Lifelong Learning Programme

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Title of the Experience
Logarithmic functions
Name of the teacher
Viera Kolbaská
Country where it took place
School typology
High Secondary School
Thematic Area
Experience typology
Teaching in class
Type of contact
Description of the Experience
The aim of this course topic is using axial symmetry to create graphs of inverse functions of the various functions that pupils know; analyze to which functions and what conditions exist inverse functions and consequently lead students to the knowledge of logarithmic functions as an inverse function of the exponential function. At the same time the students read graphs of the function definition, domain values and characteristics (monotony of the limitations and features of pairing and un-pairing of the functions).

The thematic unit of Logarithmic function (2nd year, second semester of the school year) follows the teaching of a unit of Exponential functions and Exponential equation. Previously, however, the students got familiar with the concept of function, fields of functions, features of the functions such as monotony, pairing and un-pairing, the limitations and the maximum and minimum of functions (2nd year, the first half of school year ). Students also know from the first grade the function kinds such as the constant, the linear, and the quadratic functions with absolute value.
Students are introduced to the problems of curriculum in a discussion about the axial and central symmetries, which were bound in terms in the 2nd year with pairing and un=pairing of the functions. This is followed by the construction of graphs of linear, quadratic and exponential functions, functions with absolute value (without a PC), which is under the y axis, the x axis. The axis of the coordinate system is given by the equation y = x of the constructed graph of each particular function. Consequently, students are introduced to the concept of an inverse function, inverse function graph properties and functions inverse to each other (study of the functions and the limitations of the monotony of the functions and its pairing and un-pairing properties. Teaching this curriculum is guided through brainstorming, conceptual mapping, problem dialogue, worksheets and PowerPoint presentations, which are alternated and adjusted according to the level of pupils' skills and knowledge.
Use of the worksheets is either individually or in pairs, when there is also a space for discussion among students.

This thematic unit is in lessons conducted without a PC. Solving problems by using PC is recommended to pupils at home in preparation for the upcoming classes of and in preparation for written verification of knowledge of the thematic unit.

To teach a curriculum topic designed this way is needed at least 5 teaching hours.

To prepare for a class students were again able to use the website.
I started preparing the documents of the website according to their wish so that the worksheets were at the beginning of the core elements of the curriculum and part of the task was solved.

For a successful management of the curriculum it is necessary to cope well with the curriculum of the first year of axial symmetry, linear and quadratic functions and functions with absolute value.
Challenges to the successful implementation of teaching this subject matter were similar to the previous study topics:
1. Little knowledge of axial symmetry
2. Insecure knowledge of the subject matter of the abovementioned functions

Students had problems especially in meeting the challenges of the quadratic function, and the functions with absolute value. They constructed graphs on the basis of determining the values of several functions without sufficient knowledge of the top of the graph of the function, minimum and maximum functions, intersections of the functions of the coordinate axes and the monotony property of the functions.
Therefore, the number of teaching hours was enlarged by those needed for rehearsing and further understanding of the functions. They were a part of the lessons as well as the consultation time outside the classroom.

Recommended website:
I must continue to say that pupils made use of the website as well as the possibility of extracurricular time "to remove their lack of understanding" in small scale.
It was again the most effective to address the challenges of worksheets and especially let them work them out individually and for additional points in the evaluation.
After previous experience, I allow students to use their own "cheat sheets - formulas", which was on their side positively evaluated. This tool also allows better communication between students and the teacher.
Of pupils' comments is worth mentioning that they saw the possibility of using the lessons learned in vocational subjects. These findings will be used at the beginning of the 3rd year.
Curriculum on the functions they generally did not like. Much rather they solve different tasks in the field equations.

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Dissemination Seminar in Florence

31 October 2015 The seminar has been held in ITIS “A. Meucci” one of the schools involved within Goerudio project activities. Its main aim was to promote the results of the project toward a broad sample of stakeholders even overcrossing the number of people directly involved in the production of project outcomes. This purpose has been totally achieved especially thanks to the participation of students and teachers coming from different schools or from other classes instead of those ones directly involved within the project activities.