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The Associations between Mathematical Skills, Cognitive Performance, and Language Background in Elementary School Children. A Two-Year Follow-Up Study

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Title: The Associations between Mathematical Skills, Cognitive Performance, and Language Background in Elementary School Children. A Two-Year Follow-Up Study
Language: English
Authors: Tanja Linnavalli (ORCID 0000-0003-1775-5795), Pinja Jylänki (ORCID 0000-0003-4438-8986), Julia Kainulainen, Mari Tervaniemi (ORCID 0000-0002-9651-2929), Minna Törmänen (ORCID 0000-0002-6907-4396)
Source: Scandinavian Journal of Educational Research. 2025 69(6):1304-1318.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 15
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Early Childhood Education
Elementary Education
Grade 3
Primary Education
Grade 4
Intermediate Grades
Descriptors: Foreign Countries, Cognitive Tests, Memory, Intelligence Tests, Short Term Memory, Mathematics Skills, Mathematics Achievement, Arithmetic, Word Problems (Mathematics), Grade 3, Grade 4, Elementary School Students, Thinking Skills, Native Language, Gender Differences, Longitudinal Studies, Followup Studies
Geographic Terms: Finland
Assessment and Survey Identifiers: Wechsler Intelligence Scales Short Forms, Digit Span Test, Block Design Test
DOI: 10.1080/00313831.2024.2419063
ISSN: 0031-3831
1470-1170
Abstract: Early mathematical skills contribute to later school performance and socio-economic status. Working memory is related to mathematical skills, but spatial and language skills have independent effects on separate areas of mathematical skills such as solving word problems or arithmetic skills. In this study, 9- to 10-year-old children's (N = 57) cognitive and mathematical skills were assessed three times over 2 years. Spatial reasoning was associated with performance in solving word problems and working memory with performance in the arithmetic test. Regarding word problems, girls outperformed boys. Also, the second-language learners performed similarly to the native speakers in the beginning and in the end of the third grade, but worse in the end of the fourth grade. The results suggest that the students' inadequate mastery of the school language may lead to underachievement in mathematics, implying that further efforts should be invested in supporting their language learning.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1484413
Database: ERIC
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  Value: <anid>AN0188100221;55b01oct.25;2025Sep23.08:04;v2.2.500</anid> <title id="AN0188100221-1">The associations between mathematical skills, cognitive performance, and language background in elementary school children. a two-year follow-up study </title> <p>Early mathematical skills contribute to later school performance and socio-economic status. Working memory is related to mathematical skills, but spatial and language skills have independent effects on separate areas of mathematical skills such as solving word problems or arithmetic skills. In this study, 9- to 10-year-old children's (N = 57) cognitive and mathematical skills were assessed three times over 2 years. Spatial reasoning was associated with performance in solving word problems and working memory with performance in the arithmetic test. Regarding word problems, girls outperformed boys. Also, the second-language learners performed similarly to the native speakers in the beginning and in the end of the third grade, but worse in the end of the fourth grade. The results suggest that the students' inadequate mastery of the school language may lead to underachievement in mathematics, implying that further efforts should be invested in supporting their language learning.</p> <p>Keywords: Mathematical skills; working memory; language skills; spatial skills; second-language learners</p> <hd id="AN0188100221-2">Introduction</hd> <p>Mathematical skills are a predictor of academic success at school (Duncan et al., [<reflink idref="bib16" id="ref1">16</reflink>]) and are strongly related to socio-economic status in later life (Ritchie & Bates, [<reflink idref="bib55" id="ref2">55</reflink>]). Even if more advanced skills are not needed in one's occupation, they are still essential for coping with our daily lives: we calculate prices, dates, and the time it takes to drive somewhere. The learning of mathematical skills starts before formal schooling begins, and many studies have focused on the earlier years of mathematical development (e.g., Aunio et al., [<reflink idref="bib7" id="ref3">7</reflink>]; Aunola et al., [<reflink idref="bib9" id="ref4">9</reflink>]). Since difficulties in mathematical learning have been found to accumulate during school years (e.g., Aubrey et al., [<reflink idref="bib6" id="ref5">6</reflink>]), it is also important to study the development of mathematical skills in elementary school-aged children.</p> <p>Important mathematical skills in elementary school-aged children include skills such as arithmetic (i.e., addition, subtraction, multiplication, and division), and skills in solving word problems (i.e., the ability to solve verbally presented mathematical problems; Geary, [<reflink idref="bib21" id="ref6">21</reflink>]). Children demonstrate a variety of individual differences in their mathematical skills that can be explained by domain-specific skills (i.e., previously measured skills in maths; Aunola et al., [<reflink idref="bib9" id="ref7">9</reflink>]; Geary et al., [<reflink idref="bib23" id="ref8">23</reflink>]; Jordan et al., [<reflink idref="bib29" id="ref9">29</reflink>]; Lee & Bull, [<reflink idref="bib36" id="ref10">36</reflink>]) and domain-general skills such as cognitive skills (Geary et al., [<reflink idref="bib23" id="ref11">23</reflink>]; Träff et al., [<reflink idref="bib59" id="ref12">59</reflink>]). Cognitive skills, including working memory, spatial, and language skills, have been proposed as important factors in mathematical development (e.g., Lee & Bull, [<reflink idref="bib36" id="ref13">36</reflink>]; LeFevre et al., [<reflink idref="bib37" id="ref14">37</reflink>]; Träff et al., [<reflink idref="bib59" id="ref15">59</reflink>]), yet results have been somewhat inconsistent.</p> <p>Considering the importance of mathematical skills in later life, and the fact that previous studies have focused more on the earlier years or have found inconsistent results, more studies are needed to better understand mathematical development in elementary school children. Thus the present study focuses on the development of arithmetic and word problem solving skills in 9- to 10-year-old children, and their association with working memory, spatial, and language skills, as well as the significance of background variables (i.e., language status and gender) for this development.</p> <hd id="AN0188100221-3">Mathematical and cognitive skills</hd> <p></p> <hd id="AN0188100221-4">Working memory</hd> <p>Working memory (WM), the capacity to keep information in mind while processing it (Baddeley, [<reflink idref="bib10" id="ref16">10</reflink>]), has been found to be connected to elementary school children's mathematical skills in numerous studies (Allen et al., [<reflink idref="bib3" id="ref17">3</reflink>]; Alloway & Alloway, [<reflink idref="bib4" id="ref18">4</reflink>]; Friso-van den Bos et al., [<reflink idref="bib19" id="ref19">19</reflink>]; Geary, [<reflink idref="bib22" id="ref20">22</reflink>]; Kleemans et al., [<reflink idref="bib32" id="ref21">32</reflink>]; Lee & Bull, [<reflink idref="bib36" id="ref22">36</reflink>]; Pina et al., [<reflink idref="bib51" id="ref23">51</reflink>]). WM is needed, for instance, when learning new mathematical skills or when solving mathematical problems based on existing mathematical knowledge (Lee & Bull, [<reflink idref="bib36" id="ref24">36</reflink>]) since many mathematical tasks require simultaneous information processing and storage (Peng et al., [<reflink idref="bib50" id="ref25">50</reflink>]). The connection between WM and mathematical skills has been found to vary between different mathematical skills, showing a stronger connection between WM, arithmetic, and solving word problems (see meta-analysis by Peng et al., [<reflink idref="bib50" id="ref26">50</reflink>]). Indeed, studies have shown that verbal and visual–spatial WM is associated with arithmetic and word problem solving skills in second to fourth graders (Wu et al., [<reflink idref="bib63" id="ref27">63</reflink>]), and verbal WM with more complex word problem solving skills in fourth to sixth graders (Pina et al., [<reflink idref="bib51" id="ref28">51</reflink>]). However, the strength of the connection is found to be dependent on the children's age (Peng et al., [<reflink idref="bib50" id="ref29">50</reflink>]). For example, the link between (combined verbal and visual–spatial) WM and arithmetic skills appeared to be stronger during early (i.e., grades 1 and 2) compared to later elementary school years (Lee & Bull, [<reflink idref="bib36" id="ref30">36</reflink>]).</p> <p>In addition to the association between WM and mathematical skills, studies have found that WM can be a good predictor of later mathematical skills. For example, Alloway and Alloway ([<reflink idref="bib4" id="ref31">4</reflink>]) showed that verbal WM at the age of five predicted – independently of measured intelligence – arithmetic and reasoning skills at the age of 11. Furthermore, Geary ([<reflink idref="bib22" id="ref32">22</reflink>]) found that the verbal WM in first-grade predicted achievement in arithmetic skills 4 years later. More recently, Allen and Giofrè ([<reflink idref="bib2" id="ref33">2</reflink>]) found that third graders' verbal and visual–spatial WM contributed differently to mathematics achievement, with visual–spatial WM being a stronger predictor in mathematics components with visual elements, and verbal WM in tasks requiring factual recall and basic mathematical skills. However, there is also contradictory evidence for such links. For example, Fuchs et al. ([<reflink idref="bib20" id="ref34">20</reflink>]) did not find WM to be an independent predictor of arithmetic or word problem solving in third graders.</p> <p>Taken together, it appears that WM plays a role in mathematical development. However, it is still unclear what kind of WM, visual–spatial or verbal, contributes to arithmetic and word problem solving skills in elementary years.</p> <hd id="AN0188100221-5">Spatial skills</hd> <p>Several studies support the existence of a link between spatial (i.e., spatial perception, mental rotation, and spatial visualization; Linn & Petersen, [<reflink idref="bib40" id="ref35">40</reflink>]) and mathematical skills (Gunderson et al., [<reflink idref="bib25" id="ref36">25</reflink>]; Mix et al., [<reflink idref="bib43" id="ref37">43</reflink>]; Mix et al., [<reflink idref="bib42" id="ref38">42</reflink>]; Xie et al., [<reflink idref="bib64" id="ref39">64</reflink>]). It has been suggested that all these skills activate the same neural regions in the brain (see Hawes & Ansari, [<reflink idref="bib26" id="ref40">26</reflink>]) and the shared processes may explain the link between these abilities. A link between spatial and mathematical skills has been found even before formal schooling (Xie et al., [<reflink idref="bib64" id="ref41">64</reflink>]), and spatial skills have been found to predict children's later mathematical skills. For example, Zhang and colleagues ([<reflink idref="bib65" id="ref42">65</reflink>]) found that spatial skills in kindergarten predicted the level and growth of arithmetic skills from 1<sups>st</sups> to 3<sups>rd</sups> grade, even after controlling for gender and parental education.</p> <p>More specifically, in elementary school children, spatial skills measured by the Block Design test (visual–spatial reasoning, Wechsler, [<reflink idref="bib61" id="ref43">61</reflink>]) have shown an association with arithmetic skills (Clifford, [<reflink idref="bib14" id="ref44">14</reflink>]; Mix et al., [<reflink idref="bib43" id="ref45">43</reflink>]; Passolunghi et al., [<reflink idref="bib48" id="ref46">48</reflink>]) and solving word problems (Mix et al., [<reflink idref="bib43" id="ref47">43</reflink>]). Thus it seems that spatial skills are connected to more than one kind of mathematical skill. However, there is also contradictory evidence for the link between spatial and mathematical skills (e.g., Carr et al., [<reflink idref="bib12" id="ref48">12</reflink>]). For example, Xie et al. ([<reflink idref="bib64" id="ref49">64</reflink>]) concluded in their meta-analysis that the link between spatial and arithmetic skills is weaker than that between spatial skills and mathematical reasoning. More research is therefore needed on the relationship between arithmetic, word problem solving, and spatial skills to better understand this phenomenon.</p> <hd id="AN0188100221-6">Language skills</hd> <p>According to recent meta-analyses, language and mathematical skills are related (Koponen et al., [<reflink idref="bib33" id="ref50">33</reflink>]; Peng et al., [<reflink idref="bib49" id="ref51">49</reflink>]). Koponen et al. ([<reflink idref="bib33" id="ref52">33</reflink>]) demonstrated a relationship between rapid automatic naming and mathematics skills. More recently, Peng et al. ([<reflink idref="bib49" id="ref53">49</reflink>]) demonstrated in their meta-analysis a relationship between language and mathematical skills in a broader manner. In addition, single studies have shown that many aspects of language skills, such as phonological awareness, listening comprehension, vocabulary, reading skills, and verbal reasoning, seem to be associated with (Alloway & Passolunghi, [<reflink idref="bib5" id="ref54">5</reflink>]; Durand et al., [<reflink idref="bib17" id="ref55">17</reflink>]; Kleemans et al., [<reflink idref="bib32" id="ref56">32</reflink>]) or even predict (Aunola et al., [<reflink idref="bib9" id="ref57">9</reflink>]; Erbeli et al., [<reflink idref="bib18" id="ref58">18</reflink>]; Hecht et al., [<reflink idref="bib27" id="ref59">27</reflink>]; Kikas et al., [<reflink idref="bib31" id="ref60">31</reflink>]; Krajewski & Schneider, [<reflink idref="bib34" id="ref61">34</reflink>]) mathematical skills in elementary school children.</p> <p>Although some studies suggest that language skills (e.g., vocabulary and verbal reasoning skills) are linked to arithmetic skills in elementary school children (Alloway & Passolunghi, [<reflink idref="bib5" id="ref62">5</reflink>]; Kikas et al., [<reflink idref="bib31" id="ref63">31</reflink>]; Kleemans et al., [<reflink idref="bib32" id="ref64">32</reflink>]), much research seems to support the view that language skills contribute to word problem solving but not so much to arithmetic skills. For instance, a recent meta-analysis (Peng et al., [<reflink idref="bib49" id="ref65">49</reflink>]) showed that word problem solving had a stronger association with language skills than basic arithmetic skills. This may be explained by the fact that more complex mathematical skills such as word problem skills require more complex and semantically oriented language skills (e.g., language comprehension) compared to simpler mathematical skills (Peng et al., [<reflink idref="bib49" id="ref66">49</reflink>]).</p> <p>Thus, based on the literature, it appears that language skills are connected with mathematical skills, and more clearly to word problem solving than arithmetic skills in elementary school children.</p> <hd id="AN0188100221-7">Mathematical skills, language status, and gender</hd> <p></p> <hd id="AN0188100221-8">Children's language status</hd> <p>The number of children attending school in a second language is rising in Finland, and it is predicted that by 2035, almost 25% of pupils in the Helsinki Metropolitan Area will be of immigrant origin (Helsingin kaupunginkanslia, [<reflink idref="bib28" id="ref67">28</reflink>]). According to Finland's PISA (the OECD Programme for International Student Assessment) 2022 results (OECD, [<reflink idref="bib46" id="ref68">46</reflink>]), ninth-grade students who were first- or second-generation immigrants scored significantly lower in mathematical tests than their peers without an immigrant background (Leino et al., [<reflink idref="bib38" id="ref69">38</reflink>]). This is not surprising given that mathematical learning includes many specific mathematical words and expressions that may be challenging for second-language learners (Moschkovich, [<reflink idref="bib45" id="ref70">45</reflink>]). Indeed, previous studies have found that learning mathematical skills at school appears to be more challenging for second-language learners than for native speakers, and the level of language proficiency seems to influence this association (de Araujo et al., [<reflink idref="bib15" id="ref71">15</reflink>]). Another explanation for the challenges that second-language learners face in learning mathematics may be the difficulties entailed in using a second language to think about mathematics: when doing mathematics, second-language learners need to switch between their first and second language, and especially in more difficult tasks, this switching can take cognitive resources away from doing the mathematics (Peng et al., [<reflink idref="bib49" id="ref72">49</reflink>]). Based on the literature, it seems that the second-language learner status can affect mathematical performance at least in those tasks involving language elements (e.g., word problem solving).</p> <hd id="AN0188100221-9">Gender differences</hd> <p>Gender differences in mathematical skills have been widely investigated. Aunola et al. ([<reflink idref="bib9" id="ref73">9</reflink>]) followed children from preschool to second grade and found no differences in mathematical performance between the genders, although boys did show a steeper developmental curve during these years than girls. In line with studies finding minimal or non-existent gender differences in school-aged children's mathematical skills (e.g., Kikas et al., [<reflink idref="bib31" id="ref74">31</reflink>]; Lachance & Mazzocco, [<reflink idref="bib35" id="ref75">35</reflink>]; Moè, [<reflink idref="bib44" id="ref76">44</reflink>]; Scafidi & Bui, [<reflink idref="bib57" id="ref77">57</reflink>]), meta-analyses also concluded that girls and boys appear to perform at a similar level in mathematical tests in elementary school (Lindberg et al., [<reflink idref="bib39" id="ref78">39</reflink>]; Reilly et al., [<reflink idref="bib54" id="ref79">54</reflink>]). However, slight differences favouring males have been found in later school years (i.e., high school and college; Lindberg et al., [<reflink idref="bib39" id="ref80">39</reflink>]; Reilly et al., [<reflink idref="bib54" id="ref81">54</reflink>]). Such an advantage has also been observed for ninth-graders in OECD countries in the most recently published PISA results (OECD, [<reflink idref="bib46" id="ref82">46</reflink>]). However, PISA results vary depending on the country, and in Finland, for example, girls have recently overtaken boys in performance on mathematical tasks, although the difference is not considerable (Leino et al., [<reflink idref="bib38" id="ref83">38</reflink>]). Thus it seems that gender differences are minimal or non-existent in elementary school children, and possible differences occur at later school levels.</p> <hd id="AN0188100221-10">The present study</hd> <p>Theoretical models and longitudinal studies of mathematical development highlight the importance of domain-specific skills such as arithmetic and word problem solving skills, as well as domain-general abilities such as cognitive skills (Lee & Bull, [<reflink idref="bib36" id="ref84">36</reflink>]; LeFevre et al., [<reflink idref="bib37" id="ref85">37</reflink>]; Träff et al., [<reflink idref="bib59" id="ref86">59</reflink>]). Despite the well-documented importance of cognitive skills, there is still contradictory evidence on what kind of cognitive skills are related to each mathematical skill in the age group of the studied sample. Thus the aim of this present study was to investigate how WM, spatial, and language skills contributed to mathematical performance in arithmetic and word problem solving tasks over two school years in 9- to 10-year-old children. We focused on arithmetic and word problem solving as they are among the most essential areas of mathematics and play a central role in the teaching of mathematics in elementary schools (Geary, [<reflink idref="bib21" id="ref87">21</reflink>]). Furthermore, we were interested in the associations between language status and gender in the development of these skills. Our longitudinal design allowed us to investigate whether the possible associations and differences exist during both the third and fourth grades, or whether the inspected groups (language status, gender, special needs education) show differential developmental trajectories regarding the inspected variables. Furthermore, the measures were conducted in the children's natural environment, namely at their school, enhancing the validity and impact of the results. Based on the literature, we hypothesize that (i) WM, spatial, and language skills are associated with word problem-solving skills, and WM with arithmetic skills during the third and fourth grades, (ii) second-language learners perform less well than their peers in word problem solving but not in arithmetic skills during the third and fourth grades, and (iii) there is no gender difference in mathematical performance and its development during the third and fourth grades.</p> <hd id="AN0188100221-11">Methods</hd> <p>The data for the study were collected in an ArtsEqual project (www.artsequal.fi; Academy of Finland https://<ulink href="http://www.aka.fi/en/strategic-research/),">www.aka.fi/en/strategic-research/),</ulink> which aimed to investigate the effects of movement and music activities on children's academic and cognitive skills, as well as their motivation. The class teachers were trained to conduct three weekly music, movement, or music and movement sessions. However, the interventions were sub-optimally conducted by all teachers, and the number of participating children per class remained low. The preliminary results showed no essential differences between the compared classes.</p> <hd id="AN0188100221-12">Participants</hd> <p>Initially, all the children in four parallel classes (<emph>N =</emph> 92 in total) in one municipal elementary school, representing a lower-middle-class region in the Helsinki Metropolitan Area, were invited to participate in the study. Of these, 57 third-graders (32 boys; mean age 9.25 years, <emph>SD =</emph> 4.3 months) participated in all investigations in this longitudinal research with the consent of the children and their guardians. Forty-three children (22 boys) spoke Finnish and 14 some other language(s) at home. Twenty-five children (18 boys) had special educational needs (SEN).[<reflink idref="bib1" id="ref88">1</reflink>] None of the children had been diagnosed with severe developmental disabilities. In accordance with Finland's tiered framework for special needs education, all the children participated in general education, where intensified support is provided by special educators if general support is insufficient. Ten children with SEN (8 boys) had a language other than Finnish as their home language.</p> <p>The children gave their verbal assent before the experiment and the guardians signed the informed consent. The study was approved by the University of Helsinki Ethical Review Board in the Humanities and Social and Behavioural Sciences, in Helsinki, Finland, and carried out in accordance with the committee's guidelines and regulations, as well as with those of the Helsinki Declaration.</p> <hd id="AN0188100221-13">Procedure</hd> <p>The longitudinal follow-up lasted 2 academic years, during which the reported measures were conducted three or four times, depending on the measure: autumn (September–October), winter (January) and spring (May) of the first year, and spring (April–May) of the second year. The first, third and fourth test results were included in the analyses. The tests for cognitive skills were conducted during the school day in a separate room. The test took approximately 30 minutes per child. Children were offered biscuits and a soft drink and received a sticker after participation. Their performance in mathematical tests was measured during the school classes and supervised by the class teacher. All test material was in Finnish, and the researchers made sure that the children understood the instructions for the tests.</p> <hd id="AN0188100221-14">Tests for mathematical skills</hd> <p></p> <hd id="AN0188100221-15">Word problem solving test</hd> <p>MATTE is a test that assesses the ability of third to fifth graders (9- to 11-year-old children) to solve verbal mathematical problems (Kajamies et al., [<reflink idref="bib30" id="ref89">30</reflink>]). The task descriptions include a large amount of text and non-essential information, including numbers that are not necessary for solving the problems. Hence, the tasks require good reading comprehension, and the mere finding of keywords does not automatically lead to the correct calculations. Some tasks also require converting units of measurement, which is deemed to be challenging for children. An example of a MATTE task could be: "Your uncle gives you and your two friends 11 euros and 10 cents to buy sweets. You divide the money equally. How much money will each of you get?". The individual tasks are scored according to how the child notes down his/her thinking, and it is possible to get some points for an inaccurate answer if the problem solving has proceeded accurately. The inter-rater reliability of the individual tasks ranges between 0.70 and 1.0 (Kajamies et al., [<reflink idref="bib30" id="ref90">30</reflink>]). The pupils completed different versions of MATTE four times during the 2 academic years, each time within a 45-minute lesson, supervised by their class teacher. To decrease the emergence of learning effects due to multiple testing, MATTE has two task sets that were utilised in the present study. The maximum score is 40.</p> <hd id="AN0188100221-16">Arithmetic test</hd> <p>RMAT is a paper and pencil test that assesses arithmetic skills for third to sixth graders (Räsänen, [<reflink idref="bib53" id="ref91">53</reflink>]). RMAT comprises 56 items, with most of them assessing basic arithmetic skills, such as addition, subtraction, multiplication, and division with one- and multi-digits. In addition, the test includes some calculations with fractions and decimals, measurement scale conversions, and algebraic tasks. RMAT is based on the maths tasks in The Wide-Range Achievement Test (WRAT: Robertson, [<reflink idref="bib56" id="ref92">56</reflink>]; Wilkinson & Robertson, [<reflink idref="bib62" id="ref93">62</reflink>]). It has been modified to accommodate Finland's school culture and includes more basic maths problems than WRAT, with which it shows correlations of.55−.66. The test-retest reliability of RMAT is reported to be between.65 and.83, depending on the compared grades, with the time interval between the measurement points being 6−19 months. Internal consistency of RMAT has been reported to be between.92 and.95, depending on the grade. In the present study, RMAT was administered in classrooms supervised by the teacher three times during the follow-up: the first autumn, the first spring, and the second spring. According to RMAT guidelines, children were given 10 minutes to complete the test. Each accurately answered separate task was scored with one point, resulting in a maximum of 56 points.</p> <hd id="AN0188100221-17">Tests for cognitive skills</hd> <p>The children's cognitive performance was measured with subtests of Wechsler's Intelligence Scale for Children IV test battery (WISC-IV; Wechsler, [<reflink idref="bib61" id="ref94">61</reflink>]).</p> <hd id="AN0188100221-18">Working memory</hd> <p>The Digit Span Backward test assesses verbal working memory capacity. The experimenter reads the child a set of numbers and she/he repeats them in the opposite order. The list size increases after each successfully performed level, starting with two numbers. Successful performance requires encoding and manipulating information.</p> <hd id="AN0188100221-19">Spatial skills</hd> <p>The Block Design test assesses spatial perception, visual abstract processing, and problem solving. The experimenter shows the child a pattern drawn on paper and the child must create a similar pattern with given blocks. The test has a two-minute time limit for each pattern. Both perception and motor abilities contribute to performance in the test.</p> <hd id="AN0188100221-20">Language skills</hd> <p>In the Word Reasoning subtest, the child is given clues with which she/he must guess which objects or things they refer to. The clue would be, e.g., "You see with this part of your head" and the right answer "eye(s)". The test measures abstract verbal reasoning and verbal concept formation and therefore relates to overall language comprehension and general reasoning.</p> <hd id="AN0188100221-21">Statistical analyses</hd> <p>The statistical analyses were conducted with IBM SPSS Statistics 27 (IBM Corporation, New York, USA). Raw scores from three test points for both mathematical tests, as well as for cognitive tests were used in the analyses.</p> <p>The change over time in the mathematical tests was analysed separately for both tests using linear mixed-model analyses with restricted maximum likelihood, and Bayesian information criteria were used to define model fit. We tested the varying intercepts across the classes by running basic models with time as a fixed factor, including participant and school class as random factors with random intercept. The effect of time varied significantly in intercepts across participants in both models (<emph>p <</emph> 0.001), as the effect of class did not. Based on this, each child was treated as a random factor with a random intercept when predicting word problem solving and arithmetic skills. While maths test scores acted as dependent variables in subsequent linear mixed models, time, gender, special needs education status, class, and all cognitive test scores acted as factors in the model. As children's development is not always linear, at least on an individual level, we used cognitive scores from each measurement point instead of baseline measurements in the models. Both models were inspected for normality of residuals, homoscedasticity, and multicollinearity, and violations of the assumptions were not found.</p> <p>Significant interactions were further investigated with one-way analyses of variance using Scheffé's procedure or, when appropriate, Mann–Whitney <emph>U</emph> tests. The alpha level was set at <emph>p</emph> <.05.</p> <hd id="AN0188100221-22">Results</hd> <p>Table 1 shows the mean, standard deviation, and minimum and maximum values for all variables.</p> <p>Table 1. Mean and standard deviations for all tests (raw scores) at three measurement points. T1 = third-grade autumn, T2 = third-grade spring, T3 = fourth-grade spring, Digit Span Backward<emph></emph>= working memory, Block Design = spatial skills.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>Mean</td><td>Standard deviation</td><td>Minimum</td><td>Maximum</td></tr></thead><tbody><tr><td><italic>Word problem solving</italic></td><td char="." /><td char="." /><td /><td /></tr><tr><td>T1 (<italic>N =</italic> 56)</td><td char=".">5.2</td><td char=".">6.3</td><td char=".">0</td><td char=".">24</td></tr><tr><td>T2 (<italic>N =</italic> 54)</td><td char=".">10.6</td><td char=".">8.8</td><td char=".">0</td><td char=".">30</td></tr><tr><td>T3 (<italic>N =</italic> 48)</td><td char=".">15.3</td><td char=".">9.9</td><td char=".">1</td><td char=".">35</td></tr><tr><td><italic>Arithmetic test</italic></td><td char="." /><td char="." /><td /><td /></tr><tr><td>T1 (<italic>N =</italic> 56)</td><td char=".">19.6</td><td char=".">5.1</td><td char=".">8</td><td char=".">29</td></tr><tr><td>T2 (<italic>N =</italic> 55)</td><td char=".">25.0</td><td char=".">6.4</td><td char=".">7</td><td char=".">38</td></tr><tr><td>T3 (<italic>N =</italic> 50)</td><td char=".">30.1</td><td char=".">5.4</td><td char=".">20</td><td char=".">44</td></tr><tr><td><italic>Digit Span Backward</italic></td><td char="." /><td char="." /><td /><td /></tr><tr><td>T1 (<italic>N =</italic> 56)</td><td char=".">6.1</td><td char=".">1.3</td><td char=".">4</td><td char=".">9</td></tr><tr><td>T2 (<italic>N =</italic> 57)</td><td char=".">6.4</td><td char=".">1.6</td><td char=".">3</td><td char=".">10</td></tr><tr><td>T3 (<italic>N =</italic> 51)</td><td char=".">6.7</td><td char=".">1.5</td><td char=".">4</td><td char=".">10</td></tr><tr><td><italic>Block Design</italic></td><td char="." /><td char="." /><td /><td /></tr><tr><td>T1 (<italic>N =</italic> 56)</td><td char=".">30.6</td><td char=".">10.9</td><td char=".">10</td><td char=".">57</td></tr><tr><td>T2 (<italic>N =</italic> 57)</td><td char=".">39.6</td><td char=".">10.3</td><td char=".">18</td><td char=".">63</td></tr><tr><td>T3 (<italic>N =</italic> 51)</td><td char=".">40.8</td><td char=".">10.6</td><td char=".">18</td><td char=".">64</td></tr><tr><td><italic>Word Reasoning</italic></td><td char="." /><td char="." /><td /><td /></tr><tr><td>T1 (<italic>N =</italic> 56)</td><td char=".">12.1</td><td char=".">3.2</td><td char=".">4</td><td char=".">18</td></tr><tr><td>T2 (<italic>N =</italic> 57)</td><td char=".">13.5</td><td char=".">3.3</td><td char=".">5</td><td char=".">20</td></tr><tr><td>T3 (<italic>N =</italic> 51)</td><td char=".">14.6</td><td char=".">3.2</td><td char=".">5</td><td char=".">20</td></tr></tbody></table> </ephtml> </p> <hd id="AN0188100221-23">Effects of cognitive performance on math skills</hd> <p>Time had a significant main effect on both word problem-solving and arithmetic skills [<emph>F</emph> (<reflink idref="bib2" id="ref95">2</reflink>, 103) = 5.16, <emph>p </emph>=.007; <emph>F</emph> (<reflink idref="bib2" id="ref96">2</reflink>, 105) = 44.85, <emph>p </emph><.001, respectively]. Test scores increased between each time point (all <emph>p</emph>s <.020). Spatial skills were significantly related to the children's word problem solving [<emph>F</emph> (<reflink idref="bib1" id="ref97">1</reflink>, 117) = 4.61, <emph>p </emph>=.034], with one point's increase in spatial skills corresponding to an increase of 0.14 word problem-solving points. In addition, working memory showed a significant main effect on the children's arithmetic scores [<emph>F</emph> (<reflink idref="bib1" id="ref98">1</reflink>, 135) = 9.68, <emph>p </emph>=.002], with one point in the working memory test increasing them by 0.91 points. All main effects and interactions are shown in Table 2.</p> <p>Table 2. Main effects and interactions of cognitive measures and background variables on word problem solving and arithmetic tests. T1 = third-grade autumn, T2 = third-grade spring, T3 = fourth-grade spring, SEN = children with special needs education status, No-SEN = children without special educational needs. The four school classes are named A, B, C, and D. The significant results are in bold. Digit Span Backward<emph></emph>= working memory, Block Design = spatial skills.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td><italic>df</italic>, <italic>df</italic></td><td><italic>F</italic></td><td><italic>p</italic></td><td><italic>post hocs</italic></td></tr></thead><tbody><tr><td><italic>Word problem solving</italic></td><td /></tr><tr><td>Time</td><td>2, 103</td><td char=".">5.16</td><td char=".">.<bold>007</bold></td><td>T2 > T1: t (96) = - 3.73, <bold><italic>p </italic><.001</bold> T3 > T2: t (100) = - 2.56, <bold><italic>p =</italic>.012</bold></td></tr><tr><td>Digit Span Backward</td><td>1, 128</td><td char=".">1.95</td><td char=".">.165</td><td /></tr><tr><td>Block Design</td><td>1, 117</td><td char=".">4.61</td><td char=".">.<bold>034</bold></td><td /></tr><tr><td>Word Reasoning</td><td>1, 128</td><td char=".">2.97</td><td char=".">.087</td><td /></tr><tr><td>Language</td><td>1, 50</td><td char=".">1.15</td><td char=".">.288</td><td /></tr><tr><td>Gender</td><td>1, 48</td><td char=".">4.52</td><td char=".">.<bold>039</bold></td><td>girls > boys: t (156) = - 3.01, <bold><italic>p =</italic>.003</bold></td></tr><tr><td>Special needs education</td><td>1, 62</td><td char=".">2.15</td><td char=".">.147</td><td /></tr><tr><td>Class</td><td>3, 49</td><td char=".">4.17</td><td char=".">.<bold>010</bold></td><td>A > C; t (86) = 3.11, <bold><italic>p =</italic>.003</bold> A > D: t (89) = 3.97, <bold><italic>p <</italic>.001</bold> B > D: t (50) = 2.14, <bold><italic>p =</italic>.037</bold></td></tr><tr><td>Time * Language</td><td>2, 89</td><td char=".">5.10</td><td char=".">.<bold>008</bold></td><td>T1 & T2: <italic>NS</italic> T3: Native speakers > Second- language learners: <italic>U</italic> = 83.5; <bold><italic>p </italic>=.015</bold></td></tr><tr><td>Time * Gender</td><td>2, 88</td><td char=".">1.20</td><td char=".">.306</td><td /></tr><tr><td>Time * Special needs education</td><td>2, 87</td><td char=".">1.69</td><td char=".">.191</td><td /></tr><tr><td>Time * Class</td><td>6, 88</td><td char=".">2.04</td><td char=".">.069</td><td /></tr><tr><td>Special needs education * Language</td><td>1, 50</td><td char=".">0.220</td><td char=".">.641</td><td /></tr><tr><td><italic>Arithmetic test</italic></td><td /><td char="." /><td char="." /><td /></tr><tr><td>Time</td><td>2, 105</td><td char=".">44.84</td><td char="."><bold><.001</bold></td><td>T2 > T1: t (109) = - 4.90, <bold><italic>p </italic><.001</bold> T3 > T2: t (103) = - 4.42, <bold><italic>p </italic><.001</bold></td></tr><tr><td>Digit Span Backward</td><td>1, 135</td><td char=".">9.68</td><td char=".">.<bold>002</bold></td><td /></tr><tr><td>Block Design</td><td>1, 108</td><td char=".">0.09</td><td char=".">.768</td><td /></tr><tr><td>Word Reasoning</td><td>1, 117</td><td char=".">0.07</td><td char=".">.789</td><td /></tr><tr><td>Language</td><td>1, 49</td><td char=".">1.55</td><td char=".">.220</td><td /></tr><tr><td>Gender</td><td>1, 47</td><td char=".">< 0.01</td><td char=".">.966</td><td /></tr><tr><td>Special needs education</td><td>1, 63</td><td char=".">16.08</td><td char="."><bold><.001</bold></td><td>No-SEN > SEN: t (159) = 5.63, <bold><italic>p </italic><.001</bold></td></tr><tr><td>Class</td><td>3, 48</td><td char=".">2.63</td><td char=".">.061</td><td /></tr><tr><td>Time * Language</td><td>2, 91</td><td char=".">0.03</td><td char=".">.970</td><td /></tr><tr><td>Time * Gender</td><td>2, 89</td><td char=".">0.45</td><td char=".">.638</td><td /></tr><tr><td>Time * Special needs education</td><td>2, 90</td><td char=".">.35</td><td char=".">.708</td><td /></tr><tr><td>Time * Class</td><td>6, 90</td><td char=".">2.43</td><td char=".">.<bold>032</bold></td><td><italic>NS</italic></td></tr><tr><td>Special needs education * Language</td><td>1, 49</td><td char=".">2.93</td><td char=".">.093</td><td /></tr></tbody></table> </ephtml> </p> <hd id="AN0188100221-24">Effects of the children's background variables on math skills</hd> <p>Whereas language status did not have a main effect on either of the maths tests, there was a significant interaction between language status and time on word problem solving [<emph>F</emph> (<reflink idref="bib2" id="ref99">2</reflink>, 89) = 5.10, <emph>p </emph>=.008]. Regarding this test, the conducted non-parametric Mann–Whitney <emph>U-</emph>tests revealed that there was no significant difference between native Finnish speakers and second-language learners in the first or second measurement (<emph>U</emph> = 235.5, <emph>p </emph>=.257; <emph>U</emph> = 182.0, <emph>p </emph>=.144, respectively). However, a significant difference was found in the third measurement (<emph>U</emph> = 83.5, <emph>p </emph>=.015), with native speakers of Finnish scoring higher (<emph>M</emph> = 17.0, <emph>SD =</emph> 9.7) than their second-language learner peers (<emph>M</emph> = 8.3, <emph>SD =</emph> 7.8).</p> <p>Regarding the language status and cognitive measures, additional analyses indicated that language status had a main effect on word reasoning [<emph>F</emph> (<reflink idref="bib1" id="ref100">1</reflink>, 56) = 7.41, <emph>p </emph>=.009], but not on working memory or spatial skills scores. Interaction between language status and time was significant for spatial skills and Word Reasoning [<emph>F</emph> (<reflink idref="bib4" id="ref101">4</reflink>, 105) = 27.09, <emph>p </emph><.001; <emph>F</emph> (<reflink idref="bib4" id="ref102">4</reflink>, 104) = 11.41, <emph>p </emph><.001, respectively], with post-hoc analyses revealing that the only significant difference between the groups emerged for Word Reasoning, at the first time point (<emph>p </emph>=.024).</p> <p>Girls achieved higher overall scores than boys (<emph>M</emph> = 12.5, <emph>SD =</emph> 9.7; <emph>M</emph> = 8.13, <emph>SD =</emph> 8.5, respectively) in word problem solving [<emph>F</emph> (<reflink idref="bib1" id="ref103">1</reflink>, 48) = 4.52, <emph>p </emph>=.039], but no difference between genders was found regarding arithmetic skills [<emph>F</emph> (<reflink idref="bib1" id="ref104">1</reflink>, 47) = 0.002, <emph>p </emph>=.966]. Figure 1 shows the development of word problem-solving and arithmetic skills for inspected groups.</p> <p>Graph: Figure 1. The group-specific increase in word problem-solving test and arithmetic test mean scores during the follow-up. T1 = third-grade autumn, T2 = third-grade spring, T3 = fourth-grade spring, * = significant difference between the groups. The error bars represent the 95% confidence interval.</p> <p>Special educational needs status had a significant main effect on arithmetic skills [<emph>F</emph> (<reflink idref="bib1" id="ref105">1</reflink>, 63) = 16.08, <emph>p </emph><.001], with these children scoring lower overall (<emph>M</emph> = 21.3, <emph>SD =</emph> 6.5) than their typically developing peers (<emph>M</emph> = 27.1, <emph>SD =</emph> 6.5).</p> <hd id="AN0188100221-25">Discussion</hd> <p>Our aim was to investigate the associations between cognitive abilities and two types of mathematical tasks, and the effect of language status and gender on this performance and its development over two school years. Whereas the Block Design test measuring visual–spatial reasoning and problem solving was associated with word problem solving, verbal working memory capacity was linked to arithmetic skills. Girls scored higher than boys in the word-problem test, but not in the arithmetic test. The development in word problem solving diverged between the language groups: unlike in the first two measurements, the second-language learners scored lower in the third measurement of the word-problem task than their native-speaker peers. Furthermore, children with special educational needs scored lower overall in arithmetic problems than their typically developing peers.</p> <p>Our first hypothesis was partly confirmed by the results. During the third and fourth grades, visual–spatial reasoning was linked only to word problem solving, and WM to arithmetic skills. Regarding the association between word problem solving and visual–spatial skills, our result aligns with several studies (Casey et al., [<reflink idref="bib13" id="ref106">13</reflink>]; Gilligan et al., [<reflink idref="bib24" id="ref107">24</reflink>]; Mix et al., [<reflink idref="bib43" id="ref108">43</reflink>]; Oostermeijer et al., [<reflink idref="bib47" id="ref109">47</reflink>]), and upgrades them by demonstrating that the visual–spatial skills are not linked to arithmetic skills. This result coincides with a meta-analysis suggesting that spatial skills show stronger links with mathematical reasoning than with numerical and arithmetical skills (Xie et al., [<reflink idref="bib64" id="ref110">64</reflink>]). As the meta-analysis indicated, solving logical reasoning problems and spatial problems requires complex processing of numerical, verbal, and spatial features, whereas arithmetic problem solving requires only numerical processing. Thus the association may be due to both spatial skills and more general reasoning ability needed in Block Design and word problem solving, but not in arithmetic tasks.</p> <p>Contradicting our expectations and some previous studies (Alloway & Alloway, [<reflink idref="bib4" id="ref111">4</reflink>]; Pina et al., [<reflink idref="bib51" id="ref112">51</reflink>]; Wu et al., [<reflink idref="bib63" id="ref113">63</reflink>]), WM was not independently connected to the children's capacity to solve word problems. Instead, the hypothesised and found connection between verbal WM and arithmetic skills upgrades the previous results (Allen & Giofrè, [<reflink idref="bib2" id="ref114">2</reflink>]; Alloway & Alloway, [<reflink idref="bib4" id="ref115">4</reflink>]; Geary, [<reflink idref="bib22" id="ref116">22</reflink>]; Lee & Bull, [<reflink idref="bib36" id="ref117">36</reflink>]) in suggesting that verbal WM is associated specifically with arithmetic skills but not with word problem solving.</p> <p>Also contrary to our expectations, language skills were not independently connected to the children's capacity to solve word problems. According to the analyses, the Word Reasoning test did show a trend in predicting word problem solving and a larger sample size might have shown a significant association. However, in addition to verbal reasoning, Word Reasoning measures concept formation, and may therefore not be comparable to reading comprehension tests in previous studies showing results contradictory to the present study (Björn et al., [<reflink idref="bib11" id="ref118">11</reflink>]; Pongsakdi et al., [<reflink idref="bib52" id="ref119">52</reflink>]; Wu et al., [<reflink idref="bib63" id="ref120">63</reflink>]).</p> <p>Strictly speaking, the second hypothesis was only partly confirmed by our results: language status had no effect on solving arithmetic problems and, overall, the second-language learners did not perform lower in word problem solving in the first two measurements conducted in the third grade. However, performance development in word problem solving was different in the two groups: the scores increased steadily for the native speakers' group but ceased to increase after the third year spring for the second-language learners' group. As a result, the second-language learners performed lower than their peers at the end of the follow-up. This difference does not seem to be linked to the tested Word Reasoning ability, as it showed an opposite pattern regarding the language status: the groups differed initially but not on later measurement points.</p> <p>The difference emerging only at the end of the follow-up may be due to low scores for all at the beginning: the MATTE test is challenging for third graders. However, native speakers improved their performance faster than second-language learners, and thus it seems that the ability of abstract thinking needed in verbally presented problems develops earlier in native language speakers than in second-language learners. This result aligns with previous international literature (Abedi & Lord, [<reflink idref="bib1" id="ref121">1</reflink>]; Vukovic & Lesaux, [<reflink idref="bib60" id="ref122">60</reflink>]; see de Araujo et al., [<reflink idref="bib15" id="ref123">15</reflink>]) and with the Finnish PISA results (Leino et al., [<reflink idref="bib38" id="ref124">38</reflink>]). The fact that no difference emerged between language groups in arithmetic problems emphasises the role of language skills in verbally presented reasoning tasks. Second-language learners may have difficulties in comprehending the problems due to inadequate understanding of syntactic structures or linguistic concepts, or even just basic maths-specific language. Alternatively, learning more abstract mathematical thinking might be more challenging for this group. Instead of simply not understanding the presented problem properly, second-language learners may not have learned the basics of mathematical deduction in the first place. In any case, this is a worrying result, calling for attention in educational systems.</p> <p>Our third hypothesis was not totally confirmed: we expected to find no gender difference in performance and its development in either mathematical test, but this was only true regarding arithmetic skills. Although there was no difference in the developmental trajectory of the word problem solving between genders, the girls outperformed the boys in all measurement points. This result contradicts many previous studies either not finding a difference between genders (Abedi & Lord, [<reflink idref="bib1" id="ref125">1</reflink>]; Aunola et al., [<reflink idref="bib9" id="ref126">9</reflink>]; Kikas et al., [<reflink idref="bib31" id="ref127">31</reflink>]; Lachance & Mazzocco, [<reflink idref="bib35" id="ref128">35</reflink>]; Moè, [<reflink idref="bib44" id="ref129">44</reflink>]; Scafidi & Bui, [<reflink idref="bib57" id="ref130">57</reflink>]; see Lindberg et al., [<reflink idref="bib39" id="ref131">39</reflink>]) or showing that boys perform better in maths (OECD, [<reflink idref="bib46" id="ref132">46</reflink>]; Reilly et al., [<reflink idref="bib54" id="ref133">54</reflink>]). However, Finnish PISA results have found a slight advantage for girls in mathematical skills and a clearer difference in reading skills, and it seems that the gender differences may at least be partly due to differences in cultures and education systems between countries (OECD, [<reflink idref="bib46" id="ref134">46</reflink>]; Shen et al., [<reflink idref="bib58" id="ref135">58</reflink>]). Although verbal reasoning skills were not linked to word problem-solving skills in the present study, it may be that the better reading skills of girls (Lachance & Mazzocco, [<reflink idref="bib35" id="ref136">35</reflink>]; Leino et al., [<reflink idref="bib38" id="ref137">38</reflink>]; OECD, [<reflink idref="bib46" id="ref138">46</reflink>]) contribute to this discrepancy.</p> <p>The quality of education and didactics in mathematics is essential for the development of mathematical skills (Aunio et al., [<reflink idref="bib8" id="ref139">8</reflink>]; MacDonald & Carmichael, [<reflink idref="bib41" id="ref140">41</reflink>]). Since the language status appears to affect these skills in childhood, it would be of utmost importance to develop tools to support the non-native children's learning early on. Student teachers should learn about the importance of children understanding the meaning of mathematical expressions and concepts, and the possibility of supporting non-native children's mathematical skills, for example by using picture cards to enhance understanding of word problems. In sum, it should be emphasised that mathematics is not an isolated subject but related to language skills and cognitive skills, such as working memory and spatial reasoning. Thus our results set requirements not only for attitudes when aiming for inclusivity in education and society, but importantly for teacher education.</p> <hd id="AN0188100221-26">Limitations</hd> <p>The present study partly confirms and upgrades previous knowledge of the connections between cognitive abilities and two types of mathematical skills during a two-year follow-up. However, the small sample size limits the generalisability of the results. Moreover, the difference in group sizes between native speakers and second-language learners calls for caution when interpreting the results.</p> <hd id="AN0188100221-27">Conclusion</hd> <p>The inadequate mastery of school language may lead to underachievement in mathematical skills at school. Therefore, more emphasis needs to be placed on teaching the school language and maths-specific language to second-language learners in elementary schools. This may be accomplished by increasing the number of weekly language lessons, more inclusive teaching methods, or the overall quality of education.</p> <hd id="AN0188100221-28">Acknowledgements</hd> <p>The authors wish to thank Professor Eeva Anttila, Professor Marja-Leena Juntunen, Dr Kaisa Tiippana, laboratory engineer Tommi Makkonen and Ms Laura Ginström, MA, for their comments and help, and the teachers, children, and their families for participating.</p> <hd id="AN0188100221-29">Disclosure statement</hd> <p>No potential conflict of interest was reported by the author(s).</p> <hd id="AN0188100221-30">Data availability</hd> <p>The data are available on request from the corresponding author. The data are not publicly available to protect the privacy of the participating children.</p> <ref id="AN0188100221-31"> <title> References </title> <blist> <bibl id="bib1" idref="ref88" type="bt">1</bibl> <bibtext> Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. 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Legislation directs the Finnish education system to be based on principles of equality, equity in learning, and inclusion.</bibtext> </blist> </ref> <aug> <p>By Tanja Linnavalli; Pinja Jylänki; Julia Kainulainen; Mari Tervaniemi and Minna Törmänen</p> <p>Reported by Author; Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib16" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib55" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib21" firstref="ref6"></nolink> <nolink nlid="nl4" bibid="bib23" firstref="ref8"></nolink> <nolink nlid="nl5" bibid="bib29" firstref="ref9"></nolink> <nolink nlid="nl6" bibid="bib36" firstref="ref10"></nolink> <nolink nlid="nl7" bibid="bib59" firstref="ref12"></nolink> <nolink nlid="nl8" bibid="bib37" firstref="ref14"></nolink> <nolink nlid="nl9" bibid="bib10" firstref="ref16"></nolink> <nolink nlid="nl10" bibid="bib19" firstref="ref19"></nolink> <nolink nlid="nl11" bibid="bib22" firstref="ref20"></nolink> <nolink nlid="nl12" bibid="bib32" firstref="ref21"></nolink> <nolink nlid="nl13" bibid="bib51" firstref="ref23"></nolink> <nolink nlid="nl14" bibid="bib50" firstref="ref25"></nolink> <nolink nlid="nl15" bibid="bib63" firstref="ref27"></nolink> <nolink nlid="nl16" bibid="bib20" firstref="ref34"></nolink> <nolink nlid="nl17" bibid="bib40" firstref="ref35"></nolink> <nolink nlid="nl18" bibid="bib25" firstref="ref36"></nolink> <nolink nlid="nl19" bibid="bib43" firstref="ref37"></nolink> <nolink nlid="nl20" bibid="bib42" firstref="ref38"></nolink> <nolink nlid="nl21" bibid="bib64" firstref="ref39"></nolink> <nolink nlid="nl22" bibid="bib26" firstref="ref40"></nolink> <nolink nlid="nl23" bibid="bib65" firstref="ref42"></nolink> <nolink nlid="nl24" bibid="bib61" firstref="ref43"></nolink> <nolink nlid="nl25" bibid="bib14" firstref="ref44"></nolink> <nolink nlid="nl26" bibid="bib48" firstref="ref46"></nolink> <nolink nlid="nl27" bibid="bib12" firstref="ref48"></nolink> <nolink nlid="nl28" bibid="bib33" firstref="ref50"></nolink> <nolink nlid="nl29" bibid="bib49" firstref="ref51"></nolink> <nolink nlid="nl30" bibid="bib17" firstref="ref55"></nolink> <nolink nlid="nl31" bibid="bib18" firstref="ref58"></nolink> <nolink nlid="nl32" bibid="bib27" firstref="ref59"></nolink> <nolink nlid="nl33" bibid="bib31" firstref="ref60"></nolink> <nolink nlid="nl34" bibid="bib34" firstref="ref61"></nolink> <nolink nlid="nl35" bibid="bib28" firstref="ref67"></nolink> <nolink nlid="nl36" bibid="bib46" firstref="ref68"></nolink> <nolink nlid="nl37" bibid="bib38" firstref="ref69"></nolink> <nolink nlid="nl38" bibid="bib45" firstref="ref70"></nolink> <nolink nlid="nl39" bibid="bib15" firstref="ref71"></nolink> <nolink nlid="nl40" bibid="bib35" firstref="ref75"></nolink> <nolink nlid="nl41" bibid="bib44" firstref="ref76"></nolink> <nolink nlid="nl42" bibid="bib57" firstref="ref77"></nolink> <nolink nlid="nl43" bibid="bib39" firstref="ref78"></nolink> <nolink nlid="nl44" bibid="bib54" firstref="ref79"></nolink> <nolink nlid="nl45" bibid="bib30" firstref="ref89"></nolink> <nolink nlid="nl46" bibid="bib53" firstref="ref91"></nolink> <nolink nlid="nl47" bibid="bib56" firstref="ref92"></nolink> <nolink nlid="nl48" bibid="bib62" firstref="ref93"></nolink> <nolink nlid="nl49" bibid="bib13" firstref="ref106"></nolink> <nolink nlid="nl50" bibid="bib24" firstref="ref107"></nolink> <nolink nlid="nl51" bibid="bib47" firstref="ref109"></nolink> <nolink nlid="nl52" bibid="bib11" firstref="ref118"></nolink> <nolink nlid="nl53" bibid="bib52" firstref="ref119"></nolink> <nolink nlid="nl54" bibid="bib60" firstref="ref122"></nolink> <nolink nlid="nl55" bibid="bib58" firstref="ref135"></nolink> <nolink nlid="nl56" bibid="bib41" firstref="ref140"></nolink>
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  Label: Page Count
  Group: Src
  Data: 15
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Early+Childhood+Education%22">Early Childhood Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+3%22">Grade 3</searchLink><br /><searchLink fieldCode="EL" term="%22Primary+Education%22">Primary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+4%22">Grade 4</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Tests%22">Cognitive Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Memory%22">Memory</searchLink><br /><searchLink fieldCode="DE" term="%22Intelligence+Tests%22">Intelligence Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Short+Term+Memory%22">Short Term Memory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Achievement%22">Mathematics Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Arithmetic%22">Arithmetic</searchLink><br /><searchLink fieldCode="DE" term="%22Word+Problems+%28Mathematics%29%22">Word Problems (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+3%22">Grade 3</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+4%22">Grade 4</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Thinking+Skills%22">Thinking Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Native+Language%22">Native Language</searchLink><br /><searchLink fieldCode="DE" term="%22Gender+Differences%22">Gender Differences</searchLink><br /><searchLink fieldCode="DE" term="%22Longitudinal+Studies%22">Longitudinal Studies</searchLink><br /><searchLink fieldCode="DE" term="%22Followup+Studies%22">Followup Studies</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Finland%22">Finland</searchLink>
– Name: SubjectThesaurus
  Label: Assessment and Survey Identifiers
  Group: Su
  Data: <searchLink fieldCode="SU" term="%22Wechsler+Intelligence+Scales+Short+Forms%22">Wechsler Intelligence Scales Short Forms</searchLink><br /><searchLink fieldCode="SU" term="%22Digit+Span+Test%22">Digit Span Test</searchLink><br /><searchLink fieldCode="SU" term="%22Block+Design+Test%22">Block Design Test</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1080/00313831.2024.2419063
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0031-3831<br />1470-1170
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Early mathematical skills contribute to later school performance and socio-economic status. Working memory is related to mathematical skills, but spatial and language skills have independent effects on separate areas of mathematical skills such as solving word problems or arithmetic skills. In this study, 9- to 10-year-old children's (N = 57) cognitive and mathematical skills were assessed three times over 2 years. Spatial reasoning was associated with performance in solving word problems and working memory with performance in the arithmetic test. Regarding word problems, girls outperformed boys. Also, the second-language learners performed similarly to the native speakers in the beginning and in the end of the third grade, but worse in the end of the fourth grade. The results suggest that the students' inadequate mastery of the school language may lead to underachievement in mathematics, implying that further efforts should be invested in supporting their language learning.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2025
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1484413
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1484413
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  BibEntity:
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      – Type: doi
        Value: 10.1080/00313831.2024.2419063
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 1304
    Subjects:
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Cognitive Tests
        Type: general
      – SubjectFull: Memory
        Type: general
      – SubjectFull: Intelligence Tests
        Type: general
      – SubjectFull: Short Term Memory
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Mathematics Achievement
        Type: general
      – SubjectFull: Arithmetic
        Type: general
      – SubjectFull: Word Problems (Mathematics)
        Type: general
      – SubjectFull: Grade 3
        Type: general
      – SubjectFull: Grade 4
        Type: general
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Thinking Skills
        Type: general
      – SubjectFull: Native Language
        Type: general
      – SubjectFull: Gender Differences
        Type: general
      – SubjectFull: Longitudinal Studies
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      – SubjectFull: Followup Studies
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      – SubjectFull: Finland
        Type: general
      – SubjectFull: Wechsler Intelligence Scales Short Forms
        Type: general
      – SubjectFull: Digit Span Test
        Type: general
      – SubjectFull: Block Design Test
        Type: general
    Titles:
      – TitleFull: The Associations between Mathematical Skills, Cognitive Performance, and Language Background in Elementary School Children. A Two-Year Follow-Up Study
        Type: main
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      – PersonEntity:
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            NameFull: Tanja Linnavalli
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            NameFull: Pinja Jylänki
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            NameFull: Julia Kainulainen
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            NameFull: Mari Tervaniemi
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            NameFull: Minna Törmänen
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 0031-3831
            – Type: issn-electronic
              Value: 1470-1170
          Numbering:
            – Type: volume
              Value: 69
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: Scandinavian Journal of Educational Research
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