Benefits of Integrating an Explicit Self-Efficacy Intervention With Calculation Strategy Training for Low-Performing Elementary Students

This study examined the malleability of math self-efficacy (SE) among children with poor calculation fluency via an intervention that targeted four sources of SE (mastery experiences, vicarious experiences, social persuasions, and emotional and physiological states). The effect of pure strategy training was contrasted with an intervention that integrated strategy training and explicit SE support. Moreover, the changes in SE source experiences and their relation with math SE, as well as the relation between math-SE profiles and calculation fluency development, were examined. In a quasi-experimental design, 60 Finnish children with calculation fluency problems in Grades 2 to 4 participated in…

Counting and RAN: Predictors of arithmetic calculation and reading fluency.

This study examined whether counting and rapid automatized naming (RAN) could operate as significant predictors of both later arithmetic calculation and reading fluency. The authors also took an important step to clarify the cognitive mechanisms underlying these predictive relationships by controlling for the effect of phonological awareness and verbal short-term memory. Due to rather strong covariance between verbal short-term memory and phonological awareness, short-term memory could be controlled only partially. Participants, 200 children from a longitudinal study, were followed from age 5 to 10 years. Structural equation modeling showed counting to be a strong predictor, not only of lat…

Development of Numeracy and Literacy Skills in Early Childhood—A Longitudinal Study on the Roles of Home Environment and Familial Risk for Reading and Math Difficulties

This study examines the direct and indirect effects of home numeracy and literacy environment, and parental factors (parental reading and math difficulties, and parental education) on the development of several early numeracy and literacy skills. The 265 participating Finnish children were assessed four times between ages 2.5 and 6.5. Children’s skills in counting objects, number production, number sequence knowledge, number symbol knowledge, number naming, vocabulary, print knowledge, and letter knowledge were assessed individually. Parents (N = 202) reported on their education level, learning difficulties in math and reading (familial risk, FR), and home learning environment separately fo…

Basic numeracy in children with specific language impairment: heterogeneity and connections to language.

Purpose This study examined basic numerical skills in children with specific language impairment (SLI) and how well linguistic factors explain the variance in these children’s number skills. Method The performance of children with SLI ( n = 29) was compared with that of typically developing children along a continuum ranging from preschool to 3rd grade ( n = 20, 47, 40, and 33). This facilitated both linguistic and educational age comparisons. To study number skills within the SLI group more closely, this group was divided into subgroups on the basis of their performance in verbal and nonverbal numerical skills. The performance of the different SLI subgroups on the linguistic and nonverbal…

Longitudinal and situational associations between math anxiety and performance among early adolescents

Studies have found math anxiety and achievement to be related from the beginning of formal schooling, but the knowledge regarding the direction of the relationship is vague. The purpose of the present study was to study this relationship. We investigated math anxiety from two points of view: trait and state anxiety. In the first substudy, we investigated the longitudinal relationship between math anxiety and performance from sixth to seventh grade (n = 848) with cross-lagged modeling. In the second substudy, we investigated the situational relationship of anxiety and performance by giving the participants (n = 149) challenging and nonchallenging math tasks adapted to their skill level, and …

Calculation and language : diagnostic and intervention studies

Tuire Koponen selvitti väitöskirjassaan kielellisten taitojen yhteyttä matemaattisten perustaitojen, erityisesti peruslaskutaidon, kehittymiseen. Hän tutki sekä 9-11-vuotiaita lapsia, joilla oli kielellisiä erityisvaikeuksia, että laajempaa, 10-vuotiaiden koko ikäluokkaa edustavaa joukkoa.Lapsilla, joilla oli kielellisiä erityisvaikeuksia, oli myös selvästi enemmän vaikeuksia usealla eri alueella matematiikan perustaidoissa. Heitä verrattiin 2-3- luokkalaisiin lapsiin, joiden matematiikan opetussisällöt olivat samantasoisia.- Nämä lapset eivät kuitenkaan muodosta yhtenäistä ryhmää matemaattisten perustaitojen suhteen, vaan yksilöllistä arviointia tarvitaan kunkin kielihäiriöisen lapsen tait…

Prematurity and overlap between reading and arithmetic: The cognitive mechanisms behind the association

It is well-known that very preterm children perform at lower levels than full-term children in reading and arithmetic at school. Whether the lower performance levels of preterm children in these two separate domains have the same or different origins, however, is not clear. The present study examined the extent to which prematurity is associated with the overlap (i.e., common variance) of reading and arithmetic among Finnish school beginners. We also examined the extent to which the association of prematurity with the overlap between reading and arithmetic is due to different prereading skills, basic number skills, and general cognitive abilities. The participants (age 6-7) consisted of 193…

Verbal counting skill predicts later math performance and difficulties in middle school

This study examined the role of verbal counting skill as an early predictor of math performance and difficulties (at or below −1.5 standard deviation in basic math skills) in middle school. The role of fourth-grade level arithmetical skills (i.e., calculation fluency, multi-digit arithmetic i.e. procedural calculation, and word problem solving) as mediators was also investigated. The participants included 207 children in central Finland who were studied from kindergarten to the seventh grade. Path modeling showed that verbal counting in kindergarten is a strong predictor for basic math performance in seventh grade, explaining even 52% of the variance in these skills after controlling for th…

A meta-analysis of the relation between RAN and mathematics.

Several studies have shown that rapid automatized naming (RAN) is a significant predictor of mathematics, but the nature of their relationship remains elusive. Thus, the purpose of this meta-analysis was to estimate the size of their relationship and determine the conditions under which they correlate. We used a random-effects model analysis of data from 38 studies (33 unique samples, 151 correlations, 7,135 participants) to examine the size of the RAN–mathematics relationship and the role of different moderators (i.e., math measure and variable, type of RAN task, math age, study design, and sample characteristics). The results showed a significant correlation between RAN and mathematics (r…

Parental influences on the development of single and co-occurring difficulties in reading and arithmetic fluency

This study investigated how single and co-occurring difficulties in reading and arithmetic fluency developed among Finnish children across Grades 1–9 (N = 2151). Latent profile analysis among 391 children who had reading and/or arithmetic fluency difficulties in Grade 9 revealed profiles that followed three distinct patterns: reading difficulties (N = 121), mathematical difficulties (N = 94), and comorbid difficulties (N = 176). The profiles and typical performers were compared on parental reading and mathematical difficulties, parental education, the early home learning environment, and parental assistance with school homework across Grades 1–9. Results showed that although parents whose c…

Response-To-Intervention in Finland and the United States: Mathematics Learning Support as an Example

Response to Intervention (RTI) was accepted in the early 2000s as a new framework for identifying learning difficulties (LD) in the U.S. In Finland, a similar multi-tiered framework has existed since 2010. In the present study, these frameworks are presented from the viewpoint of the role of assessment and instruction as expressed in documents that describe the frameworks, as it seems that these two components of RTI are the most disparate between the U.S. and Finland. We present a suggestion for the Finnish framework as an example of support in mathematics learning that incorporates principles of RTI (such as systematized assessment and instruction, cyclic support, and modifiable instructi…

Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge

Utilizing a longitudinal sample of Finnish children (ages 6-10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are …

Development of math anxiety and its longitudinal relationships with arithmetic achievement among primary school children

Abstract The aim of this study is to examine the development of two separable aspects of math anxiety, anxiety about math-related situations and anxiety about failure in math, and their cross-lagged relationship with arithmetic achievement. The mean level of anxiety about math-related situations decreased among second, third, and fourth graders, and the level of anxiety about failure in math declined among third, fourth, and fifth graders. The rank-order of individuals was more stable in arithmetic achievement than in either aspect of math anxiety. Arithmetic achievement predicted later anxiety about failure in math, but neither aspect of math anxiety predicted later achievement. The result…

Can reading fluency and self-efficacy of reading fluency be enhanced with an intervention targeting the sources of self-efficacy?

Abstract The first aim of the study was to analyze whether reading fluency and self-efficacy of reading fluency (SE-rf) are malleable for children (Grades 3–5) with deficits in fluent reading via a 12-week special education program targeting both reading fluency and the sources of SE-rf (SE-program). The second aim was to investigate whether changes in SE-rf are related to changes in reading fluency. The SE-program (n = 40) was contrasted with the SKILL-program (n = 42) providing training solely in reading fluency. The groups showed equal improvements in reading fluency. Positive change in SE-rf emerged only in the SE-group, and this change was associated with changes in fluency, but the as…

Cognitive skills, self-beliefs and task interest in children with low reading and/or arithmetic fluency

This study examined the identifiability and early cognitive and motivational markers of low reading and arithmetic fluency. Comparisons of these characteristics between Finnish third graders (n = 197) with low fluency in reading, arithmetic, or both revealed, first, that the majority of third graders with low arithmetic fluency showed low arithmetic skills already at first-grade spring, whereas children with low reading fluency were identified from the second-grade fall onward. Second, all groups with low fluency showed low rapid automatized naming and counting skills across the primary school years, while in other cognitive skills these groups showed different patterns. Third, all groups w…

Individuality in the Early Number Skill Components Underlying Basic Arithmetic Skills

Early number skills underlie success in basic arithmetic. However, very little is known about the skill profiles among children in preprimary education and how the potential profiles are related to arithmetic development. This longitudinal study of 440 Finnish children in preprimary education (mean age: 75 months) modeled latent performancelevel profile groups for the early number skill components that are proposed to be key predictors of arithmetic (symbolic number comparison, mapping, and verbal counting skills). Based on three assessment time points (September, January, and May), four profile groups were found: the poorest-performing (6%), low-performing (16%), nearaverage-performing (33…

The Many Faces of Special Education Within RTI Frameworks in the United States and Finland

Response to intervention (RTI) can be considered an everyday practice in many parts of the United States, whereas, in Finland, only recently has a new framework for support in learning taken shape. Choosing Finland as the comparative partner for this policy paper is justified as its educational system has been widely referenced on the basis of good Programme for International Student Assessment (PISA) results. The results of the present comparative article showed first, that the U.S. RTI was primarily intended for diagnosing and preventing learning disabilities whereas the Finnish RTI is mainly an administrative structure for support. Second, the U.S. RTI includes clear definitions regardin…

Preventive Support for Kindergarteners Most At-Risk for Mathematics Difficulties: Computer-Assisted Intervention

Weaknesses in early number skills have been found to be a risk factor for later difficulties in mathematical performance. Nevertheless, only a few intervention studies with young children have been published. In this study, the responsiveness to early support in kindergarteners with most severe difficulties was examined with two different computer programs. Two intervention groups were matched by age, visuo-spatial, and phonological working memory, as well as early number skills. After a short and intensive computerized intervention, the results indicated significant intervention effects for verbal counting Wilcoxon ES (r) = 0.46, and dot counting fluency, r = 0.52, when practiced with Grap…

Trajectories of change in reading self-efficacy: A longitudinal analysis of self-efficacy and its sources

The beliefs children hold about their capabilities as readers are known to influence their reading achievement. The aim of this study was to extend previous work by examining trajectories of change in reading self-efficacy among primary school students (N = 1327) and the relations between the trajectories of self-efficacy and their hypothesized sources over 11 months. Using growth mixture modeling, we identified four trajectories of change in reading self-efficacy, involving increasing, stable, and declining trends. These trajectories of change in reading self-efficacy were associated with students’ varying experiences with the four sources of self-efficacy over time. Higher levels of maste…

Early Cognitive Precursors of Children's Mathematics Learning Disability and Persistent Low Achievement: A 5-Year Longitudinal Study.

Mathematical difficulties have been distinguished as mathematics learning disability (MLD) and persistent low achievement (LA). Based on 1,880 Finnish children who were followed from kindergarten (age 6) to fourth grade, this study examined the early risk factors for MLD and LA. Distinct groups of MLD (6.0% of the sample) and LA (25.7%) children were identified on the basis of their mathematics performance between first and fourth grades with latent class growth modeling. Impairment in the same set of cognitive skills, including language, spatial, and counting skills, was found to underlie MLD and LA. The finding highlights the importance of monitoring mathematical development across the ea…

Comorbid Fluency Difficulties in Reading and Math: Longitudinal Stability Across Early Grades

We examined the prevalence of comorbidity of dysfluent reading and math skills longitudinally in a representative sample ( N = 1,928) and the stability of comorbid and single difficulties from first to fourth grades. The findings indicated that half the children who showed very low performance in one skill also evidenced low or very low performance in the other. Comorbid difficulties had somewhat higher prevalence in third and fourth graders than in first and second graders. The stability of comorbid difficulties was found to be established from Grade 2 onward, but the stability of single difficulties increased steadily across grades. Overall, the findings emphasize the relatively strong s…

Cognitive predictors of single-digit and procedural calculation skills and their covariation with reading skill.

Abstract This study examined the extent to which children’s cognitive abilities in kindergarten and their mothers’ education predict their single-digit and procedural calculation skills and the covariance of these with reading skill in Grade 4. In kindergarten, we assessed children’s (N = 178) basic number skills, linguistic skills, and visual attention. In Grade 4, we assessed their calculation and reading skills. Data on children’s cognitive ability at 5 years of age and their mothers’ level of education were also collected. The results showed that both of the core components of calculation, single-digit and procedural calculation, as well as their covariance with reading, were predicted …

Early Cognitive Profiles Predicting Reading and Arithmetic Skills in Grades 1 and 7

The aim of this study was to investigate cognitive profiles composed of skills predicting the overlap between reading and arithmetic in kindergarten (phonological awareness, letter knowledge, rapid automatized naming, and counting sequence knowledge) and the relation of these profiles to reading and arithmetic skills at Grades 1 and 7. A total of four distinct cognitive profiles were identified in an unselected sample of 1,710 children aged 5–6 years: (1) high linguistic and high counting skills (39.2%), (2) low linguistic and low counting skills (25.4%), (3) high counting skills in relation to linguistic skills (15.3%), and (4) low counting skills in relation to linguistic skills (20.1%). …

Tyttöjen ja poikien väliset osaamiserot matematiikassa

Individual variance in responsiveness to early computerized mathematics intervention

Abstract We examined the effects of short, intensive computerized intervention in early number skills for kindergarteners with poor addition skills (below 1.5 SD ). The mathematical content of the software was hierarchically organized, starting from one-to-one correspondence, comparing and ordering, and proceeding via number concept and counting to basic addition. The results showed positive within-group effects for basic addition (Wilcoxon ES ( r ) = .59), verbal counting (.56), and the Number Sets Test (.45; see Geary, Bailey, & Hoard, 2009 ). The effects remained stable over a 9-week follow-up period. However, there was no significant between-group difference in terms of gain scores as c…

A pilot study of the effects of RightStart instruction on early numeracy skills of children with specific language impairment

This pilot study investigated the effects of an early numeracy program, RightStart Mathematics (RS), on Finnish kindergartners with specific language impairment (SLI). The study applied a pre-test-instruction-post-test design. The children with SLI (n=9, Mage=82.11 months) received RS instruction two to three times a week for 40 min over seven months, which replaced their business-as-usual mathematics instruction. Mathematical skill development among children with SLI was examined at the individual and group levels, and compared to the performance of normal language-achieving age peers (n=32, Mage=74.16 months) who received business-as-usual kindergarten mathematics instruction. The childre…

A Review of Early Numeracy Interventions for Children at Risk in Mathematics

This study reviewed early numeracy interventions for four- to seven-year-old children at risk for mathematics difficulties. The search yielded 19 peer-reviewed studies with pre- and post-treatment control designs. The interventions were categorised as either core or supplemental instruction. The study analysed the effectiveness and identified the pedagogical components of the interventions: setting, duration, numeracy content used for intervention training and progress measurement, conductor and professional developmental support offered, and instructional design features. The interventions showed, to various degrees, the promising effect of improving the early numeracy skills of at-risk ch…

Self-regulatory efficacy and sources of efficacy in elementary school pupils: Self-regulatory experiences in a population sample and pupils with attention and executive function difficulties

In this study, we examined self-regulatory efficacy and sources of self-efficacy (mastery experiences, vicarious experiences, social persuasion and physiological/emotional states) and the relationships between self-efficacy and its sources among elementary school pupils. Two groups were compared: a population sample (PS, N = 1284) and pupils with difficulties in attention and executive functions (AED, N = 61). Data gathered from self-report questionnaires indicated that pupils in the PS group had more positive efficacy beliefs and mastery experiences and fewer negative physiological/emotional states than the AED group. Analyses showed strong connections between sources and self-regulatory e…

Covariation between reading and arithmetic skills from grade 1 to grade 7

This study examined the extent to which reading and arithmetic skills show covariation at Grade 1 and at Grade 7, to what extent this covariation is time-invariant or time-specific, and to what extent different antecedents will predict these time-invariant and time-specific portions of the covariation. The reading and arithmetic skills of a total of 1335 Finnish children were assessed at the end of Grade 1 and then again at the end of Grade 7. Phonological awareness, letter knowledge, rapid automatized naming (RAN), counting, and parental education levels were measured in kindergarten; working memory at Grade 1 and nonverbal reasoning at Grade 3. The results showed that reading and arithmet…

Counting and rapid naming predict the fluency of arithmetic and reading skills

Understanding of the factors that underlie the development of fluency in reading and arithmetic is limited. This longitudinal study examined whether verbal counting and rapid automatized naming (RAN) were predictors of arithmetic and reading fluency in a population-based sample and to what extent related early emerging cognitive abilities and socioeconomic background accounted for the predictive power of counting and RAN. In addition, in order to examine the uniqueness of counting as a numerical predictor of reading fluency, the influence of another early number skill—number concept—was controlled. Three hundred and seventy-eight Finnish children were followed from kindergarten to Grade 3 (…

Interventiovastemallien tarjoamat mahdollisuudet kolmiportaisen tuen mallin kehittämiseen : esimerkkinä matematiikan oppimisen tuki

Tässä katsausartikkelissa esitellään Yhdysvalloissa monin paikoin käytössä olevaa interventiovastemallia (Response to Intervention, RTI), joka sisältää tutkimusperustaisen näkökulman koulussa annettavaan oppimisen tukeen. Ennen kaikkea pohditaan interventiovastemallille ominaisen tuen tiheyden, keston ja arvioinnin merkitystä ja hyödynnettävyyttä suomalaisessa kolmiportaisen tuen mallissa. Lopuksi esitetään jatkokeskustelua ja -tutkimusta varten matematiikan oppimisen tuen kolmivaihemalli, johon on yhdistelty RTI-lähestymistapaa matematiikan oppimisvaikeuksiin annettavan tuen osalta ja joka kuitenkin on suomalaisen lainsäädännön mukainen. Kolmivaihemalli pohjaa yksityiskohdiltaan yhdysvalta…

Math anxiety and its relationship with basic arithmetic skills among primary school children

Background Children have been found to report and demonstrate math anxiety as early as the first grade. However, previous results concerning the relationship between math anxiety and performance are contradictory, with some studies establishing a correlation between them while others do not. These contradictory results might be related to varying operationalizations of math anxiety. Aims In this study, we aimed to examine the prevalence of math anxiety and its relationship with basic arithmetic skills in primary school children, with explicit focus on two aspects of math anxiety: anxiety about failure in mathematics and anxiety in math-related situations. Sample The participants comprised 1…

Minäuskomukset ja matematiikan oppiminen : Matematiikan Maailmaan -hankkeen kokemuksia

Matematiikan taitojen kehitystä ohjaavat taitojen oppimiseen liittyvien alkuvalmiuksien ohella erilaiset emotionaaliset tekijät, kuten oppilaan uskomukset itsestään matematiikan osaajana. Nämä uskomukset alkavat muodostua jo varhain suunnaten matematiikan oppimiseen liittyvää kiinnostusta ja vaikuttaen työskentelyyn oppimistilanteissa. Matematiikkaan liittyvien minäuskomusten muodostumiseen esi- ja alkuopetusiässä on kuitenkin tähän saakka kiinnitetty vähän huomiota. Jyväskylän yliopiston opettajankoulutuslaitoksen Matematiikan Maailmaan (MaMa) -kehittämishankkeen tavoitteena oli Opettajankoulutusfoorumin opettajankoulutuksen kehittämisohjelman periaatteiden mukaisesti vahvistaa opettajanko…

Cognitive Correlates of the Covariance in Reading and Arithmetic Fluency: Importance of Serial Retrieval Fluency

This study examines the core predictors of the covariance in reading and arithmetic fluency and the domain-general cognitive skills that explain the core predictors and covariance. Seven-year-old Finnish children (N = 200) were assessed on rapid automatized naming (RAN), phonological awareness, letter knowledge, verbal counting, number writing, number comparison, memory skills, and processing and articulation speed in the spring of Grade 1 and on reading and arithmetic fluency in the fall of Grade 2. RAN and verbal counting were strongly associated, and a constructed latent factor, serial retrieval fluency (SRF), was the strongest unique predictor of the shared variance. Other unique predic…

Conceptual knowledge‐based strategy training in single‐digit calculation: a single case intervention study in a child with specific language impairment

The aim of this single‐case intervention study was to examine whether a conceptual knowledge‐based strategy training would improve the accuracy of single‐digit arithmetical calculation in a child with specific language impairment. The intervention concerned an11‐year‐old Finnish‐speaking child with specific language impairment. He was trained individually once a week for three months. On the basis of his baseline performance single‐digit arithmetical problems were divided into ‘well‐known arithmetical problems’ and ‘error‐prone arithmetical problems’. Error‐prone problems were taught in meaningful relation to well‐known problems, which he repeatedly solved correctly by using arithmetical fa…

Cognitive Skills, Math-Related Emotions, and Beliefs Explaining Response to Arithmetic Fluency Intervention

We examined the associations of cognitive skills, math-related emotions and beliefs, and gender with responses to an arithmetic fluency intervention. Elementary school children with dysfluent arithmetic skills (N=69) participated in an arithmetic fluency intervention (with and without self-efficacy support) implemented in small groups in schools for 12 weeks. Hierarchical regression models including cognitive skills or math-related emotions and beliefs predicted 21% to 50% of the variation in the intervention response, i.e., improvement in arithmetic fluency. Cognitive skills were associated with the response mainly among boys, whereas math-related emotions and beliefs explained more among …

Cognitive predictors of counting skills

Rote counting skills have found to be a strong predictor of later arithmetic and reading fluency. However, knowledge of the underlying cognitive factors influencing counting skill is very limited. Present study examined to what extent language skills (phonology, vocabulary, and morphology), nonverbal reasoning skills, and memory at the age of five could explain counting skill at the beginning of first grade. Gender, parents’ education level and child’s persistence were included as control variables. The question was examined in a longitudinal sample (N = 101) with a structural equation model. Results showed that language skills together with memory, nonverbal reasoning skills and parent’s e…