Tuire Koponen

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 consistent with the hypothesis that linguistic and spatial skills can improve arithmetic development by enhancing childrens number-related knowledge.

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 regarding the intensity, duration, and content of support provided within each tier whereas the Finnish version contains no explicit guidelines for support. Third, the U.S. RTI assumes no special educational services in the first two tiers, but the Finnish framework includes special educational services from the onset of support. Implications for policy and practice are discussed.

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 = .37; 95% confidence interval [CI] [.33–.42]) as well as a large heterogeneity of individual correlations. The results also revealed that RAN produced stronger correlations with arithmetic calculation tasks than with general achievement tests; stronger correlations with single-digit calculation tasks than multidigit calculation tasks; and stronger correlations with math fluency tasks than math accuracy tasks. The effect of these moderators suggests that part of the reason why RAN predicts mathematics is that they both require quick access to and retrieval of phonological representations from long-term memory. Our findings also suggest that RAN objects or colors can be used as early predictors of mathematical skill, especially of arithmetic fluency.

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 GraphoGame Math, as well as for basic arithmetic, r = 0.63, when practiced with Number Race. The findings suggest that a targeted computerized practice can produce specific training effects in kindergarteners most at-risk for mathematics difficulties. The results are discussed with regard to practical implications for educational game development.

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 fact knowledge. An intervention study design was used consisting of six baseline and three follow‐up assessments. The results show that the participant calculated additions, subtractions and multiplications more accurately after the intervention was applied. In subtraction he also used more retrieval‐based strategies after than before the intervention. The results suggest that an intervention programme targeted at improving calculation skill based on conceptual knowledge is beneficial, especially when children have weaknesses in use of counting procedures and in direct memory retrieval.

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 children with SLI began kindergarten with significantly weaker early numeracy skills compared to their peers. Immediately after the instruction phase, there was no significant difference between the groups in counting skills. In Grade 1, the children with SLI performed similarly to their peers in addition and subtraction skills (accuracy) and multi-digit number comparison, but showed weaker skills in arithmetical reasoning and in matching spoken and printed multi-digit numbers. Our pilot study showed encouraging signs that the early numeracy skills of children with SLI can be improved successfully in a kindergarten small-classroom setting with systematic instruction emphasizing visualization.

Knowing, Applying, and Reasoning about Arithmetic: Roles of Domain-General and Numerical Skills in Multiple Domains of Arithmetic Learning.

The longitudinal relations of domain-general and numerical skills at ages 6–7 years to 3 cognitive domains of arithmetic learning, namely knowing (written computation), applying (arithmetic word problems), and reasoning (arithmetic reasoning) at age 11, were examined for a representative sample of 378 Finnish children. The results showed that domain-general skills, including spatial visualization, language, rapid automatized naming, and working memory, contributed independently to arithmetic learning. These relations were mostly mediated via basic number competence (i.e., counting sequence and number system knowledge), although spatial visualization remained predictive of arithmetic outcomes. The findings underscore a similar developmental course of arithmetic learning across different cognitive domains where domain-general skills build a launchpad for advanced arithmetic via enhancing basic number competence.

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 education explained only 22% of the variance in counting at the beginning of the first grade. Vocabulary, morphology, and verbal short-term memory were found to be interchangeable predictors, each explaining approximately 7%–9%, of counting skill. These findings challenge the interpretation of counting as a strongly language-based number skill. However, additional analysis among children with dyslexia revealed that memory and language skills, together with a child’s persistence and gender, had a rather strong predictive value, explaining 34%–46% of counting skill. Together these results suggest that verbal short-term memory and language skills at the age of five have not the same predictive value on counting skill at the beginning of school among a population-based sample as found in subjects with language impairment or learning difficulties, and thus, other cognitive factors should be taken into account in further research related to typical development of counting skill.

Does Multi-Component Strategy Training Improve Calculation Fluency Among Poor Performing Elementary School Children?

The aim of the present study was to extend the previous intervention research in math by examining whether elementary school children with poor calculation fluency benefit from strategy training focusing on derived fact strategies and following an integrative framework, i.e., integrating factual, conceptual, and procedural arithmetic knowledge. It was also examined what kind of changes can be found in frequency of using different strategies. A quasi-experimental design was applied, and the study was carried out within the context of the school and its schedules and resources. Twenty schools in Finland volunteered to participate, and 1376 children were screened in for calculation fluency problems. Children from second to fourth grades were recruited for the math intervention study. Children with low performance (below the 20th percentile) were selected for individual assessment, and indications of using counting-based strategies were the inclusion criteria. Altogether, 69 children participated in calculation training for 12 weeks. Children participated in a group based strategy training twice a week for 45 min. In addition, they had two short weekly sessions for practicing basic addition skills. Along with pre- and post-intervention assessments, a 5-month follow-up assessment was conducted to exam the long-term effects of the intervention. The results showed that children with dysfluent calculation skills participating in the intervention improved significantly in their addition fluency during the intervention period, showing greater positive change than business-as-usual or reading intervention controls. They also maintained the reached fluency level during the 5-month follow-up but did not continue to develop in addition fluency after the end of the intensive training program. There was an increase in fact retrieval and derived fact/decomposition as the preferred strategies in math intervention children and a decrease of the use of counting-based strategies, which were the most common strategies for them before the intervention. No transfer effect was found for subtraction fluency.

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 instruction). Finally, recommendations are presented for further refining and developing assessment and instruction policies in the two countries.