| 1. |
- Johansson, Maria, et al.
(author)
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Student teachers' definitions of the concept “teaching mathematics in preschool”
- 2019
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In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11). - : ERME. ; , s. 2277-2284
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Conference paper (other academic/artistic)abstract
- This article reports on how a group of preschool and primary student teachers define the concept “teaching mathematics in preschool” in the beginning of their studies. The background for this pilot-study is the recent change in the Swedish curriculum, which means a shift from play-based to more teaching oriented activities, and the actual Swedish debate on the role of teaching in preschool.
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| 2. |
- Tossavainen, Timo, et al.
(author)
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Swedish Primary and Preprimary Student Teachers' Views Of Using Digital Tools in Preprimary Mathematics Education
- 2018
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In: Journal of Technology and Information Education. - : Palacky University Olomouc. - 1803-537X .- 1803-6805. ; 10:2, s. 16-23
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Journal article (peer-reviewed)abstract
- Our study surveys Swedish primary and preprimary student teachers' (n=94) views of content and methods of mathematics education in preschool and, especially, of using digital tools in preprimary mathematics education. The views related to digital tools turned out to be clearly positive in general. Students who are strongly for using digital tools are also more sure in saying that mathematics education in preschool should be fun. However, they agree less with the claims such as mathematics lessons should be structured, or that the responsibility for the mathematics education of small children belongs mainly to their parents. Those students who were quite strongly for using digital tools agreed less with the claim that mathematics is one of the most important areas of preprimary education. The willingness to take responsibility for children's mathematical education from the parents was the most significant single factor to explain the participants' opinions about using digital tools.
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| 3. |
- Attorps, Iiris, 1955-, et al.
(author)
-
Erfarenheter av ”Learning Studies” som ett pedagogiskt verktyg i skola och högskola
- 2010
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In: Toisensa kohtaavat ainedidaktiikat [Möte med ämnesdidaktik]. - Tampere : Juvenes Print. ; , s. 25-33
-
Conference paper (peer-reviewed)abstract
- I detta dokument diskuterar vi pågående projekt i matematikdidaktik vid Högskolan i Gävle. Syftet med projektet är att utveckla och testa metoder för att förbättra lärande i matematik från förskolan till universitetsnivån. Dessutom är syftet att utveckla en forskningsmiljö för lärande i matematik som kan fungera som en plattform för att utveckla lärarnas kompetens i matematik. Den övergripande forskningsfrågan är: Hur påverkar lärarens sätt att hantera lärandeobjekt (t.ex. funktionsbegrepp, integralbegrepp etc.) i klassrummet elevens/studentens lärande? Vilka är de kritiska aspekterna för studenternas lärande? Som ett teoretiskt ramverk använder vi Learning Study modellen designad av Marton et al. (2004). Modellen bygger på variationsteorin (Marton et al. 2004), som härrör från den fenomenografiska forskningstraditionen och som introducerades i Sverige under senare delen av 1960-talet och i början av 1970-talet. Resultaten av studierna antyder bl.a. att det är betydligt enklare att hitta olika typer av konkreta men användbara representationer av lärandeobjektet i undervisningen av den elementära matematiken jämfört med undervisningen av den högre matematiken. Troligen beror det på att universitetsmatematik är mer abstrakt och bygger på den tidigare erhållna kunskapen.
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| 4. |
- Attorps, Iiris, 1955-, et al.
(author)
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Is there always truth in equation?
- 2009
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In: Nordic Research in Mathematics Education. Proceedings from NORMA 08. - Rotterdam : Sense Publishers. ; , s. 143-149
-
Conference paper (peer-reviewed)abstract
- In this study we analyse conceptions that prospective teachers in mathematics have about equations and how these conceptions are related to the truth value (of mathematical statements). Our phenomenographic research reveals that there exists a large variety of fundamentally different conceptions about equations and that in students’ actual concept image of equation it is commonly assumed that a mathematical expression must possess the truth value ‘true’ in order to be an equation in spite of the fact that any consideration related to the truth value only rarely appears in concept definitions given by students.
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| 5. |
- Attorps, Iiris, et al.
(author)
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Is there equality in equation?
- 2007
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In: European research in mathematics education 5.
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Conference paper (peer-reviewed)
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| 6. |
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| 7. |
- Attorps, Iiris, 1955-, et al.
(author)
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The Learning Study Model and the Teaching of the Definite Integral Concept
- 2010
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In: <em></em>Reports and Studies in Education, Humanities, and Theology. - Joensuu : University of Eastern Finland. ; , s. 77-86
-
Conference paper (peer-reviewed)abstract
- In recent years, there have been several studies in mathematics education basing on the variation theory and the model of Learning Study that involves co-operation between teachers and researchers in an iterative process. Most of these studies have focused on the teaching and learning of elementary school mathematics rather than topics in advanced mathematics. In this paper, we discuss some challenges and possibilities of the Learning Study model and the variation theory when developing the teaching of mathematics at advanced levels. More precisely, we report on a series of teaching experiments on the definite integral concept. The experiments were carried out at a Swedish university. The data of this study consists of the documents on the observation of three lectures and the students’ answers to pre and post tests. Both engineering and teacher students participated. In the analysis of the data, we applied statistical methods. Although the series consisted only of three lectures, it revealed that the students’ understanding about certain – but not necessarily all – aspects of the definite integral concept can be enhanced by using the Learning Study model.
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| 8. |
- Attorps, Iiris, 1955-, et al.
(author)
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Varied ways to teach the definite integral concept
- 2013
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In: International Electronic Journal of Mathematics Education. - Turkey : Gökkuşağı Ltd. Şti., Turkey. - 1306-3030. ; 8:2-3, s. 81-99
-
Journal article (peer-reviewed)abstract
- In this paper, we report on a collaborative teaching experiment based on the Learning Study model (LS model) which grounds on the Variation Theory. Until today, most of such studies have focused on the teaching and learning of elementary school mathematics; ours was carried out in undergraduate mathematics education. In the following, we discuss how we managed to promote students’ conceptual learning by varying the treatment of the object of learning (the concept of definite integral and the Fundamental Theorem of Calculus) during three lectures on an introductory course in calculus. We also discuss the challenges and possibilities of the LS model and the Variation Theory in the development of the teaching of tertiary mathematics in general. The experiment was carried out at aSwedish university. The data of the study consists of the documents of the observation of three lectures and the students’ answers to the pre- and post-tests of each lesson. The analysis of learning results revealed some critical aspects of the definite integral concept and patterns of variations that seem to be effective to a significant degree. For example, we found several possibilities to use GeoGebra to enrich students’ learning opportunities.
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| 9. |
- Bergqvist, Erik, et al.
(author)
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An Analysis of High and Low Intercorrelations between Mathematics Self-Efficacy, Anxiety, and Achievement Variables : A Prerequisite for a Reliable Factor Analysis
- 2020
-
In: Education Research International. - : Hindawi Publishing Corporation. - 2090-4002 .- 2090-4010. ; 2020
-
Journal article (peer-reviewed)abstract
- This paper draws on data from a quantitative study of upper secondary students' general mathematical self-efficacy, anxiety towards mathematics, and their relationship to achievement in mathematics. The main objective of this article is to discuss the type of information that may be lost if potential problems of validity and extreme multicollinearity in exploratory factor analysis would be solved by only removing variables without doing a profound analysis. We also describe a method that treats Likert items in the questionnaire as ordinal variables that may represent the underlying continuous variable. Our study shows, for example, that removal of problematic variables without a profound analysis leads to a loss of significant information about test anxiety. Our qualitative analysis of problematic variables also led to an unexpected finding regarding the relationship between general mathematical self-efficacy and motivational values in mathematics.
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| 10. |
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| 11. |
- Gothóni, Ralf, et al.
(author)
-
Miten lahjakas kasvaa menestyjäksi
- 2018
-
In: Kanava. - : Yhtyneet Kuvalehdet Oy. - 0355-0303. ; 46:4, s. 6-10
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Journal article (peer-reviewed)abstract
- The article discusses what kind of processes are related to educating or, more precisely, bringing up a talented musician into a successful performing artist. The processes are similar when the giftedness concerns mathematics or other fields who operate with non-concrete content and abstract values.
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| 12. |
- Haukkanen, Pentti, et al.
(author)
-
Arithmetic Subderivatives : Discontinuity and Continuity
- 2019
-
In: Journal of Integer Sequences. - Ontario, Canada : University of Waterloo. - 1530-7638. ; 22:7
-
Journal article (peer-reviewed)abstract
- We first prove that any arithmetic subderivative of a rational number defines a function that is everywhere discontinuous in a very strong sense. Second, we show that although the restriction of this function to the set of integers is continuous (in the relative topology), it is not Lipschitz continuous. Third, we see that its restriction to a suitable infinite set is Lipschitz continuous. This follows from the solutions of certain arithmetic differential equations.
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| 13. |
- Haukkanen, Pentti, et al.
(author)
-
Arithmetic Subderivatives : p-adic Discontinuity and Continuity
- 2020
-
In: Journal of Integer Sequences. - : University of Waterloo. - 1530-7638. ; 23:7
-
Journal article (peer-reviewed)abstract
- In a previous paper, we proved that the arithmetic subderivative DS is discontinuous at any rational point with respect to the ordinary absolute value. In the present paper, we study this question with respect to the p-adic absolute value. In particular, we show that DS is in this sense continuous at the origin if S is finite or p not in S.
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| 14. |
- Haukkanen, Pentti, et al.
(author)
-
Asymptotics of partial sums of the Dirichlet series of the arithmetic derivative
- 2020
-
In: Mathematical Communications. - : Department of Mathematics, University of Osijek. - 1331-0623 .- 1848-8013. ; 25:1, s. 107-115
-
Journal article (peer-reviewed)abstract
- For ∅ ̸= P ⊆ P, let DP be the arithmetic subderivative function with respect to P on Z+, let ζDP be the function defined by the Dirichlet series of DP , and let σDP denote its abscissa of convergence. Under certain assumptions concerning s and P, we present asymptotic formulas for the partial sums of ζDP (s) and show that σDP = 2. We also express ζDP (s), s > 2, using the Riemann zeta function.
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| 15. |
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| 16. |
- Haukkanen, Pentti, et al.
(author)
-
The arithmetic derivative and Leibniz-additive functions
- 2018
-
In: Notes on Number Theory and Discrete Mathematics. - : “Marin Drinov” Academic Publishing House of the Bulgarian Academy of Sciences. - 1310-5132 .- 2367-8275. ; 24:3, s. 68-76
-
Journal article (peer-reviewed)abstract
- An arithmetic function ? is Leibniz-additive if there is a completely multiplicative function ℎ? such that ?(??) = ?(?)ℎ? (?) + ?(?)ℎ? (?) for all positive integers ? and ?. A motivation for the present study is the fact that Leibnizadditive functions are generalizations of the arithmetic derivative ?; namely, ? is Leibnizadditive with ℎ?(?) = ?. We study the basic properties of Leibniz-additive functions and, among other things, show that a Leibniz-additive function ? is totally determined by the values of ? and ℎ? at primes. We also find connections of Leibniz-additive functions to the usual product, composition and Dirichlet convolution of arithmetic functions. The arithmetic partial derivative is also considered.
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| 17. |
- Haukkanen, Pentti, et al.
(author)
-
The Arithmetic Jacobian Matrix and Determinant
- 2017
-
In: Journal of Integer Sequences. - : University of Waterloo. - 1530-7638. ; 20:9
-
Journal article (peer-reviewed)abstract
- Let a1,..., am be real numbers that can be expressed as a finite product of prime powers with rational exponents. Using arithmetic partial derivatives, we define the arithmetic Jacobian matrix Ja of the vector a = (a1,..., am) analogously to the Jacobian matrix Jf of a vector function f. We introduce the concept of multiplicative independence of {a1,..., am} and show that Ja plays in it a similar role as Jf does in functional independence. We also present a kind of arithmetic implicit function theorem and show that Ja applies to it somewhat analogously as Jf applies to the ordinary implicit function theorem.
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| 18. |
- Hiidenmaa, Pirjo, et al.
(author)
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Reading culture as shared ethos: A study of Finnish self-identified readers
- 2024
-
In: Poetics. - : Elsevier. - 0304-422X .- 1872-7514. ; 105
-
Journal article (peer-reviewed)abstract
- This article advances understanding about book reading as a sociocultural phenomenon in the 2020s. We make a contribution to the cultural sociology of reading by investigating Finnish self-identified book readers by analysing the significance of sociodemographic variables (gender, education, age, and place of residence) in terms of reading activity and access to books. Our study is placed in the context of Finnish reading culture that is characterised by a particular appreciation of reading and measures promoting equal access to culture. Based on an online survey of 955 respondents conducted in 2021, our statistical analyses show that the social stratification of book reading activity that is prominent in population level does not recur within the specific group of people who identify themselves as readers. Among Finnish self-identified book readers, education, gender, and place of residence do not induce significant differences in reading activity. Our analysis that foregrounds inclination instead of quantity as a criterion for readers sheds light on reader equality from a different direction than previous research into nationwide reading habits or descriptive studies on avid readers.
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| 19. |
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| 20. |
- Johansson, Claes, et al.
(author)
-
Programmering på gymnasiet
- 2021
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In: Nämnaren. - : Nationellt centrum för matematikutbildning (NCM). - 0348-2723. ; :4, s. 43-48
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Journal article (pop. science, debate, etc.)
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| 21. |
- Joutsenlahti, Jorma, et al.
(author)
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Matemaattisen ajattelun kielentäminen ja siihen ohjaaminen koulussa
- 2018
-
In: Matematiikan opetus ja oppiminen. - Jyväskylä : Niilo Mäki Institute. - 9789513975845 ; , s. 410-430
-
Book chapter (peer-reviewed)abstract
- Matematiikan opiskelussa on hedelmällistä lähestyä uusia käsitteitä ja algoritmeja tarkastelemalla niiden merkityksiä monipuolisesti. Joustavalla luonnollisen kielen, kuviokielen ja matematiikan symbolikielen käytöllä voidaan opiskeltavista kohteista luoda merkityksellisiä tietorakenteita. Opiskelijalle matemaattisen ajattelun esittäminen (kielentäminen) mainittujen kielten avulla on oiva keino tehdä omaa ajattelua muille opiskelijoille ymmärrettäväksi. Toisaalta opettajalle opiskelijoiden monipuolinen kielten käyttö luo tärkeän pohjan oppimisen arvioinnille ja siten opetuk-sen suunnittelulle. Tarkastelemme matemaattisen ajattelun kielentämistä sekä suullisessa että kirjallisessa työskentelyssä. Esittelemme joitakin tut-kimuspohjaisesti kehitettyjä peruskoulun kielentämisharjoituksia, joita voi soveltaen käyttää korkeakouluopintoihin asti. Lopuksi esittelemme kielentämisen eräänä sovelluksena variaatioteoriaan perustuvan learning study -mallin.
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| 22. |
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| 23. |
- Jumppanen, Pauli, et al.
(author)
-
Ilmastonmuutoksen ja energiankäytön didaktiikkaa
- 2021
-
In: Dimensio. - : MAOL ry.
-
Journal article (other academic/artistic)abstract
- Ilmastonmuutoksesta ja energiankäytöstä puhutaan paljon mediassa. Pääviesti on jo selvä: maailmanlaajuista energian tuotantoa ja kulutusta on muutettava merkittävästi, jotta ilmaston lämpenemistä pystyttäisiin hillitsemään. Mutta miten näistä asioista pitäisi puhua koulussa?
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| 24. |
- Lehtinen, Matti, et al.
(author)
-
Matematiikan opetuksen ihanteet : [On the ideals of mathematics teacher]
- 2019
-
In: Tieteessä tapahtuu. - Helsinki : Tieteellisten seurain valtuuskunta. - 0781-7916 .- 1239-6540. ; 37:5, s. 3-10
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Journal article (other academic/artistic)abstract
- Useimmilla meistä on pysyviä muistoja joistakin tietyistä oppiaineista ja niiden opettajapersoonista. Eräitä matematiikanopettajia muistellaan vielä vuosikymmeniä heidän kuolemansa jälkeen – niin hyvällä kuin pahallakin. Nämä muistot kertovat myös siitä, millaisia odotamme opettajiemme olevan.
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| 25. |
- Madej, Lars
(author)
-
X - men sen då? Algebrans stora idéer från första klass till högre matematik : Med fokus på tidig algebra i Sverige
- 2021
-
Doctoral thesis (other academic/artistic)abstract
- The overall aim of this thesis is to increase the knowledge of the state of algebraic thinking in the earlier years, so called early algebra, in the Swedish primary school. First, using the Big Ideas of Algebra (Blanton et al., Journal for Research in Mathematics Education, 46(1), 39–87, 2015) as a theoretical framework, the thesis investigates which types of algebraic thinking can be identified in the Swedish mathematics curriculum and in two textbooks series for Grades 1-6. Second, as students’ understanding of the equal sign as a symbol for a relation is an important factor for algebraic success, students’ knowledge of it is studied by using an assessment form based on Matthews et al. (Journal for Research in Mathematics Education, 43(3), 316-350, 2012).The results of the empirical studies show that Equivalences, Expressions, Equations, and Inequalities (EEEI) were the most prominent Big Idea in the Swedish context. The Big Idea of Generalized Arithmetic (GA) is not represented in the Central content in Grades 1-6 and only slightly represented in the textbooks. Furthermore, there are big differences between the two textbook series, both regarding the total amount of algebraic content and regarding how well each Big Idea is represented in the textbooks. As textbooks are important artefacts in Swedish mathematics classrooms, opportunities to learn early algebra in a classroom might depend on which textbook is used. Concerning students’ understanding of the equal sign, the study shows that they, in general, are able to describe the meaning of the equal sign as relational, but they are less able to use the relational structure of an equality. This implies that “the meaning of the equal sign”, which is part of the algebraic content in the Swedish mathematics curriculum in Grades 1-3, might be learnt as a definition by word rather than by its implications in mathematics. Besides the empirical contributions, the thesis also offers a discussion whether the Big Ideas can be found in mathematics at the university level and in research in abstract algebra and it is argued that algebraic thinking is present in all levels of mathematics, from early algebra in lower primary school to research in mathematics.
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| 26. |
- Mattila, Mika, et al.
(author)
-
Maximal perpendicularity in certain Abelian groups
- 2017
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In: Acta Universitatis Sapientiae, Mathematica. - : Walter de Gruyter. - 2066-7752. ; 9:1, s. 235-247
-
Journal article (peer-reviewed)abstract
- We define perpendicularity in an Abelian group G as a binary relation satisfying certain five axioms. Such a relation is maximal if it is not a subrelation of any other perpendicularity in G. A motivation for the study is that the poset (P, ⊆) of all perpendicularities in G is a lattice if G has a unique maximal perpendicularity, and only a meet-semilattice if not. We study the cardinality of the set of maximal perpendicularities and, on the other hand, conditions on the existence of a unique maximal perpendicularity in the following cases: G ≅ ℤn, G is finite, G is finitely generated, and G = ℤ ⊕ ℤ ⊕⋯. A few such conditions are found and a few conjectured. In studying ℝn, we encounter perpendicularity in a vector space.
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| 27. |
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| 28. |
- Merikoski, Jorma K., et al.
(author)
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Arithmetic subderivatives and Leibniz-additive functions
- 2019
-
In: Annales Mathematicae et Informaticae. - Hungary : Eszterházy Károly College. - 1216-6014 .- 1787-5021 .- 1787-6117. ; 50, s. 145-157
-
Journal article (peer-reviewed)abstract
- We introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. In order to generalize these notions a step further, we define that an arithmetic function ? is Leibniz-additive if there is a nonzero-valued and completely multiplicative function ℎ? satisfying ?(??) = ?(?)ℎ? (?) + ?(?)ℎ? (?) for all positive integers ? and ?. We study some basic properties of such functions. For example, we present conditions when an arithmetic function is Leibniz-additive and, generalizing the well-known bounds for the arithmetic derivative, we establish bounds for a Leibniz-additive function.
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| 29. |
- Merikoski, Jorma K., et al.
(author)
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Complete Additivity, Complete Multiplicativity, and Leibniz-additivity on Rationals
- 2021
-
In: Integers. - : Colgate University. - 1553-1732. ; 21
-
Journal article (peer-reviewed)abstract
- Completely additive (c-additive in short) functions and completely multiplicative (c-multiplicative in short) functions are ordinarily defined for positive integers but sometimes on larger domains. We survey this matter by extending these functions first to nonzero integers and thereafter to nonzero rationals. Then we can similarly extend Leibniz-additive (L-additive in short) functions. (A function is L-additive if it is a product of a c-additive and a c-multiplicative function.) We study some properties of these functions. The role of an L-additive function as a generalized arithmetic derivative is our special interest.
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| 30. |
- Merikoski, Jorma K., et al.
(author)
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On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix
- 2018
-
In: Special Matrices. - : Walter de Gruyter. - 2300-7451. ; 6, s. 23-36
-
Journal article (peer-reviewed)abstract
- Consider the recursion g0 = a, g1 = b, gn = gn−1 + gn−2, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g0, . . . , gn−1. We also give three lower bounds (with equality conditions) for the spectral norm of this matrix. For this purpose, we present three ways to estimate the spectral norm from below in general.
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| 31. |
- Merikoski, Jorma K., et al.
(author)
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The spectral norm of a circulant matrix
- 2018
-
In: JP Journal of Algebra, Number Theory and Applications. - : PUSHPA PUBLISHING HOUSE. - 0972-5555. ; 40:4, s. 495-500
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Journal article (peer-reviewed)
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| 32. |
- Rensaa, Ragnhild Johanne, et al.
(author)
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Norwegian freshmen engineering students' self-efficacy, motivation, and view of mathematics in light of task performance
- 2022
-
In: Nordic Journal of STEM Education. - : NTNU Norwegian University of Science and Technology. - 2535-4574. ; 6:1
-
Journal article (peer-reviewed)abstract
- We report on 71 Norwegian freshmen engineering students' self-efficacy and motivation in mathematics. Students' responses to five-point Likert scales were analysed across three groups corresponding to different performance levels on a set of mathematical tasks. The groups were investigated to trace differences in self-efficacy, motivation, and the epistemological beliefs about the nature of mathematics. Results show that the Norwegian first-year engineering students' self-efficacy is closely related to task performance, but there is not a similar correspondence between task performance and the motivational values. The amount of higher performing students who regard mathematics as a set of (ready-made) tools for solving tasks is a little higher than the amount of lower performing students, while in the case of valuing problem-solving processes in mathematics, the distribution of students is opposite with lower performing students being a majority. The task performance levels are a significant predictor of how dynamic the distribution of the epistemological beliefs is.
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| 33. |
- Schneider, Thomas, et al.
(author)
-
Evaluation and control of occupational health risks from nanoparticles
- 2007
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Reports (peer-reviewed)abstract
- Rapid growth in the nanoparticle industry is anticipated in the Nordic countries owing to highly focused national research and investment initiatives. Knowledge on consequences for occupational exposures to engineered nanoparticles and appropriate technical control levels is still limited. This report explores existing knowledge on exposure risks and technical control approaches. The report concludes that data are too limited to allow general conclusions to be drawn regarding risks of exposure to engineered nanoparticles.Engineering techniques for controlling nanoparticle exposure can build on the current knowledge and approaches to control exposure to e.g. welding fume and carbon black. There is a need for improving the quality of information provided in Material Safety Data Sheets.
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| 34. |
- Stén, Johan, et al.
(author)
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Osmo Pekonen (1960–2022)
- 2023
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In: The Mathematical intelligencer. - : Springer Nature. - 0343-6993 .- 1866-7414. ; 45:1, s. 1-4
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Journal article (other academic/artistic)
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| 35. |
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| 36. |
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| 37. |
- Tossavainen, Timo, et al.
(author)
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Ajasta ja mittaamisesta musiikissa ja matematiikassa
- 2021
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In: Kanava. - Helsinki : Otava Publishing Company Ltd.. - 0355-0303. ; 49:1, s. 28-32
-
Journal article (other academic/artistic)abstract
- This article discusses a mathematical foundation of the measurement of distances from various perspectives. As an application we consider the measurement of time in music.
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| 38. |
- Tossavainen, Timo, et al.
(author)
-
Aloittavien diplomi-insinööriopiskelijoiden motivaatio, matematiikkakäsitys ja menestys matemaattisissa tehtävissä
- 2020
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In: Arkhimedes – Tidskrift för fysik och matematik. - : Suomen Fyysikkoseura. - 0004-1920. ; :2-3, s. 13-20
-
Journal article (peer-reviewed)abstract
- Tässä artikkelissa tarkastellan Tampereen yliopistossa DI-koulutukessa aloittaneiden opiskelijoiden (N=272) matematiikkaan liityvää motivaatiota, käsityksiä oppiaineen luonteesta ja menestystä lukiotasoisissa matematiikan tehtävissä. Kiinostus matematiikkaa kohtaan ja hyvä käsitys itsestä matematiikan oppijana ovat vahvimpia osaamisen selittäjiä. Vaikka erilaisilla käsityksillä matematiikan luonteesta ei ollut suurta vaikutusta testitehtävissä menestymiseen, käsitteiden määritelmien ymmärtämiseen ja päättelytaitojen kehittymiseen panostaminen vaikuttaa paremmalta keinolta kehittää matematiikan opetusta kuin matematiikan hyötyarvon korostaminen tai keskittyminen reseptinomaisiin ohjeisiin matematiikan soveltamisessa.
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| 39. |
- Tossavainen, Timo, et al.
(author)
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An investigation of Swedish pre-service preschool teachers’ knowledge about the negative numbers
- 2020
-
In: Journal of Early Childhood Education Research. - : Association for Finnish Early Childhood Education. - 2323-7414. ; 9:2, s. 420-436
-
Journal article (peer-reviewed)abstract
- In this paper, we examine the Swedish pre-service preschool teachers’ knowledge about the negative numbers, which is one of the central content areas in their compulsory mathematics course. Our results show that almost a half of the pre-service preschool teachers can give a reasonable definition for the negative numbers, but only a few of them set the negative numbers in relation to the other common number sets. The participants’ performance in a set of mathematical tasks related to the negative numbers follows the qualitative variance in their definitions of the negative numbers, yet this relation is not completely direct; there were also such participants who were not able to give a definition but succeeded well in the tasks. Those who gave a vague definition performed weaker than the others. Although the participants’ knowledge about the negative numbers is, perhaps, not satisfactory with every respect, it does not significantly differ from that of a control group that consists of (non-mathematician) university teachers from their study programme.
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| 40. |
- Tossavainen, Timo
(author)
-
Cryptography based on algebraic perpendicularities
- 2023
-
In: Mathematical Gazette. - : Cambridge University Press. - 0025-5572 .- 2056-6328. ; 107:568, s. 65-69
-
Journal article (peer-reviewed)abstract
- Cryptography, the mathematics of protecting secret or sensitive information, is a continuously evolving area of interest. A concrete example of this is the fact that worldwide spending on information security and risk management technology and services has been estimated to reach over $150 billion in 2021. Modern cryptography is actually not a single separate domain of mathematics but an advanced encryption scheme can be based on applications of results in number theory, such as the Euler–Fermat Theorem, or involve the discrete logarithm problem using either a primitive root of a large prime or an element of an elliptic curve over a prime field. In the background, probability theory, statistics, studies on computational models and finite geometries, etc. play a major role. Recent research has considered even DNA-based molecular cryptography systems.
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| 42. |
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| 43. |
- Tossavainen, Timo, et al.
(author)
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Explorations of Finnish mathematics students' beliefs about the nature of mathematics
- 2017
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In: Far East Journal of Mathematical Education. - : Pushpa Publishing House. - 0973-5631. ; 17:3, s. 105-120
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Journal article (peer-reviewed)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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| 44. |
- Tossavainen, Timo, et al.
(author)
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Factors that influence engineering students' motivation to study mathematics
- 2024
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In: 1st International Conference on Math Education and Technology 2023 (ICMET 2023): book of abstracts. - Aveiro, Portugal. - 9789727899081 ; , s. 49-50
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Conference paper (peer-reviewed)abstract
- Students' motivation plays a crucial role in studying mathematics. A recent Swedish study on engineering students' mathematical self-concept and its dependency on their views of mathematics and study habits showed that engineering students' motivation to study mathematics varies across the years. In order to understand better this variation, we conducted interviews with eleven engineering students from a Swedish university. Our primary focus is to understand the underlying reasons for these changes in engineering students’ motivation throughout their university journey, as well as to explore their opinions on how to sustain motivation to study mathematics.
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| 45. |
- Tossavainen, Timo, et al.
(author)
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First-year engineering students’ mathematics task performance and its relation to their motivational values and views about mathematics
- 2021
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In: European Journal of Engineering Education. - : Taylor & Francis. - 0304-3797 .- 1469-5898. ; 46:4, s. 604-617
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Journal article (peer-reviewed)abstract
- This study investigates Finnish, Norwegian, and Swedish first-year engineering students’ task performance in mathematics and examines how it relates to their motivational values and beliefs about the nature of mathematics. In a set of seven mathematical tasks, female students outperformed male students, for example, in the simplification of symbolic expressions. Our findings also show that female students set more demanding learning goals for themselves. Further, they expressed higher intrinsic motivational values, whereas male students emphasised utility values, which correlated negatively with task performance. Problem-solving and discovering structures and regularities dominate engineering students’ views of mathematics. The ‘toolbox’ view of mathematics is the best predictor of task performance; the stronger this view is, the poorer is the task performance. However, neither motivational values nor views about mathematics are especially strong predictors of task performance. Based on the findings of this study, it is recommended that, in engineering mathematics courses, greater emphasis is placed on learning fundamental reasoning strategies and discussing the theoretical foundations of the main results. This seems to lead to a better result even in applying mathematics than if one focuses only on learning how to use ready-made mathematical tools in concrete examples.
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| 46. |
- Tossavainen, Timo
(author)
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Matemaattisia keskusteluja tekoälyn kanssa – Onko ChatGPT:stä oppaaksi matematiikan oppimisessa?
- 2023
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In: Tieteessä tapahtuu. - Helsinki : Tieteellisten seurain valtuuskunta. - 0781-7916 .- 1239-6540. ; 41:2, s. 39-46
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Journal article (other academic/artistic)abstract
- Tekoäly on tulossa osaksi oppimisen arkea. Kävin keskusteluja tekoälyn kanssa muun muassa eräiden matemaattisten lauseiden todistamisesta selvittääkseni, miten tekoälyä voisi käyttää matematiikan oppimisen tukena. Millaisia mahdollisuuksia tai uhkakuvia tekoälyn käyttöön liittyy?
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| 47. |
- Tossavainen, Timo, et al.
(author)
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Matematiikan opettajien ja opettajaksi opiskelevien matemaattisesta osaamisesta
- 2018
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In: Matematiikan opetus ja oppiminen. - Jyväskylä : Niilo Mäki Institute. - 9789513975845 ; , s. 294-304
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Book chapter (peer-reviewed)abstract
- Tässä luvussa tarkastellaan suomalaisten matematiikan opettajien ja opettajaopiskelijoiden matemaattista osaamista sekä 2010-luvulla tehdyn tutkimuksen että muun käytettävissä olevan aineiston valossa. Lisäksi artikkelissa pohditaan eräitä opettajankoulutuksen järjestämiseen liittyviä mahdollisuuksia vahvistaa peruskoulun matematiikan opettajien matemaattista osaamista.
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| 48. |
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| 49. |
- Tossavainen, Timo, et al.
(author)
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Norwegian, Swedish, and Finnish first-year engineering students' motivational values and beliefs about the nature of mathematics
- 2022
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In: Bringing Nordic mathematics education into the future. - : Svensk förening för MatematikDidaktisk Forskning. ; , s. 233-240
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Conference paper (peer-reviewed)abstract
- We report from a Nordic research project that has investigated first-year engineering students in Norway, Sweden, and Finland, and the relationships between their task performance, motivational values, and beliefs about the nature of mathematics. The present paper focuses on the covariance between their motivational values and beliefs from the perspectives of gender and nationality. The results show that female students' motivational values are more strongly related to their beliefs than is the case for male students. Further, the Finnish students' motivational values are only weakly related to their beliefs, whereas the Norwegian and the Swedish students' motivation to mathematics is quite strongly related to how much they appreciate the applications of mathematics.
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| 50. |
- Tossavainen, Timo, et al.
(author)
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On mathematics students' understanding of the equation concept
- 2011
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In: Far East Journal of Mathematical Education. - Allahabad : Pushpa Publishing House. - 0973-5631. ; 6:2, s. 127-147
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Journal article (peer-reviewed)abstract
- We analyze data on mathematics students’ understanding of the concept of equation. A majority of the participants (N = 128) studies in teacher education programs in Finland, Sweden and South Africa. The data reveals a variety of fundamentally different concept definitions of equation, of which only a half can be seen to be correct. In the students’ concept image of equation, it is commonly assumed that every equation must possess the truth value ‘true’ in spite of the fact that any considerations related to the truth value only rarely appear in their concept definitions. Also the presence of a variable is regularly assumed in the participants’ concept images. Both a chain of equations and a pair of equivalent equations are surprisingly often seen being a single equation. Finally, the incomplete understanding of the reflexive and symmetric properties of equality often hindersstudents from identifying equations. The study is based on both phenomenographic andquantitative analyses of the students’ answers to a questionnaire. .
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