conscious and active citizenship are indispensable

Lecture-style instruction. As far as possible, students may be required to expose suggestions and remarks on the various topics and to try to solve exercises and to suggest mathematical models for simple problematic contexts.
Through the student reception, topics chosen by students will be discussed and deepen in individual way and any question can be posed to the teacher.
Mandatory activities in laboratory require active participation, relational skills, full individual involvement.

Attendance in laboratory activities is mandatory and requires individual documentable activities and the development of customized reports and materials.
Although not mandatory, class attendance is strongly recommended, because of the relevance of relational aspects in teaching-learning processes both with other students and with the teacher.
Teaching takes advantage of MOODLE platform, which is obligatory for all students and can be particularly useful for students having motivated difficulties in attending classes with regularity.
During the course, the student reception is encouraged for any discussion on mathematical topics and for any individual in-depth analysis.

Before the examination, it is required to fulfill successfully all requirements of the laboratory. The evaluation of the laboratory contributes to the determination of the final vote.
Written exam, followed by an oral exam.
Although it is impossible to make a strict separation between the two types, it is possible to state that subjects of particular examination of the written exam are all the skills required between the objectives with particular regard to the basic knowledge of the topics addressed and those of the type operational and problem-solving applications and modeling of problem situations, while the subject of particular examination of the oral examination is all the skills required between the objectives with particular regard to linguistic and communicative skills and the ability to structure hierarchically the mathematical knowledge learned by enhancing The originality and autonomy of mathematical thought.
In order to pass the exam, it is necessary at all stages to demonstrate to possess all basic elementary knowledge and basic skills in the execution of standard algorithms, which are taught in primary school.

Logic and language; elements of propositional calculus and quantifiers. Equivalence and order relations.
Elementary probability theory. Combinatorial calculus. Different meanings of probability. Basic probabilistic formulas. Conditional probability.
First topics of descriptive statistics. Measures of position and of dispersion. Representation of statistical data.
Topics of plane geometry. Lines in a plane. Parallelism and perpendicularity. Examples of plane geometrical figures. Polygons, circles and related properties.
Topics of space geometry. Lines and planes in the space. Parallelism and perpendicularity. Examples of space geometrical figures. Polyhedra. Convex and regular polyhedral and their generalizations.
Geometric transformations.