Izvleček
Učenje in poučevanje matematike v velikem delu temelji na razumevanju in osmišljanju matematičnih vsebin, ki se jih učenci in dijaki učijo. Proces izgrajevanja razumevanja je dolgoročen in kompleksen, učinkovito pa ga lahko regulira učitelj s premišljeno pripravo nalog in dejavnosti v podporo izgradnji in uporabi matematičnih pojmov in konceptov. Rutar Ilc (Rutar Ilc v Suban Ambrož 2012) navaja, da učenje z razumevanjem »poteka s pomočjo miselnih aktivnosti, s katerimi gradimo odnos in povezave med dejstvom in idejami ter ustvarjamo mentalne modele«. Za matematiko je vzpostavljanje odnosov in povezav med matematičnimi pojmi in koncepti zelo pomembno, saj je narava matematičnega znanja kumulativna. Z uporabo različnih reprezentacij, aktivacijo notranjih povezav med pojmi, povezovanju z drugimi področji, aktivnostjo dijakov lahko vzpodbujamo razumevanje in omogočimo osmišljeno uporabo matematičnega znanja. Reševanje problemskih nalog, ki jih dijak rešuje na različne načine (npr. s konkretnimi pripomočki, s tehnologijo, analitično), je lahko učinkovit način za razvijanje razumevanja matematičnih vsebin in njihovo uporabo. Predstavljamo tri primere nalog s prepogibanjem papirja, ki omogočajo uporabo matematičnega znanja in preverjanje ter razvijanje razumevanja nekaterih pojmov iz geometrije.
Abstract
Using and Making Sense of Mathematical Content in the Light of Complexity: Three Paper Folding Examples
Learning and teaching mathematics is based to a large extent on the understanding and making sense of
mathematical content taught to primary and secondary school students. The process of developing this understanding is complex and takes time, while it can be effectively regulated by the teacher with a well-thought-out preparation of tasks and activities that supports the building and use of mathematical notions and concepts. Rutar Ilc (Rutar Ilc in Suban Ambrož 2012) states that learning by understanding is a process that »uses mental activities that help build the relationships and connections between facts and ideas, creating mental models.« Establishing relationships and connections between mathematical notions and concepts is very important in mathematics due to the cumulative nature of mathematical knowledge. Using various representations, activating inner connections between the concepts, linking other areas and engaging students can contribute to the understanding and logical use of mathematical knowledge. Various ways of problem solving (e.g. using practical tools, technology or analytics) can be an effective method to develop the understanding and use of mathematical content. The article introduces three paper folding examples as ways of using mathematical knowledge as well as testing and developing the understanding of certain geometric concepts.