Speaker
Description
Učitelj lahko načrtuje in izvede pouk matematike tudi drugače od klasičnega frontalnega načina, pri katerem so dijaki pasivni, ker le prepisujejo iz table v zvezke in se pri tem dolgočasijo. Raziskovalni pouk jih na aktiven način zaposli v razredu, doma, na terenu, v delavnici in v računalniški učilnici. Za iskanje podatkov, izdelavo tabel in za risanje grafov funkcij uporabljajo dijaki sodobno informacijsko komunikacijsko tehnologijo (pametne telefone z ustreznimi aplikacijami ter prenosne računalnike), kar jih še bolj pritegne k delu. V članku je opisano izkustveno in raziskovalno proučevanje grafov in parametrov kvadratne funkcije s pomočjo različnih računalniških aplikacij in fizikalnih eksperimentov. Dijaki drugega letnika programa SSI so na projektnih dnevih s programom za videoanalizo Tracker in z matematično aplikacijo GeoGebra raziskovali vrste in oblike parabol ter računali njihove funkcijske zapise, ničle, začetne vrednosti in temena. Iz videoanalize pridobljene podatke so vnesli v elektronsko preglednico Excel, narisali grafe funkcij ter jih medsebojno primerjali. Pouk je zahteval od dijakov kompetence snemanja in obdelave videoposnetkov, snemanja zaslona, uporabo elektronskih preglednic, uporabo naprednejših funkcij programa GeoGebra ter teoretično znanje o kvadratni funkciji. Izdelali so plakate in skice z definicijami parametrov kvadratne funkcije ter izvajali in dokumentirali fizikalne eksperimente, ki prikažejo nastanek in oblike različnih parabol. Namesto klasičnih nalog iz zbirke nalog so dijaki s fizikalnimi poskusi modelirali lastne parabole in zapisali njihove funkcijske predpise. Vsem eksperimentalno pridobljenim funkcijam so dijaki s svinčnikom na papir ročno preračunali funkcijske predpise, ničle, začetne vrednosti in temena ter na koncu vse preverili z vnosom parametrov v program GeoGebra.
Ključne besede: družina krivulj, GeoGebra, kvadratna funkcija in graf, videoanaliza.
Abstract
The teacher can plan and execute mathematics lessons in a different way than the classical frontal method, in which the students are passive because they just write from the blackboard into notebooks and get bored doing so. Experimental learning teaching actively engages them in the classroom, at home, in the field, in the workshop or the computer lab. Students use modern information and communication technology (smartphones with appropriate apps and laptops) to search for data, create tables and draw graphs of functions. This interactive type of work gives them motivation to work harder. The article describes the experiential and research study of graphs and parameters of the quadratic function with the help of various computer applications and physical experiments. During the project days, students of the second year of the SSI program used the video analysis program Tracker and the mathematical application GeoGebra to investigate the types and shapes of parabolas. Function parameters, zeroes, initial values and extremes were calculated. The data obtained from the video analysis was put into an electronic Excel spreadsheet and graphs of the various functions were drawn and compared. The learning process required different competencies such as video recording and editing, screen capturing, use of electronic spreadsheets, use of the GeoGebra program’s advanced functions, and theoretical knowledge of the quadratic function. Students made posters and sketches with the definitions of the quadratic function. They performed and video-documented physical experiments that show the formation and shapes of different parabolas. The students modeled their own parabolas with the use of physical experiments and wrote down their function formulas using different software. In the end, the students manually derived the function formulas, zeros, initial values and vertexes and then checked everything by entering the parameters into the GeoGebra program.
Keywords: family of curves, GeoGebra, quadratic function and graph, video analysis.
