Laskemisen sujuvuus osana matemaattisia taitoja : Sujuvuuden seuranta ja matemaattisten taitojen tukeminen alakoulussa

The first purpose of this thesis was to investigate the development of calculation fluency, and the relationship between reading fluency and naming speed in Finnish children from second to fifth grade. The second purpose of this thesis was to investigate the effectiveness of two mathematical intervention programmes on learning of low-performing children. The main aim of the first longitudinal study (Study III) was to follow up the development of calculation fluency from second to fourth grade in two classes. The second aim was to predict children´s later calculation fluency with previous calculation fluency, reading fluency, naming speed, gender, and parent´s level of education. In the second longitudinal study (Study IV), children were classifield as non-fluent in calculation, non-fluent in reading, and fluent in both academic skills. Calculation and reading fluency of all three groups were followed up to grade 5. The groups were also compared on naming speed. In this thesis, there were two intervention studies. The first intervention study (Study I) was conducted with children from three grades (2nd, 3rd, and 4th). The intervention programme used in Study I was designed based on previous intervention studies (Bryant, Bryant, Gersten, Scammacca & Chavez, 2008; Fuchs, Compton, Fuchs, Paulsen, Bryant & Hamlett, 2005). Study II was conducted with children from the first grade. The intervention programme used in Study II was adapted from the “I count too!” programme (Minakin lasken) (Van Luit, Aunio & Räsänen, 2010). In Studies I and IV, the results were also examined from the perspective of individual differences. In the longitudinal studies (Study III and IV), the differences between groups in calculation fluency were stable during the research period. If a child had difficulties in calculation fluency, they most likely had problems also in reading fluency. Calculation fluency was best predicted by previous calculation fluency. The results suggest that calculation fluency in second grade predicts over 65 % of the variance in calculation fluency in fourth grade. In grade 5, the children, who had separate problems in calculation or reading fluency had closed their gap to their classmates´ fluency. Children who had co-occurring fluency problems on reading and calculation fluency had slower naming speed. The results from the intervention studies (Study I and II) show that intensified instruction can be used successfully to support mathematical skills in elementary school. It is necessary to identify low performance early enough, because in the intervention study (Study II) conducted with first grade children, the instruction group experienced significant development, especially in counting skills. However, there were significant differences between children in the intervention group in both studies. In both intervention studies, the development was most significant in the children who had no severe learning difficulties. Findings suggest that systematic monitoring of the developmental process in calculation is necessary in the elementary school years. There are some potentially shared components in calculation and reading fluency. The screening for at-risk development in reading and calculation should be done at the same time, and screening should be continued after the early school years. It should be noticed early enough, if the child has co-occuring problems in calculation and reading fluency.Tässä väitöstutkimuksessa seurattiin laskemisen sujuvuuden kehitystä toiselta viidennelle luokalle ja sen yhteyttä lukemisen sujuvuuden ja nimeämisnopeuden kanssa. Lisäksi tarkasteltiin kahden alakouluikäisille suunnatun harjoitusohjelman kykyä vaikuttaa lasten matemaattisiin taitoihin. Ensimmäisessä seurantatutkimuksessa seurattiin kahden koululuokan lasten laskutaidon muutosta toiselta neljännelle luokalle sekä pyrittiin selittämään myöhempää laskemisen sujuvuutta aiemman laskemisen sujuvuuden, lukemisen sujuvuuden, sukupuolen, nimeämisnopeuden ja vanhempien koulutuksen avulla (osatutkimus III). Toisessa seurantatutkimuksessa (osatutkimus IV) lapsista muodostettiin toisella luokalla arvioidun laskemisen ja lukemisen sujuvuuden perusteella sujuvuusryhmät (ei-sujuva laskija, ei-sujuva lukija, sujuva molemmissa taidoissa), joiden sujuvuutta sekä laskemisessa että lukemisessa seurattiin viidennen luokan syksyyn saakka. Ryhmiä verrattiin toisiinsa myös nimeämisnopeuden suhteen. Interventiotutkimuksia oli kaksi. Niistä ensimmäisessä (osatutkimus I) osallistujat olivat saman koulun kolmelta luokka-asteelta (2., 3. ja 4.), ja harjoitusohjelma perustui aiempiin interventiotutkimuksiin (mm. Bryant, Bryant, Gersten, Scammacca & Chavez, 2008; Fuchs, Compton, Fuchs, Paulsen, Bryant & Hamlett, 2005). Toisessa interventiotutkimuksessa (osatutkimus II) osallistujat olivat ensimmäisellä luokalla. Tässä osatutkimuksessa käytetty harjoitusohjelma oli muokattu Minäkin lasken! –harjoitusohjelmasta (Van Luit, Aunio & Räsänen, 2010). Osatutkimuksissa I ja IV kuvattiin myös lasten yksilöllistä kehitystä tutkituissa taidoissa. Laskemisen sujuvuus eri luokka-asteilla oli voimakkaasti yhteydessä keskenään. Ääneen lukemisen sujuvuus oli yhteydessä päässä laskettavien tehtävien kanssa, äänetön sanantunnistus sekä päässä että algoritmien avulla laskettavien tehtävien sujuvuuden kanssa. Lapset, jotka olivat sujuvuudeltaan heikkoja laskijoita, olivat usein suhteellisen heikkoja myös lukemisen sujuvuudessa. Lasten myöhempää laskemisen sujuvuutta kyettiin parhaiten selittämään aiemmalla laskemisen sujuvuudella. Toisen luokan talvella arvioidulla laskemisen sujuvuudella kyettiin selittämään 2/3 kolmannen luokan kevään laskemisen sujuvuudesta ja 1/5 neljännen luokan kevään laskemisen sujuvuudesta. Viidennellä luokalla alkujaan pelkästään laskemisessa tai lukemisessa ei-sujuvat lapset olivat saavuttaneet laskemisen sujuvuudessa luokka-asteensa tason. Interventiotutkimukset (osatutkimukset I ja II) osoittivat, että lasten matemaattisia taitoja voidaan tukea alakoulussa erilaisin systemaattisin harjoitusohjelmin. Parhaita tuloksia saadaan varhaisessa vaiheessa toteutetuilla interventioilla. 1. luokalla toteutetussa interventiossa harjoitusryhmän lapset saavuttivat varhaisissa matemaattisissa taidoissa vertailuryhmän lapset. Toisessa osatutkimuksessa tuesta vaikutti olevan merkittävintä hyötyä 2. luokalla. Yksittäisten lasten välillä oli eroja siinä, miten he hyötyivät interventiosta. Molemmissa interventioissa tuesta hyötyminen oli merkittävintä lapsilla, joilla matemaattisissa taidoissa ilmeneviin heikkouksiin ei liittynyt muuta oppimiseen vaikuttavaa pulmaa. Tutkimuksen perusteella laskemisen sujuvuuden kehitystä olisi tärkeä seurata systemaattisesti koko alakoulun ajan. Varsinkin toisen luokan aikana arvioitu laskemisen sujuvuus ennakoi varsin hyvin myöhempää sujuvuutta, myös algoritmien avulla laskettaessa. Seurannassa kannattaa ottaa huomioon myös lukemisen sujuvuus. Tällöin kiinnitetään jo varhaisessa vaiheessa huomiota myös päällekkäisiin sujuvuuspulmiin

Alakoululaisten laskemisen ja lukemisen sujuvuuden seuranta

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Mathematical intervention for low performing first graders

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Differential Effects of Virtual and Concrete Manipulatives in a Fraction Intervention on Fourth and Fifth Grade Students’ Fraction Skills

Fraction knowledge has been found to predict later mathematical performance, but many students have difficulty with fractions. Virtual manipulatives (VM) and concrete manipulatives (CM) are effective approaches to teaching fractions, but previous research has not been able to reach a consensus on which manipulatives are the most effective. This quasi-experimental study employed a pre- and posttest design to investigate the differential effects of VM and CM in a fraction intervention on students’ fraction skills. In addition to fraction skills, students’ arithmetic fluency was measured. Fidelity of intervention, social validity, and time-efficiency of the manipulatives were also investigated. Fourth- and fifth-grade participants (N= 115) from Southern Finland were assigned to VM and CM intervention groups. The intervention was implemented during six 45-minute lessons over 2 weeks. Results revealed that the CM group outperformed the VM group in fraction skills, which suggests that CM should be favored in fraction interventions.Fraction knowledge has been found to predict later mathematical performance, but many students have difficulty with fractions. Virtual manipulatives (VM) and concrete manipulatives (CM) are effective approaches to teaching fractions, but previous research has not been able to reach a consensus on which manipulatives are the most effective. This quasi-experimental study employed a pre- and posttest design to investigate the differential effects of VM and CM in a fraction intervention on students’ fraction skills. In addition to fraction skills, students’ arithmetic fluency was measured. Fidelity of intervention, social validity, and time-efficiency of the manipulatives were also investigated. Fourth- and fifth-grade participants (N= 115) from Southern Finland were assigned to VM and CM intervention groups. The intervention was implemented during six 45-minute lessons over 2 weeks. Results revealed that the CM group outperformed the VM group in fraction skills, which suggests that CM should be favored in fraction interventions.Peer reviewe

Virtuaalisten ja konkreettisten apuvälineiden käytön vaikutus viidesluokkalaisten murtolukujen oppimiseen

Tämän tutkimuksen tarkoituksena on selvittää virtuaalisten ja konkreettisten apuvälineiden käytön vaikutuksia neljäs- ja viidesluokkalaisille suunnatussa murtolukuinterventiossa. Oppimistulosten lisäksi tutkimme apuvälineiden aikatehokkuutta sekä sitä, kuinka hyödyllisenä ja helppokäyttöisenä oppilaat pitävät apuvälineitä. Esittelemme tutkimuksemme pilotoinnin tuloksia.Peer reviewe

New Delivery Chair for Vaginal Delivery

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Effects of Gender on Basic Numerical and Arithmetic Skills : Pilot Data From Third to Ninth Grade for a Large-Scale Online Dyscalculia Screener

In this study, we analyzed the development and effects of gender on basic number skills from third to ninth grade in Finland. Because the international comparison studies have shown slightly different developmental trends in mathematical attainment for different language groups in Finland, we added the language of education as a variable in our analysis. Participants were 4,265 students from third to ninth grade in Finland, representing students in two national languages (Finnish, n = 2,833, and Swedish, n = 1,432). Confirmatory factor analyses showed that the subtasks in the dyscalculia screener formed two separate factors, namely, number-processing skills and arithmetic fluency. We found a linear development trend across age cohorts in both the factors. Reliability and validity evidence of the measures supported the use of these tasks in the whole age group from 9 to15 years. In this sample, there was an increasing gender difference in favor of girls and Swedish-speaking students by grade levels in number-processing skills. At the same time, boys showed a better performance and a larger variance in tasks measuring arithmetic fluency. The results indicate that the gender ratio within the group with mathematical learning disabilities depends directly on tasks used to measure their basic number skills.Peer reviewe

Effects of Gender on Basic Numerical and Arithmetic Skills: Pilot Data From Third to Ninth Grade for a Large-Scale Online Dyscalculia Screener

In this study, we analyzed the development and effects of gender on basic number skills from third to ninth grade in Finland. Because the international comparison studies have shown slightly different developmental trends in mathematical attainment for different language groups in Finland, we added the language of education as a variable in our analysis. Participants were 4,265 students from third to ninth grade in Finland, representing students in two national languages (Finnish, n = 2,833, and Swedish, n = 1,432). Confirmatory factor analyses showed that the subtasks in the dyscalculia screener formed two separate factors, namely, number-processing skills and arithmetic fluency. We found a linear development trend across age cohorts in both the factors. Reliability and validity evidence of the measures supported the use of these tasks in the whole age group from 9 to15 years. In this sample, there was an increasing gender difference in favor of girls and Swedish-speaking students by grade levels in number-processing skills. At the same time, boys showed a better performance and a larger variance in tasks measuring arithmetic fluency. The results indicate that the gender ratio within the group with mathematical learning disabilities depends directly on tasks used to measure their basic number skills.</p

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A nationwide study on parathyroid carcinoma

Background: Parathyroid carcinoma (PC) is rare and diagnostically challenging. Reported outcomes are rather poor and the incidence might be increasing.Material and methods: We performed a nationwide study on all cases (n=32) diagnosed in 2000-2011 in Finland, and compared clinical and histopathological characteristics and outcome to atypical parathyroid (APA; n=28) and parathyroid adenomas (PA; n=72). The incidence in years 1955-1999 was compared to that in 2000-2013.Results: Preoperatively, calcium and parathyroid hormone concentrations were higher in PC compared to APA and PA (1.76, 1.56 and 1.44mmol/l, pPeer reviewe