Lifelong Learning Programme

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Title of the Experience
Exponential 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 thematic unit is to combine knowledge of power, which use within the field of study is mainly in operations with units of different variables (conversion of units of large and small numbers using 10 squares of numbers and operations with them) as well as the formation of new relationships in physics and electronics implementing expressions in relationships with functional relationships powers and exponent and the graphical representation of various exponential functions to help students become proficient in drawing graphs depicting relationships between variables in electronics and mechanical engineering.

1. Function – the term function, domain range and range values of functions, function graph (use of the task files on the website within the home preparation time, solving worksheets)
2. Constant, linear, and quadratic functions (repeating of the first year curriculum) - graph, domain range and range of the function values, the monotony of functions (presentation in PowerPoint - basic information about the features, conceptual mapping, worksheets)
3. Power law functions - graph, domain range and the range of function values, monotony functions, pairing and unpairing of the functions, the limitations of functions, maximum and minimum of functions (repetition of a power of knowledge - worksheet and a set of tasks on the website for home preparation, marked in italics are those properties of functions that are a newly acquired knowledge)
After follow these steps:
1. Definition of an exponential function - problem teaching, activities with calculator - define the concept, graphical representation of functions and function ranges
2. Properties of exponential functions – making graphs using the PC and reading from them the properties at determined functions they already know from previous time
3. Setting the homework as a preparation for the review test by a set of tasks from the website, consultations in extracurricular time to the topic of websites tasks
4. Written verification of the newly acquired knowledge, written test

Solving the exponential functions is the curriculum that is taught at the beginning of the second semester of the second year of secondary school. For the successful management of the curriculum it is necessary to cope with the curriculum of the square and solving linear and quadratic equations and inequalities of the first year (intersections of function graphs with axes coordinate system and determining the domain of functions in more complex tasks).
Challenges to the successful implementation of teaching this curriculum are:
1. Lack of knowledge about the activities with squares (pupils achieve during the course of the first year only average or below average rating)
2. Insecure knowledge of the curriculum of equations and inequalities of various kinds, intervals as a set of domain functions
3. Low skills in drawing graphs taught during the 1st year(linear, quadratic and constant functions)

Recommended webpage:
I must say that pupils in small scale used the website. Either they did not bring teaching aids (calculators, spreadsheets, textbooks) to the classroom.
The most effective solution to problems was using the worksheets either individually, in pairs or in groups.
The best motivation for most students was receiving additional points to their summative evaluation.
Students positively evaluated those lessons aiming at rehearsing the curricular topics as well as the opportunity to use the “cheating notes- formulas”. They liked the gradation of the classes from the most simple to the challenging tasks in which they had to use higher mind operations. They liked the opportunity to consult with the teacher outside the classroom time and the openness of the discussions during the class hours.

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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.