NOMAD 13(2), 2008. Finnish mathematics teacher students’ informal and formal arguing skills in the case of derivative



In this study, formal and informal reasoning skills of 146 Finnish subject-teacher students in mathematics are investigated. The students participated in a test in which they were asked to argue two claims concerning derivative both informally and formally. The results show that the success in the formal tasks and the success in the informal tasks were dependent. However, there were several students who did well in the formal tasks despite succeeding poorly in the informal tasks. The success both in the formal tasks and in the informal tasks was dependent also on the amount of passed studies in mathematics and on the success in these studies. Moreover, these factors could have a stronger effect on the formal than on the informal reasoning skills.


I denna studie undersöktes den formella och informella argumentationsfärdigheten hos 146 finska blivande ämneslärare i matematik. Studenterna deltog i ett test, där de skulle argumentera både formellt och informellt för två påståenden gällande derivatan. Resultaten visar, att framgången i formella uppgifter och i informella uppgifter beror av varandra. Studenterna kunde emellertid klara sig bra i formella uppgifter utan att ha likadan framgång i informella.
Resultaten i båda uppgiftstyperna var beroende både av mängden av och framgången i tidigare matematikstudier. Dessutom kan de här faktorerna ha haft en starkare effekt på de formella argumentationsfärdigheterna.

Antti Viholainen is a PhD candidate at University of Jyväskylä, Finland. Since the year 2003, he has worked as a researcher in the area of mathematics education. His main interests are the nature of mathematical knowledge, informal and formal reasoning and the coherence of mental structures. In his studies, he has especially concentrated on the informal and formal representations regarding the concept of derivative.