Naslov
A different approach to solving linear Diophantine equations. An experimental study on using multiple strategies to solve linear Diophantine equations

Autori
Lončarević, Radomir

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Scientific Conference “Research in Mathematics Education” / - , 2019, 87-102

ISBN
978-86-6447-017-9

Skup
Znanstvena konferencija "Istraživanja u matematičkom obrazovanju"

Mjesto i datum
Beograd, Srbija, 10.05.2019. - 11.05.2019

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
metode istraživanja, znanje koje se zadržava, proceduralna fleksibilnost, linearne diofantske jednadžbe, Fareyev niz
(Research methodes, retained knowledge, procedural flexibility, linear Diophantine equations, Farey sequence)

Sažetak
The most common methods for solving the linear Diophantine equations (LDE) of form 𝑎𝑥+𝑏𝑦= 𝑐, 𝑎, 𝑏, 𝑐 ∈ℤ that students learn in advanced classes in primary schools are Euclid alghorithm, Euler method and solving by guessing or inspection. This paper introduces an alternative method in solving LDE of form 𝑎𝑥+𝑏𝑦=𝑐, 𝑎, 𝑏, 𝑐 ∈ℤ. The LDE is solved using the properties of Farey sequence and in this paper the algorithm for solving LDE is given. In the second part of the paper an experimental study is described and the answer on the following question is given. Can using multiple strategies lead to greater gain in solving LDE, or does it lead to confusion? The experimental study was conducted on 124 seventh-grade students, who had been divided in four groups. Each group of students were acquainted with different numbers of methods for solving linear Diophantine equations. Post-test results show an interesting difference in solving LDE from group to group. Also, in this paper we present the main reasons for using the specific method to solve LDE from students’ point of view. One year later we conducted measurement in retained knowledge and procedural flexibility and here we present our findings.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Pedagogija, Obrazovne znanosti (psihologija odgoja i obrazovanja, sociologija obrazovanja, politologija obrazovanja, ekonomika obrazovanja, antropologija obrazovanja, neuroznanost i rano učenje, pedagoške discipline)

POVEZANOST RADA