59 research outputs found
Matemaattiset interventiot : Matemaattisilta taidoiltaan heikkojen lasten tukeminen ennen koulunaloitusta ja ensimmäisinä kouluvuosina
The purpose of this thesis was to investigate the effectiveness of early mathematics interventions for young children with low performance in mathematics. Previous research has indicated that early mathematics skills are a strong predictor of later mathematics performance. The goal of early mathematics support by means of interventions is to improve mathematics performance, and consequently, to diminish the possibility of mathematics learning disability emerging later on. This thesis sought to complement and extend previous research in the field of early mathematics interventions, by reviewing early mathematics interventions, and investigating the effectiveness of two early mathematics intervention programmes.
Study I reviewed mathematics interventions (N = 19) aimed at 4–7-year-old children with low performance in mathematics. For each intervention, effect sizes were calculated for mathematics outcome measures, and the pedagogical implementation was described. The effectiveness of the RightStart Mathematics (RS) (Cotter, 2001) instruction was investigated in Studies II and III. In Study II, the instruction was provided for Finnish kindergartners (RS group: n = 38, comparison group: n = 32) in general education classrooms, with focus on low-performing children. In Study III, the RS instruction was provided in special education classrooms for children with a specific language impairment (SLI group: n = 9, comparison group: n = 32). In Study IV, a mathematics intervention programme Improving Mathematics Skills in the Second Grade (IMS-2) (Mononen & Aunio, 2012) was developed, and its effectiveness for second graders performing low in mathematics was examined (IMS-2 group: n = 11, low-performing controls: n = 13 and typically performing controls: n = 64). In Studies II-IV, quantitative methods were used for analysing the interventions’ effects.
According to the results of the review, in the majority of the interventions, the mathematics skills of the participating children improved more than the skills of the children in control groups, with effect sizes varying from small to large. Progress in mathematics learning was evident when instruction included one or more of the following instructional features: explicit instruction, peer-assisted instruction, applying a concrete-representational-abstract sequence, computer assisted instruction, or games. Study II showed that the RS instruction was as effective as the typical Finnish kindergarten mathematics instruction. The counting skills of the initially low-performing children improved to the level of their typically performing peers. Follow-up in the first grade revealed performance differences between the initially low- and typically performing children, highlighting the importance of continuously monitoring progress, and providing intensified support. In Study III, children with a SLI receiving RS instruction improved their counting skills to the level of their peers. In the first grade follow-up, the children with SLI performed similarly to their peers in addition and subtraction skills (accuracy) and multi-digit number comparison. In Study IV, the mathematics skills of the second graders participating in the IMS-2 intervention did not improve more than the skills of the children in control groups. However, the study provided valuable information about the functionality of the IMS-2 programme’s intensity and content.
To conclude, in general, the results indicate that rather than waiting for children to fail, mathematics interventions can be used successfully to promote the early mathematics skills of children with low performance in mathematics, already before the onset of formal schooling and in the early grades. Therefore, identifying low performance in mathematics and providing sufficient support should be emphasised already in early childhood education, in accordance with the Finnish three-tiered educational support system.
Keywords: early mathematics skills, low performance in mathematics, mathematics learning disability, mathematics intervention, review, specific language impairment, educational supportTämän väitöstutkimuksen tarkoituksena oli tarkastella matemaattisten interventioiden vaikuttavuutta lapsilla, joilla on heikot matemaattiset taidot. Aiempi tutkimus on osoittanut, että matemaattisilla taidoilla ennen kouluikää on vahva yhteys myöhempään matematiikan osaamiseen. Varhaisella matemaattisten taitojen tukemisella pyritään kohentamaan matemaattisen osaamisen tasoa ja siten ennaltaehkäisemään matematiikan oppimisvaikeuksien syntymistä. Tämä tutkimus täydentää ja laajentaa nykyistä tietämystä matemaattisista interventioista kirjallisuuskatsauksella matemaattisista interventioista, jotka on suunnattu matemaattisesti heikkojen lasten tukemiseen. Lisäksi tutkittiin kahden matemaattisen interventio-ohjelman vaikuttavuutta.
Osatutkimuksen I kirjallisuuskatsaus tarkasteli matemaattisia interventioita (N = 19), jotka oli suunnattu 4–7-vuotiaille lapsille, joilla on heikot matemaattiset taidot. Jokaisen intervention matemaattisten taitojen osaamistuloksille laskettiin efektikoot ja intervention pedagoginen toteutus kuvailtiin. Osatutkimuksissa II ja III tutkittiin RightStart Matematiikka (RS) (Cotter, 2001) ohjelman vaikuttavuutta. Osatutkimuksessa II RS-opetusta annettiin suomalaisille esiopetusikäisille lapsille (RS-ryhmä: n = 38, verrokkiryhmä: n = 32) yleisopetuksen esiopetusryhmissä. Tarkastelun kohteena olivat myös matemaattisilta taidoiltaan heikot lapset. Osatutkimuksessa III RS-opetusta annettiin erityisopetuksen ryhmissä lapsille, joilla oli kielellinen erityisvaikeus (SLI-ryhmä: n = 9, verrokkiryhmä: n = 32). Osatutkimuksessa IV kehitettiin interventio-ohjelma Matemaattisten taitojen tukeminen toisella luokalla (MTT-2) (Mononen & Aunio, 2012) ja sen vaikuttavuutta tutkittiin toisluokkalaisilla, joilla oli heikot matemaattiset taidot (MTT-2-ryhmä: n = 11, heikot verrokkiryhmä: n = 13, tavanomaisesti osaavat verrokkiryhmä: n = 64). Osatutkimuksissa II-IV interventioiden vaikuttavuutta analysoitiin määrällisillä tutkimusmenetelmillä.
Kirjallisuuskatsauksen perusteella suurin osa matemaattisista interventioista näytti kohentavan taidoiltaan heikkojen lasten matemaattisia taitoja, efektikokojen vaihdellessa pienestä suureen. Taidot paranivat selkeästi, kun interventiossa käytettiin yhtä tai useampaa seuraavista opetustavoista: eksplisiittinen opetus, oppilasparityöskentely, opetuksen eteneminen konkreettinen-kuva-abstrakti -jatkumolla, tietokoneavusteinen opetus tai pelit. Osatutkimus II osoitti, että RS-opetus oli yhtä tehokasta kuin tavanomainen suomalainen esiopetuksen matematiikan opetus. Esiopetusvuoden jälkeen heikkojen lasten laskemisen taidot olivat nousseet samalle tasolle tavanomaisesti osaavien kanssa. Ensimmäisellä luokalla taitoeroja esiintyi jälleen alun perin heikkojen ja tavanomaisesti osaavien lasten välillä. Tämä tulos korostaa sitä, että lasten matemaattisia taitoja tulisi arvioida säännöllisesti, ja lisätukea tulisi tarjota niille, jotka sitä näyttävät tarvitsevan. Osatutkimuksessa III RS-opetusta saaneiden lasten, joilla oli kielellinen erityisvaikeus, laskemisen taidot olivat kohentuneet tavanomaisesti osaavien lasten tasolle esiopetusvuoden lopussa. Ensimmäisellä luokalla nämä lapset suoriutuivat samalla tasolla tavanomaisesti osaavien lasten kanssa yhteen- ja vähennyslaskuissa (oikeellisuus) sekä moninumeroisten lukujen vertailussa. Osatutkimuksessa IV MTT-2 interventiota saaneiden matemaattisilta taidoiltaan heikkojen toisluokkalaisten osaamisen kasvu matemaattisissa taidoissa ei eronnut verrokkiryhmien lasten taitojen osaamisen kasvusta. Tämä osatutkimus antoi arvokasta tietoa MTT-2 intervention toimivuuteen vaikuttavista asioista, kuten interventio-ohjelman sisällöstä ja kestosta.
Yhteenvetona voidaan todeta, että yleisesti ottaen matemaattisten interventioiden avulla voidaan tukea onnistuneesti jo ennen koulunaloitusta ja ensimmäisinä kouluvuosina niitä lapsia, jotka ovat matemaattisilta taidoiltaan heikkoja. Tästä syystä, ja suomalaista kolmiportaisen tuen mallia mukaillen, lasten heikot matemaattiset taidot tulisi pystyä tunnistamaan arvioinnin keinoin jo ennen koulunaloitusta ja tarjota tukea sitä tarvitseville.
Avainsanat: esi- ja alkuopetus, heikko matemaattinen osaaminen, kielellinen erityisvaikeus, kirjallisuuskatsaus, matemaattiset interventiot, matemaattiset taidot, matematiikan oppimisvaikeude
LukiMat ja Mavalka: Matemaattisten taitojen tuen tarpeen tunnistaminen esiopetuksessa
In Finland, there are only a few mathematical assessment tools suitable for pre-primary education. There is still very little research on their effectiveness and reliability. This study examined two of the most common pre-primary school mathematics assessment tools in Finland: the LukiMat pre-primary school mathematics - Identifying need of support and the Mathematical Skills Inventory (Mavalka) 2. The aim of the study was to find out what kind of mathematical skills children have at the beginning of the pre-primary school year, whether these assessment tools find the children whose mathematical skills are weak, that is below the 25th percentile, and what kind of math performance profiles low-performing children have. In addition, the study looked at the self-concept and interest in mathematics of pre-primary school children and their relationship with mathematical performance. Seventy-two pre-primary school-age children participated in the study. They were given the LukiMat and Mavalka assessments and a questionnaire measuring their self-concept and interest in mathematics at the beginning of the pre-primary school year. The correlation between LukiMat and Mavalka was found to be strong, with 15 (65.2%) of the same children found to have weak skills. The performance profile of each child in need of support was individual, highlighting the importance of assessing mathematical subskills to guide teaching and support. Regression analysis showed that self-concept and interest were not related to mathematical skills. The study showed that LukiMat and Mavalka are reliable assessment tools for assessing pre-primary school children's mathematical skills.Suomessa on käytössä vain muutamia esiopetukseen soveltuvia matemaattisten taitojen arviointivälineitä. Niiden toimivuudesta ja luotettavuudesta on vielä varsin vähän tutkimustietoa. Tässä tutkimuksessa tarkasteltiin kahta Suomessa yleisintä esiopetuksessa käytössä olevaa matemaattisten taitojen arviointivälinettä: LukiMat esiopetus matematiikka – Tuen tarpeen tunnistaminen ja Matemaattisten valmiuksien kartoitus 2 (Mavalka). Pyrimme selvittämään, millaisia matemaattisia taitoja lapsilla on esiopetusvuoden alussa, löytävätkö kyseiset arviointivälineet ne samat lapset, joiden matemaattiset valmiudet ovat keskimääräistä heikommat, eli osaaminen jää alle 25. persentiilin, ja millaisia osaamisprofiileja heillä on matemaattisissa osataidoissa. Lisäksi tutkittiin, miten lasten matematiikan minäkäsitys ja kiinnostus on yhteydessä matemaattiseen osaamiseen. Tutkimukseen osallistui 72 esiopetusikäistä lasta. Heille tehtiin LukiMat- ja Mavalka-arvioinnit sekä matematiikan minäkäsitystä ja kiinnostusta mittaava kysely. LukiMatin ja Mavalkan välinen yhteys osoittautui korrelaatioanalyysissä vahvaksi ja arviointivälineillä löydettiin 15 (65.2 %) taidoiltaan heikkoa samaa lasta. Jokaisen tukea tarvitsevan lapsen osaamisprofiili oli yksilöllinen, mikä korostaa eri matemaattisten osataitojen arviointia opetuksen ja tuen suuntaamiseksi. Regressioanalyysi osoitti, että minäkäsityksellä ja kiinnostuksella ei ollut yhteyttä esiopetusikäisten lasten matemaattiseen osaamiseen. Tutkimus osoitti, että LukiMat ja Mavalka ovat luotettavia arviointivälineitä esiopetusikäisten lasten matemaattisten taitojen arviointiin
Predicting Mathematical Learning Difficulties Status : The Role of Domain-Specific and Domain-General Skills
AbstractThis study investigated which domain-specific and domain-general skills measured at grade 1 predict mathematical learning difficulties (MLD) status at grade 3. We used different cut-off criteria and measures of mathematics performance for defining the MLD status. Norwegian children’s (N = 206) numeracy, cognitive, and language skills were measured at grade 1 and arithmetic fluency and curriculum-based mathematics (CBM) at grade 3. Logistic regression analyses showed that symbolic numerical magnitude processing, verbal counting, and rapid automatized naming predicted MLD25 status (performance ≤ 25th percentile) based on arithmetic fluency, whereas verbal counting skills and nonverbal reasoning predicted the status based on CBM. The same predictors were found for MLD10 status (performance ≤ 10th percentile), and in addition, rapid automatized naming also predicted the status based on CBM. Only symbolic numerical magnitude processing and verbal counting predicted LOW status (performance between 11–25th percentile) based on arithmetic fluency, whereas nonverbal reasoning and working memory predicted LOW status based on CBM. Different cut-off scores and mathematics measures used for the definition of MLD status are important to acknowledge, as these seem to lead to relatively significant variation in which students are identified as having MLD and which factors contribute to the MLD status.Abstract
This study investigated which domain-specific and domain-general skills measured at grade 1 predict mathematical learning difficulties (MLD) status at grade 3. We used different cut-off criteria and measures of mathematics performance for defining the MLD status. Norwegian children’s (N = 206) numeracy, cognitive, and language skills were measured at grade 1 and arithmetic fluency and curriculum-based mathematics (CBM) at grade 3. Logistic regression analyses showed that symbolic numerical magnitude processing, verbal counting, and rapid automatized naming predicted MLD25 status (performance ≤ 25th percentile) based on arithmetic fluency, whereas verbal counting skills and nonverbal reasoning predicted the status based on CBM. The same predictors were found for MLD10 status (performance ≤ 10th percentile), and in addition, rapid automatized naming also predicted the status based on CBM. Only symbolic numerical magnitude processing and verbal counting predicted LOW status (performance between 11–25th percentile) based on arithmetic fluency, whereas nonverbal reasoning and working memory predicted LOW status based on CBM. Different cut-off scores and mathematics measures used for the definition of MLD status are important to acknowledge, as these seem to lead to relatively significant variation in which students are identified as having MLD and which factors contribute to the MLD status
The effects of educational computer game on low-performing children’s early numeracy skills – an intervention study in a preschool setting
The aim of this study was to determine the effects of an educational computer game, Lola’s World, on low-performing children’s early numeracy skills. Four preschools with 33 children from families of low socio-economic status (Mage = 5.5 years) took part in this study. Of the 33 children, 23 were split randomly into two groups: an intervention group playing a numeracy game (Lola’s World) and an active control group playing an early reading skills game (Lola’s ABC party). The remaining 10 children served as a passive control group. The intervention phase lasted three weeks, during which time the children played the games daily for about 15 min. The children’s numeracy skills were measured using the Early Numeracy Test. Those children (n = 22) who exhibited low numeracy (i.e. at risk for learning difficulties in mathematics) were included in the analyses. The three groups did not differ in terms of parental educational levels or home languages. They were comparable in terms of nonverbal reasoning and the amount of time spent playing. The Lola’s World group improved its early numeracy performance from pretest to post-test. No between-group differences were found. The results are discussed in relation to providing game-based support for low-performing preschoolers.Peer reviewe
A comparative study of variations in arithmetic fluency between Norwegian and Finnish third graders
The study aimed to investigate variations in addition and subtraction fluency by observing grade three students in Norway (n = 253, M-age = 8.38 y.) and Finland (n = 209, M-age = 9.35 y.) while controlling for their age and non-verbal reasoning. Gender differences were also examined. The focus of the study was on the performance of the low-achieving (LA) students in comparison to the typically achieving (TA) group, not neglecting differences in how early educational support was organised across the two countries. Two-minute speed tests in both addition and subtraction within the 1-20 number range were used to assess fluency. The Finnish students outperformed students in the Norwegian sample both in addition and subtraction fluency. There were more Norwegian students in the LA group (i.e. performance at or below the 25th percentile) in both addition (37.9% vs. 20.1%) and subtraction (39.1% vs. 15.8%). In comparison to the TA students, the LA students made more errors and skipped over more arithmetic tasks in an attempt to solve them. Observed differences are discussed in relation to both country characteristics concerning early mathematics education and early educational support.Peer reviewe
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