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Identifying Word-Problem Difficulty: An Item Response Analysis of an Additive Word-Problem Screener

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Title: Identifying Word-Problem Difficulty: An Item Response Analysis of an Additive Word-Problem Screener
Language: English
Authors: Alison M. Hardy (ORCID 0009-0002-5197-9223), J. E. Miller (ORCID 0000-0002-9258-8774), Sarah R. Powell (ORCID 0000-0002-6424-6160), Nancy Scammacca (ORCID 0000-0002-7484-5976)
Source: Psychology in the Schools. 2025 62(10):3912-3925.
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: 14
Publication Date: 2025
Sponsoring Agency: Institute of Education Sciences (ED)
Contract Number: R324A150078
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Secondary Education
Descriptors: Elementary School Students, Word Problems (Mathematics), Mathematics Education, Secondary School Students, Mathematics Skills, Difficulty Level, Learning Problems, Mathematics Tests, Screening Tests, Test Theory, Computation, Identification, Intervention
DOI: 10.1002/pits.23582
ISSN: 0033-3085
1520-6807
Abstract: Students encounter hundreds of word problems throughout the elementary grades and on standardized assessments through high school. To demonstrate proficiency on these measures of mathematics competency, students must be skilled in solving word problems. Early detection of word-problem difficulty is essential, and screeners play an important role in early detection. There are, however, a limited number of word-problem screeners and very few nonproprietary brief screeners. Thus, this paper examines the "Additive Word-Problem Screener"--a 12-min, free-to-use, eight-problem screener. Through examination of classical test theory and calculation of item response theory statistics, we determined that the "Additive Word-Problem Screener" is a promising short-form screener for identifying students with word-problem difficulty.
Abstractor: As Provided
IES Funded: Yes
Entry Date: 2025
Accession Number: EJ1483433
Database: ERIC
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  Value: <anid>AN0187949505;pis01oct.25;2025Sep16.03:20;v2.2.500</anid> <title id="AN0187949505-1">Identifying Word‐Problem Difficulty: An Item Response Analysis of an Additive Word‐Problem Screener </title> <p>Students encounter hundreds of word problems throughout the elementary grades and on standardized assessments through high school. To demonstrate proficiency on these measures of mathematics competency, students must be skilled in solving word problems. Early detection of word‐problem difficulty is essential, and screeners play an important role in early detection. There are, however, a limited number of word‐problem screeners and very few nonproprietary brief screeners. Thus, this paper examines the Additive Word‐Problem Screener—a 12‐min, free‐to‐use, eight‐problem screener. Through examination of classical test theory and calculation of item response theory statistics, we determined that the Additive Word‐Problem Screener is a promising short‐form screener for identifying students with word‐problem difficulty.</p> <p>Summary: This freely available screener can be used to identify Grades 2–5 students with word‐problem difficulty (piratemathequationquest.com/data.html).A classroom can be screened in about 12 min and scoring is straightforward.Early identification of word‐problem difficulty is crucial so students can receive targeted word‐problem instruction and intervention.</p> <p>Keywords: item response theory; mathematics; word problems</p> <hd id="AN0187949505-2">Introduction</hd> <p>Word problems are text‐based mathematical scenarios in which students must use the presented information to answer one or more questions. Students begin solving word problems as early as kindergarten, and with each grade level, word problems increase in difficulty (CCSSM; National Governors Association Center for Best Practices and Council of Chief State School Officers [<reflink idref="bib33" id="ref1">33</reflink>]). An example of a Grade 3 word problem is: <emph>Last month, the school store sold 107 T‐shirts and 88 sweatshirts. How many more T‐shirts were sold than sweatshirts?</emph> (State of Texas Assessments of Academic Readiness [<reflink idref="bib53" id="ref2">53</reflink>]). Students solve hundreds of word problems such as this throughout the elementary grades. Moreover, on national‐ (e.g., the National Assessment of Educational Progress) and state‐level mathematics assessments, students demonstrate their mathematics competency largely through solving word problems.</p> <p>In an analysis of released items from state‐level mathematics tests, Powell et al. ([<reflink idref="bib47" id="ref3">47</reflink>]) identified 92.5% of items as word problems. Of these, 69% of the word problems were categorized as <emph>directive word problems</emph>. Directive word problems involve text‐based directions to answer a question (e.g., <emph>What is the value of 341,562 when rounded to the nearest ten thousand?</emph>). The other 31% were categorized as <emph>routine word problem</emph>s, like the word problem about the school store. In this paper, unless otherwise specified, we use the term word problem to refer to <emph>routine</emph> word problems. With the overwhelming majority of test items presented as directive or routine word problems, students must develop strong word‐problem skills to demonstrate their mathematics knowledge. In this study, we examined the technical properties of a word‐problem screener that researchers and educators could use to quickly identify students experiencing difficulty with additive (i.e., addition and subtraction) word problems, making it possible to provide timely intervention.</p> <hd id="AN0187949505-3">Framework for the Study</hd> <p>Our study is grounded in a framework related to problem solving that involves recognizing the underlying structure of a problem to determine the appropriate steps to solve the problem. Sweller ([<reflink idref="bib56" id="ref4">56</reflink>]) asserted that students' awareness of <emph>schemas</emph>, the ability to group problems by their underlying structure, is the determining factor that distinguishes successful problem solvers from unsuccessful problem solvers. Schemas are directly connected to the conceptual underpinning of a problem (Riley et al. [<reflink idref="bib49" id="ref5">49</reflink>]). Once students recognize the schema of a problem, they can use a schema‐specific representation (e.g., graphic organizer, equation) to organize and solve the problem (Willis and Fuson [<reflink idref="bib60" id="ref6">60</reflink>]). Furthermore, an understanding of schemas is essential for transfer from simpler problems to more complex problems (Cooper and Sweller [<reflink idref="bib9" id="ref7">9</reflink>]).</p> <p>Concerning word problems in particular, researchers have analyzed the structure of routine word problems in which students would use addition or subtraction for the computation with the problem, and they have identified three reliable additive schemas (e.g., Carpenter et al. [<reflink idref="bib5" id="ref8">5</reflink>]; Corte and Verschaffel [<reflink idref="bib10" id="ref9">10</reflink>]; Kintsch and Greeno [<reflink idref="bib28" id="ref10">28</reflink>]; Nesher et al. [<reflink idref="bib34" id="ref11">34</reflink>]; Willis and Fuson [<reflink idref="bib60" id="ref12">60</reflink>]). Importantly, all routine word problems that require addition or subtraction computation can be categorized by the three schemas described in the next paragraph.</p> <p>In alignment with the recent literature on word‐problem instruction, we refer to the three additive schemas as Total, Difference, and Change (e.g., Fuchs et al. [<reflink idref="bib17" id="ref13">17</reflink>]; Powell et al. [<reflink idref="bib44" id="ref14">44</reflink>], [<reflink idref="bib46" id="ref15">46</reflink>]; Stevens et al. [<reflink idref="bib54" id="ref16">54</reflink>]). In Total problems, parts are put together for a total (e.g., <emph>The cafeteria served 156 hot lunches and 49 cold lunches. How many lunches did they serve altogether?</emph>). Total problems may have an unknown <emph>total</emph> or an unknown <emph>part</emph>. Total problems are sometimes referred to as <emph>combine, group</emph>, or <emph>part‐part‐whole</emph> problems (Carpenter et al. [<reflink idref="bib5" id="ref17">5</reflink>]; Jitendra et al. [<reflink idref="bib25" id="ref18">25</reflink>]; Riley et al. [<reflink idref="bib49" id="ref19">49</reflink>]; Van de Walle et al. [<reflink idref="bib58" id="ref20">58</reflink>]). In Difference problems, two amounts are compared for a difference (e.g., <emph>Mr. Atkin's class drank 12 cartons of chocolate milk and 9 cartons of white milk. How many fewer cartons of white milk were there than chocolate?)</emph>. Difference problems may have an unknown <emph>difference, lesser amount</emph>, or <emph>greater amount</emph>. Difference problems are sometimes referred to as <emph>compare</emph> problems (Carpenter et al. [<reflink idref="bib5" id="ref21">5</reflink>]; Van de Walle et al. [<reflink idref="bib58" id="ref22">58</reflink>]). In Change problems, a start amount increases or decreases to a new end amount (e.g., <emph>There were 75 slices of pizza. Mr. Atkin's class went through the line and took 12 slices. How many slices are left?)</emph>. Change problems may have an unknown <emph>start amount, change amount</emph>, or <emph>end amount</emph>. When describing Change problems, the terms <emph>joining</emph> and <emph>separating</emph> are sometimes used (Carpenter et al. [<reflink idref="bib5" id="ref23">5</reflink>]; Van de Walle et al. [<reflink idref="bib58" id="ref24">58</reflink>]).</p> <p>Students solve Total, Difference, and Change problems throughout elementary school, and with each grade level, the complexity of such problems increases (CCSSM [<reflink idref="bib33" id="ref25">33</reflink>]). For example, in kindergarten, students solve additive word problems that require addition and subtraction within 10. In Grade 1, students begin solving word problems in which the location of the unknown value can vary (e.g., a Total problem with a missing <emph>part</emph>, a Change problem with a missing <emph>start amount</emph>). In Grade 3, students solve additive word problems that require addition and subtraction of whole numbers within 1000. By the end of Grade 5, students solve additive word problems that require addition and subtraction of fractions with unlike denominators. Considering how quickly word problems grow in complexity throughout the elementary grades, educators need to be able to quickly identify students who experience difficulty with word problems. In the next section, we describe these students and recent efforts to support them.</p> <hd id="AN0187949505-4">Supporting Students With Word‐Problem Difficulty</hd> <p>Students who experience difficulty with mathematics often demonstrate lower performance on word problems than students who do not experience mathematics difficulty (Peake et al. [<reflink idref="bib37" id="ref26">37</reflink>]; van Garderen et al. [<reflink idref="bib18" id="ref27">18</reflink>]). In this paper, we use <emph>word‐problem difficulty</emph> to describe such students. Word problems require a confluence of skills, and as such, students with word‐problem difficulty may struggle with one or many of the required skills. To solve a word problem, students have to read and comprehend text, access and organize information, develop a plan for the solution, complete the calculation(s), and check for the reasonableness of their solution (Boonen et al. [<reflink idref="bib3" id="ref28">3</reflink>]). Moreover, some students may experience difficulties with working memory or long‐term memory, which can impede success (Lee et al. [<reflink idref="bib30" id="ref29">30</reflink>]; Thevenot and Oakhill [<reflink idref="bib57" id="ref30">57</reflink>]). Finally, many word problems contain irrelevant information, information accessed through charts or graphs, or require multiple steps. These factors can contribute to the complexity of word‐problem solving (Arsenault and Powell [<reflink idref="bib1" id="ref31">1</reflink>]).</p> <p>Without focused instruction on how to set up and solve word problems, students with word‐problem difficulty are likely to have limited and ineffective strategies. First, some students may begin adding or subtracting the numbers in the word problems without carefully reading and comprehending the problem (Van Dooren et al. [<reflink idref="bib11" id="ref32">11</reflink>]). Other students may use superficial cues in the word problem, such as keywords, to solve a word problem (Shum and Chan [<reflink idref="bib52" id="ref33">52</reflink>]). Problematically, keywords lead to a correct problem solution in less than half of single‐step word problems and less than 10% of multi‐step word problems (Powell et al. [<reflink idref="bib47" id="ref34">47</reflink>]). Some students with word‐problem difficulty may use irrelevant information presented within the word problem in their problem solution (Jarosz and Jaeger [<reflink idref="bib24" id="ref35">24</reflink>]; Ng et al. [<reflink idref="bib35" id="ref36">35</reflink>]; Wang et al. [<reflink idref="bib59" id="ref37">59</reflink>]). Moreover, even after constructing the appropriate equation to solve a word problem, students can make computational mistakes (Haghverdi et al. [<reflink idref="bib21" id="ref38">21</reflink>]; Sharpe et al. [<reflink idref="bib51" id="ref39">51</reflink>]).</p> <p>When students experience word‐problem difficulty, educators can implement a handful of evidence‐based practices to support these students (Cook et al. [<reflink idref="bib8" id="ref40">8</reflink>]; Jitendra et al. [<reflink idref="bib26" id="ref41">26</reflink>]; Kong et al. [<reflink idref="bib29" id="ref42">29</reflink>]). One such evidence‐based practice is schema instruction. A breadth of studies have demonstrated that schema instruction can improve word‐problem outcomes for students with word‐problem difficulty (Flores et al. [<reflink idref="bib14" id="ref43">14</reflink>]; Fuchs et al. [<reflink idref="bib16" id="ref44">16</reflink>]; Griffin et al. [<reflink idref="bib20" id="ref45">20</reflink>]; Peltier et al. [<reflink idref="bib41" id="ref46">41</reflink>]; Powell et al. [<reflink idref="bib46" id="ref47">46</reflink>]; Swanson et al. [<reflink idref="bib55" id="ref48">55</reflink>]; Xin et al. [<reflink idref="bib61" id="ref49">61</reflink>]; Zheng et al. [<reflink idref="bib62" id="ref50">62</reflink>]).</p> <p>In schema instruction, students are explicitly taught to recognize word problems as belonging to a specific schema and use a schema‐specific model to determine a problem solution (Carpenter et al. [<reflink idref="bib5" id="ref51">5</reflink>]; Fuchs et al. [<reflink idref="bib16" id="ref52">16</reflink>]; Griffin et al. [<reflink idref="bib20" id="ref53">20</reflink>]). The positive results of schema instruction are in alignment with the hypothesis of Sweller ([<reflink idref="bib56" id="ref54">56</reflink>]) that the processes of solving word problems and forming an understanding of the schemas are largely separate from one another. Thus, students, particularly those with word‐problem difficulty, may benefit from word‐problem instruction focused on schemas.</p> <hd id="AN0187949505-5">Identifying Students With Word‐Problem Difficulty</hd> <p>To identify which students may have word‐problem difficulty so as to provide timely word‐problem intervention, researchers and educators should have access to an efficient word‐problem screening measure. An efficient screener would be able to quickly screen a large number of students to identify which students may require additional word‐problem support through small‐group instruction or within multi‐tiered frameworks. Moreover, to support researchers and educators in implementing schema instruction, word‐problem screening measures should include all relevant schemas (e.g., Total, Difference, and Change) with unknowns in various locations.</p> <p>Currently, there are a number of commercially‐available measures that could be used to screen for word‐problem difficulty. For example, researchers and educators could use the <emph>Applied Problem Solving</emph> or <emph>Foundations of Problem Solving</emph> subtests of the KeyMath3 (Connolly [<reflink idref="bib7" id="ref55">7</reflink>]). Researchers and educators could also administer the <emph>Applied Problems</emph> subtest of the Woodcock‐Johnson Test of Achievement (WJ‐IV; Schrank et al. [<reflink idref="bib50" id="ref56">50</reflink>]). These measures include a wide variety of mathematics problems designed for students in prekindergarten and beyond (see Table 1 for additional details). However, these measures have a few limitations. First, these measures must be individually and orally administered. Thus, they are time‐intensive and complicated for classroom teachers to administer. Second, to administer these subtests, one must purchase the testing kits, which for the KeyMath3 costs upwards of $600 and for the WJ‐IV costs upwards of $2300. Finally, because these measures cover a variety of mathematics content for a wide range of grade levels, the inclusion of word problems with additive schemas (i.e., Total, Difference, and Change) varies.</p> <p>1 Table Summary of existing word‐problem screeners.</p> <p> <ephtml> <table><thead valign="bottom"><tr valign="bottom"><th>Screener</th><th>Description</th><th>Single‐step additive word problems with whole numbers within 1000</th><th>Administration</th><th>Price range</th></tr></thead><tbody valign="top"><tr><td>Applied Problem Solving – KeyMath3 (Connolly <xref ref-type="bibr" rid="bibr7">2007</xref>)</td><td>35 items; mathematics‐related prompts, directive word problems, and routine word problems designed for students in prekindergarten through Grade 5. Most routine word problems are orally presented with visuals. Problems are single‐ and multi‐step, require all four operations, and include irrelevant information.</td><td>3 Total0 Difference1 Change</td><td>Individual, oral (5 min)</td><td>Kit: $57925 Forms: $113</td></tr><tr><td>Applied Problems – Woodcock‐Johnson Test of Achievement (WJ‐IV; Schrank et al. <xref ref-type="bibr" rid="bibr50">2014</xref>)</td><td>56 items; mathematics‐related prompts, directive word problems, and routine word problems designed for students in prekindergarten through adulthood. Some routine word problems are orally presented with visuals. Problems are single‐ and multi‐step, require all four operations, and include irrelevant information.</td><td>1 Total2 Difference10 Change</td><td>Individual, oral and written (5 min)</td><td>Kit: $225025 Forms: $284</td></tr><tr><td>Foundations of Problem Solving – KeyMath3 (Connolly <xref ref-type="bibr" rid="bibr7">2007</xref>)</td><td>27 items; mathematics‐related prompts, directive word problems, and routine word problems designed for students in prekindergarten through Grade 5. Some routine word problems are orally presented with visuals, and many questions require students to explain problem‐solving strategies.</td><td>0 Total1 Difference1 Change</td><td>Individual, oral (5 min)</td><td>Kit: $57925 Forms: $113</td></tr><tr><td>Mathematics Problem Solving, Primary 3 – Stanford Achievement Test (SAT10; Pearson <xref ref-type="bibr" rid="bibr39">2019</xref>)</td><td>46 items; directive and routine word problems designed for students in Grade 3. Problems are single‐ and multi‐step and require all four operations.</td><td>1 Total1 Difference0 Change</td><td>Whole group, written (40–50 min)</td><td>Kit: $8210 Forms: $255</td></tr><tr><td>Math Problem Solving – Wechsler Individual Achievement Test (WIAT‐4; Pearson <xref ref-type="bibr" rid="bibr40">2020</xref>)</td><td>71 items; mathematics‐related prompts, directive word problems, and routine word problems designed for students in prekindergarten through adulthood. Problems are single‐ and multi‐step and require all four operations. Some routine word problems are orally presented with visuals.</td><td>1 Total0 Difference2 Change</td><td>Whole group, oral (30 min)</td><td>Kit: $90725 Forms: $216</td></tr><tr><td>Single‐Digit Word Problems (Pennies Test; Jordan and Hanich <xref ref-type="bibr" rid="bibr27">2000</xref>)</td><td>14 items; routine word problems that require addition and subtraction within 10.</td><td>2 Total4 Difference6 Change</td><td>Whole group, written (10 min)</td><td>Free from author</td></tr><tr><td>Word Problems – Test of Mathematical Abilities (TOMA‐3; Brown et al. <xref ref-type="bibr" rid="bibr4">2012</xref>)</td><td>30 items; directive and routine word problems designed for students ages 8 through 18. Problems are single‐ and multi‐step, require all four operations, and include irrelevant information.</td><td>3 Total2 Difference2 Change</td><td>Whole group, written (30 min)</td><td>Kit: $21625 Forms: $79</td></tr></tbody></table> </ephtml> </p> <p>1 <emph>Note:</emph> The listed prices were retrieved in February 2024.</p> <p>Several commercially available measures can be implemented in a whole‐group setting. Two of them, the <emph>Math Problem Solving</emph> subtest of the Wechsler Individual Achievement Test (WIAT‐4; Pearson [<reflink idref="bib40" id="ref57">40</reflink>]) and the <emph>Word Problems</emph> subtest of the Test of Mathematical Abilities (TOMA‐3; Brown et al. [<reflink idref="bib4" id="ref58">4</reflink>]), are similar to the previous measures in that they cover a variety of mathematics content and are appropriate for a wide range of grade levels. For example, the subtest of the WIAT‐4 includes 71 items, but only three of them are additive word problems typical of Grade 3 (i.e., require addition and subtraction of whole numbers within 1000). Thus, these measures have a limited capacity for the early identification of word‐problem difficulty.</p> <p>The <emph>Mathematics Problem Solving</emph> subtest of the Stanford Achievement Test (SAT10; Pearson [<reflink idref="bib39" id="ref59">39</reflink>]) has grade‐level specific measures. For example, researchers and educators could administer Primary 3 of the SAT10 to target Grade 3 knowledge and skills. However, even these grade‐level specific measures include a small proportion of single‐step additive word problems. Moreover, these measures are expensive. Beyond the cost of testing kits, researchers and educators would have to order testing booklets. For example, 10 SAT10 Primary 3 test booklets cost $255, which means a school would spend at least $500 to screen one classroom of students in the elementary grades.</p> <p>One researcher‐created measure that has been widely implemented is <emph>Single‐Digit Word Problems</emph> (<emph>Pennies Test</emph>; Jordan and Hanich [<reflink idref="bib27" id="ref60">27</reflink>]). This measure is freely available through the authors, can be administered in a whole‐group setting, and, with only 14 items, can be administered quickly (i.e., 12 min or less). All three additive schemas (i.e., Total, Difference, and Change) are represented, and unknowns are in various locations. However, one limitation is that this measure only requires addition and subtraction within ten. Thus, the questions may not be difficult enough to detect word‐problem difficulty at Grade 3 or beyond.</p> <p>As part of an Institute of Education Sciences efficacy trial (Powell et al. [<reflink idref="bib46" id="ref61">46</reflink>]), our research team developed the <emph>Additive Word‐Problem Screener</emph> to help educators quickly identify elementary students who may benefit from additional word‐problem support. This measure is available for free on our project's website (piratemathequationquest.com/data.html) so that researchers and educators can efficiently screen a classroom of students without having to invest in costly and more difficult‐to‐administer measures. We designed the <emph>Additive Word‐Problem Screener</emph> to represent addition and subtraction whole‐number word problems students may set up and solve in the elementary grades, most often in Grades 2, 3, and 4.</p> <p>Although the students who participated in this study were in Grade 3, the items on the screener were in alignment with Grade 2 mathematics standards (CCSSM [<reflink idref="bib33" id="ref62">33</reflink>]). Thus, this screener could be used to identify students with word‐problem difficulty beginning in Grade 2. Still, the measure could be used at additional grade levels (e.g., Grades 4 and 5) if students experience difficulty solving additive word problems with whole numbers.</p> <hd id="AN0187949505-6">Purpose of the Study</hd> <p>The main objective of this study was to examine the psychometric properties of Powell and Berry's ([<reflink idref="bib43" id="ref63">43</reflink>]) <emph>Additive Word‐Problem Screener</emph> to determine whether we could encourage teachers to use the screener to quickly identify students with word‐problem difficulty. We used a combination of classical test theory (CTT) and item response theory (IRT) to examine the psychometric properties of the word‐problem screener in categorizing student word‐problem difficulty.</p> <hd id="AN0187949505-7">Methods</hd> <p></p> <hd id="AN0187949505-8">Setting</hd> <p>After receiving approval from The University of Texas at Austin's Institutional Review Board and school district for conducting research in public schools, we recruited elementary schools from a large urban school district in the Southwest of the U.S. This public school district served over 80,000 students. On average, the district reported 55.5% of students as Hispanic, 29.6% as White, 7.1% as African American, and 7.7% as belonging to another race or ethnic category. Overall, 27.1% of students identified as dual‐language learners, 52.4% qualified as economically disadvantaged, and 12.1% received special education services. The district's graduation rate was 90.7%.</p> <hd id="AN0187949505-9">Sample</hd> <p>We collected this data as part of an efficacy trial focused on word‐problem intervention with Grade 3 students (Powell et al. [<reflink idref="bib46" id="ref64">46</reflink>]). We recruited Grade 3 teachers and the students in their classrooms across three school years. In the first year, we worked with 62 classrooms from 14 schools. In Year 2, we worked with 53 classrooms from 13 schools. In Year 3, we worked with 51 classrooms in 13 schools. Table 2 provides the demographics of the participating students. The total sample included 2,841 Grade 3 students.</p> <p>2 Table Student demographics.</p> <p> <ephtml> <table><thead valign="bottom"><tr valign="bottom"><th>Group Variable</th><th>Groups</th><th>Percentage</th></tr></thead><tbody valign="top"><tr><td>Word‐problem ability status</td><td>Typical</td><td>76%</td></tr><tr><td /><td>Word‐problem difficulty</td><td>24%</td></tr><tr><td>Gender</td><td>Females</td><td>51%</td></tr><tr><td>Dual‐language learner</td><td>Yes</td><td>41%</td></tr><tr><td>Race</td><td>African American</td><td>10%</td></tr><tr><td /><td>Hispanic/Latine</td><td>47%</td></tr><tr><td /><td>White</td><td>29%</td></tr><tr><td /><td>Asian</td><td>5%</td></tr><tr><td /><td>Multi‐racial</td><td>7%</td></tr><tr><td /><td>Other</td><td>2%</td></tr></tbody></table> </ephtml> </p> <p>As part of the efficacy trial, we identified students with mathematics difficulty using <emph>Single‐Digit Word Problems</emph> (Jordan and Hanich [<reflink idref="bib27" id="ref65">27</reflink>]). For study eligibility, we identified students who answered seven or fewer items correctly (out of 14) as experiencing word‐problem difficulty. This cut‐off score represented performance at or below the 25th percentile, a common cut‐off score in research related to the identification of mathematics difficulty (Geary et al. [<reflink idref="bib19" id="ref66">19</reflink>]; Hecht and Vagi [<reflink idref="bib22" id="ref67">22</reflink>]; Locuniak and Jordan [<reflink idref="bib31" id="ref68">31</reflink>]). Based on the initial screening, we identified 692 students with word‐problem difficulty and 2,149 without word‐problem difficulty.</p> <hd id="AN0187949505-10">Screener Development</hd> <p>We developed the <emph>Additive Word‐Problem Screener</emph> to identify or confirm students with word‐problem difficulty (Powell and Berry [<reflink idref="bib43" id="ref69">43</reflink>]). The screener included eight items that surveyed the word‐problem schemas of Total, Difference, and Change. On the <emph>Additive Word‐Problem Screener</emph>, students solved one Total problem (WP3) with an unknown part. Students solved three Difference problems, with the greater amount unknown (WP2), the difference unknown (WP5), and the lesser amount unknown (WP7). The Screener also included four Change problems. Two involved an increase with an unknown end amount (WP1) and an unknown start amount (WP6), whereas two involved a decrease with an unknown start amount (WP4) and an unknown change amount (WP8). Table 3 shows each of the eight word problems. We included one Total problem because there are only two variations (i.e., an unknown total or part). We did not include a Total problem with an unknown total because of students' propensity to add numbers from a word problem together. We included three Difference problems because there are several variations (i.e., unknown difference, greater amount, or lesser amount). Finally, we included four Change problems because there are six variations. Change problems can involve an increase or a decrease and have an unknown start amount, change amount, or end amount.</p> <p>3 Table Additive word‐problem screener questions.</p> <p> <ephtml> <table><thead valign="bottom"><tr valign="bottom"><th>Item</th><th>Question</th><th>Schema</th></tr></thead><tbody valign="top"><tr><td>WP1</td><td>Alfred drove 59 miles, and then he stopped for gas. Then, Alfred drove 34 more miles before stopping for lunch. How far did Alfred drive?</td><td>Change—Increase (unknown end amount)</td></tr><tr><td>WP2</td><td>The library has 23 books about dinosaurs. The library has 14 more books about space. How many books about space does the library have?</td><td>Difference (unknown greater amount)</td></tr><tr><td>WP3</td><td>The farmer has 61 sheep and cows. If 25 of the animals are sheep, how many are cows?</td><td>Total (unknown part)</td></tr><tr><td>WP4</td><td>Frances poured cups of lemonade. She sold 38 cups and has 19 cups left. How many cups did Frances pour?</td><td>Change—Decrease (unknown start amount)</td></tr><tr><td>WP5</td><td>Mr. Jones delivers packages. He delivered 26 packages on Thursday and 85 packages on Friday. How many more packages did he deliver on Friday?</td><td>Difference (unknown difference)</td></tr><tr><td>WP6</td><td>There were some students on the school bus. Then, 19 more students got on the bus. There are now 34 students on the bus. How many students were on the bus to start with?</td><td>Change—Increase (unknown start amount)</td></tr><tr><td>WP7</td><td>The grocery store has 22 fewer peaches than apples. If the grocery has 74 apples, how many peaches does the store have?</td><td>Difference (unknown lesser amount)</td></tr><tr><td>WP8</td><td>Jack had $38, and then he bought a shirt. Now, Jack has $14. How much did the shirt cost?</td><td>Change—Decrease (unknown change amount)</td></tr></tbody></table> </ephtml> </p> <hd id="AN0187949505-11">Procedures</hd> <p>Each year, a research team of 13 to 15 graduate students administered the <emph>Additive Word‐Problem Screener</emph> and several other tests as part of an ongoing research project (Powell et al. [<reflink idref="bib46" id="ref70">46</reflink>]). During a 45‐min screening session, the examiners administered five measures: <emph>Single‐Digit Word Problems</emph> (Jordan and Hanich [<reflink idref="bib27" id="ref71">27</reflink>]), the <emph>Additive Word‐Problem Screener</emph>, a test of equation solving, a test of equal‐sign knowledge, and a computation measure. This analysis focused on the second measure—the <emph>Additive Word‐Problem Screener</emph>.</p> <p>After participating in a 2‐h training in which the project lead reviewed administration protocols and practiced administration with the team, examiners administered the <emph>Additive Word‐Problem Screener</emph> in a group setting with whole classrooms of Grade 3 students. Examiners read from a screening protocol. At the beginning of the screening session, examiners explained to students that they would do some mathematics activities but that these activities were not for a classroom grade. At the beginning of the <emph>Additive Word‐Problem Screener</emph>, examiners said they would read a word problem aloud. If students wanted the word problem read again, students could raise their hand, and the examiner would read the problem again (for a total of reading each problem two times). Then, examiners read each word problem item aloud to reduce differences in reading ability. The total administration of the <emph>Additive Word‐Problem Screener</emph> lasted approximately 12 min. Among 10 randomly selected audio recordings of the screening sessions, the shortest duration for this measure was 9 min, and the longest was 14 min, with an average duration of 12 min.</p> <p>Examiners scored each item in a database by scoring 1 as correct, 0 as incorrect, and blank as no response. Two teams scored all items in two separate databases, compared the two databases, and rectified any discrepancies. Original scoring reliability was 99.9% (Powell et al. [<reflink idref="bib46" id="ref72">46</reflink>]).</p> <hd id="AN0187949505-12">Data Analysis</hd> <p>As described, the <emph>Additive Word‐Problem Screener</emph> consisted of eight items. We used a combination of classical test theory and item response theory in these analyses. The combination of information allows for a more holistic picture of the relationship between student mathematics ability and their item response.</p> <hd id="AN0187949505-13">IRT Analyses</hd> <p>We conducted IRT analyses using the mirt package in R (v1.35.1; Chalmers [<reflink idref="bib6" id="ref73">6</reflink>]). Initial CTT psychometric work explored reliability and correlations between items. Three IRT models were analyzed to determine fit: a Rasch model, a 2‐parameter logistic model (2PL), and a multidimensional 2PL (2PL‐2).</p> <p>The Rasch model assumed each item has a single parameter of item difficulty. Difficulty was the easiness of an item compared to a set of items. However, in the mirt package, the modeling software assumes multidimensional or multi‐trait data, and the difficulty parameter represented easiness of item as the reverse score compared to other software. Therefore, lower values represented more difficult items, and higher values represented easier items.</p> <p>The 2PL models included an additional parameter, discrimination, which represented the extent to which the item effectively determines a student's underlying word‐problem solving ability. Multidimensional 2PL explored whether the model is explained better by multiple latent traits instead of a single latent trait. We used likelihood ratio tests (LRTs) to determine the best‐fitting model. A significant LRT represented a need for a more parameterized, complex model versus a less parameterized, simpler model. The inclusion and examination of information criterion and parameter significance further supported model selection.</p> <p>In this report, we compared a Rasch versus a 2PL model and a 2PL versus a multidimensional 2PL model with two potential latent traits. Parameter estimates were explored in all three models to determine if the models converged appropriately. Further asymptotic constraints such as 3 parameter logistic models (3PL, e.g., guessing) were not considered given the item format was not multiple choice.</p> <p>After model selection, we calculated both the overall test information ( <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0001" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>I</mi><mo>(</mo><mi mathvariant="normal">θ</mi></mrow></mrow></semantics></math> </ephtml> )) and standard error ( <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0002" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="italic">SE</mi><mo>(</mo><mi mathvariant="normal">θ</mi></mrow></mrow></semantics></math> </ephtml> )). These metrics help with determining how well the word problem screener captures the underlying latent trait(s). Peaks of the test information curve between +3 standard deviations indicate adequate modeling. In addition, we calculated the IRT reliability as the empirical reliability given the latent trait estimates and their associated standard errors.</p> <p>Listwise deletion was used based on missing student data. Scores in the final data set were correct or incorrect, with missing responses scored as incorrect for the IRT analyses presented here. Correctly labeling the answer (e.g., 40 apples instead of 40) was not required for a response to be considered correct.</p> <hd id="AN0187949505-14">IRT DIF</hd> <p>We conducted differential item functioning (DIF) tests comparing typical students versus students with word‐problem difficulty and female versus male students. DIF occurs when students from different groups who have the same underlying latent ability level (e.g., word‐problem solving ability) have a different probability of a correct response (Finch and French [<reflink idref="bib12" id="ref74">12</reflink>]). In this study, researchers administered another psychometrically sound mathematics difficulty screener (Single‐Digit Word Problems; Jordan and Hanich [<reflink idref="bib27" id="ref75">27</reflink>]) to determine word‐problem difficulty status for each student. Item DIF was tested through LRT where a single item was constrained and all other items were freely estimated between dichotomous groups versus a model where all items are freely estimated between groups. Here, a significant LRT represents DIF between groups on a particular item. Lastly, anchor items—test items believed to be free of the effects DIF between groups—were not used due to the exploratory nature of the test. In other words, it was unclear a priori which items would not have DIF between groups.</p> <hd id="AN0187949505-15">Concurrent Validity</hd> <p>Students completed three additional assessments after taking the <emph>Additive Word‐Problem Screener</emph>: the <emph>Single‐Digit Word Problems (Pennies Test)</emph> assessment, the <emph>Open Equations</emph> assessment (Powell [<reflink idref="bib42" id="ref76">42</reflink>]), and the <emph>Test of Equal Sign Understanding</emph> (Matthews and Rittle‐Johnson [<reflink idref="bib32" id="ref77">32</reflink>]). The <emph>Open Equations</emph> assessment featured 30 equations in which students solved for the unknown (e.g., 3 + _ = 8; 9 – 6 = 7 – _). The reliability for this assessment was 0.86 (Powell et al. [<reflink idref="bib46" id="ref78">46</reflink>]). The <emph>Test of Equal Sign Understanding</emph> measured students' understanding of the equal sign and equivalence. The reliability for this assessment was 0.64 (Powell et al. [<reflink idref="bib46" id="ref79">46</reflink>]). The correlations between the <emph>Additive Word‐Problem Screener</emph> and these assessments ranged from 0.542 to 0.663. The magnitude of the correlations show that the <emph>Additive Word‐Problem Screener</emph> is related to but distinct from these measures of mathematics skills.</p> <hd id="AN0187949505-16">Results</hd> <p>Bivariate correlations between all item scores ranged between 0.21 to 0.54 (see Table 4). The lowest correlation occurred between WP4 and WP8. Cronbach's alpha and omega reliability statistics were performed on the <emph>Additive Word‐Problem Screener</emph>. Cronbach's alpha indicated adequate reliability at 0.80 (95% CI: 0.79, 0.81), and omega was similar at 0.81 (95% CI: 0.80 to 0.82). We systematically dropped items and recalculated overall alpha reliabilities to determine if dropping any items improved or worsen the alpha reliability (see Table 4). Cronbach's alpha did not change in a meaningful way if we removed any items from the test.</p> <p>4 Table Word problem item scores' bivariate correlation.</p> <p> <ephtml> <table><thead valign="bottom"><tr valign="bottom"><th>Item</th><th>WP1</th><th>WP2</th><th>WP3</th><th>WP4</th><th>WP5</th><th>WP6</th><th>WP7</th><th>Increase to alpha</th></tr></thead><tbody valign="top"><tr><td>WP1</td><td /><td /><td /><td /><td /><td /><td /><td>0.78</td></tr><tr><td>WP2</td><td>0.31<ext-link href="***" /></td><td /><td /><td /><td /><td /><td /><td>0.80</td></tr><tr><td>WP3</td><td>0.29<ext-link href="***" /></td><td>0.22<ext-link href="***" /></td><td /><td /><td /><td /><td /><td>0.78</td></tr><tr><td>WP4</td><td>0.27<ext-link href="***" /></td><td>0.23<ext-link href="***" /></td><td>0.24<ext-link href="***" /></td><td /><td /><td /><td /><td>0.80</td></tr><tr><td>WP5</td><td>0.31<ext-link href="***" /></td><td>0.22<ext-link href="***" /></td><td>0.52<ext-link href="***" /></td><td>0.26<ext-link href="***" /></td><td /><td /><td /><td>0.77</td></tr><tr><td>WP6</td><td>0.31<ext-link href="***" /></td><td>0.23<ext-link href="***" /></td><td>0.49<ext-link href="***" /></td><td>0.23<ext-link href="***" /></td><td>0.54<ext-link href="***" /></td><td /><td /><td>0.77</td></tr><tr><td>WP7</td><td>0.40<ext-link href="***" /></td><td>0.31<ext-link href="***" /></td><td>0.44<ext-link href="***" /></td><td>0.28<ext-link href="***" /></td><td>0.49<ext-link href="***" /></td><td>0.46<ext-link href="***" /></td><td /><td>0.76</td></tr><tr><td>WP8</td><td>0.38<ext-link href="***" /></td><td>0.28<ext-link href="***" /></td><td>0.33<ext-link href="***" /></td><td>0.21<ext-link href="***" /></td><td>0.36<ext-link href="***" /></td><td>0.36<ext-link href="***" /></td><td>0.54<ext-link href="***" /></td><td>0.78</td></tr></tbody></table> </ephtml> </p> <p>2 *** <emph>p</emph> < 0.0001 "Increase to alpha" represents the increase of alpha if the item is dropped from the test set and reliability is recalculated.</p> <hd id="AN0187949505-17">IRT Analyses</hd> <p>Rasch, 2PL, and 2PL‐2 model fit estimates can be found in Table 5. Using structural equation modeling cut off criterion for fit parameters (Hu and Bentler [<reflink idref="bib23" id="ref80">23</reflink>]), the results supported adequate fit for the Rasch model (0.05 < RMSEA < 0.10, CFI > 0.95), and good model fit statistics for both the 2PL and 2PL‐2 (RMSEA < 0.07, CFI > 0.95).</p> <p>5 Table IRT fit measures and model comparison.</p> <p> <ephtml> <table><thead valign="bottom"><tr valign="bottom"><th /><th align="center">Goodness of fit</th></tr><tr valign="bottom"><th /><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0004" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="normal">M</mi><mn>2</mn></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0005" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="italic">df</mi></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0006" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="italic">p</mi></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0007" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>CFI</mtext></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0008" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>TLI</mtext></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0009" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>SRMSR</mtext></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0010" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>RMSEA</mtext></mrow></mrow></semantics></math></p></th><th align="center"><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0011" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>RMSEA</mtext><mspace width="1em" /><mn>95</mn><mo>%</mo><mtext>CI</mtext></mrow></mrow></semantics></math></p></th></tr></thead><tbody valign="top"><tr><td>Rasch</td><td>80.29</td><td>27.00</td><td>0.00</td><td>0.92</td><td>0.92</td><td>0.10</td><td>0.10</td><td>0.09</td><td>0.11</td></tr><tr><td>2PL</td><td>165.94</td><td>20.00</td><td>0.00</td><td>0.99</td><td>0.98</td><td>0.03</td><td>0.05</td><td>0.04</td><td>0.06</td></tr><tr><td>2PL‐2</td><td>165.94</td><td>20.00</td><td>0.00</td><td>0.99</td><td>0.98</td><td>0.03</td><td>0.05</td><td>0.04</td><td>0.06</td></tr></tbody></table> </ephtml> </p> <p></p> <p> <ephtml> <table><thead valign="bottom"><tr><th /><th align="center">Model comparison</th></tr><tr><th /><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0012" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>AIC</mtext></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0013" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>SABIC</mtext></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0014" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>HQ</mtext></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0015" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mtext>BIC</mtext></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0016" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="italic">LL</mi></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0017" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="bold">Δ</mi><msup><mi mathvariant="normal">χ</mi><mn>2</mn></msup></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0018" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="italic">Δdf</mi></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0019" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="bold">Δ</mi><mi mathvariant="italic">p</mi></mrow></mrow></semantics></math></p></th><th /></tr></thead><tbody valign="top"><tr><td>Rasch</td><td>23,891.36</td><td>23,916.33</td><td>2391.68</td><td>23,944.92</td><td>−11,936.68</td><td /><td /><td /><td /></tr><tr><td>2PL</td><td>23,363.48</td><td>23,407.87</td><td>23,397.83</td><td>23,458.71</td><td>−11,665.74</td><td>541.88</td><td>7</td><td>0.00</td><td /></tr><tr><td>2PL‐2</td><td>23,297.85</td><td>23,361.67</td><td>23,347.23</td><td>23,434.75</td><td>−11,625.93</td><td>79.63</td><td>7</td><td>0.00</td><td /></tr></tbody></table> </ephtml> </p> <p>3 <emph>Note:</emph> M2 = overall goodness of fit metric. <emph>df</emph> = degrees of freedom. <emph>p</emph> = <emph>p‐value</emph> for M2. CFI = comparative fit index. TLI = Tucker–Lewis fit index. SRMSR = standardized root mean square residual. RMSEA = root mean squared error approximation. RMSEA <emph>95% CI</emph> = RMSEA confidence intervals. AIC = Akaike information criterion. <emph>SABIC</emph> = sample size adjusted BIC. BIC = Bayesian information criterion. HQ = Hannan–Quinn criterion. <emph>LL</emph> = log likelihood. <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0020" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="bold">Δ</mi><mi mathvariant="bold">χ</mi><mn mathvariant="bold">2</mn></mrow></mrow></semantics></math> </ephtml>  = difference of LRT. <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0021" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>Δ</mi><mi>df</mi><mo>=</mo><mi>difference in number of parameter between tests</mi><mo>.</mo><mi>Δ</mi><mi>p</mi><mo>=</mo><mspace width="0.25em" /><mi mathvariant="italic">p</mi><mo>−</mo><mi>value for the LRT</mi><mo>.</mo></mrow></mrow></semantics></math> </ephtml></p> <p>We performed likelihood ratio tests comparing Rasch versus 2PL and 2PL versus 2PL‐2. Both model tests produced significant results (<emph>p</emph> < 0.01; see Table 5) indicating that the best‐fitting model was the 2PL‐2 as supported by the information criterion. Yet, careful examination of the second latent trait difficulty parameters within the 2PL‐2 model revealed several near‐zero, nonsignificant effect size parameters. It is possible these additional parameters were noise (i.e., spurious error) and led to a false positive regarding model fit. In other words, these items did not contribute significantly to an additional, theorized, latent trait.</p> <p>Other measurement research on commonly used psychometric measures call for careful examination of the quality of items over the use of a "fit contest" or a "model champion" (Reise et al. [<reflink idref="bib48" id="ref81">48</reflink>], p. 836). The combination of the small discrepancies between model fit and information criterion support picking a model based on the quality of item estimates. Here, we assume a 2PL, single‐trait framework for the remaining analyses with these items given the low amount of information added by including 2PL‐2's additional parameters.</p> <hd id="AN0187949505-18">IRT Parameter Estimates</hd> <p>The 2PL model provided discrimination and difficulty parameter estimates for each item. The first two items (WP1 and WP2) were more difficult than the remaining items. In the future, it may be advantageous to move these items toward the end of the test. WP5 had the best ability to discriminate with WP7 being second best. WP4 was the easiest and least informative item and could potentially be removed from the test. Further justification for removing it is discussed in the item misfit section. We present item characteristics curves for each word‐problem item in Figure 1. The <emph>x</emph>‐axis represents math ability ( <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0023" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>θ</mi></mrow></mrow></semantics></math> </ephtml> ), and the <emph>y</emph>‐axis represents probability of correctly answer the item given one's math ability ( <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0024" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>P</mi><mo>(</mo><mi>θ</mi><mo>)</mo><mo>)</mo></mrow></mrow></semantics></math> </ephtml> . Generally, all items, except WP4, represented a sigmoidal curve ('S' shape) characteristic of adequate IRT items. The flatness of the sigmoidal curve for WP4 compared to other items represented the low difficulty of the item.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/PIS/01oct25/pits23582-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="pits23582-fig-0001.jpg" title="1 Item characteristic curves." /> </p> <p></p> <p>Based on the overall test information curve, which showed peak test information between +3 standard deviations (see Figure 2), and the standard error, the <emph>Additive Word‐Problem Screener</emph> adequately assessed latent word‐problem ability. The empirical reliability for the overall test was 0.79.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/PIS/01oct25/pits23582-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="pits23582-fig-0002.jpg" title="2 Test information and standard error." /> </p> <p></p> <p>Three items could be considered for removal based on misfit with the data using Orlando and Thissen ([<reflink idref="bib36" id="ref82">36</reflink>]) corrected chi‐square fit statistics ( <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0025" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><msub><mi>S</mi><msup><mi>χ</mi><mn>2</mn></msup></msub><mi>;</mi></mrow></mrow></semantics></math> </ephtml> see Table 6). However, based on the low <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0026" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="italic">RMSE</mi><msub><mi>A</mi><msub><mi>S</mi><msup><mi>χ</mi><mn>2</mn></msup></msub></msub></mrow></mrow></semantics></math> </ephtml> values and the observation that the items' Item Characteristic Curves (ICCs) largely adhere to the expected sigmoidal shape required by the 2PL model, we believe that two of the three flagged items remain valid and appropriate for inclusion in the test. The RMSEA values indicate excellent fit ( <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0027" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mrow><mo><</mo><mn>0.05</mn></mrow><mo>)</mo></mrow></mrow></semantics></math> </ephtml> ; Hu and Bentler [<reflink idref="bib23" id="ref83">23</reflink>]) suggesting that the degree of misfit is minimal and unlikely to compromise the measure's overall validity. Additionally, the ICCs demonstrate that two of these three items function as intended across groups, maintaining the model's assumptions and supporting their continued use as part of the test. However, the third item, WP4, was a potential misfit to the overall <emph>Additive Word‐Problem Screener. WP4 ICC does not meet the assumptions of a sigmoidal logistic regression curve and appears to be relatively easy adding little psychometric information and potentially introducing item misfit to the model's assumptions</emph>. Thus, we view the misfit here for two of three items as ignorable given the short length of the test.</p> <p>6 Table 2PL IRT model parameters and misfit.</p> <p> <ephtml> <table><thead valign="bottom"><tr valign="bottom"><th>Items</th><th>Discrimination</th><th>Difficulty</th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0028" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><msub><mi>S</mi><msup><mi>χ</mi><mn>2</mn></msup></msub></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0029" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi>d</mi><msub><mi>f</mi><msub><mi>S</mi><msup><mi>χ</mi><mn>2</mn></msup></msub></msub></mrow></mrow></semantics></math></p></th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0030" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><mi mathvariant="italic">RMSE</mi><msub><mi>A</mi><msub><mi>S</mi><msup><mi>χ</mi><mn>2</mn></msup></msub></msub></mrow></mrow></semantics></math></p></th></tr></thead><tbody valign="top"><tr><td>WP1</td><td>1.63<ext-link href="*" /></td><td>−0.38<ext-link href="*" /></td><td>5.42</td><td>5</td><td>0.01</td></tr><tr><td>WP2</td><td>1.06<ext-link href="*" /></td><td>−0.52<ext-link href="*" /></td><td>4.46</td><td>5</td><td>0.00</td></tr><tr><td>WP3</td><td>2.56<ext-link href="*" /></td><td>0.83<ext-link href="*" /></td><td>6.40</td><td>5</td><td>0.01</td></tr><tr><td>WP4</td><td>1.01<ext-link href="*" /></td><td>1.04<ext-link href="*" /></td><td>26.08<ext-link href="*" /></td><td>5</td><td>0.04</td></tr><tr><td>WP5</td><td>3.64<ext-link href="*" /></td><td>0.81<ext-link href="*" /></td><td>0.70</td><td>4</td><td>0.00</td></tr><tr><td>WP6</td><td>2.60<ext-link href="*" /></td><td>0.68<ext-link href="*" /></td><td>19.50<ext-link href="*" /></td><td>5</td><td>0.03</td></tr><tr><td>WP7</td><td>3.40<ext-link href="*" /></td><td>0.13<ext-link href="*" /></td><td>11.17</td><td>5</td><td>0.02</td></tr><tr><td>WP8</td><td>2.26<ext-link href="*" /></td><td>−0.28<ext-link href="*" /></td><td>19.25<ext-link href="*" /></td><td>5</td><td>0.03</td></tr></tbody></table> </ephtml> </p> <p>4 * <emph>p <</emph> 0.05. <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0031" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><msub><mi mathvariant="bold-italic">S</mi><msup><mi mathvariant="bold-italic">χ</mi><mn mathvariant="bold-italic">2</mn></msup></msub></mrow></mrow></semantics></math> </ephtml>  = Orlando and Thissen ([<reflink idref="bib36" id="ref84">36</reflink>]) misfit test criterion. <ephtml> <math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0032" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="bold-italic">RMSE</mi><msub><mi mathvariant="bold-italic">A</mi><msub><mi mathvariant="bold-italic">S</mi><msup><mi mathvariant="bold-italic">χ</mi><mn mathvariant="bold-italic">2</mn></msup></msub></msub></mrow></mrow></semantics></math> </ephtml>  = adequate fit of the overall item to the data. Lower difficulty values indicate more difficult items.</p> <hd id="AN0187949505-21">IRT DIF</hd> <p>Students identified with a word‐problem difficulty had different discrimination and difficulty parameter estimates for all word problem items compared to typical students. Testing indicated that all items contained some DIF for word‐problem difficulty status between students (see Table 7). All eight items had difficulty parameters below 0 (indicating high difficulty) for the students with mathematics difficulty. Difficulty parameters in the DIF IRT analysis differed compared to the original test structure. Particularly, the first item is easier for typical students compared to students with mathematics difficulty. Discrimination parameters were quite similar between groups (see Table 7). Specifically, the item characteristic curves represent similarly shaped curves for each item supporting similar discrimination values; however, the lack of overlap or the separation between the two curves indicate differences in difficulty (see Figure 3). Students with word‐problem difficulty had item characteristic curves centered higher on word‐problem difficulty compared to students without word‐problem difficulty. In other words, students with word‐problem difficulty needed greater word‐problem ability to answer the item correctly compared to typical students.</p> <p>7 Table DIF IRT parameters.</p> <p> <ephtml> <table><thead valign="bottom"><tr valign="bottom"><th>Group</th><th /><th /><th>Students with word‐problem difficulty</th><th align="center">Typical students</th></tr><tr valign="bottom"><th>Items</th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0033" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><msubsup><mi>χ</mi><mi mathvariant="normal">Δ</mi><mn>2</mn></msubsup></mrow></mrow></semantics></math></p></th><th><italic>df</italic></th><th>Discrimination</th><th>Difficulty</th><th>Discrimination</th><th>Difficulty</th></tr></thead><tbody valign="top"><tr><td>WP1</td><td>386.91<ext-link href="*" /></td><td>2</td><td>1.50</td><td>−1.27</td><td>1.25</td><td>1.15</td></tr><tr><td>WP2</td><td>243.66<ext-link href="*" /></td><td>2</td><td>0.90</td><td>−0.69</td><td>0.80</td><td>0.92</td></tr><tr><td>WP3</td><td>321.33<ext-link href="*" /></td><td>2</td><td>1.58</td><td>−4.68</td><td>2.17</td><td>−1.31</td></tr><tr><td>WP4</td><td>114.84<ext-link href="*" /></td><td>2</td><td>1.17</td><td>−2.21</td><td>0.85</td><td>−0.75</td></tr><tr><td>WP5</td><td>316.30<ext-link href="*" /></td><td>2</td><td>3.43</td><td>−7.82</td><td>3.15</td><td>−1.87</td></tr><tr><td>WP6</td><td>348.34<ext-link href="*" /></td><td>2</td><td>2.71</td><td>−5.57</td><td>2.15</td><td>−0.93</td></tr><tr><td>WP7</td><td>622.39<ext-link href="*" /></td><td>2</td><td>2.17</td><td>−3.99</td><td>2.69</td><td>0.64</td></tr><tr><td>WP8</td><td>495.86<ext-link href="*" /></td><td>2</td><td>1.20</td><td>−1.50</td><td>1.83</td><td>1.35</td></tr></tbody></table> </ephtml> </p> <p></p> <p> <ephtml> <table><thead valign="bottom"><tr><th /><th /><th /><th>Female students</th><th align="center">Male students</th></tr><tr><th>Items</th><th><p><math altimg="urn:x-wiley:00333085:media:pits23582:pits23582-math-0034" display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics xmlns=""><mrow><mrow><msubsup><mi>χ</mi><mi mathvariant="normal">Δ</mi><mn>2</mn></msubsup></mrow></mrow></semantics></math></p></th><th><italic>df</italic></th><th>Discrimination</th><th>Difficulty</th><th>Discrimination</th><th>Difficulty</th></tr></thead><tbody valign="top"><tr><td>WP1</td><td>3.18</td><td>2</td><td>1.80</td><td>0.67</td><td>1.49</td><td>0.50</td></tr><tr><td>WP2</td><td>1.15</td><td>2</td><td>1.04</td><td>0.57</td><td>1.08</td><td>0.46</td></tr><tr><td>WP3</td><td>2.48</td><td>2</td><td>2.48</td><td>−2.32</td><td>2.58</td><td>−2.08</td></tr><tr><td>WP4</td><td>3.09</td><td>2</td><td>0.93</td><td>−0.97</td><td>1.07</td><td>−1.19</td></tr><tr><td>WP5</td><td>4.72</td><td>2</td><td>4.05</td><td>−3.48</td><td>2.93</td><td>−2.52</td></tr><tr><td>WP6</td><td>2.10</td><td>2</td><td>2.38</td><td>−1.81</td><td>2.63</td><td>−1.70</td></tr><tr><td>WP7</td><td>5.52</td><td>2</td><td>3.06</td><td>−0.74</td><td>3.55</td><td>−0.36</td></tr><tr><td>WP8</td><td>2.95</td><td>2</td><td>2.26</td><td>0.47</td><td>2.20</td><td>0.74</td></tr></tbody></table> </ephtml> </p> <p>5 * <emph>p <</emph> 0.05. Lower difficulty values indicate easier items.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/PIS/01oct25/pits23582-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="pits23582-fig-0003.jpg" title="3 Item characteristic curves for typical students versus students with word‐problem difficulty." /> </p> <p></p> <p>DIF based on students' gender was not present for any of the word‐problem items. Both discrimination and difficulty parameters in the multigroup analysis had similar estimates and item characteristics curves (see Table 7 and Figure 4, respectively). This finding is further supported by the non‐significant LRT results. Thus, the results generalize to a heterogenous population of both female and male students.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/PIS/01oct25/pits23582-fig-0004.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="pits23582-fig-0004.jpg" title="4 Item Characteristic curves for student gender." /> </p> <p></p> <p>Students responded to three additional assessments after taking the word problems screener: the Single‐Digit Word Problems (Pennies Test) assessment, the Open Equations assessment, and the Test of Equal Sign Understanding. The correlations between the word problems screener and these assessments ranged from 0.542 to 0.663. The magnitude of the correlations show that the word problems screener is related to but distinct from these measures of math skills.</p> <hd id="AN0187949505-24">Discussion</hd> <p>The psychometric analyses reported here support several general conclusions. First, the IRT results suggested that the <emph>Additive Word‐Problem Screener</emph> measured a single latent trait of word‐problem ability. The 2PL model with difficulty and discrimination parameters best described this screener. Though a multidimensional model fit the data better, the near zero, nonsignificant effect size parameters on the second trait and the small difference between model fit estimates indicated the fit may not be the best determinate in model selection. As argued by Bollen and Long ([<reflink idref="bib2" id="ref85">2</reflink>], p. 8), "test statistics and fit indices are very beneficial, but they are no replacement for sound judgment and substantive expertise."</p> <p>Second, the psychometric properties of the <emph>Additive Word‐Problem Screener</emph> supported adequate model fit and captured the word‐problem ability distribution being modeled. Both CTT and IRT reliability statistics corroborated the consistency of most items (barring WP4). Third, all but one item on the <emph>Additive Word‐Problem Screener</emph> had adequate fit and discrimination and difficulty parameters. WP4 seemed to fit poorly on multiple psychometric properties across the sample. The low discrimination and difficulty parameters indicated that this item had little ability to capture students' overall word‐problem ability regardless of students' mathematics difficulty status. In addition to the item misfit, both students with and without mathematics difficulty had a high chance of answering the item correctly. Removing any item from a test of this length can significantly impact the overall reliability and validity of the measured domain (Finch and French [<reflink idref="bib13" id="ref86">13</reflink>]). After carefully evaluating the psychometric properties of each flagged item, we recommend removing this particular item over the others to preserve the measure's integrity and balance. Thus, we believe future research should evaluate removing this item (WP4) and re‐examining the psychometric properties of the test with a new sample to see if the other items are flagged again as misfit.</p> <p>Lastly, the <emph>Additive Word‐Problem Screener</emph> supported different probability of correct response for different groups. DIF was not found when comparing female and male students, but each item contained DIF when comparing typical students and with word‐problem difficulty. We would expect students with word‐problem difficulty to have a lower probability of answering a word problem correctly. We would not expect a difference in probability between female and male Grade 3 students. Generally, the psychometric properties, except for WP4, support use of the measure as a screener for word‐problem difficulty.</p> <hd id="AN0187949505-25">Implications for Practice</hd> <p>As described, the <emph>Additive Word‐Problem Screener</emph> is a free, brief measure of word‐problem solving that has adequate statistical properties and allows for easy, effective administration in a classroom setting. The measure takes about 12 min to administer to an entire classroom of students. The items are scored as correct or incorrect based on the numerical responses, making scoring for a classroom of students a quick and straightforward task for teachers. In terms of identifying students with word‐problem difficulty, educators may want to examine the word‐problem performance of students who correctly answer fewer than half (i.e., four) of the eight items on the <emph>Additive Word‐Problem Screener</emph>. These students would likely benefit from targeted word‐problem intervention.</p> <p>The items on this screener require addition and subtraction within 100, which aligns with Grade 2 mathematics standards (CCSSM [<reflink idref="bib33" id="ref87">33</reflink>]). Thus, Grade 2 teachers might administer the screener after providing instruction on additive word problems and addition and subtraction within 100. This screener could help determine which students would benefit from additional small‐group instruction. Alternatively, Grade 3 teachers might administer the screener at the beginning of the school year to determine if whole‐group reteaching or small‐group intervention might be necessary. Finally, Grades 4 and 5 teachers might administer the screener to identify students who require immediate intervention in solving additive word problems. As the complexity and rigor of word problems increase throughout the elementary grades, Grades 4 and 5 students who perform poorly on this screener should receive intensive intervention and have their progress monitored closely.</p> <p>Furthermore, this screener may be a helpful tool in implementing schema instruction. Many of the aforementioned commercially available word‐problem measures include a combination of mathematics‐related prompts, directive word problems, and routine word problems that span grade‐level expectations for preschool through Grade 12. The <emph>Additive Word‐Problem Screener</emph> has a narrower focus on routine additive word problems that require addition and subtraction of whole numbers. Educators could look at item‐level performance to understand how students solve Total, Difference, or Change problems. Such an analysis could inform existing or future schema instruction.</p> <p>The alignment of this screener with schema instruction is significant because although schema instruction has been determined to be an evidence‐based practice (e.g., Fuchs et al. [<reflink idref="bib15" id="ref88">15</reflink>]), many elementary teachers do not implement it (Powell et al. [<reflink idref="bib45" id="ref89">45</reflink>]). Instead, elementary word‐problem instruction often focuses on the ineffective keywords strategy (Pearce et al. [<reflink idref="bib38" id="ref90">38</reflink>]). Thus, we hope that the <emph>Additive Word‐Problem Screener</emph>, a quick and freely available screener, will support teachers in identifying which students would benefit the most from a schema‐based intervention. In turn, we hope this screener will help teachers understand the merit of schema instruction and bring research to practice.</p> <hd id="AN0187949505-26">Conclusion</hd> <p>Because every student in the U.S. solves word problems to demonstrate their mathematics competency (Powell et al. [<reflink idref="bib47" id="ref91">47</reflink>]), it is essential for educators to have tools to help identify which students have difficulty with word‐problem solving. A quick and freely available screener could be one data source for educators to use to identify which students (a) have difficulty with word‐problem solving and (b) may require targeted word‐problem support, either through small‐group instruction in the general education mathematics classroom, or through tiered small‐group or individual interventions provided through an MTSS framework. The <emph>Additive Word‐Problem Screener</emph> shows promise for use as a screener when educators want to gauge speedily the performance of their students on whole‐number addition and subtraction word problems, which are prevalent throughout the elementary grades.</p> <hd id="AN0187949505-27">Acknowledgments</hd> <p>This research was supported in part by Grant R324A150078 from the Institute of Education Sciences in the U.S. Department of Education to The University of Texas at Austin. The content is solely the responsibility of the authors and does not necessarily represent the official views of the U.S. Department of Education.</p> <hd id="AN0187949505-28">Data Availability Statement</hd> <p>The data that support the findings of this study are available from the corresponding author upon reasonable request.</p> <ref id="AN0187949505-29"> <title> References </title> <blist> <bibl id="bib1" idref="ref31" type="bt">1</bibl> <bibtext> Arsenault, T. L., and S. R. Powell. 2022. " Word‐Problem Performance Differences by Schema: A Comparison of Students With and Without Mathematics Difficulty." Learning Disabilities Research & Practice 37, no. 1 : 37 – 50. https://doi.org/10.1111/ldrp.12273.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref85" type="bt">2</bibl> <bibtext> Bollen, K. A., and J. S. Long. 1993. Testing Structural Equations Models. Sage.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref28" type="bt">3</bibl> <bibtext> Boonen, A. J. H., B. B. de Koning, J. Jolles, and M. van der Schoot. 2016. " Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training." Frontiers in Psychology 7 : 191. https://doi.org/10.3389/fpsyg.2016.00191.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref58" type="bt">4</bibl> <bibtext> Brown, V., M. E. Cronin, and D. P. Bryant 2012. Test of Mathematical Abilities – Third Edition. Pro‐Ed.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref8" type="bt">5</bibl> <bibtext> Carpenter, T. P., J. Hiebert, and J. M. Moser. 1981. " Problem Structure and First‐Grade Children's Initial Solution Processes for Simple Addition and Subtraction Problems." Journal for Research in Mathematics Education 12, no. 1 : 27 – 39. https://doi.org/10.2307/748656.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref73" type="bt">6</bibl> <bibtext> Chalmers, R. P. 2012. " Mirt: A Multidimensional Item Response Theory Package for the R Environment." Journal of Statistical Software 48, no. 6 : 1 – 29. https://doi.org/10.18637/jss.v048.i06.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref55" type="bt">7</bibl> <bibtext> Connolly, A. J. 2007. KeyMath3. Pearson.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref40" type="bt">8</bibl> <bibtext> Cook, S. C., L. W. Collins, L. L. Morin, and P. J. Riccomini. 2020. " Schema‐Based Instruction for Mathematical Word Problem Solving: An Evidence‐Based Review for Students With Learning Disabilities." Learning Disability Quarterly 43, no. 2 : 75 – 87. https://doi.org/10.1177/0731948718823080.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref7" type="bt">9</bibl> <bibtext> Cooper, G., and J. Sweller. 1987. " Effects of Schema Acquisition and Rule Automation on Mathematical Problem‐Solving Transfer." Journal of Educational Psychology 79, no. 4 : 347 – 362. https://doi.org/10.1037/0022-0663.79.4.347.</bibtext> </blist> <blist> <bibtext> Corte, E. D., and L. Verschaffel. 1987. " The Effect of Semantic Structure on First Graders' Strategies for Solving Addition and Subtraction Word Problems." Journal for Research in Mathematics Education 18, no. 5 : 363 – 381. https://doi.org/10.2307/749085.</bibtext> </blist> <blist> <bibtext> Van Dooren, W., D. De Bock, and L. Verschaffel. 2010. " From Addition to Multiplication...and Back: The Development of Students' Additive and Multiplicative Reasoning Skills." Cognition and Instruction 28, no. 3 : 360 – 381. https://doi.org/10.1080/07370008.2010.488306.</bibtext> </blist> <blist> <bibtext> Finch, W. H., and B. F. French. 2015. Latent Variable Modeling With R. Routledge.</bibtext> </blist> <blist> <bibtext> Finch, W. H., and B. F. French. 2018. Educational and Psychological Measurement. Routledge.</bibtext> </blist> <blist> <bibtext> Flores, M. M., V. M. Hinton, and M. E. Burton. 2016. " Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete‐Representational‐Abstract Sequence and Schema‐Based Instruction." Preventing School Failure: Alternative Education for Children and Youth 60, no. 4 : 345 – 355. https://doi.org/10.1080/1045988X.2016.1164117.</bibtext> </blist> <blist> <bibtext> Fuchs, L. S., N. Bucka, B. Clarke, et al. 2021. Assisting Students Struggling With Mathematics: Intervention in the Elementary Grades. Educator's Practice Guide. What Works Clearinghouse. https://ies.ed.gov/ncee/wwc/PracticeGuide/26.</bibtext> </blist> <blist> <bibtext> Fuchs, L. S., S. R. Powell, P. T. Cirino, et al. 2014. " Does Calculation or Word‐Problem Instruction Provide a Stronger Route to Pre‐Algebraic Knowledge? " Journal of Educational Psychology 106, no. 4 : 990 – 1006. https://doi.org/10.1037/a0036793.</bibtext> </blist> <blist> <bibtext> Fuchs, L. S., R. O. Zumeta, R. F. Schumacher, et al. 2010. " The Effects of Schema‐Broadening Instruction on Second Graders' Word‐Problem Performance and Their Ability to Represent Word Problems With Algebraic Equations: A Randomized Control Study." Elementary School Journal 110, no. 4 : 446 – 463. https://doi.org/10.1086/651191.</bibtext> </blist> <blist> <bibtext> van Garderen, D., A. Scheuermann, and C. Jackson. 2012. " Examining How Students With Diverse Abilities Use Diagrams to Solve Mathematics Word Problems." Learning Disability Quarterly 36, no. 3 : 145 – 160. https://doi.org/10.1177/0731948712438558.</bibtext> </blist> <blist> <bibtext> Geary, D. C., M. K. Hoard, L. Nugent, and D. H. Bailey. 2012. " Mathematical Cognition Deficits in Children With Learning Disabilities and Persistent Low Achievement: A Five‐Year Prospective Study." Journal of Educational Psychology 104, no. 1 : 206 – 223. https://doi.org/10.1037/a0025398.</bibtext> </blist> <blist> <bibtext> Griffin, C. C., J. C. Gagnon, M. H. Jossi, T. G. Ulrich, and J. A. Myers. 2018. " Priming Mathematics Word Problem Structures in a Rural Elementary Classroom." Rural Special Education Quarterly 37, no. 3 : 150 – 163. https://doi.org/10.1177/8756870518772164.</bibtext> </blist> <blist> <bibtext> Haghverdi, M., A. S. Semnani, and M. Seifi. 2012. " The Relationship Between Different Kinds of Students' Errors and the Knowledge Required to Solve Mathematics Word Problems." Bolema: Boletim de Educação Matemática 26 : 649 – 666. https://doi.org/10.1590/s0103-636x2012000200012.</bibtext> </blist> <blist> <bibtext> Hecht, S. A., and K. J. Vagi. 2010. " Sources of Group and Individual Differences in Emerging Fraction Skills." Journal of Educational Psychology 102, no. 4 : 843 – 859. https://doi.org/10.1037/a0019824.</bibtext> </blist> <blist> <bibtext> Hu, L., and P. M. Bentler. 1999. " Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives." Structural Equation Modeling: A Multidisciplinary Journal 6 : 1 – 55. https://doi.org/10.1080/10705519909540118.</bibtext> </blist> <blist> <bibtext> Jarosz, A. F., and A. J. Jaeger. 2019. " Inconsistent Operations: A Weapon of Math Disruption." Applied Cognitive Psychology 33, no. 1 : 124 – 138. https://doi.org/10.1002/acp.3471.</bibtext> </blist> <blist> <bibtext> Jitendra, A. K., D. N. Dupuis, M. C. Rodriguez, et al. 2013. " A Randomized Controlled Trial of the Impact of Schema‐Based Instruction on Mathematical Outcomes for Third‐Grade Students With Mathematics Difficulties." Elementary School Journal 114, no. 2 : 252 – 276. https://doi.org/10.1086/673199.</bibtext> </blist> <blist> <bibtext> Jitendra, A. K., S. Petersen‐Brown, A. E. Lein, et al. 2015. " Teaching Mathematical Word Problem Solving: The Quality of Evidence for Strategy Instruction Priming the Problem Structure." Journal of Learning Disabilities 48, no. 1 : 51 – 72. https://doi.org/10.1177/0022219413487408.</bibtext> </blist> <blist> <bibtext> Jordan, N. C., and L. B. Hanich. 2000. " Mathematical Thinking in Second‐Grade Children With Different Forms of LD." Journal of Learning Disabilities 33, no. 6 : 567 – 578. https://doi.org/10.1177/002221940003300605.</bibtext> </blist> <blist> <bibtext> Kintsch, W., and J. G. Greeno. 1985. " Understanding and Solving Word Arithmetic Problems." Psychological Review 92, no. 1 : 109 – 129. https://doi.org/10.1037/0033-295X.92.1.109.</bibtext> </blist> <blist> <bibtext> Kong, J. E., C. Yan, A. Serceki, and H. L. Swanson. 2021. " Word‐Problem‐Solving Interventions for Elementary Students With Learning Disabilities: A Selective Meta‐Analysis of the Literature." Learning Disability Quarterly 44, no. 4 : 248 – 260. https://doi.org/10.1177/0731948721994843.</bibtext> </blist> <blist> <bibtext> Lee, K., S. F. Ng, and R. Bull. 2018. " Learning and Solving Algebra Word Problems: The Roles of Relational Skills, Arithmetic, and Executive Functioning." Developmental Psychology 54 : 1758 – 1772. https://doi.org/10.1037/dev0000561.</bibtext> </blist> <blist> <bibtext> Locuniak, M. N., and N. C. Jordan. 2008. " Using Kindergarten Number Sense to Predict Calculation Fluency in Second Grade." Journal of Learning Disabilities 41, no. 5 : 451 – 459. https://doi.org/10.1177/0022219408321126.</bibtext> </blist> <blist> <bibtext> Matthews, P., and B. Rittle‐Johnson. 2009. " In Pursuit of Knowledge: Comparing Self‐Explanations, Concepts, and Procedures as Pedagogical Tools." Journal of Experimental Child Psychology 104, no. 1 : 1 – 21. https://doi.org/10.1016/j.jecp.2008.08.004.</bibtext> </blist> <blist> <bibtext> National Governors Association Center for Best Practices & Council of Chief State School Officers. 2010. Common Core State Standards for Mathematics.</bibtext> </blist> <blist> <bibtext> Nesher, P., J. G. Greeno, and M. S. Riley. 1982. " The Development of Semantic Categories for Addition and Subtraction." Educational Studies in Mathematics 13 : 373 – 394. https://doi.org/10.1007/bf00366618.</bibtext> </blist> <blist> <bibtext> Ng, J., K. Lee, and K. H. Khng. 2017. " Irrelevant Information in Math Problems Need Not be Inhibited: Students Might Just Need to Spot Them." Learning and Individual Differences 60 : 46 – 55. https://doi.org/10.1016/j.lindif.2017.09.008.</bibtext> </blist> <blist> <bibtext> Orlando, M., and D. Thissen. 2000. " Likelihood‐Based Item Fit Indices for Dichotomous Item Response Theory Models." Applied Psychological Measurement 24, no. 1 : 50 – 64. https://doi.org/10.1177/01466216000241003.</bibtext> </blist> <blist> <bibtext> Peake, C., J. E. Jiménez, C. Rodríguez, E. Bisschop, and R. Villarroel. 2015. " Syntactic Awareness and Arithmetic Word Problem Solving in Children With and Without Learning Disabilities." Journal of Learning Disabilities 48, no. 6 : 593 – 601. https://doi.org/10.1177/0022219413520183.</bibtext> </blist> <blist> <bibtext> Pearce, D. L., F. Bruun, K. Skinner, and C. Lopez‐Mohler. 2013. " What Teachers Say About Student Difficulties Solving Mathematical Word Problems in Grades 2–5." International Electronic Journal of Mathematics Education 8, no. 1 : 3 – 19. https://doi.org/10.29333/iejme/271.</bibtext> </blist> <blist> <bibtext> Pearson, A. 2019. Stanford Achievement Test Series – Tenth Edition.</bibtext> </blist> <blist> <bibtext> Pearson, A. 2020. Wechsler Individual Achievement Test.</bibtext> </blist> <blist> <bibtext> Peltier, C., T. E. Sinclair, J. M. Pulos, and A. Suk. 2020. " Effects of Schema‐Based Instruction on Immediate, Generalized, and Combined Structured Word Problems." Journal of Special Education 54, no. 2 : 101 – 112. https://doi.org/10.1177/0022466919883397.</bibtext> </blist> <blist> <bibtext> Powell, S. R. 2007. Open Equations. Available from S. R. Powell, 1912 Speedway, D5300, Austin, TX 78712.</bibtext> </blist> <blist> <bibtext> Powell, S. R., and K. A. Berry. 2015. Additive Word‐Problem Screener. Available from S. R. Powell, 1912 Speedway, D5300, Austin, TX 78712.</bibtext> </blist> <blist> <bibtext> Powell, S. R., K. A. Berry, and M. A. Barnes. 2019. " The Role of Pre‐Algebraic Reasoning Within a Word‐Problem Intervention for Third‐Grade Students With Mathematics Difficulty." ZDM 52 : 151 – 163. https://doi.org/10.1007/s11858-019-01093-1.</bibtext> </blist> <blist> <bibtext> Powell, S. R., K. A. Berry, and S. A. Benz. 2020. " Analyzing the Word‐Problem Performance and Strategies of Students Experiencing Mathematics Difficulty." Journal of Mathematical Behavior 58 : 100759. https://doi.org/10.1016/j.jmathb.2020.100759.</bibtext> </blist> <blist> <bibtext> Powell, S. R., K. A. Berry, A.‐M. Fall, G. Roberts, L. S. Fuchs, and M. A. Barnes. 2021. " Alternative Paths to Improved Word‐Problem Performance: An Advantage for Embedding Pre‐Algebraic Reasoning Instruction Within Word‐Problem Intervention." Journal of Educational Psychology 113, no. 5 : 898 – 910. https://doi.org/10.1037/edu0000513.</bibtext> </blist> <blist> <bibtext> Powell, S. R., J. M. Namkung, and X. Lin. 2022. " An Investigation of Using Keywords to Solve Word Problems." Elementary School Journal 122, no. 3 : 452 – 473. https://doi.org/10.1086/717888.</bibtext> </blist> <blist> <bibtext> Reise, S. P., D. S. Kim, M. Mansolf, and K. F. Widaman. 2016. " Is the Bifactor Model a Better Model or Is It Just Better at Modeling Implausible Responses? Application of Iteratively Reweighted Least Squares to the Rosenberg Self‐Esteem Scale." Multivariate Behavioral Research 51, no. 6 : 818 – 838. https://doi.org/10.1080/00273171.2016.1243461.</bibtext> </blist> <blist> <bibtext> Riley, M. S., J. G. Greeno, and J. I. Heller. 1984. " Development of Children's Problem‐Solving Ability in Arithmetic." In The Development of Mathematical Thinking, edited by H. P. Ginsburg, 153 – 196. Academic Press.</bibtext> </blist> <blist> <bibtext> Schrank, R. A., K. S. McGrew, and N. Mather. 2014. Woodcock‐Johnson IV. Riverside.</bibtext> </blist> <blist> <bibtext> Sharpe, S. T., R. Fults, and J. Krawec. 2014. " The Effects of a Mathematical Problem‐Solving Intervention on the Errors Made by Middle School Students With and Without Learning Disabilities." Middle Grades Research Journal 9 : 43 – 59.</bibtext> </blist> <blist> <bibtext> Shum, H. Y., and W. W. L. Chan. 2020. " Young Children's Inhibition of Keyword Heuristic in Solving Arithmetic Word Problems." Human Behavior and Brain 1, no. 2 : 43 – 48.</bibtext> </blist> <blist> <bibtext> State of Texas Assessments of Academic Readiness. 2023. Grade 3 mathematics. State of Texas. https://tea.texas.gov/student-assessment/testing/staar/staar-released-test-questions.</bibtext> </blist> <blist> <bibtext> Stevens, E. A., A. J. Leroux, M. H. Mowbray, and G. S. Lee. 2022. " Evaluating the Effects of Adding Explicit Vocabulary Instruction to a Word‐Problem Schema Intervention." Exceptional Children 89, no. 3 : 275 – 293. https://doi.org/10.1177/00144029221112290.</bibtext> </blist> <blist> <bibtext> Swanson, H. L., M. J. Orosco, and C. M. Lussier. 2014. " The Effects of Mathematics Strategy Instruction for Children With Serious Problem‐Solving Difficulties." Exceptional Children 80, no. 2 : 149 – 168. https://doi.org/10.1177/001440291408000202.</bibtext> </blist> <blist> <bibtext> Sweller, J. 1988. " Cognitive Load During Problem Solving: Effects on Learning." Cognitive science 12, no. 2 : 257 – 285. https://doi.org/10.1016/0364-0213(88)90023-7.</bibtext> </blist> <blist> <bibtext> Thevenot, C., and J. Oakhill. 2006. " Representations and Strategies for Solving Dynamic and Static Arithmetic Word Problems: The Role of Working Memory Capacities." European Journal of Cognitive Psychology 18, no. 5 : 756 – 775. https://doi.org/10.1080/09541440500412270.</bibtext> </blist> <blist> <bibtext> Van de Walle, J. A., K. S. Karp, and J. M. Bay‐Williams. 2022. Elementary and Middle School Mathematics: Teaching Developmentally. Pearson.</bibtext> </blist> <blist> <bibtext> Wang, A. Y., L. S. Fuchs, and D. Fuchs. 2016. " Cognitive and Linguistic Predictors of Mathematical Word Problems With and Without Irrelevant Information." Learning and Individual Differences 52 : 79 – 87. https://doi.org/10.1016/j.lindif.2016.10.015.</bibtext> </blist> <blist> <bibtext> Willis, G. B., and K. C. Fuson. 1988. " Teaching Children to Use Schematic Drawings to Solve Addition and Subtraction Word Problems." Journal of Educational Psychology 80, no. 2 : 192 – 201. https://doi.org/10.1037/0022-0663.80.2.192.</bibtext> </blist> <blist> <bibtext> Xin, Y. P., D. Zhang, J. Y. Park, K. Tom, A. Whipple, and L. Si. 2011. " A Comparison of Two Mathematics Problem‐Solving Strategies: Facilitate Algebra‐Readiness." Journal of Educational Research 104 : 381 – 395. https://doi.org/10.1080/00220671.2010.487080.</bibtext> </blist> <blist> <bibtext> Zheng, X., L. J. Flynn, and H. L. Swanson. 2013. " Experimental Intervention Studies on Word Problem Solving and Math Disabilities: A Selective Analysis of the Literature." Learning Disability Quarterly 36, no. 2 : 97 – 111. https://doi.org/10.1177/0731948712444277.</bibtext> </blist> </ref> <aug> <p>By Alison M. Hardy; J. E. Miller; Sarah R. Powell and Nancy Scammacca</p> <p>Reported by Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib33" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib53" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib47" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib56" firstref="ref4"></nolink> <nolink nlid="nl5" bibid="bib49" firstref="ref5"></nolink> <nolink nlid="nl6" bibid="bib60" firstref="ref6"></nolink> <nolink nlid="nl7" bibid="bib10" firstref="ref9"></nolink> <nolink nlid="nl8" bibid="bib28" firstref="ref10"></nolink> <nolink nlid="nl9" bibid="bib34" firstref="ref11"></nolink> <nolink nlid="nl10" bibid="bib17" firstref="ref13"></nolink> <nolink nlid="nl11" bibid="bib44" firstref="ref14"></nolink> <nolink nlid="nl12" bibid="bib46" firstref="ref15"></nolink> <nolink nlid="nl13" bibid="bib54" firstref="ref16"></nolink> <nolink nlid="nl14" bibid="bib25" firstref="ref18"></nolink> <nolink nlid="nl15" bibid="bib58" firstref="ref20"></nolink> <nolink nlid="nl16" bibid="bib37" firstref="ref26"></nolink> <nolink nlid="nl17" bibid="bib18" firstref="ref27"></nolink> <nolink nlid="nl18" bibid="bib30" firstref="ref29"></nolink> <nolink nlid="nl19" bibid="bib57" firstref="ref30"></nolink> <nolink nlid="nl20" bibid="bib11" firstref="ref32"></nolink> <nolink nlid="nl21" bibid="bib52" firstref="ref33"></nolink> <nolink nlid="nl22" bibid="bib24" firstref="ref35"></nolink> <nolink nlid="nl23" bibid="bib35" firstref="ref36"></nolink> <nolink nlid="nl24" bibid="bib59" firstref="ref37"></nolink> <nolink nlid="nl25" bibid="bib21" firstref="ref38"></nolink> <nolink nlid="nl26" bibid="bib51" firstref="ref39"></nolink> <nolink nlid="nl27" bibid="bib26" firstref="ref41"></nolink> <nolink nlid="nl28" bibid="bib29" firstref="ref42"></nolink> <nolink nlid="nl29" bibid="bib14" firstref="ref43"></nolink> <nolink nlid="nl30" bibid="bib16" firstref="ref44"></nolink> <nolink nlid="nl31" bibid="bib20" firstref="ref45"></nolink> <nolink nlid="nl32" bibid="bib41" firstref="ref46"></nolink> <nolink nlid="nl33" bibid="bib55" firstref="ref48"></nolink> <nolink nlid="nl34" bibid="bib61" firstref="ref49"></nolink> <nolink nlid="nl35" bibid="bib62" firstref="ref50"></nolink> <nolink nlid="nl36" bibid="bib50" firstref="ref56"></nolink> <nolink nlid="nl37" bibid="bib40" firstref="ref57"></nolink> <nolink nlid="nl38" bibid="bib39" firstref="ref59"></nolink> <nolink nlid="nl39" bibid="bib27" firstref="ref60"></nolink> <nolink nlid="nl40" bibid="bib43" firstref="ref63"></nolink> <nolink nlid="nl41" bibid="bib19" firstref="ref66"></nolink> <nolink nlid="nl42" bibid="bib22" firstref="ref67"></nolink> <nolink nlid="nl43" bibid="bib31" firstref="ref68"></nolink> <nolink nlid="nl44" bibid="bib12" firstref="ref74"></nolink> <nolink nlid="nl45" bibid="bib42" firstref="ref76"></nolink> <nolink nlid="nl46" bibid="bib32" firstref="ref77"></nolink> <nolink nlid="nl47" bibid="bib23" firstref="ref80"></nolink> <nolink nlid="nl48" bibid="bib48" firstref="ref81"></nolink> <nolink nlid="nl49" bibid="bib36" firstref="ref82"></nolink> <nolink nlid="nl50" bibid="bib13" firstref="ref86"></nolink> <nolink nlid="nl51" bibid="bib15" firstref="ref88"></nolink> <nolink nlid="nl52" bibid="bib45" firstref="ref89"></nolink> <nolink nlid="nl53" bibid="bib38" firstref="ref90"></nolink>
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  Data: Identifying Word-Problem Difficulty: An Item Response Analysis of an Additive Word-Problem Screener
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  Data: <searchLink fieldCode="AR" term="%22Alison+M%2E+Hardy%22">Alison M. Hardy</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0002-5197-9223">0009-0002-5197-9223</externalLink>)<br /><searchLink fieldCode="AR" term="%22J%2E+E%2E+Miller%22">J. E. Miller</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-9258-8774">0000-0002-9258-8774</externalLink>)<br /><searchLink fieldCode="AR" term="%22Sarah+R%2E+Powell%22">Sarah R. Powell</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-6424-6160">0000-0002-6424-6160</externalLink>)<br /><searchLink fieldCode="AR" term="%22Nancy+Scammacca%22">Nancy Scammacca</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-7484-5976">0000-0002-7484-5976</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22Psychology+in+the+Schools%22"><i>Psychology in the Schools</i></searchLink>. 2025 62(10):3912-3925.
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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: Institute of Education Sciences (ED)
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  Data: Journal Articles<br />Reports - Research
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  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Word+Problems+%28Mathematics%29%22">Word Problems (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Students%22">Secondary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Difficulty+Level%22">Difficulty Level</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Problems%22">Learning Problems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Tests%22">Mathematics Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Screening+Tests%22">Screening Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Test+Theory%22">Test Theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computation%22">Computation</searchLink><br /><searchLink fieldCode="DE" term="%22Identification%22">Identification</searchLink><br /><searchLink fieldCode="DE" term="%22Intervention%22">Intervention</searchLink>
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  Data: 10.1002/pits.23582
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  Data: 0033-3085<br />1520-6807
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Students encounter hundreds of word problems throughout the elementary grades and on standardized assessments through high school. To demonstrate proficiency on these measures of mathematics competency, students must be skilled in solving word problems. Early detection of word-problem difficulty is essential, and screeners play an important role in early detection. There are, however, a limited number of word-problem screeners and very few nonproprietary brief screeners. Thus, this paper examines the "Additive Word-Problem Screener"--a 12-min, free-to-use, eight-problem screener. Through examination of classical test theory and calculation of item response theory statistics, we determined that the "Additive Word-Problem Screener" is a promising short-form screener for identifying students with word-problem difficulty.
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  Data: 2025
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  Data: EJ1483433
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        Value: 10.1002/pits.23582
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 14
        StartPage: 3912
    Subjects:
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Word Problems (Mathematics)
        Type: general
      – SubjectFull: Mathematics Education
        Type: general
      – SubjectFull: Secondary School Students
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Difficulty Level
        Type: general
      – SubjectFull: Learning Problems
        Type: general
      – SubjectFull: Mathematics Tests
        Type: general
      – SubjectFull: Screening Tests
        Type: general
      – SubjectFull: Test Theory
        Type: general
      – SubjectFull: Computation
        Type: general
      – SubjectFull: Identification
        Type: general
      – SubjectFull: Intervention
        Type: general
    Titles:
      – TitleFull: Identifying Word-Problem Difficulty: An Item Response Analysis of an Additive Word-Problem Screener
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              Value: 62
            – Type: issue
              Value: 10
          Titles:
            – TitleFull: Psychology in the Schools
              Type: main
ResultId 1