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.

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 quasiexperimental 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.

Tämän tutkimuksen tavoitteena oli selvittää erityisopettajiksi opiskelevien verkkopalvelujen käyttöä opiskelujen ja työn tukena sekä heidän näkemyksiään ThinkMath-verkkopalvelusta ja sen kehittämistarpeista. Tutkimus on osa Matematiikan maailmaan –matematiikan opettajankoulutuksen kehittämishanketta. Kehittämistutkimuksen tässä osassa selvitettiin opiskelijoiden kokemuksia verkkomateriaalien käytöstä, erityisesti ThinkMath-verkkopalvelusta. Tutkimuksen osallistujat olivat Matemaattiset oppimisvaikeudet -kurssin opiskelijoita (N = 66). Opiskelijat tutustuivat yhdellä kurssin harjoituskerralla ThinkMath-harjoitusmateriaaleihin. Tietoa kerättiin kyselylomakkeilla kurssin alkaessa ja päättyessä. Tuloksissa käytetään kuvailevia tunnuslukuja sekä ristiintaulukointia. Tulosten perusteella erityisopettajaopiskelijat suhtautuvat verkkomateriaalien käyttöön varsin positiivisesti eikä eroja ollut eri ikä- tai työkokemusryhmien välillä. ThinkMath –verkkopalvelu tunnettiin ennalta varsin heikosti. Kurssin päättyessä opiskelijat kokivat sivuston antavan varsin hyvin tietoa matemaattisten taitojen kehityksestä. Heikoimmin sivuston koettiin antavan tietoa matemaattisten oppimisvaikeuksien arvioinnista ja taustatekijöistä. Verkkopalvelun käytettävyydessä kehitettävää ilmeni erityisesti tiedon löytämisen helpottamisessa. Tutkimus antaa tietoa paitsi tämän verkkopalvelun kehittämiseen myös yleensä opettajille suunnatun verkkomateriaalin suunnitteluun.   Special education teacher students as users of online materials. Survey to develop ThinkMath web services Abstract The aim of this study was to find out how special educational needs teacher students use online materials in their studies. In addition, we asked how much they have used online materials in their teacher work before their studies. We were also interested in their specific expectations for the development of ThinkMath -web services. The research is part of the Teacher Training Project 'Matematiikan maailmaan' ('Math World'), which is funded by the Ministry of Education and Culture.  In our project, we follow educational design research (EDR) principles with several data collection and development cycles. In this paper, we report the results from the first EDR cycle, in which we explored students' experiences with the use of online materials, especially the ThinkMath web service. The participants of the study were students in the Mathematical Learning Difficulty course (N = 66). Students were introduced to ThinkMath online materials as a part of this course. The data was collected by questionnaires at the beginning and at the end of the course. The results use descriptive indicators and cross-tabulation.  On the basis of the results, special educational needs teacher students are quite positive about the use of online materials. There were no differences between age or work experience groups. The ThinkMath web service was known poorly in advance. At the end of the course, the students felt that the ThinkMath web service provided quite good information on the development of mathematical skills. Students suggested adding more information about background factors of mathematical learning difficulties, and ways of evaluating mathematical learning. Students also felt that search-functions in the ThinkMath web service needed to be better.  Our study showed the benefit of involving users to the developmental work of online materials, for example, ThinkMath web services. Keywords: online materials, special educational needs teacher students, educational design research, ThinkMath, web services