Terhi Kaarakka | Tampere University (original) (raw)

Papers by Terhi Kaarakka

International journal of education in mathematics, science and technology :, May 31, 2024

This study investigates the relationship between first-year higher education students' (N = 405) ... more This study investigates the relationship between first-year higher education students' (N = 405) approaches to learning and academic performance on engineering mathematics courses. In addition, we study what combinations of approaches to learning students apply, how these combinations change over time, and whether they are linked to the pedagogical design. The students were divided into an intervention group taught with an instructional model based on flipped learning, and a control group taught with a modern lecture-based model. The students' approaches to learning were measured five times during one academic year. Multiple linear regression, dominance analysis and cluster analysis were used in analyzing the data. We found that a high level of organized studying and a low level of surface approach to learning were positively linked to exam performance, but a deep approach to learning was not linked to performance. In the last three measurements, the students in the intervention group were overrepresented in the cluster with the most desirable profile in terms of approaches to learning. In the long term, flipped learning seemed to foster deep approach learning and organized studying better than the lecture-based model.

Communications on Stochastic Analysis, 2011

In this monograph, we are mainly studying Gaussian processes, in particularly three different typ... more In this monograph, we are mainly studying Gaussian processes, in particularly three different types of fractional Ornstein-Uhlenbeck processes. Pioneers in this field may be mentioned, e.g. Kolmogorov (1903-1987) and Mandelbrot (1924-2010). 2 , 1), we find out the covariance kernel of increment process of Y (α) , and using that we investicate the covariance of Y (α) and the variance of Y (α) , when t tends to infinity. One of our main results is that the increment process of Y (α) is short-range dependent. We also study weak convergence and tightness and then i ii Abstract finally prove that 1 √ a Y (α) at converges weakly to scaled Brownian motion. In the case H ∈ (1 2 , 1), fractional Brownian motion and the fractional Ornstein-Uhlenbeck process of the first kind both exhibit a long-range dependence, but the fractional Ornstein-Uhlenbeck process of the second kind exhibits a short-range dependence. This offers more opportunities to model network traffic or economic time series via tractable fractional processes. The fractional Ornstein-Uhlenbeck process of the first kind and the fractional Ornstein-Uhlenbeck process of the second kind are quite similar to simulate, since they can both be represented via stochastic differential equations.

European Journal of Engineering Education

In this monograph, we are mainly studying Gaussian processes, in particularly three different typ... more In this monograph, we are mainly studying Gaussian processes, in particularly three different types of fractional Ornstein – Uhlenbeck processes. Pioneers in this field may bementioned, e.g. Kolmogorov (1903-1987) and Mandelbrot (1924-2010).The Ornstein – Uhlenbeck diffusion can be constructed from Brownian motion via a Doobtransformation and also from a solution of the Langevin stochastic differential equation. Both of these processes have the same finite dimensional distributions. However the solution of the Langevin stochastic differential equation, which driving process is fractionalBrownian motion and a Doob transformation of fractional Brownian motion do not havesame finite dimensional distributions. Indeed we verify, that the covariance of the fractionalOrnstein – Uhlenbeck process of the first kind (which we call the solution of the Langevin stochastic differential equation in which the driving process is fractional Brownian motion) behaves at infinity like a power function ...

Le Centre pour la Communication Scientifique Directe - HAL - Université de Nantes, Feb 2, 2022

ANNUAL CONFERENCE OF THE EUROPEAN SOCIETY FOR ENGINEERING EDUCATION, 2016

European Journal of Mechanics - A/Solids, 2021

In this article, the continuum-based high-cycle fatigue analysis method, introduced by Ottosen, S... more In this article, the continuum-based high-cycle fatigue analysis method, introduced by Ottosen, Stenström and Ristinmaa in 2008, is extended to cases where the stress history is a stochastic process. The basic three-parameter Ornstein–Uhlenbeck process is chosen for stress description. As a practical example, the theory is applied in both finite and infinite life cases. A definition for the safety factor is introduced, which is reduced to a minimization problem of the value for the endurance surface. In the stochastic case, the values of the endurance surface form a stochastic process and the cumulative distribution function can be constructed for its maximum values.publishedVersionPeer reviewe

Tiivistelmä. Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastist... more Tiivistelmä. Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastista laajennusta. Esitetty malli on muodostettu yleisten kontinuumimekaniikan periaatteiden mukaisesti ja on siten luonnostaan moniakselinen ja käsittelee kaikki jännityskomponentit ekvivalentilla tavalla. Malli soveltuu myös mielivaltaiselle kuormitushistorialle. Esimerkkinä tarkastellaan yksinkertaista valkoisella kohinalla häirityn säännöllisen kuormituksen aiheuttaman elinikäennusteen jakaumaa.

FMSERA Journal, Oct 31, 2017

Rakenteiden Mekaniikka

Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastista laajennusta... more Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastista laajennusta. Esitetty malli on muodostettu yleisten kontinuumimekaniikan periaatteiden mukaisesti ja on siten luonnostaan moniakselinen ja käsittelee kaikki jännityskomponentit ekvivalentilla tavalla. Malli soveltuu myos mielivaltaiselle kuormitushistorialle. Esimerkkinä tarkastellaan yksinkertaista valkoisella kohinalla häirityn säännollisen kuormituksen aiheuttaman elinikäaennusteen jakaumaa.

International Journal of Mathematical Education in Science and Technology, 2021

Integration is seen as a main factor for students to stay in university and eventually graduate. ... more Integration is seen as a main factor for students to stay in university and eventually graduate. In conventional lecture-based teaching, students might avoid asking for academic help from teachers,...

Matemaattisten tehtavien ratkaisujen kirjoittaminen digitaaliseen muotoon yleistyy koko ajan ylio... more Matemaattisten tehtavien ratkaisujen kirjoittaminen digitaaliseen muotoon yleistyy koko ajan ylioppilaskirjoitusten, sahkoisen tenttimisen ja avointen verkkokurssien takia. Samalla tarve ratkaisujen automaattiseen arviointiin kasvaa. Vaikka monet peruskurssitason harjoitustehtavat tarkistetaan jo nyt sahkoisesti, olisi hyodyllista voida tarkistaa opiskelijan koko paattelyketju pelkan vastauksen sijaan. Tassa julkaisussa saadaan luokiteltua, millaisia virheita opiskelijat tekevat yhdessa tehtavassa ja pohditaan, kuinka tata voidaan hyodyntaa opiskelijoille annettavassa, automatisoidussa palautteessa siten, etta palautteella ohjataan opiskelijan matemaattisen ajattelun kehittymista. Lisaksi TTY:lla on pitkaan testattu ensimmaisen vuoden opiskelijoiden matemaattisia perustaitoja, joten osaamme kohdentaa tukitoimet keskeisiin ongelma-alueisiin, kuten trigonometriaan.

Mechanical fatigue phenomenon of materials has inherently stochastic features. For irregular load... more Mechanical fatigue phenomenon of materials has inherently stochastic features. For irregular loading histories, the classical method to predict a life time is the Rainflow method, which is based on a construction of an equivalent cycle. The method is essentially one dimensional, but can be extended to the multiaxial case considering an equivalent stress criteria. It could also be extended to a stochastic case. A common process is to estimate the autocorrelation function from measured stress data, then the spectral density function can be found by using the fast Fourier transform, and the life time can be approximated with a level crossing formula, usually the so called Rice’s formula. In this paper a truly stochastic approach is described for an evolution equation based multiaxial highcycle fatigue model applicable for arbitrary loading histories. The stochastic version of an evolution equation based continuum HCF-model is not only a particular method, but a broad concept to handle ...

Tiivistelmä Artikkelissa tarkastellaan äärettömään elinikään liittyvää varmuuskertoimen laskentaa... more Tiivistelmä Artikkelissa tarkastellaan äärettömään elinikään liittyvää varmuuskertoimen laskentaa kontinuumimekaniikkaan perustuvassa jännitysväsymismallissa. Jännityshistoria voi olla joko deterministinen tai stokastinen. Varmuuskertoimen laskenta redusoituu kestävyysfunktion maksimiarvon etsimiseen. Stokastisen jännityshistorian tapauksessa myös kestävyysfunktion arvot muodostavat stokastisen prosessin, jonka maksimiarvon todennäköisyysjakauma voidaan muodostaa. Menetelmää havainnollistetaan sekä yksinkertaisella yksidimensioisella että moniakselisella teollisella esimerkkilaskennalla.

European Journal of Mechanics - A/Solids

LUMAT: International Journal on Math, Science and Technology Education

MathCheck is a relatively new online tool that gives students feedback on their solutions to elem... more MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if the step is incorrect. It has been in student use since the autumn of 2015 and under design-based research from the first online day. The main research questions of this study are the following. 1) How can the usage of MathCheck support the aspects of conceptual understanding and procedural fluency of constructivism learning? 2) How can MathCheck empower both students and teachers in the education of mathematics? This paper presents the results of five pedagogical experiments considering both students’ and teachers’ point of views. In each experiment, the students have suggested improvements, which have affected the further development of Ma...

International journal of education in mathematics, science and technology :, May 31, 2024

This study investigates the relationship between first-year higher education students' (N = 405) ... more This study investigates the relationship between first-year higher education students' (N = 405) approaches to learning and academic performance on engineering mathematics courses. In addition, we study what combinations of approaches to learning students apply, how these combinations change over time, and whether they are linked to the pedagogical design. The students were divided into an intervention group taught with an instructional model based on flipped learning, and a control group taught with a modern lecture-based model. The students' approaches to learning were measured five times during one academic year. Multiple linear regression, dominance analysis and cluster analysis were used in analyzing the data. We found that a high level of organized studying and a low level of surface approach to learning were positively linked to exam performance, but a deep approach to learning was not linked to performance. In the last three measurements, the students in the intervention group were overrepresented in the cluster with the most desirable profile in terms of approaches to learning. In the long term, flipped learning seemed to foster deep approach learning and organized studying better than the lecture-based model.

Communications on Stochastic Analysis, 2011

In this monograph, we are mainly studying Gaussian processes, in particularly three different typ... more In this monograph, we are mainly studying Gaussian processes, in particularly three different types of fractional Ornstein-Uhlenbeck processes. Pioneers in this field may be mentioned, e.g. Kolmogorov (1903-1987) and Mandelbrot (1924-2010). 2 , 1), we find out the covariance kernel of increment process of Y (α) , and using that we investicate the covariance of Y (α) and the variance of Y (α) , when t tends to infinity. One of our main results is that the increment process of Y (α) is short-range dependent. We also study weak convergence and tightness and then i ii Abstract finally prove that 1 √ a Y (α) at converges weakly to scaled Brownian motion. In the case H ∈ (1 2 , 1), fractional Brownian motion and the fractional Ornstein-Uhlenbeck process of the first kind both exhibit a long-range dependence, but the fractional Ornstein-Uhlenbeck process of the second kind exhibits a short-range dependence. This offers more opportunities to model network traffic or economic time series via tractable fractional processes. The fractional Ornstein-Uhlenbeck process of the first kind and the fractional Ornstein-Uhlenbeck process of the second kind are quite similar to simulate, since they can both be represented via stochastic differential equations.

European Journal of Engineering Education

In this monograph, we are mainly studying Gaussian processes, in particularly three different typ... more In this monograph, we are mainly studying Gaussian processes, in particularly three different types of fractional Ornstein – Uhlenbeck processes. Pioneers in this field may bementioned, e.g. Kolmogorov (1903-1987) and Mandelbrot (1924-2010).The Ornstein – Uhlenbeck diffusion can be constructed from Brownian motion via a Doobtransformation and also from a solution of the Langevin stochastic differential equation. Both of these processes have the same finite dimensional distributions. However the solution of the Langevin stochastic differential equation, which driving process is fractionalBrownian motion and a Doob transformation of fractional Brownian motion do not havesame finite dimensional distributions. Indeed we verify, that the covariance of the fractionalOrnstein – Uhlenbeck process of the first kind (which we call the solution of the Langevin stochastic differential equation in which the driving process is fractional Brownian motion) behaves at infinity like a power function ...

Le Centre pour la Communication Scientifique Directe - HAL - Université de Nantes, Feb 2, 2022

ANNUAL CONFERENCE OF THE EUROPEAN SOCIETY FOR ENGINEERING EDUCATION, 2016

European Journal of Mechanics - A/Solids, 2021

In this article, the continuum-based high-cycle fatigue analysis method, introduced by Ottosen, S... more In this article, the continuum-based high-cycle fatigue analysis method, introduced by Ottosen, Stenström and Ristinmaa in 2008, is extended to cases where the stress history is a stochastic process. The basic three-parameter Ornstein–Uhlenbeck process is chosen for stress description. As a practical example, the theory is applied in both finite and infinite life cases. A definition for the safety factor is introduced, which is reduced to a minimization problem of the value for the endurance surface. In the stochastic case, the values of the endurance surface form a stochastic process and the cumulative distribution function can be constructed for its maximum values.publishedVersionPeer reviewe

Tiivistelmä. Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastist... more Tiivistelmä. Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastista laajennusta. Esitetty malli on muodostettu yleisten kontinuumimekaniikan periaatteiden mukaisesti ja on siten luonnostaan moniakselinen ja käsittelee kaikki jännityskomponentit ekvivalentilla tavalla. Malli soveltuu myös mielivaltaiselle kuormitushistorialle. Esimerkkinä tarkastellaan yksinkertaista valkoisella kohinalla häirityn säännöllisen kuormituksen aiheuttaman elinikäennusteen jakaumaa.

FMSERA Journal, Oct 31, 2017

Rakenteiden Mekaniikka

Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastista laajennusta... more Artikkelissa tarkastellaan evoluutioyhtälöpohjaisen jännitysväsymismallin stokastista laajennusta. Esitetty malli on muodostettu yleisten kontinuumimekaniikan periaatteiden mukaisesti ja on siten luonnostaan moniakselinen ja käsittelee kaikki jännityskomponentit ekvivalentilla tavalla. Malli soveltuu myos mielivaltaiselle kuormitushistorialle. Esimerkkinä tarkastellaan yksinkertaista valkoisella kohinalla häirityn säännollisen kuormituksen aiheuttaman elinikäaennusteen jakaumaa.

International Journal of Mathematical Education in Science and Technology, 2021

Integration is seen as a main factor for students to stay in university and eventually graduate. ... more Integration is seen as a main factor for students to stay in university and eventually graduate. In conventional lecture-based teaching, students might avoid asking for academic help from teachers,...

Matemaattisten tehtavien ratkaisujen kirjoittaminen digitaaliseen muotoon yleistyy koko ajan ylio... more Matemaattisten tehtavien ratkaisujen kirjoittaminen digitaaliseen muotoon yleistyy koko ajan ylioppilaskirjoitusten, sahkoisen tenttimisen ja avointen verkkokurssien takia. Samalla tarve ratkaisujen automaattiseen arviointiin kasvaa. Vaikka monet peruskurssitason harjoitustehtavat tarkistetaan jo nyt sahkoisesti, olisi hyodyllista voida tarkistaa opiskelijan koko paattelyketju pelkan vastauksen sijaan. Tassa julkaisussa saadaan luokiteltua, millaisia virheita opiskelijat tekevat yhdessa tehtavassa ja pohditaan, kuinka tata voidaan hyodyntaa opiskelijoille annettavassa, automatisoidussa palautteessa siten, etta palautteella ohjataan opiskelijan matemaattisen ajattelun kehittymista. Lisaksi TTY:lla on pitkaan testattu ensimmaisen vuoden opiskelijoiden matemaattisia perustaitoja, joten osaamme kohdentaa tukitoimet keskeisiin ongelma-alueisiin, kuten trigonometriaan.

Mechanical fatigue phenomenon of materials has inherently stochastic features. For irregular load... more Mechanical fatigue phenomenon of materials has inherently stochastic features. For irregular loading histories, the classical method to predict a life time is the Rainflow method, which is based on a construction of an equivalent cycle. The method is essentially one dimensional, but can be extended to the multiaxial case considering an equivalent stress criteria. It could also be extended to a stochastic case. A common process is to estimate the autocorrelation function from measured stress data, then the spectral density function can be found by using the fast Fourier transform, and the life time can be approximated with a level crossing formula, usually the so called Rice’s formula. In this paper a truly stochastic approach is described for an evolution equation based multiaxial highcycle fatigue model applicable for arbitrary loading histories. The stochastic version of an evolution equation based continuum HCF-model is not only a particular method, but a broad concept to handle ...

Tiivistelmä Artikkelissa tarkastellaan äärettömään elinikään liittyvää varmuuskertoimen laskentaa... more Tiivistelmä Artikkelissa tarkastellaan äärettömään elinikään liittyvää varmuuskertoimen laskentaa kontinuumimekaniikkaan perustuvassa jännitysväsymismallissa. Jännityshistoria voi olla joko deterministinen tai stokastinen. Varmuuskertoimen laskenta redusoituu kestävyysfunktion maksimiarvon etsimiseen. Stokastisen jännityshistorian tapauksessa myös kestävyysfunktion arvot muodostavat stokastisen prosessin, jonka maksimiarvon todennäköisyysjakauma voidaan muodostaa. Menetelmää havainnollistetaan sekä yksinkertaisella yksidimensioisella että moniakselisella teollisella esimerkkilaskennalla.

European Journal of Mechanics - A/Solids

LUMAT: International Journal on Math, Science and Technology Education

MathCheck is a relatively new online tool that gives students feedback on their solutions to elem... more MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if the step is incorrect. It has been in student use since the autumn of 2015 and under design-based research from the first online day. The main research questions of this study are the following. 1) How can the usage of MathCheck support the aspects of conceptual understanding and procedural fluency of constructivism learning? 2) How can MathCheck empower both students and teachers in the education of mathematics? This paper presents the results of five pedagogical experiments considering both students’ and teachers’ point of views. In each experiment, the students have suggested improvements, which have affected the further development of Ma...