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Psychometric Evaluation of the Preschool Early Numeracy Skills Test--Brief Version within the Item Response Theory Framework

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Title: Psychometric Evaluation of the Preschool Early Numeracy Skills Test--Brief Version within the Item Response Theory Framework
Language: English
Authors: Tsigilis, Nikolaos (ORCID 0000-0002-2388-959X), Krousorati, Katerina (ORCID 0000-0001-7481-3336), Gregoriadis, Athanasios (ORCID 0000-0002-3026-6614), Grammatikopoulos, Vasilis (ORCID 0000-0001-7556-6162)
Source: Educational Measurement: Issues and Practice. Sum 2023 42(2):32-41.
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 10
Publication Date: 2023
Document Type: Journal Articles
Reports - Research
Education Level: Early Childhood Education
Preschool Education
Descriptors: Psychometrics, Preschool Education, Numeracy, Item Response Theory, Test Validity, Gender Differences, Preschool Children, Foreign Countries
Geographic Terms: Greece
DOI: 10.1111/emip.12536
ISSN: 0731-1745
1745-3992
Abstract: The Preschool Early Numeracy Skills Test--Brief Version (PENS-B) is a measure of early numeracy skills, developed and mainly used in the United States. The purpose of this study was to examine the factorial validity and measurement invariance across gender of PENS-B in the Greek educational context. PENS-B was administered to 906 preschool children (473 boys, 433 girls), randomly selected from 84 kindergarten classrooms. A 2PL unidimensional and multidimensional item response theory analysis, using cross-validation procedures, were used to analyze the data. Results showed that responses to 20 items can be adequately explained by a two-dimensional model (Numbering Relations and Arithmetic Operations). Application of differential item functioning procedures did not detect any gender bias. Numeracy Relation comprises 16 items, which assess low levels of this latent trait. On the other hand, four items capture average levels of Arithmetic Operations. Total information curves revealed that both dimensions measure with precision only a small area of their underlying latent trait.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1380345
Database: ERIC
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  Value: <anid>AN0164231916;ems01jun.23;2023Jun13.07:39;v2.2.500</anid> <title id="AN0164231916-1">Psychometric Evaluation of the Preschool Early Numeracy Skills Test–Brief Version Within the Item Response Theory Framework </title> <p>The Preschool Early Numeracy Skills Test–Brief Version (PENS‐B) is a measure of early numeracy skills, developed and mainly used in the United States. The purpose of this study was to examine the factorial validity and measurement invariance across gender of PENS‐B in the Greek educational context. PENS‐B was administered to 906 preschool children (473 boys, 433 girls), randomly selected from 84 kindergarten classrooms. A 2PL unidimensional and multidimensional item response theory analysis, using cross‐validation procedures, were used to analyze the data. Results showed that responses to 20 items can be adequately explained by a two‐dimensional model (Numbering Relations and Arithmetic Operations). Application of differential item functioning procedures did not detect any gender bias. Numeracy Relation comprises 16 items, which assess low levels of this latent trait. On the other hand, four items capture average levels of Arithmetic Operations. Total information curves revealed that both dimensions measure with precision only a small area of their underlying latent trait.</p> <p>Keywords: cross‐validation approach; early childhood education; multidimensional item response theory; numeracy skills</p> <p>The early mathematical skills of young children are recognized as fundamental abilities for their future academic achievement (LeFevre et al., [<reflink idref="bib30" id="ref1">30</reflink>]; National Council of Teachers of Mathematics, 2006). Recent studies showed the association between preschool children's mathematical competence and math achievement in later grades (Nguyen et al., [<reflink idref="bib42" id="ref2">42</reflink>]; Watts et al., [<reflink idref="bib54" id="ref3">54</reflink>]), with research evidence suggesting that early mathematical knowledge is a strong predictor for later mathematical outcomes, even stronger than early reading skills (Duncan et al., [<reflink idref="bib20" id="ref4">20</reflink>]). Mathematical knowledge holds a critical position in Early Childhood Education (ECE) as children are very competent in mathematics from their early years (Clements & Sarama, [<reflink idref="bib14" id="ref5">14</reflink>]). The timely identification of children with deficits in aspects of mathematical knowledge is a key prerequisite for enhancing their competencies effectively (Raghubar & Barnes, [<reflink idref="bib48" id="ref6">48</reflink>]). Measures with sound theoretical and psychometric characteristics are essential to ensure that children have acquired the crucial components of mathematical knowledge.</p> <p>Mathematical knowledge comprises several components, such as basic knowledge of numbers, memory for arithmetical facts, understanding of mathematical concepts, and the ability to follow procedures (Aunola et al., [<reflink idref="bib4" id="ref7">4</reflink>]). Early numeracy skills constitute the foundational abilities on which further mathematical development is built (Aunio et al., [<reflink idref="bib3" id="ref8">3</reflink>]). Three core domains have been identified as the most representative of the early numeracy skills: relational skills, counting skills (including numbering skills), and arithmetic operations (Charitaki et al., [<reflink idref="bib12" id="ref9">12</reflink>]). Despite the importance of early numeracy competence for children's later mathematical development, a consensus view among researchers regarding the structure of early numeracy is still unclear (Devlin et al., [<reflink idref="bib18" id="ref10">18</reflink>]). Some researchers propose a three‐factor model to describe the structure of numeracy skills in typically developing children, which includes relational skills, arithmetic operations, and either numbering skills (e.g., Lopez‐Pedersen et al., 2021; Purpura & Lonigan, [<reflink idref="bib45" id="ref11">45</reflink>]) or counting skills (e.g., Hellstrand et al., [<reflink idref="bib26" id="ref12">26</reflink>]; Milburn et al., [<reflink idref="bib37" id="ref13">37</reflink>]; Tzouriadou et al., [<reflink idref="bib52" id="ref14">52</reflink>]). Alternatively, other research suggests a two‐factor model for the structure of early numeracy, including numbering with relational skills as the first factor and arithmetic operations as the second factor (e.g., Jordan et al., [<reflink idref="bib28" id="ref15">28</reflink>]; National Research Council, [<reflink idref="bib41" id="ref16">41</reflink>]). The variations in the factor structure of early numeracy may be attributed to the different research tools that exist in the literature and the applied statistical techniques (Charitaki et al., [<reflink idref="bib12" id="ref17">12</reflink>]), such as classical test theory (CTT) or item response theory (IRT).</p> <p>Several measures have been developed for the assessment of either discrete numeracy skills (e.g., Floyd et al., [<reflink idref="bib21" id="ref18">21</reflink>]; Hellstrand et al., [<reflink idref="bib26" id="ref19">26</reflink>]; Van de Rijt et al., [<reflink idref="bib53" id="ref20">53</reflink>]) or broad mathematical ability (e.g., Clements et al., [<reflink idref="bib15" id="ref21">15</reflink>]; Ginsburg & Baroody, [<reflink idref="bib23" id="ref22">23</reflink>]; Starkey et al., [<reflink idref="bib50" id="ref23">50</reflink>]). Apart from their strong psychometric characteristics, mathematical measures for early childhood instruments should also follow a developmentally appropriate administration (Clements & Sarama, [<reflink idref="bib14" id="ref24">14</reflink>]; Dong et al., [<reflink idref="bib19" id="ref25">19</reflink>]). However, several existing measures have been criticized for being complicated to administer (demanding additional materials like cards, blocks, tokens) and time‐consuming (Hellstrand et al., [<reflink idref="bib26" id="ref26">26</reflink>]; Purpura & Lonigan, [<reflink idref="bib46" id="ref27">46</reflink>]). For instance, tests that are individually administered via interviews demand a session of at least 20 minutes to be completed (e.g., Ginsburg & Baroody, [<reflink idref="bib23" id="ref28">23</reflink>]; Starkey et al., [<reflink idref="bib50" id="ref29">50</reflink>]; Van de Rijt et al., [<reflink idref="bib53" id="ref30">53</reflink>]).</p> <p>In an attempt to overcome the limitations of the existing measures, Purpura et al. ([<reflink idref="bib47" id="ref31">47</reflink>]) developed the Preschool Early Numeracy Skills Test–Brief Version (PENS‐B), a broad‐content screener measure of early numeracy skills across the preschool age. An essential advantage of PENS‐B, among others, lies in two key features. First, PENS‐B offers researchers who administer it the possibility of applying a ceiling rule, as defined by three or more errors in a row, to reduce the administrative time without reducing its reliability. Second, the measure can identify children at risk of mathematical difficulties using the three age‐based cut‐offs (children aged 3, 4, and 5 years old).</p> <p>The IRT framework was used for the PENS‐B development. In previous work, Purpura and Lonigan ([[<reflink idref="bib45" id="ref32">45</reflink>]]) developed PENS comprising 143 separate early numeracy assessment tasks measuring skills in relations, numbering, and arithmetic operations. PENS‐B's items were derived from PENS by following three steps: First, a dichotomous two‐parameter logistic (2‐PL) IRT model was employed for calculating the difficulty (<emph>b</emph>) and discrimination (<emph>α</emph>) parameters of the items. Difficulty parameters ranged from –2.00 to 2.00 and discrimination parameters ranged from.10 to 2.16. Second, items that included manipulatives or were difficult to administer were removed. Purpura et al. ([<reflink idref="bib47" id="ref33">47</reflink>]) showed that items deletion did not significantly influence the difficulty and discrimination parameters (<emph>b</emph> from –1.52 to 1.63 and <emph>α</emph> from.32 to 1.87). Third, the summed score of the retained 24 items was highly correlated (<emph>r</emph> =.94) with a latent factor score of all the original assessment tasks; thus, it was considered that the measure of PENS‐B functioned similarly to the initial assessment tasks. The one‐factor solution of PENS‐B had high internal consistency (<emph>α</emph> =.93) and the IRT standard errors for theta scores indicated that it is a reliable test. Furthermore, PENS‐B exhibited strong evidence of convergent validity with another numeracy measure (Ginsburg & Baroody, [<reflink idref="bib23" id="ref34">23</reflink>]) and high discriminant validity with two literacy measures (Lonigan & Wilson, [<reflink idref="bib33" id="ref35">33</reflink>]; Martin & Brownell, [<reflink idref="bib36" id="ref36">36</reflink>]).</p> <p>Several studies (e.g., Beisly et al., [<reflink idref="bib7" id="ref37">7</reflink>]; Lin et al., [<reflink idref="bib31" id="ref38">31</reflink>]) have used the PENS‐B to evaluate preschoolers' numeracy skills due to its psychometric properties. Insofar, the available studies using the PENS‐B applied it mainly to North America. To the best of our knowledge, only one study (Kung et al., [<reflink idref="bib29" id="ref39">29</reflink>]) administered PENS‐B in Chinese children (<emph>n</emph> = 91). In addition, the studies mentioned above did not examine the PENS‐B factorial structure, but they took it for granted. According to Anderson and Gerbing ([<reflink idref="bib1" id="ref40">1</reflink>]), the structure of the construct being measured should be first well understood before its meaning can be tested. Furthermore, cross‐national comparisons of preschoolers' mathematical skills have shown that children's numeracy varies across countries and languages (Cankaya & LeFevre, [<reflink idref="bib9" id="ref41">9</reflink>]; Tzouriadou et al., [<reflink idref="bib52" id="ref42">52</reflink>]). Thus, culturally robust instruments with sound psychometric properties are required. Given that PENS‐B was developed and validated in North America, its generalizability remains to be further examined in different cultural contexts.</p> <p>As far as Greece is concerned, the national early childhood curriculum acknowledges the crucial role of children's engagement with math‐related activities. According to the official curriculum of preschool, educators should engage children in structured mathematical activities based on their experiences. Among the plethora of competencies that children need to develop, the official curriculum suggests that children need to become familiar with mathematical concepts and relationships, (e.g., classifications, comparisons), ordering of numbers from 1 to 10, counting, and understanding simple arithmetic operations (e.g., addition, subtraction, etc.) (Ministry of Education/Pedagogical Institute, [<reflink idref="bib38" id="ref43">38</reflink>]). Attending kindergarten in Greece is compulsory and the 2‐year attendance starts at the age of four (Gregoriadis et al., [<reflink idref="bib25" id="ref44">25</reflink>]). Therefore, it is expected that children will develop basic numeracy skills by the age of 6 years old due to their attendance in preschool education. To assess the effectiveness of the curriculum in mathematics, measures with sound theoretical and psychometric characteristics are essential. To the best of our knowledge, in the Greek ECE, there is only one measure of early numeracy (the Utrecht Early Mathematical Competence Scales; Van de Rijt et al., [<reflink idref="bib53" id="ref45">53</reflink>]), which has been validated (Barbas et al., [<reflink idref="bib6" id="ref46">6</reflink>]). This instrument belongs to the category of measures that includes forty tasks and demands a considerable amount of time to be completed. Another instrument used in the Greek ECE is the TEMA‐3 (the Test of Early Mathematics Ability; Ginsburg & Baroody, [<reflink idref="bib23" id="ref47">23</reflink>]), which has not been validated (Manolitsis et al., [<reflink idref="bib35" id="ref48">35</reflink>]; Papadakis et al., [<reflink idref="bib44" id="ref49">44</reflink>]). Thus, there is a need for additional research endeavors to measure numeracy skills that are suitable for early childhood and not time‐consuming.</p> <p>The purpose of this study was to examine the psychometric properties of the Greek version of the PENS‐B using the IRT framework. The main research question of the study focused on whether the Greek version of the PENS‐B has adequate psychometric properties for assessing numeracy skills within the Greek cultural and ECE context. In particular, we examined the dimensionality of the PENS‐B, estimated its items' parameters (namely, the difficulty and the discrimination) and evaluated the level of precision when assessing preschoolers' numeracy skills. An additional purpose of this study focused on the invariance of PENS‐B across gender.</p> <p>Prior research findings regarding gender differences in children's math performance are contradictory (Hutchison et al., [<reflink idref="bib27" id="ref50">27</reflink>]). As mathematics and science have been characterized as stereotyped male domains (Lindberg et al., 2010), several studies show small but statistically significant differences in math performance, which mainly favored boys (e.g., Chang et al., [<reflink idref="bib10" id="ref51">10</reflink>]; Jordan et al., [<reflink idref="bib28" id="ref52">28</reflink>]). In contrast, there are studies in which girls are favored (e.g., Aunio et al., [<reflink idref="bib2" id="ref53">2</reflink>]). However, some prior studies using various measures did not report any gender differences in children's basic numerical skills (e.g., Aunola et al., [<reflink idref="bib4" id="ref54">4</reflink>]; Hutchison et al., [<reflink idref="bib27" id="ref55">27</reflink>]). This finding was also replicated in studies employing the PENS‐B (e.g., Napoli & Purpura, [<reflink idref="bib39" id="ref56">39</reflink>]; Purpura et al., [<reflink idref="bib47" id="ref57">47</reflink>]). With regard to the Greek educational context, study showed that preschool children's performance in mathematical competence seems to be independent of gender in some studies (Papadakis et al., [<reflink idref="bib44" id="ref58">44</reflink>]). In our study, we did not expect gender differences in the Greek preschoolers' numeracy performance in PENS‐B.</p> <hd id="AN0164231916-2">Method</hd> <p></p> <hd id="AN0164231916-3">Participants</hd> <p>The maximum number of students allowed in a Greek kindergarten classroom is 25 children (the number of children per class usually ranges from 18 to 25 children). Participants were recruited by a random selection of ten children per classroom from eighty‐four Greek public kindergarten classes in North Greece. In some classes with restricted number of students (e.g., 11–13 students), where parents provided signed consent forms, all students were included in the study. The sample consisted of 906 children (473 boys, 433 girls) aged between 4 and 6 years (<emph>M</emph> = 64.43 months, <emph>SD</emph> = 7.08).</p> <hd id="AN0164231916-4">Measures</hd> <p>The PENS‐B (Purpura et al., [<reflink idref="bib47" id="ref59">47</reflink>]) was used to measure the broad numeracy skills in preschool students. PENS‐B consists of 24 easy‐to‐administer items that do not require the use of manipulatives. The assessment areas include one‐to‐one counting, counting a subtest, numeral comparison, identifying numerals, number order, ordinality, relative size, set comparison, set to numerals, story problems, and number combinations. For twenty‐one tasks, the examiner shows to the child a picture and asks a question about it (e.g., "How many dogs are there?" while displaying an image of three dogs). Three items include story problems that the examiner tells the child (e.g., "If Jimmy has one book, Michele has one book, and Jimmy gives Michele his book, how many books does Michele have now?"). The scoring method is based on a binary form (0–1), in which children receive one point for each correct response and a score of zero for each wrong answer or nonanswer. The possible total score on the PENS‐B ranges between 0 and 24. Upon permission from the PENS‐B principal developer, the scale was transferred to the Greek language, followed by a back‐translation into English. Next, a bilingual scholar reviewed the two versions, correcting any discrepancies.</p> <hd id="AN0164231916-5">Procedure</hd> <p>The Greek Ministry of Education approved the ethics of the study and issued permission to access kindergarten schools. Children's parents were informed about the study's purpose and signed consent forms. Finally, children were informed about the study and that participation was voluntary. Following the procedure described in Purpura's et al. ([<reflink idref="bib47" id="ref60">47</reflink>]) study, the children were administered the scale individually in a quiet area outside the classroom. The process for the completion of the PENS‐B lasted approximately 10 minutes.</p> <hd id="AN0164231916-6">Data Analysis Strategy</hd> <p>The <emph>mirt</emph> library for the R environment ver. 1.37.1 (Chalmers, [<reflink idref="bib11" id="ref61">11</reflink>]) was used to calibrate the 24 items comprising PENS‐B using a 2PL model. A cross‐validation approach was employed by splitting the data set into two‐equal groups (group‐A, group‐B). Preliminary analysis showed no differences between the two groups in relation to students' age (<emph>t</emph><subs>902</subs> =.549, <emph>p</emph> =.583) and gender (<emph>χ</emph><sups>2</sups><subs>1</subs> =.054, <emph>p</emph> =.817).</p> <p>In the case of parametric IRT, the assumptions of appropriate dimensionality, local independence, and correct model specification should be satisfied (DeMars, [<reflink idref="bib17" id="ref62">17</reflink>]; Toland, [<reflink idref="bib51" id="ref63">51</reflink>]). The first assumption means that the employed IRT model contains the correct number of continuous latent traits. According to de Ayala ([<reflink idref="bib16" id="ref64">16</reflink>]), before choosing an IRT model, the dimensionality of the data should be thoroughly inspected. However, if a violation from the assumption of unidimensionality appears to exist, then the use of an exploratory or confirmatory multi‐dimensional IRT (MIRT) model may be warranted (de Ayala, [<reflink idref="bib16" id="ref65">16</reflink>]; Wirth & Edwards, [<reflink idref="bib55" id="ref66">55</reflink>]).</p> <p>Another assumption closely related to dimensionality is local independence (LI). LI postulates that items are not related after conditioning on the latent trait. If LI is not met, then estimated item parameters may be seriously distorted (DeMars, [<reflink idref="bib17" id="ref67">17</reflink>]; Toland, [<reflink idref="bib51" id="ref68">51</reflink>]). According to DeMars ([<reflink idref="bib17" id="ref69">17</reflink>], p. 48), "If the item responses are not locally independent under a unidimensional model, another dimension must be causing the dependence." The standardized local dependence (LD) <emph>χ</emph><sups>2</sups> (Chen & Thissen, [<reflink idref="bib13" id="ref70">13</reflink>]) was used to examine the LI assumption. Finally, the third assumption implies that items responses follow the selected IRT model (e.g., 1PL, 2PL). The S‐<emph>χ</emph><sups>2</sups> (Orlando & Thissen, [<reflink idref="bib43" id="ref71">43</reflink>]) was employed to test this assumption. Nonsignificant S‐<emph>χ</emph><sups>2</sups> suggest that the assumption of correct model specification is met.</p> <hd id="AN0164231916-7">Results</hd> <p>Prior to items calibration, the appropriate dimensionality of PENS‐B was tested. Based on the Purpura et al. ([<reflink idref="bib47" id="ref72">47</reflink>]) study, a unidimensional model was first examined. Initial calibration on group‐A converged fast, with no issues (Table 1). Items fit using the S‐<emph>χ</emph><sups>2</sups> (Orlando & Thissen, [<reflink idref="bib43" id="ref73">43</reflink>]) showed that its value could not be estimated for four items (<emph>x</emph>1, <emph>x</emph>2, <emph>x</emph>3, <emph>x</emph>5). It should be noted that these items yielded exceptionally high success percentages (Table 2). In addition, examination of the local independence (LI) assumption employing the standardized local dependence (LD) <emph>χ</emph><sups>2</sups> (Chen & Thissen, [<reflink idref="bib13" id="ref74">13</reflink>]) revealed that several leftover associations, after accounting for the latent trait, were well above the recommended cut‐off point of |10| (Toland, [<reflink idref="bib51" id="ref75">51</reflink>]), suggesting the existence of additional dimension (DeMars, [<reflink idref="bib17" id="ref76">17</reflink>]). The largests LD values were associated with items <emph>x</emph>19, <emph>x</emph>21, <emph>x</emph>23, <emph>x</emph>24 (e.g., <emph>x</emph>21–<emph>x</emph>8 = 19.39, <emph>x</emph>24–<emph>x</emph>10 = 18.84). Thus, it was decided (a) to discard the four items with exceptionally high success percentages and (b) to refit a unidimensional model along with an exploratory two‐dimensional IRT model. In exploratory IRT analysis, a researcher defines only the number of dimensions and items are free to load to any of the dimensions without posing any constraints, whereas in confirmatory IRT, items are related only to a specific dimension (mirt v.1.37.1, Chalmers, [<reflink idref="bib11" id="ref77">11</reflink>]).</p> <p>1 Table Fit Indices of the Examined PENS‐B Models</p> <p> <ephtml> <table><thead><tr><th /><th>–2LL</th><th>AIC</th><th>BIC</th><th>M2 (<italic>df</italic>)</th><th>RMSEA</th><th>CFI</th></tr></thead><tbody><tr><td>Group‐A (453)</td><td>Exploratory IRT</td></tr><tr><td>1f, 24 items</td><td>5115.0</td><td>5211.0</td><td>5408.6</td><td>1032.1<sup>*</sup> (252)</td><td>.083</td><td>.946</td></tr><tr><td>1f, 20 items</td><td>5069.7</td><td>5149.7</td><td>5314.8</td><td>675.9<sup>*</sup> (170)</td><td>.081</td><td>.949</td></tr><tr><td>2f, 20 items</td><td>4815.1</td><td>4933.1</td><td>5175.9</td><td>217.4<sup>*</sup> (151)</td><td>.033</td><td>.993</td></tr><tr><td>Group‐B (453)</td><td>Confirmatory IRT</td></tr><tr><td>1f, 20 items</td><td align="center">5198.9</td><td>5278.9</td><td>5443.6</td><td>546.5<sup>*</sup> (170)</td><td>.070</td><td>.961</td></tr><tr><td>2f, 20 items</td><td align="center">4992.9</td><td>5074.9</td><td>5243.6</td><td>285.9<sup>*</sup> (169)</td><td>.039</td><td>.988</td></tr><tr><td>Total sample</td><td /><td /><td /><td /><td /><td /></tr><tr><td>2f, 20 items</td><td>9916.9</td><td>9998.9</td><td>10196.1</td><td>370.5<sup>*</sup> (169)</td><td>.036</td><td>.990</td></tr></tbody></table> </ephtml> </p> <p>1 <sups>*</sups><emph>p</emph> <.001.</p> <p>2 Table Descriptive Statistics and Items Fit of the PENS‐B</p> <p> <ephtml> <table><thead><tr><th /><th>Wrong (%)</th><th>Correct (%)</th><th>S‐<italic>χ</italic><sup>2</sup>(<italic>df</italic>)</th><th><italic>p</italic> Value</th></tr></thead><tbody><tr><td>1. Count 3 dots</td><td>.7 %</td><td>99.3 %</td><td>ΝΑ</td><td>‐</td></tr><tr><td>2. Count 3 pictures from a larger set</td><td>.8 %</td><td>99.2 %</td><td>ΝΑ</td><td>‐</td></tr><tr><td>3. Identify 8 dots as largest of 4 sets</td><td>.6 %</td><td>99.4 %</td><td>ΝΑ</td><td>‐</td></tr><tr><td>4. Identify the numeral 1</td><td>3.2 %</td><td>96.8 %</td><td>3.45 (4)</td><td>.484</td></tr><tr><td>5. Connect the numeral 1 to 1 dot</td><td>.6 %</td><td>99.4 %</td><td>ΝΑ</td><td>‐</td></tr><tr><td>6. Count 6 dots</td><td>2.5 %</td><td>97.5 %</td><td>4.80 (3)</td><td>.187</td></tr><tr><td>7. Identify 3 dots as largest of 4 sets</td><td>1.2 %</td><td>98.8 %</td><td>5.24 (2)</td><td>.073</td></tr><tr><td>8. Connect the numeral 3 to 3 dots</td><td>6.4 %</td><td>93.6 %</td><td>7.28 (9)</td><td>.608</td></tr><tr><td>9. Count 11 dots</td><td>9.9%</td><td>90.1 %</td><td>15.85 (12)</td><td>.197</td></tr><tr><td>10. Connect the numeral 5 to 5 dots</td><td>8.7 %</td><td>91.3 %</td><td>14.87 (9)</td><td>.094</td></tr><tr><td>11. Identify number before 5</td><td>8.4 %</td><td>91.6 %</td><td>7.50 (5)</td><td>.187</td></tr><tr><td>12. Identify number closest to 4 from 4 options</td><td>20.0 %</td><td>80.0 %</td><td>15.50 (12)</td><td>.213</td></tr><tr><td>13. Story problems 1 + 1 =</td><td>4.3 %</td><td>95.7 %</td><td>6.70 (12)</td><td>.876</td></tr><tr><td>14. Identify number after 9</td><td>12.7 %</td><td>87.3 %</td><td>13.15 (10)</td><td>.216</td></tr><tr><td>15. Identify numeral 8 as largest of 4 numerals</td><td>17.8 %</td><td>82.2 %</td><td>13.08 (12)</td><td>.363</td></tr><tr><td>16. Story problems 1 – 1 =</td><td>33.1 %</td><td>66.9 %</td><td>21.50 (13)</td><td>.064</td></tr><tr><td>17. Identify number closest to 9 from 4 options</td><td>32.0 %</td><td>68.0 %</td><td>14.44 (9)</td><td>.105</td></tr><tr><td>18. Story problems 4 – 1 =</td><td>10.2 %</td><td>89.8 %</td><td>15.59 (13)</td><td>.271</td></tr><tr><td>19. 1 + 1 =</td><td>39.3 %</td><td>60.7 %</td><td>9.31 (8)</td><td>.317</td></tr><tr><td>20. Count 20 pictures from of a larger set</td><td>32.1 %</td><td>67.9 %</td><td>13.98 (12)</td><td>.302</td></tr><tr><td>21. 2 + 2 =</td><td>51.2 %</td><td>48.8 %</td><td>19.27 (7)</td><td>.007</td></tr><tr><td>22. Identify eighth object</td><td>15.0 %</td><td>85.0 %</td><td>9.64 (11)</td><td>.562</td></tr><tr><td>23. 0 + 2 =</td><td>72.2 %</td><td>27.8 %</td><td>8.39 (3)</td><td>.038</td></tr><tr><td>24. 1 + 3 =</td><td>59.7 %</td><td>40.3 %</td><td>11.15 (6)</td><td>.082</td></tr></tbody></table> </ephtml> </p> <p>2 <emph>Note</emph>. The <emph>p</emph> values of the S‐<emph>χ</emph><sups>2</sups> were obtained from the two‐dimensional model from the total sample, based on 20 items.</p> <p>Fit indices of both models are presented in Table 1. Their comparison showed that the two‐dimensional model fit significantly better to the data than the unidimensional model (Δ<emph>χ</emph><sups>2</sups> = 254.6, Δ<emph>df</emph> = 19, <emph>p</emph> <.001). The AIC and BIC values provided the same conclusion. Moreover, the M2‐based RMSEA and CFI were in favor of the two‐dimensional model. The correlation between the two dimensions was significant and substantial, yielding a value of.707. Moreover, no pair of items exhibited a LD <emph>χ</emph><sups>2</sups> above |10|, suggesting that the two‐dimensional model explained well the observed associations among the 20 PENS‐B items. The first dimension included 16 items for assessing Numbering Relations (NR), whereas the second dimension included 4 items reflecting children's ability for Arithmetic Operations (AO). It should be noted that these four items were those that showed high LD values when a unidimensional model was fitted.</p> <p>The above findings clearly showed that the two‐dimensional model adequately describes students' responses to the 20 items of the PENS‐B and should be retained for further exploration using group‐B. Given the present results, a confirmatory IRT approach was employed. Similar conclusions were reached using group B, indicating the two‐dimensional model again as the most viable (Δ<emph>χ</emph><sups>2</sups> = 206.8, Δ<emph>df</emph> = 1, <emph>p</emph> <.001).</p> <p>Items calibration results of the total sample employing a 2PL confirmatory IRT are presented in Table 3. At the test level, the M2‐based RMSEA and CFI suggested an excellent fit to the data (Table 1). At the item level, the S‐<emph>χ</emph><sups>2</sups><emph>p</emph>‐values were not significant after adjusting for multiple tests (lowest <emph>p</emph>‐value.140) using the Benjamini and Hochberg ([<reflink idref="bib8" id="ref78">8</reflink>]) procedure. In addition, no local dependence issues were noticed. The association between the two dimensions was.737 (<emph>SE</emph> =.025, 95%CI.688 to.786). Regarding items' discrimination, high values above 1.34 (Baker, [<reflink idref="bib5" id="ref79">5</reflink>]) were derived, denoting that they can distinguish quite well students with similar levels of latent traits. Items intercept and multidimensional difficulties for the NR dimension clearly showed that they capture levels of that latent trait below average. On the other hand, the four arithmetic operations items measure a restricted area of the latent trait, ranging from just below average to about half of a standard deviation above average.</p> <p>3 Table Item Calibration Results of the PENS‐B 20 Items</p> <p> <ephtml> <table><thead><tr><th /><th><italic>α</italic>1</th><th><italic>α</italic>2</th><th><italic>d</italic></th><th>MDIFF</th></tr></thead><tbody><tr><td>4. Identify the numeral 1</td><td>4.269</td><td>‐</td><td>8.494</td><td>–1.990</td></tr><tr><td>6. Count 6 dots</td><td>3.871</td><td>‐</td><td>8.237</td><td>–2.128</td></tr><tr><td>7. Identify 3 dots as largest of 4 sets</td><td>1.870</td><td>‐</td><td>5.960</td><td>–3.188</td></tr><tr><td>8. Connect the numeral 3 to 3 dots</td><td>3.043</td><td>‐</td><td>5.397</td><td>–1.774</td></tr><tr><td>9. Count 11 dots</td><td>2.379</td><td>‐</td><td>3.845</td><td>–1.616</td></tr><tr><td>10. Connect the numeral 5 to 5 dots</td><td>3.803</td><td>‐</td><td>5.783</td><td>–1.521</td></tr><tr><td>11. Identify number before 5</td><td>6.111</td><td>‐</td><td>8.962</td><td>–1.466</td></tr><tr><td>12. Identify number closest to 4 from 4 options</td><td>2.874</td><td>‐</td><td>2.900</td><td>–1.009</td></tr><tr><td>13. Story problems 1 + 1 =</td><td>1.721</td><td>‐</td><td>4.280</td><td>–2.486</td></tr><tr><td>14. Identify number after 9</td><td>4.165</td><td>‐</td><td>5.282</td><td>–1.268</td></tr><tr><td>15. Identify numeral 8 as largest of 4 numerals</td><td>2.714</td><td>‐</td><td>3.045</td><td>–1.122</td></tr><tr><td>16. Story problems 1 – 1 =</td><td>1.526</td><td>‐</td><td>1.020</td><td>–.668</td></tr><tr><td>17. Identify number closest to 9 from 4 options</td><td>2.847</td><td>‐</td><td>1.612</td><td>–.566</td></tr><tr><td>18. Story problems 4 – 1 =</td><td>2.165</td><td>‐</td><td>3.584</td><td>–1.655</td></tr><tr><td>19. 1 + 1 =</td><td>‐</td><td>8.784</td><td>2.698</td><td>–.307</td></tr><tr><td>20. Count 20 pictures from of a larger set</td><td>1.976</td><td>‐</td><td>1.249</td><td>–.632</td></tr><tr><td>21. 2 + 2 =</td><td>‐</td><td>8.141</td><td>–.127</td><td>.016</td></tr><tr><td>22. Identify eighth object</td><td>3.040</td><td>‐</td><td>3.711</td><td>–1.221</td></tr><tr><td>23. 0 + 2 =</td><td>‐</td><td>5.605</td><td>–3.388</td><td>.604</td></tr><tr><td>24. 1 + 3 =</td><td>‐</td><td>6.006</td><td>–1.476</td><td>.246</td></tr></tbody></table> </ephtml> </p> <ulist> <item>3 <emph>Note</emph>. Items calibration derived from the total sample using confirmatory IRT.</item> <item>4 <emph>α</emph>1, <emph>α</emph>2 = slopes for the first and second dimension respectively, <emph>d</emph> = intercept, MDIFF = multidimensional difficulty.</item> </ulist> <p>Visual inspection of the total information function (TIF) for each dimension (Figures 1 and 2) as well as the three dimensional plots for TIF and standard errors for both dimensions (Figures 3 and 4) revealed that NA and AO measure with precision only a small area of their corresponding latent trait. NR measurement accuracy peaks around 1.5 standard deviations below average, whereas AO peaks at average. As we move away from the peaks in either direction precision rapidly decreases. The decline is more prominent for the AO dimension. Moreover, for those that prefer a single number instead of a function, Green et al. ([<reflink idref="bib24" id="ref80">24</reflink>]) developed the marginal reliability index. This type of reliability averages the scale precision across the theta range; it ranges from 0–1 and is considered analogous to reliability indices used in CTT (DeMars, [<reflink idref="bib17" id="ref81">17</reflink>]). Marginal reliability was.786 for NR and.821 for AO.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EMS/01jun23/emip12536-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="emip12536-fig-0001.jpg" title="1 Total Information Function and Standard Error Curve for the PENS‐B Numbering Relations Dimension [Colour figure can be viewed at wileyonlinelibrary.com]" /> </p> <p></p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EMS/01jun23/emip12536-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="emip12536-fig-0002.jpg" title="2 Total Information Function for the PENS‐B Arithmetic Operations Dimension [Colour figure can be viewed at wileyonlinelibrary.com]" /> </p> <p></p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EMS/01jun23/emip12536-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="emip12536-fig-0003.jpg" title="3 Contour Plot for PENS‐B Total Information FunctionNote. θ1 = Numbering Relations, θ2 = Arithmetic Operations, Higher Values Denote Higher Peaks" /> </p> <p></p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EMS/01jun23/emip12536-fig-0004.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="emip12536-fig-0004.jpg" title="4 Standard Error Surface Plot for the Two Dimensions of PENS‐B [Colour figure can be viewed at wileyonlinelibrary.com]Note. θ1 = numbering relations, θ2 = arithmetic operations." /> </p> <p></p> <p>Next, we examined whether PENS‐B items behave in a similar way across gender. Differential item functioning (DIF) procedures provided by <emph>mirt</emph> were employed, using the <emph>multipleGroup()</emph> function. An item is identified as exhibiting DIF if it yields different parameters for different groups (and hence different probability of response), when members of the groups are matched on the latent trait being measured (de Ayala, [<reflink idref="bib16" id="ref82">16</reflink>]). Three models were postulated and compared based on the Likelihood Ratio Test. The first model (M1) postulated equal structure of PENS‐B for boys and girls without posing any constraints (configural model). Thus, in the M1 model, items' parameters were allowed to be freely estimated separately for both genders. The M1 model served as the baseline model. The second model (M2) constrained item slopes to be equal across gender, while intercepts were freely estimated (metric model). Thus, M2 examined nonuniform DIF. In the case of nonuniform DIF for binary data, discrimination values are different, hence, causing item characteristic curves (ICC) of the groups to cross each other. That is, although the probability of correct response is higher for one group than the other group, this relationship is reversed after a certain point on the latent trait continuum.</p> <p>The final model (M3) posed an additional constraint of equal intercepts, to test for uniform DIF (scalar model). Uniform DIF means that an item's difficulty value is different across groups. In the case of uniform DIF for binary data the probability of correct response is constantly higher for the one group than the other group along the latent trait continuum.</p> <p>In the above models, the means and variances for boys' latent traits were set to 0 and 1 respectively, making girls the focal group. Results are presented in Table 4. Comparison of M1 with M2 and M2 with M3 yielded nonsignificant findings, suggesting no DIF for gender.</p> <p>4 Table Differential Item Functioning Results for the PENS‐B Items across Gender</p> <p> <ephtml> <table><thead><tr><th /><th>–2LL</th><th>AIC</th><th>BIC</th><th>Δ<italic>χ</italic><sup>2</sup></th><th>Δ<italic>df</italic></th><th><italic>p</italic></th><th>CFI</th><th>ΔCFI</th><th>RMSEA</th><th>ΔRMSEA</th></tr></thead><tbody><tr><td>M1</td><td>9834.5</td><td>10006.5</td><td>10419.9</td><td>‐</td><td>‐</td><td>‐</td><td>.990</td><td>‐</td><td>.025</td><td>‐</td></tr><tr><td>M2</td><td>9845.1</td><td>9977.1</td><td>10294.3</td><td>10.56</td><td>20</td><td>.957</td><td>.990</td><td>.000</td><td>.024</td><td>–.001</td></tr><tr><td>M3</td><td>9875.4</td><td>9967.4</td><td>10188.5</td><td>30.33</td><td>20</td><td>.065</td><td>.989</td><td>.001</td><td>.025</td><td>+.001</td></tr></tbody></table> </ephtml> </p> <p>5 M1 = no constraints (configural model), M2 = equal slopes (metric model), M3 = equal slopes and intercepts (scalar model).</p> <p>Given that no item of the PENS‐B exhibited DIF, it is meaningful to compare NR and AO latent means across gender. Findings showed that although girls had –.044 units lower than boys on the NR dimension, this difference was not statistically significant (95%CI –.195 to.115). However, this was not the case for the AO dimension, for which girls significantly underperformed boys by –.184 units (95%CI –.076 to –.292).</p> <hd id="AN0164231916-12">Discussion</hd> <p>There is no doubt that early numeracy is the foundation for the development of mathematical knowledge (e.g., Aunio et al., [<reflink idref="bib3" id="ref83">3</reflink>]). Toward this end, validated measures can help teachers and researchers to identify children with difficulties in mathematics and enable targeted support (Raghubar & Barnes, [<reflink idref="bib48" id="ref84">48</reflink>]). The PENS‐B is a promising instrument for assessing early numeracy skills in preschool education, and the examination of its factorial validity and measurement invariance in another cultural context is of scientific merit. Findings of the present study suggest that the 20‐items of the Greek version of the PENS‐B measures two aspects of numeracy skills in preschool students. In addition, items of both dimensions yielded high discrimination values.</p> <p>In the present study, the PENS‐B dimensionality was thoroughly tested. When a unidimensional model was fitted, there was a serious departure from the LD assumption, which, according to DeMars ([<reflink idref="bib17" id="ref85">17</reflink>]), may imply the existence of an additional dimension. Based on this result, a two dimensional model was also fitted, employing exploratory IRT, followed by confirmatory IRT. Both analyses clearly supported the tenability of the two dimensional model. It is worth noting that there were no LD issues associated with the selected model. Moreover, the fact that our findings were replicated using another sample poses additional confidence on the two dimensional model of the PENS‐B. The two dimensions were positively and strongly associated. Given that the two‐dimensional model had better fit than the unidimensional and a 95% CI around the estimated correlation between NR and AO did not include unity provides support of their discriminant validity.</p> <p>Although our results deviate from the Purpura et al. ([<reflink idref="bib47" id="ref86">47</reflink>]) unidimensional model, they align with the model proposed by Jordan et al. ([<reflink idref="bib28" id="ref87">28</reflink>]), suggesting that early numeracy involves two dimensions: basic number skills, and arithmetic operations. In addition, several authors supported multidimensional models for the informal early numeracy skills (Milburn et al., [<reflink idref="bib37" id="ref88">37</reflink>]; Purpura & Lonigan, [<reflink idref="bib45" id="ref89">45</reflink>]). Devlin et al. ([<reflink idref="bib18" id="ref90">18</reflink>]), in a review of recent studies of the factorial structure of early numeracy measures, reported that whereas some instruments were considered initially to be unidimensional, they were subsequently found to comprise more than one underlying factor. An advantage of the current study is the increased number of participants across a wide age range in comparison to the Purpura et al. ([<reflink idref="bib47" id="ref91">47</reflink>]) study, which might be a possible explanation for the emerged difference in the PENS‐B dimensionality. As the factor structure of the early numeracy remains unclear (Charitaki et al., [<reflink idref="bib12" id="ref92">12</reflink>]; Devlin et al., [<reflink idref="bib18" id="ref93">18</reflink>]), further research is needed to establish the dimensions of numeracy and how well they predict children's outcomes.</p> <p>The precision with which a test measures a latent trait represents an important psychometric property and it should be thoroughly examined. Total information function along with standard error curves revealed some notable aspects of the PENS‐B. The NR dimension seems to assess children with low to average levels of numeracy skills with adequate precision. Beyond this specific area of the continuum, NR dimension is considerably restricted in capturing average to highly skilled children on this latent trait. On the other hand, the precision of the AO dimension seems to be limited to children with average to high levels of numeracy skills. These restrictions of the current 20‐item version of PENS‐B should be taken into consideration by practitioners when they administer it to study numeracy skills in early childhood.</p> <p>Differential Item Functioning (DIF) procedures showed that PENS‐B items did not exhibit DIF across gender. This finding provides additional support to the appropriateness of PENS‐B since the absence of DIF is a highly desirable property of a measuring instrument. Thus, when it comes to gender in the Greek preschool educational context, researchers can have increased confidence in PENS‐B's ability to measure with no bias numeracy skills.</p> <p>Children's comparison, after establishing absence of DIF items in PENS‐B, showed mixed results. Thus, our expectation for the lack of gender differences in preschoolers' numeracy performance was partially confirmed. More specifically, no differences were found between boys and girls in NR. This finding is in line with the majority of existing research in early childhood education suggesting that preschool boys and girls do not differ in the numeracy skills (e.g., Aunola et al., [<reflink idref="bib4" id="ref94">4</reflink>]; Napoli & Purpura, [<reflink idref="bib39" id="ref95">39</reflink>]; Papadakis et al., [<reflink idref="bib44" id="ref96">44</reflink>]; Purpura et al., [<reflink idref="bib47" id="ref97">47</reflink>]). With regard however to the AO dimension it was found that boys outperformed girls. This result is in agreement with the study by Jordan et al. ([<reflink idref="bib28" id="ref98">28</reflink>]), who reported small but significant differences favoring boys. It should be underlined that the instrument administered by Jordan et al. ([<reflink idref="bib28" id="ref99">28</reflink>]) included tasks requiring AO skills.</p> <p>It seems that when testing instruments that mainly focus on numbering relations no gender differences occur. When, on the other hand, testing instruments include tasks targeting arithmetic operations, boys yield better scores than girls. This tendency might also be the case for the Greek educational context, since boys were more competent than girls in the PENS‐B AO dimension. Despite however the presence of gender differences in some aspects of numeracy skills, it is too early to suggest that girls are not equally equipped with numeracy competencies or not equally capable of acquiring complex mathematical skills (Hutchison et al., [<reflink idref="bib27" id="ref100">27</reflink>]). Therefore, the above mixed findings don't allow for assertive conclusions and additional research is needed to further explore gender performance regarding different aspects of numeracy skills.</p> <p>The present study is not without limitations. Our study focused on the underlying structure of the PENS‐B without presenting any associations with external related measures. In previous research, Purpura et al. ([<reflink idref="bib47" id="ref101">47</reflink>]) reported moderate correlations between PENS‐B and two measures of literacy skills, namely the Expressive One‐Word Picture Vocabulary Test–Fourth Edition (EOWPVT; Martin & Brownell, [<reflink idref="bib36" id="ref102">36</reflink>]) and the Ready to Read–Revised (GRTR; Lonigan & Wilson, [<reflink idref="bib33" id="ref103">33</reflink>]). After establishing the factorial structure of the Greek version of the PENS‐B, future studies should continue examining its association with other related measures. Toward this end, a widely applied literacy skill measure, namely the Peabody Picture Vocabulary Test‐Revised (PPVT‐R; Simos et al., [<reflink idref="bib49" id="ref104">49</reflink>]), can be employed. Moreover, the present study did not examine the temporal stability of the Greek version of the PENS‐B. The temporal stability of PENS‐B is a crucial psychometric property to correctly evaluate preschool students' numeracy skills. To the best of our knowledge, no study has examined this critical characteristic. Thus, the temporal stability of the Greek version of the PENS‐B is to be addressed. Additional research activity also seems necessary to develop items and/or replace existing ones to capture a broader range of latent traits. Such an endeavor is specifically needed for the Arithmetic Operations dimension, which comprises only four items. Based on the above research actions, researchers and practitioners will have increased confidence in assessing various levels of numeracy skills in preschool education with greater precision.</p> <p>The necessity of conducting cross‐cultural research on the development of numeracy skills is widely recognized (Aunio et al., [<reflink idref="bib2" id="ref105">2</reflink>]; Cankaya & LeFevre, [<reflink idref="bib9" id="ref106">9</reflink>]). Geary ([<reflink idref="bib22" id="ref107">22</reflink>]) maintains that mathematical development is influenced by the culture because the native language acts as a moderator for mathematical learning in preschool (Kung et al., [<reflink idref="bib29" id="ref108">29</reflink>]). The current results suggest that the PENS‐B seems to be a promising tool for assessing children's numeracy skills in cultural contexts other than the one that was initially developed. If the psychometric characteristics of PENS‐B are replicated across various cultural and educational settings, then researchers can have an instrument suitable for making thorough cross‐cultural comparisons which can lead to a more profound understanding of the development of numeracy skills.</p> <ref id="AN0164231916-13"> <title> References </title> <blist> <bibl id="bib1" idref="ref40" type="bt">1</bibl> <bibtext> Anderson, J. C., & Gerbing, D. W. (1988). 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  Group: Ti
  Data: Psychometric Evaluation of the Preschool Early Numeracy Skills Test--Brief Version within the Item Response Theory Framework
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  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Tsigilis%2C+Nikolaos%22">Tsigilis, Nikolaos</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-2388-959X">0000-0002-2388-959X</externalLink>)<br /><searchLink fieldCode="AR" term="%22Krousorati%2C+Katerina%22">Krousorati, Katerina</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-7481-3336">0000-0001-7481-3336</externalLink>)<br /><searchLink fieldCode="AR" term="%22Gregoriadis%2C+Athanasios%22">Gregoriadis, Athanasios</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-3026-6614">0000-0002-3026-6614</externalLink>)<br /><searchLink fieldCode="AR" term="%22Grammatikopoulos%2C+Vasilis%22">Grammatikopoulos, Vasilis</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-7556-6162">0000-0001-7556-6162</externalLink>)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Educational+Measurement%3A+Issues+and+Practice%22"><i>Educational Measurement: Issues and Practice</i></searchLink>. Sum 2023 42(2):32-41.
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  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
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  Data: 10
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  Data: 2023
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  Label: Document Type
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  Data: Journal Articles<br />Reports - Research
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  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Early+Childhood+Education%22">Early Childhood Education</searchLink><br /><searchLink fieldCode="EL" term="%22Preschool+Education%22">Preschool Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Psychometrics%22">Psychometrics</searchLink><br /><searchLink fieldCode="DE" term="%22Preschool+Education%22">Preschool Education</searchLink><br /><searchLink fieldCode="DE" term="%22Numeracy%22">Numeracy</searchLink><br /><searchLink fieldCode="DE" term="%22Item+Response+Theory%22">Item Response Theory</searchLink><br /><searchLink fieldCode="DE" term="%22Test+Validity%22">Test Validity</searchLink><br /><searchLink fieldCode="DE" term="%22Gender+Differences%22">Gender Differences</searchLink><br /><searchLink fieldCode="DE" term="%22Preschool+Children%22">Preschool Children</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Greece%22">Greece</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/emip.12536
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0731-1745<br />1745-3992
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The Preschool Early Numeracy Skills Test--Brief Version (PENS-B) is a measure of early numeracy skills, developed and mainly used in the United States. The purpose of this study was to examine the factorial validity and measurement invariance across gender of PENS-B in the Greek educational context. PENS-B was administered to 906 preschool children (473 boys, 433 girls), randomly selected from 84 kindergarten classrooms. A 2PL unidimensional and multidimensional item response theory analysis, using cross-validation procedures, were used to analyze the data. Results showed that responses to 20 items can be adequately explained by a two-dimensional model (Numbering Relations and Arithmetic Operations). Application of differential item functioning procedures did not detect any gender bias. Numeracy Relation comprises 16 items, which assess low levels of this latent trait. On the other hand, four items capture average levels of Arithmetic Operations. Total information curves revealed that both dimensions measure with precision only a small area of their underlying latent trait.
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  Data: 2023
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  Label: Accession Number
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  Data: EJ1380345
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1380345
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1111/emip.12536
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 10
        StartPage: 32
    Subjects:
      – SubjectFull: Psychometrics
        Type: general
      – SubjectFull: Preschool Education
        Type: general
      – SubjectFull: Numeracy
        Type: general
      – SubjectFull: Item Response Theory
        Type: general
      – SubjectFull: Test Validity
        Type: general
      – SubjectFull: Gender Differences
        Type: general
      – SubjectFull: Preschool Children
        Type: general
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Greece
        Type: general
    Titles:
      – TitleFull: Psychometric Evaluation of the Preschool Early Numeracy Skills Test--Brief Version within the Item Response Theory Framework
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Tsigilis, Nikolaos
      – PersonEntity:
          Name:
            NameFull: Krousorati, Katerina
      – PersonEntity:
          Name:
            NameFull: Gregoriadis, Athanasios
      – PersonEntity:
          Name:
            NameFull: Grammatikopoulos, Vasilis
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2023
          Identifiers:
            – Type: issn-print
              Value: 0731-1745
            – Type: issn-electronic
              Value: 1745-3992
          Numbering:
            – Type: volume
              Value: 42
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Educational Measurement: Issues and Practice
              Type: main
ResultId 1