Knowing one's own level of knowledge is an important characteristic of an individual. It enables individuals to objectively evaluate their abilities and properly adapt to their advantages and disadvantages. In this paper, we present the results of the empirical research, where pre-service teacher students had to perform self-assessment aft er their seminars and mathematics classroom performance. We compared their self-assessments to their teachers' assessments. Results show that the students' self-assessments on average deviate from their teachers' assessments. We also noticed that the Dunning-Kruger eff ect is present both for seminars and mathematics classroom performance. Th e students that received low assessment scores from their teacher provided too high self-assessment scores.
Risba kot orodje za vpogled v matematično razumevanjeAlenka Lipovec * in Manja Podgoršek Oddelek za razredni pouk, Pedagoška fakulteta, Univerza v Mariboru Povzetek: Vizualne reprezentacije omogočajo osmišljanje pomena matematičnih pojmov, odnosov in procesov, zato imajo pomembno vlogo pri pouku matematike. V predstavljeni raziskavi smo pri udeležencih preučevali razumevanje osnovnih matematičnih pojmov s pomočjo risb. Pojem je bil podan v simbolni obliki (npr. 17 -9), udeleženci pa so ga morali prikazati z risbo. Zanimalo nas je, ali dijaki oz. študenti in bodoči učitelji (N = 345) ustrezno (v skladu z matematično definicijo) narišejo podani matematični pojem. Podatke smo obdelali s kombinacijo kvantitativne in kvalitativne metodologije. Rezultati so pokazali, da udeleženci zahtevane pojme z risbo ustrezno prikazujejo, pri čemer je delež ustreznosti risb v povezavi z abstraktnostjo prikazanega pojma. Ugotovili smo tudi, da študenti 4. letnikov, ki se izobražujejo za poučevanje na razredni stopnji, pozitivno izstopajo. Po pregledu vzorca risb smo na osnovi vsebinske analize oblikovali dve temi, ki prikazujeta dva načina matematičnega razumevanja (instrumentalno in relacijsko) oz. dva tipa matematičnega znanja (proceduralni in pojmovni). Izsledki raziskave lahko služijo raziskovalcem pri oblikovanju novih raziskovalnih instrumentov za merjenje matematičnega razumevanja in učiteljem pri izbirah načina vpogleda v učenčevo razumevanje.Ključne besede: matematika, razumevanje, vizualizacija, risba, poučevanje Drawing as a tool for an insight into mathematical understanding Alenka Lipovec * and Manja Podgoršek Department of Elementary Education, Faculty of Education, University of Maribor, SloveniaAbstract: Visual representations allow us to interpret the meanings of mathematical concepts, relationships and processes, therefore they play an important role in mathematics education. In the present study, we analysed participants' understanding of basic mathematical concepts through drawings. Symbolic representation of mathematical concept was provided (e.g., 17 -9) to participants and they were asked to represent the given concept through a picture. We were interested if high school students and future teachers (N = 345) adequately (in accordance with mathematical definition) depicted given mathematical concept. The data were analysed using a combination of qualitative and quantitative analyses. The results show that participants quite adequately depicted basic mathematical concepts. Less abstract concepts were depicted more accurately. It was also noted, that 4 th year students, studying to teach at primary level, have performed better than others. In qualitative content analysis two themes emerged. Those themes illustrate two ways of mathematical understanding (instrumental and relational) and two types of mathematical knowledge (procedural and conceptual). The research results can serve researchers in the creation of new research instruments for measuring mathematical understanding and help teachers to find new approa...
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