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- Tossavainen, Timo, et al.
(författare)
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Explorations of Finnish mathematics students' beliefs about the nature of mathematics
- 2017
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Ingår i: Far East Journal of Mathematical Education. - : Pushpa Publishing House. - 0973-5631. ; 17:3, s. 105-120
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Tidskriftsartikel (refereegranskat)abstract
- According to certain surveys made in Germany, mathematics can be seen either as a stagnant structure (formalism-related orientation), a collection of rules, formulas and methods (scheme-related orientation), an active and creative construction process (process-related orientation), or as a method of describing the real world (application- related orientation). We examine how a twenty-item test of students’ orientations for students’ beliefs on the nature of mathematics, which was developed in the German context, translates to the Finnish culture remaining validity. Altogether 310 first-year students from three Finnish universities took part in the study. We apply confirmatory factor analysis to reveal that a slightly modified version the translated questionnaire is applicable also in the Finnish context. Using data collected with the translated questionnaire, we construct a binary regression models to predict students’ choosing between a technical and an ordinary university, and how probability that a student chooses teacher’s study programme slightly decreases if the static view grows stronger in his/her view of mathematics. Further, we see that all four orientations exist almost equally strong in the Finnish students’ beliefs.
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- Tossavainen, Timo, et al.
(författare)
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University mathematics students' study habits and use of learning materials
- 2020
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Ingår i: LUMAT International Journal of Math, Science and Technology Education. - : University of Helsinki, Finland and LUMA Centre Finland. - 2323-7104. ; 8:1, s. 252-270
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we study a group (N=98) of students from two campuses of one Finnish university and their responses to a questionnaire that surveyed the respondents' study habits and how they use different kinds of learning materials in university mathematics courses. Our results show that the grades in the national matriculation exams in mathematics and mother tongue do not play a significant role in one's study habits or use of learning materials. The older students are more communicative with their teachers, whereas the younger students ask for help more often from fellow students. The sociomathematical norms that constitute the local study culture have a larger impact on the study habits and on the use of learning materials. For example, the use of videos and studying lecture materials before the lectures were clearly more usual at one campus than at the other. We also found some significant differences between the groups that are based on the study programmes. The students of mathematics without an intention to become a teacher were most traditional in their study habits, whereas the students of applied physics were most active to participate in teaching. The student teachers most often lie in the middle in the issues where the other groups differ from one another.
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- Viholainen, Antti, 1977-
(författare)
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Critical features of formal and informal reasoning in the case of the concept of derivative
- 2011
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Ingår i: Proceedings of the 35<sup>th</sup> Conference of the International Group for the Psychology of Mathematics Education<em></em>. - 9789754292985 ; , s. 305-312
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Konferensbidrag (refereegranskat)abstract
- Mathematical reasoning can be categorised into formal and informal ones on the basis of the type of used arguments. Both types of reasoning are needed in mathematics, but students usually tend to restrict their reasoning either to formal or informal mode only. Three examples collected and re-analysed from earlier studies reveal some critical features of this kind of restricted reasoning: A formal reasoning may easily become dependent on memory or authoritative references or it may become superficial imitation of algorithms. Informal reasoning, for one, may easily be based on intuitive conceptions, and its validity may be difficult to evaluate.
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- Viholainen, Antti, et al.
(författare)
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Epistemological beliefs, motivational values, and study habits among students of tertiary mathematics
- 2023
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Ingår i: Eurasia Journal of Mathematics, Science and Technology Education. - : Modestum Publishing Ltd. - 1305-8215 .- 1305-8223. ; 19:5
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Tidskriftsartikel (refereegranskat)abstract
- Epistemological beliefs about the nature of mathematics affect how a student perceives mathematics in general, whereas high motivation for mathematics gives an individual a personal reason to study the subject. Epistemological beliefs and achievement motives are quite stable at individual level, but previous research has shown that there are significant differences across students with respect to them. This study concerns university students from three different study programs and investigates relations between the students' epistemological beliefs, motivational values, and study habits. The data were collected using a questionnaire and consist of responses from altogether 98 students studying mathematics courses at tertiary level. The study revealed that, when students are grouped according to their study programs, their motivational values vary across these groups more than their epistemological beliefs. The stability of epistemological beliefs was also verified in this study as the strengths of the beliefs hardly correlated with the number of passed credits or self-evaluated study success. However, several sum variables representing the motivational values and epistemological beliefs seem to predict certain study habits in linear regression models. These models can help us to design the teaching of mathematics courses favouring these study habits.
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- Viholainen, Antti, 1977-
(författare)
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Finnish mathematics teacher students' skills and tendencies to use informal and formal reasoning in the case of derivative
- 2010
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Ingår i: Ajankohtaista matemaattisten aineiden opetuksen ja oppimisen tutkimuksessa (About the actual research in teaching and learning of mathematical subjects). - Joensuu : University of Eastern Finland. - 9789526102658 ; , s. 87-102
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Konferensbidrag (refereegranskat)abstract
- The arguments constructed in mathematical reasoning may be either formal or informal: They may be based either on definitions, axioms and previously proven theorems or on concrete interpretations of mathematical concepts and situations. In addition, arguments may be superficial or deep. Results shared in this paper are from three different studies in which both students’ skills to produce informal and formal arguments and their tendencies to choose between informal and formal reasoning in problem solving situations were studied. The students in all these studies were Finnish high school pre-service mathematics teachers, and the data was collected by using a written test and videotaped interviews. The tasks used were about the concept of derivative. Results of the studies indicated that the students’ skills to produce informal and formal arguments were dependent on each other. The difference between the levels of these skills was not significant, but several students had a tendency to avoid the use of the formal definition of derivative, which led to difficulties in problem solving situations. However, this tendency could not be explained by the students’ inadequate skills to handle the definition of derivative
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- Viholainen, Antti, 1977-
(författare)
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The view of mathematics and argumentation
- 2011
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Ingår i: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education. - : University of Rzeszów. - 9788373386839 ; , s. 243-252
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Konferensbidrag (refereegranskat)abstract
- The view of mathematics affects how the role and function of argumentation is seen. If mathematics is considered as an axiomatic system, arguments have to be based on definitions, axioms and previously proven theorems, and the function of argumentation is mainly to verify and systematise a statement. On the other hand, if mathematics is seen as thinking and learning process, which requires conceptual and holistic understanding, then arguments based on more concrete representations are important. In this latter case, the function of argumentation is to engender understanding by explaining. These two types of argumentation provide a framework, which could also be applied in the design of teaching.
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- Viholainen, Antti, et al.
(författare)
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University mathematics students’ self-efficacy beliefs about proof and proving
- 2019
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Ingår i: LUMAT International Journal of Math, Science and Technology Education. - : University of Helsinki, Finland and LUMA Centre Finland. - 2323-7104. ; 7:1, s. 148-164
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Tidskriftsartikel (refereegranskat)abstract
- We examine university students’ motivation and self-efficacy beliefs about proof and proving, i.e., beliefs about personal abilities to understand, construct and present mathematical proofs, as well as their certainty about self-produced proofs. The sample of the study consists of 29 Finnish and Swedish students who were studying mathematics in tertiary level. The results show that the students were highly motivated to learn to understand and construct proofs, but they were more uncertain about their proving skills. Moreover, the study revealed reasons for the uncertainty about proving achievements. Most of the reasons are caused bydeficiencies with respect to knowledge of, understanding about or experience from proof and proving.
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- Viholainen, Antti, 1977-, et al.
(författare)
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Upper secondary school teachers' views of proof and proving : an explorative cross-cultural study
- 2010
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Ingår i: Proceedings of the 16th Conference of Mathematical Views (MAVI16).
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Konferensbidrag (refereegranskat)abstract
- This paper reports the results of initial explorations about teachers’ views of proofand proving in upper secondary school context in Sweden, Estonia and Finland. Thestudy was carried out in order to develop a questionnaire for a cross-culturalcomparative survey in Baltic countries and Nordic countries with respect of theculture of proof in school mathematics (NorBa Proof Project). The data consistsmainly of teachers’ written responses to some open questions concerning their viewsof proof and the meaning of dealing with proof in upper secondary school context.
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