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Relational Thinking: An Overlooked Component of Executive Functioning

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Title: Relational Thinking: An Overlooked Component of Executive Functioning
Language: English
Authors: Starr, Ariel (ORCID 0000-0003-0433-5003), Leib, Elena R., Younger, Jessica W., Project iLead Consortium, Uncapher, Melina R., Bunge, Silvia A.
Source: Developmental Science. May 2023 26(3).
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: 18
Publication Date: 2023
Sponsoring Agency: Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD) (DHHS/NIH)
National Science Foundation (NSF)
Contract Number: F32HD085736
NSFSLCN1540854
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Junior High Schools
Middle Schools
Secondary Education
Descriptors: Thinking Skills, Executive Function, Task Analysis, Mathematics Skills, Mathematics Achievement, Elementary School Students, Middle School Students, Mathematics Tests, Scores, Fractions, Cognitive Ability
DOI: 10.1111/desc.13320
ISSN: 1363-755X
1467-7687
Abstract: Relational thinking, the ability to represent abstract, generalizable relations, is a core component of reasoning and human cognition. Relational thinking contributes to fluid reasoning and academic achievement, particularly in the domain of math. However, due to the complex nature of many fluid reasoning tasks, it has been difficult to determine the degree to which relational thinking has a separable role from the cognitive processes collectively known as executive functions (EFs). Here, we used a simplified reasoning task to better understand how relational thinking contributes to math achievement in a large, diverse sample of elementary and middle school students (N = 942). Students also performed a set of ten adaptive EF assessments, as well as tests of math fluency and fraction magnitude comparison. We found that relational thinking was significantly correlated with each of the three EF composite scores previously derived from this dataset, albeit no more strongly than they were with each other. Further, relational thinking predicted unique variance in students' math fluency and fraction magnitude comparison scores over and above the three EF composites. Thus, we propose that relational thinking be considered an EF in its own right as one of the core, mid-level cognitive abilities that supports cognition and goal-directed behavior.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1372378
Database: ERIC
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  Value: <anid>AN0162916547;5g501may.23;2023Apr07.05:49;v2.2.500</anid> <title id="AN0162916547-1">Relational thinking: An overlooked component of executive functioning </title> <p>Relational thinking, the ability to represent abstract, generalizable relations, is a core component of reasoning and human cognition. Relational thinking contributes to fluid reasoning and academic achievement, particularly in the domain of math. However, due to the complex nature of many fluid reasoning tasks, it has been difficult to determine the degree to which relational thinking has a separable role from the cognitive processes collectively known as executive functions (EFs). Here, we used a simplified reasoning task to better understand how relational thinking contributes to math achievement in a large, diverse sample of elementary and middle school students (N = 942). Students also performed a set of ten adaptive EF assessments, as well as tests of math fluency and fraction magnitude comparison. We found that relational thinking was significantly correlated with each of the three EF composite scores previously derived from this dataset, albeit no more strongly than they were with each other. Further, relational thinking predicted unique variance in students' math fluency and fraction magnitude comparison scores over and above the three EF composites. Thus, we propose that relational thinking be considered an EF in its own right as one of the core, mid‐level cognitive abilities that supports cognition and goal‐directed behavior. Research Highlights: Relational thinking, the process of identifying and integrating relations, develops over childhood and is central to reasoning.We collected data from nearly 1000 elementary and middle schoolers on a test of relational thinking, ten standard executive function tasks, and two math tests.Relational thinking predicts unique variance in math achievement not accounted for by canonical EFs throughout middle childhood.We propose that relational thinking should be conceptualized as a core executive function that supports cognitive development and learning.</p> <p>Keywords: executive functions; reasoning; relational thinking; math; fractions; academic achievement</p> <p>Relational thinking, the process of identifying and integrating relations, develops over childhood and is central to reasoning. Using data from a sample of nearly 1,000 elementary and middle school students, we found that relational thinking predicts unique variance in math achievement not accounted for by the canonical executive functions. We propose that relational thinking should be conceptualized as a core executive function that supports cognitive development and academic achievement.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01may23/desc13320-gra-0001.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="desc13320-gra-0001.jpg" title="." /> </p> <p></p> <hd id="AN0162916547-3">INTRODUCTION</hd> <p>Relational thinking, or the process of identifying and integrating relations, is regularly invoked during reasoning (Doumas et al., [<reflink idref="bib22" id="ref1">22</reflink>]). Among other things, it enables us to draw higher‐order abstractions and generalize across situations and contexts (Gentner, [<reflink idref="bib33" id="ref2">33</reflink>]). Relational thinking is central to measures of fluid reasoning, and the terms reasoning and non‐verbal intelligence are sometimes used interchangeably to describe aspects of intelligence that are separable from crystallized intelligence (Carpenter et al., [<reflink idref="bib10" id="ref3">10</reflink>]; Cattell, [<reflink idref="bib13" id="ref4">13</reflink>]). Although some other animals can represent abstract relations between items, such as <emph>same</emph> and <emph>different</emph>, humans are unparalleled with respect to the ability to consider and integrate relations (Gentner et al., [<reflink idref="bib34" id="ref5">34</reflink>]; Penn et al., [<reflink idref="bib57" id="ref6">57</reflink>]; Thompson & Oden, [<reflink idref="bib81" id="ref7">81</reflink>]). For example, we can use analogical reasoning to intuit that the relation between a hand and a glove and is the same as that between a foot and a sock. Likewise, we can use transitive inference to deduce that if a cat is bigger than a squirrel and a squirrel is bigger than a mouse, then a cat is bigger than a mouse. Here, we argue that relational thinking is a core cognitive ability that should be considered an executive function (EF).</p> <p>EFs are construed as a constellation of domain‐general, effortful cognitive processes that are critical for goal‐directed behavior (Diamond, [<reflink idref="bib21" id="ref8">21</reflink>]), flexible thinking and problem solving (Cragg & Gilmore, [<reflink idref="bib19" id="ref9">19</reflink>]; Lehto et al., [<reflink idref="bib49" id="ref10">49</reflink>]), reasoning (Richland & Burchinal, [<reflink idref="bib63" id="ref11">63</reflink>]; Richland et al., [<reflink idref="bib66" id="ref12">66</reflink>]), and, as a result, academic performance (Best et al., [<reflink idref="bib3" id="ref13">3</reflink>]; Lawson & Farah, [<reflink idref="bib47" id="ref14">47</reflink>]; Rose et al., [<reflink idref="bib69" id="ref15">69</reflink>]). As such, they can be thought of as mid‐level cognitive processes situated between basic perceptual, attentional, and motor processes, on the one hand, and high‐level cognitive abilities (e.g., language, reading, math) on the other. Developmental psychology research on EFs commonly focuses on three putative core abilities: inhibition (the ability to selectively control attention and resist interference), working memory (the ability to hold, update, and manipulate information in mind), and cognitive flexibility (the ability to switch between perspectives, rules, and schemas as needed on a moment‐to‐moment basis; also referred to as shifting) (Diamond, [<reflink idref="bib21" id="ref16">21</reflink>]; Lehto et al., [<reflink idref="bib49" id="ref17">49</reflink>]; Miyake et al., [<reflink idref="bib56" id="ref18">56</reflink>]; Rose et al., [<reflink idref="bib69" id="ref19">69</reflink>]). These three EFs are theorized to be distinct abilities that frequently interact to support high‐level cognition and behavior. Many previous studies on the development and structure of EFs have focused on this hypothesized structure and chosen tasks that map onto these components (Hughes et al., [<reflink idref="bib40" id="ref20">40</reflink>]; Huizinga et al., [<reflink idref="bib41" id="ref21">41</reflink>]; Lee et al., [<reflink idref="bib48" id="ref22">48</reflink>]; Lehto et al., [<reflink idref="bib49" id="ref23">49</reflink>]).</p> <p>Even within these three canonical components of EF, however, there is variability in how each is conceptualized. For example, the inhibition construct combines inhibition of attention and inhibition of action, though these two types of inhibition may be cognitively and neurally distinct (Bunge et al., [<reflink idref="bib8" id="ref24">8</reflink>]; Diamond, [<reflink idref="bib21" id="ref25">21</reflink>]). Furthermore, there is no single gold‐standard definition of what makes a cognitive ability an EF, and the EF components found in any particular study are directly related to the selected tasks. More broadly, there is no agreed upon taxonomy of EFs across psychology and neuroscience.</p> <p>Like the canonical EFs, relational thinking has long been viewed as a domain‐general, effortful, mid‐level cognitive process that is central to higher‐level human cognition—in particular, various forms of reasoning (Alexander, [<reflink idref="bib1" id="ref26">1</reflink>]; Cattell, [<reflink idref="bib13" id="ref27">13</reflink>]; Halford et al., [<reflink idref="bib38" id="ref28">38</reflink>]). Despite this parallel conceptualization, relational thinking tasks have not been included in studies assessing the structure of EFs. As a result, these standard models do not involve a relational component. However, this historical precedent in and of itself does not mean that relational thinking should not be considered an EF.</p> <p>To tackle the question of whether relational thinking should be conceptualized as an EF, it is important to test whether it is distinct from the canonical EFs. Many previous studies have noted a relation between reasoning abilities and EFs (e.g., Conway et al., [<reflink idref="bib17" id="ref29">17</reflink>]; Duncan et al., [<reflink idref="bib24" id="ref30">24</reflink>]; Engle et al., [<reflink idref="bib25" id="ref31">25</reflink>]; Friedman et al., [<reflink idref="bib28" id="ref32">28</reflink>]; van Aken et al., [<reflink idref="bib83" id="ref33">83</reflink>], see Diamond, [<reflink idref="bib21" id="ref34">21</reflink>] for review). Broadly, these studies demonstrate that individuals who score higher on standard measures of EFs also tend to score higher on standard measures of reasoning. In particular, working memory and inhibitory control are frequently found to correlate positively with reasoning in both adults (Grossnickle et al., [<reflink idref="bib36" id="ref35">36</reflink>]; Krawczyk et al., [<reflink idref="bib45" id="ref36">45</reflink>]) and children (Fry & Hale, [<reflink idref="bib29" id="ref37">29</reflink>]; Richland & Burchinal, [<reflink idref="bib63" id="ref38">63</reflink>]; Richland et al., [<reflink idref="bib66" id="ref39">66</reflink>]; Starr et al., [<reflink idref="bib74" id="ref40">74</reflink>]; Thibaut & French, [<reflink idref="bib80" id="ref41">80</reflink>]; Thibaut et al., [<reflink idref="bib79" id="ref42">79</reflink>]).</p> <p>The tight relation between reasoning and EFs has led some researchers to conclude that reasoning is not actually a separable ability from EFs (Martínez et al., [<reflink idref="bib51" id="ref43">51</reflink>]), whereas others have suggested that EFs explain only about half of the variance in reasoning ability (Friedman et al., [<reflink idref="bib28" id="ref44">28</reflink>]). These arguments have been clouded by the fact that most measures of reasoning are complex and engage canonical EFs as well as relational thinking, which makes it difficult to determine whether this overlap stems from confounds in tasks themselves versus a true association between the underlying abilities.</p> <p>Breaking down the steps required to solve classic matrix reasoning tasks (Cattell, [<reflink idref="bib12" id="ref45">12</reflink>]; Raven, [[<reflink idref="bib61" id="ref46">61</reflink>]]) highlights how both relational thinking and canonical EF abilities are required for success. Matrix reasoning tasks are frequently used as a stand‐alone fluid reasoning task but are also a typical component of nonverbal intelligence tests (e.g., the Wechsler Adult Intelligence Scale; Wechsler, [<reflink idref="bib85" id="ref47">85</reflink>]). In this type of task, participants are shown a grid of visuospatial designs with one item missing, and participants must choose the correct item to complete the pattern from an array of choice items. For example, the grid may be organized such that rows of items vary along one relation (e.g., size) and the columns vary along another relation (e.g., shape). Selecting the correct item that completes the grid requires integrating the two separate relations in order to identify the item that completes the pattern in both dimensions. Therefore, in addition to identifying and integrating relations, the task also engages working memory to maintain and manipulate the different critical relations in the focus of attention and inhibitory control to resist selecting salient distractor items (Chen et al., [<reflink idref="bib14" id="ref48">14</reflink>]; Matzen & Van der Molen, [<reflink idref="bib52" id="ref49">52</reflink>]; Sternberg, [<reflink idref="bib76" id="ref50">76</reflink>]; Stevenson & Hickendorff, [<reflink idref="bib77" id="ref51">77</reflink>]). Other complex reasoning tasks similarly tap both relational thinking and canonical EFs (Richland & Morrison, [<reflink idref="bib65" id="ref52">65</reflink>]; Richland et al., [<reflink idref="bib66" id="ref53">66</reflink>]; Starr et al., [<reflink idref="bib74" id="ref54">74</reflink>]; Thibaut et al., [<reflink idref="bib79" id="ref55">79</reflink>]). Therefore, an important first step for understanding how relational thinking relates to canonical EFs is to design a task that engages relational thinking while minimizing demands on other EFs.</p> <p>EFs are often described as processes that support academic achievement; thus, exploring the unique contribution of relational thinking to math performance is germane to the question of whether it should be considered an EF. EFs are strong predictors of academic achievement throughout childhood and adolescence (Best et al., [<reflink idref="bib3" id="ref56">3</reflink>]; Cowan, [<reflink idref="bib18" id="ref57">18</reflink>]; Ferrer & McArdle, [<reflink idref="bib26" id="ref58">26</reflink>]; Ferrer et al., [<reflink idref="bib27" id="ref59">27</reflink>]; Richland et al., [<reflink idref="bib68" id="ref60">68</reflink>]; St Clair‐Thompson & Gathercole, [<reflink idref="bib75" id="ref61">75</reflink>]). This relation has been particularly well‐documented in the domain of mathematics: children who score higher on EF assessments also typically score higher on lab‐based and school‐based math assessments (Bull & Scerif, [<reflink idref="bib7" id="ref62">7</reflink>]; Fuchs et al., [<reflink idref="bib30" id="ref63">30</reflink>]; Geary, [<reflink idref="bib32" id="ref64">32</reflink>]; Green et al., [<reflink idref="bib35" id="ref65">35</reflink>]; Purpura & Ganley, [<reflink idref="bib59" id="ref66">59</reflink>]; Richland et al., [<reflink idref="bib68" id="ref67">68</reflink>]; St Clair‐Thompson & Gathercole, [<reflink idref="bib75" id="ref68">75</reflink>]; Taub et al., [<reflink idref="bib78" id="ref69">78</reflink>]). Some of the ways EFs support math achievement include helping learners maintain relevant knowledge in mind (working memory), inhibit inappropriate strategies (inhibitory control), and switching between different strategies (cognitive flexibility) (Bull & Lee, [<reflink idref="bib6" id="ref70">6</reflink>]; Cragg & Gilmore, [<reflink idref="bib19" id="ref71">19</reflink>]).</p> <p>In parallel to the research linking canonical EFs to math achievement, a number of studies have demonstrated that reasoning ability predicts both current and future math abilities (Fuchs et al., [<reflink idref="bib31" id="ref72">31</reflink>]; Green et al., [<reflink idref="bib35" id="ref73">35</reflink>]; Taub et al., [<reflink idref="bib78" id="ref74">78</reflink>]). Mathematical thinking is inherently relational (DeWolf et al., [<reflink idref="bib20" id="ref75">20</reflink>]; Miller Singley & Bunge, [<reflink idref="bib54" id="ref76">54</reflink>]; Richland et al., [<reflink idref="bib68" id="ref77">68</reflink>]). Students who conceptualize math as a relational system are more successful in tackling novel problem types and formats than students who conceptualize math as a set of explicit rules and procedures (Richland et al., [<reflink idref="bib67" id="ref78">67</reflink>]). The importance of relational thinking for math is particularly evident for concepts like equivalence, algebra, and fractions. With respect to fractions, for example, the magnitude of a fraction is equivalent to the relation between the numerator and the denominator, and comparing fractions therefore requires integrating the relation between one numerator and denominator with the relation between the other numerator and denominator (Bonato et al., [<reflink idref="bib5" id="ref79">5</reflink>]; Miller Singley & Bunge, [<reflink idref="bib54" id="ref80">54</reflink>]). Previous studies have found associations between children's performance on fraction comparison tasks and both reasoning and EF measures (DeWolf et al., [<reflink idref="bib20" id="ref81">20</reflink>]; Hecht et al., [<reflink idref="bib39" id="ref82">39</reflink>]; Kalra et al., [<reflink idref="bib43" id="ref83">43</reflink>]; Miller Singley & Bunge, [<reflink idref="bib55" id="ref84">55</reflink>]; Siegler & Pyke, [<reflink idref="bib72" id="ref85">72</reflink>]).</p> <p>However, as previously described, the complex nature of many reasoning tasks muddles the interpretation of these relations between EFs, reasoning, and math achievement. Based on the current research, it is unclear whether relational thinking and canonical EFs are explaining unique or overlapping variance in children's math achievement. Clarifying the relation between relational thinking, EFs, and math is necessary to better understand the foundational skills required for students to succeed with mathematical concepts.</p> <p>The goals of the present study were threefold. First, we aimed to assess age‐related differences and individual variability on a simplified relational thinking task in a large developmental sample. Second, we sought to examine the degree to which relational thinking can be considered a separable construct from EFs that are thought to contribute to reasoning, namely working memory and inhibitory control. Finally, we further explored the hypothesis that relational thinking should be considered a distinct EF by testing whether it independently contributes to math performance, over and above common measures of EF.</p> <p>The relational thinking task used here is a form of relational match‐to‐sample task (Christie & Genter, [<reflink idref="bib15" id="ref86">15</reflink>]; Christoff et al., [<reflink idref="bib16" id="ref87">16</reflink>]; Premack, [<reflink idref="bib58" id="ref88">58</reflink>]; Smith, [<reflink idref="bib73" id="ref89">73</reflink>]; Thompson & Oden, [<reflink idref="bib81" id="ref90">81</reflink>]). It takes the form of proportional analogies (A:B::C:D), but has no semantic component and therefore requires little or no prior knowledge (Figure 1). Briefly, this task requires participants to jointly consider the relations between two pairs of simple visual stimuli that vary along either two or three dimensions in order to determine whether the two pairs share the same relation (e.g., both match in shape). We created two levels of relational complexity (Halford et al., [<reflink idref="bib37" id="ref91">37</reflink>]) within this task. The first level requires consideration of two features, as in prior work (Christoff et al., [<reflink idref="bib16" id="ref92">16</reflink>]; Dumontheil et al., [<reflink idref="bib23" id="ref93">23</reflink>]; Wendelken et al., [<reflink idref="bib86" id="ref94">86</reflink>]); the second is a novel, more challenging level that requires consideration of three features. We designed this measure such that it can be administered efficiently in a group setting for use with large‐scale data collection (Uncapher, [<reflink idref="bib82" id="ref95">82</reflink>]).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01may23/desc13320-fig-0001.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="desc13320-fig-0001.jpg" title="1 Four sample trials from the relational thinking task. In Level 1 (top), both pairs of images must match in the same dimension to be classified as a match. In Level 2 (bottom), both pairs of images must match in two dimensions to be classified as a match. Participants must identify the dimensions along which items match; labels are shown in the figure for illustrative purposes only. The hands, also for illustrative purposes only, indicate the correct response option for each trial" /> </p> <p></p> <p>This task explicitly taps relational thinking skills, and there are critical differences in its design that reduce demand on EFs in comparison to standard reasoning tasks. First, the task contains only four elements and a two‐alternative forced‐choice answer structure to reduce demands on working memory and inhibitory control. On each trial, participants must decide only whether the items do or do not match, rather than choosing between up to eight answer choices. Second, participants are told the rules in advance and must only follow those two or three rules (depending on the level of relational complexity), rather than needing to induce multiple novel rules on their own (Carpenter et al., [<reflink idref="bib10" id="ref96">10</reflink>]). Finally, the task involves only a small set of geometric shapes, rather than familiar real‐world objects, to minimize the involvement of semantic knowledge. By reducing the number of elements—both sample and choice items—involved in the task, specifying a limited set of rules in advance, and using basic shapes, this relational thinking task is designed to isolate relational thinking while minimizing the involvement of other EFs. However, we do not consider it possible to fully eliminate demands on canonical EFs in any task that requires rule‐guided behavior (Bunge & Zelazo, [<reflink idref="bib9" id="ref97">9</reflink>]) – any more than we consider it possible to devise a "pure" EF task, as even the canonical EFs are theorized to interact with one another (Blackwell et al., [<reflink idref="bib4" id="ref98">4</reflink>]; Diamond, [<reflink idref="bib21" id="ref99">21</reflink>]).</p> <p>We addressed our aims in the context of a large, longitudinal investigation of the development of EF components across Grades 3–8. Participants in this study completed a battery of t EF tasks from the Adaptive Cognitive Evaluation (ACE) battery (Younger et al., [<reflink idref="bib88" id="ref100">88</reflink>]). A primary analysis of the ACE data, which used exploratory factor analysis methods to uncover how the different tasks grouped together, will be published separately (Younger et al., [<reflink idref="bib87" id="ref101">87</reflink>]). Based on these analyses, we used composite scores to index three putative EFs: working memory, interference resolution and response inhibition (different forms of inhibitory control, involving suppression of visual distractors and motoric responses, respectively), as well as a single measure of cognitive flexibility. In addition, participants completed the relational thinking task and a battery of scholastic achievement tasks that included of tests of math fluency and fraction comparison. The present series of analyses relate children's relational thinking task performance to individual differences in the three EF composite scores, cognitive flexibility, math fluency, and fraction comparison scores. We focus on children in 4th, 6th, and 8th grades in order to investigate how the relations between these different abilities change between elementary and middle school.</p> <hd id="AN0162916547-5">METHOD</hd> <p></p> <hd id="AN0162916547-6">Participants</hd> <p>Participants in the present study were part of Project iLead, a 2‐year, multi‐site study investigating EF development throughout elementary and middle school (Younger et al., [<reflink idref="bib88" id="ref102">88</reflink>]). Data collection took place at nine schools in northern California. In total, 1280 students participated over the course of 2 years. The data described here come from year two of the study, which included 288 fourth graders, 336 sixth graders, and 482 eighth graders. Of those participants, 243 fourth graders, 270 sixth graders, and 429 eighth graders had valid data for the relational thinking task and were included in our analyses. The demographic characteristics of our sample are detailed in Table 1.</p> <p>1 TABLE Demographic characteristics of sample</p> <p> <ephtml> <table><thead><tr><th>Variable</th><th align="left">Grade 4</th><th align="left">Grade 6</th><th align="left">Grade 8</th></tr></thead><tbody><tr><td>Age (years)</td><td align="left">9.81 (8.94, 11.90)</td><td align="left">11.75 (10.60, 13.26)</td><td align="left">13.76 (12.87, 15.35)</td></tr><tr><td>Gender</td><td /><td /><td /></tr><tr><td>Female</td><td>53%</td><td>49%</td><td>50%</td></tr><tr><td>Male</td><td>47%</td><td>51%</td><td>50%</td></tr><tr><td>Ethnicity</td><td /><td /><td /></tr><tr><td>American Indian or Alaskan Native</td><td>0%</td><td>0%</td><td>1.2%</td></tr><tr><td>Asian</td><td>50%</td><td>40%</td><td>35%</td></tr><tr><td>Black or African American</td><td>0.9%</td><td>2.5%</td><td>1.2%</td></tr><tr><td>Blank on purpose</td><td>0.5%</td><td>0%</td><td>0.2%</td></tr><tr><td>Filipino</td><td>3.3%</td><td>6.2%</td><td>7.9%</td></tr><tr><td>Hispanic or Latino</td><td>19%</td><td>28%</td><td>32%</td></tr><tr><td>Pacific Islander</td><td>0.5%</td><td>0.4%</td><td>0.2%</td></tr><tr><td>Two or more races</td><td>7.0%</td><td>3.7%</td><td>4.7%</td></tr><tr><td>White or Caucasian</td><td>19%</td><td>19%</td><td>18%</td></tr><tr><td>Eligible for free or reduced lunch</td><td>28%</td><td>35%</td><td>35%</td></tr></tbody></table> </ephtml> </p> <p>1 Because some parents opted not to share demographic data for their children, not all columns sum to 100%</p> <p>The study was performed in accordance with protocols approved by the Institutional Review Board (IRB) of the University of California, San Francisco. Written parental or guardian consent was obtained from all participants at the beginning of the study, and verbal assent from all participants was obtained before all in‐class data collection sessions. At the end of the study, all students in participating classrooms received snacks and stickers, regardless of their individual participation.</p> <hd id="AN0162916547-7">Procedure</hd> <p>Participants were tested during school hours at the beginning and end of each academic year (fall and spring) over two academic school years. EF and math fluency assessments occurred at all four time points. The reasoning and fraction tasks were part of one of two scholastic assessments that were administered to participants once per year in alternating semesters. Students were randomly assigned to complete each task set in either the fall or spring of each year. At each of the four timepoints, the EF assessments were administered first, and the scholastic assessments were administered approximately six weeks later (<emph>M</emph> = 5.7 weeks, <emph>SD</emph> = 2.4, min. = 1.9, max. = 10).</p> <p>All tasks were administered in a group setting on iPads. Each group administration was conducted by 4–12 researchers, in proportion to the student group size. A lead facilitator gave verbal instructions to the group for each task, aided by visual instructions from a 24″ × 36″ flipbook. Participants began each task at the same time, and instructions for the next task were not given until all participants completed the current task. Each task began with practice trials during which researchers monitored participants to ensure participants understood the task and were correctly following task instructions. Researchers monitored the sessions throughout administration to provide technical assistance, answer student questions, and monitor performance. Administration sessions lasted approximately 50 min.</p> <hd id="AN0162916547-8">Relational thinking task</hd> <p>The relational thinking task (Figure 1) was adapted from a task that has been used previously to study the neural correlates of relational reasoning and its development (Christoff et al., [<reflink idref="bib16" id="ref103">16</reflink>]; Dumontheil et al., [<reflink idref="bib23" id="ref104">23</reflink>]; Wendelken et al., [<reflink idref="bib86" id="ref105">86</reflink>]). The experimenter introduced the game by telling participants that in this game, "We want to see if the top row matches the bottom row using the same rule." On each trial, participants saw two pairs of items. In Level 1, the items varied in both color and shape. Participants decided whether the pairs matched along the same dimension (i.e., in both pairs, the items within each pair both matched or shape or color). If the items did match along the same direction, the participant was to press a button marked "YES" on the screen. If the items did not match along the same dimension, the participant was to press a button marked "NO" on the screen. Level 2 added the dimension of pattern: participants needed to decide whether the top and bottom pairs both followed the same two matching rules (i.e., they matched in shape and color, shape and pattern, or color and pattern). For this level, explicit instructions and practice trials made it clear that the pairs needed to match in two dimensions, and that pairs that matched in only one dimension were not matches. Participants again responded by pressing the "YES" or "NO" buttons on the screen.</p> <p>In each level, half of the trials represented matches and half of the trials were non‐matches. The order of the trials was randomized. The response window was 3.5 s in Level 1, and 4.5 s in Level 2. Participants completed three practice trials of Level 1 as a group and four practice trials individually with feedback before completing 20 Level 1 test trials without feedback. Next participants completed five Level 2 practice trials as a group and four practice trials individually, with feedback. However, only participants who achieved at least 75% accuracy on Level 1 moved onto the Level 2 test trials. Participants who scored below 75% completed Level 1 again, but only scores from the first round of gameplay were analyzed.</p> <hd id="AN0162916547-9">Math fluency task</hd> <p>Math fluency was measured using an assessment that tested participants' ability to quickly and accurately answer math problems, similar to the Math Fluency task of the Woodcock‐Johnson III Tests of Achievement (Schrank et al., [<reflink idref="bib70" id="ref106">70</reflink>]). The assessment required participants to solve single‐digit math equations (addition, subtraction, and multiplication) by typing the correct answer. Math equations were presented one at a time, and the task would not advance until a response was made for each trial. Participants were asked to solve as many equations as they were able in 3 min. Two practice trials were administered to ensure understanding. Scores were determined by the total number of correct responses.</p> <hd id="AN0162916547-10">Fraction comparison task</hd> <p>Proficiency with fractions was measured using an assessment that tested participants' ability to compare numerical magnitudes quickly and accurately. The task had three levels. Level 1 required participants to compare symbolic digits, and Levels 2 and 3 required them to compare symbolic fractions. In Levels 2 and 3, each trial presented two single‐digit fractions, side‐by‐side, and participants were instructed to indicate which fraction magnitude was larger. In Level 2, both fractions within a trial shared the same numerator or denominator (e.g., 2/3 vs. 1/3). In Level 3, the numerators and denominators always differed (e.g., 5/6 vs. 3/7). Participants responded by touching the larger fraction. Participants completed 16 trials each in Levels 2 and 3, with a response window of 4.5 s. Participants needed to answer at least 75% of the trials accurately in a given level to advance to the next level. Only data from Level 2 were included in the present analyses, because Level 1 did not involve fractions and few 4<sups>th</sups> grade students progressed to Level 3.</p> <hd id="AN0162916547-11">Executive function tasks</hd> <p>EFs were assessed with the Adaptive Cognitive Evaluation (ACE), an iPad‐based battery that assesses EF skills and is composed of ten tasks developed from commonly used EF assessments: basic response time, forward spatial span, backward spatial span, impulsive attention, sustained attention, tap and trace, color‐word Stroop, letter flanker, boxed, and task switch (Table 2; Younger et al., [<reflink idref="bib88" id="ref107">88</reflink>]). A full description of the ACE tasks and its adaptive algorithm can be found in Younger et al., [<reflink idref="bib88" id="ref108">88</reflink>].</p> <p>2 TABLE Overview of EF tasks in the ACE battery and labels provided for the EF composites derived from these tasks in the parent study (Younger et al., 2021)</p> <p> <ephtml> <table><thead><tr><th>Task name</th><th>Description</th><th>Theorized construct</th><th>EF composite</th></tr></thead><tbody><tr><td>Basic reaction time</td><td>Tap in response to visual targets</td><td>Processing speed</td><td>N/A (regressed from performance metrics of all other tasks to control for general differences in processing speed)</td></tr><tr><td>Forward spatial span</td><td>Tap to recreate cued spatial sequence of targets</td><td>Working memory</td><td>Working memory</td></tr><tr><td>Backward spatial span</td><td>Tap to recreate cued spatial sequence of targets in reverse order</td><td>Working memory</td><td>Working memory</td></tr><tr><td>Impulsive attention</td><td>Respond to frequent targets and withhold response to non‐targets</td><td>Inhibitory control</td><td>Response inhibition</td></tr><tr><td>Sustained attention</td><td>Respond to infrequent targets and withhold response to frequent non‐targets</td><td>Sustained attention</td><td>Response inhibition</td></tr><tr><td>Tap and trace</td><td>Tap with dominant hand and trace shapes with the non‐dominant hand</td><td>Dual‐task performance</td><td>Response inhibition</td></tr><tr><td>Stroop</td><td>Respond to text colors that are congruent or incongruent with semantic meaning</td><td>Inhibitory control</td><td>Interference resolution</td></tr><tr><td>Flanker</td><td>Respond to middle letters that are congruent or incongruent with flanking letters</td><td>Selective attention; Inhibitory control</td><td>Interference resolution</td></tr><tr><td>Boxed</td><td>Identify target stimuli within arrays of distractor stimuli</td><td>Visual search</td><td>Interference resolution</td></tr><tr><td>Task switch</td><td>Switch between responding to color or shape of target stimuli in response to pre‐trial cues</td><td>Cognitive flexibility</td><td>N/A (technical error prevented inclusion in factor analyses)</td></tr></tbody></table> </ephtml> </p> <p>Data from all four timepoints were previously analyzed using explanatory and confirmatory analysis methods to determine the underlying organization (Younger et al., [<reflink idref="bib87" id="ref109">87</reflink>]). These analyses revealed that a three‐factor model of EFs fit the data for all cohorts at all four timepoints. The three components were labeled response inhibition (sustained attention, impulsive attention, and tap and trace), interference resolution (Stroop, flanker, boxed), and working memory (forward and backward spatial span). Because the factor loadings varied slightly between cohorts and timepoints, we calculated composite scores for each factor by z‐scoring the individual task scores for each cohort and timepoint and then averaging the z‐scores for the tasks that comprised each factor. We used the three composite scores to index three EFs. In addition, as a measure of cognitive flexibility we used stand‐alone, z‐scored scores from the task switching task because a technical error at the first timepoint prevented scores from this task from being used in the factor analyses.</p> <hd id="AN0162916547-12">Data analysis</hd> <p>Data from the relational thinking and fraction comparison tasks were first cleaned by removing trials with response times that fell more than three median absolute deviations (MAD) above or below each participant's median response time (Leys et al., [<reflink idref="bib50" id="ref110">50</reflink>]). This removed approximately 3% of trials from relational thinking Levels 1 and 2 and approximately 4% of fraction comparison trials. For each task and level, participants needed to have valid response data (i.e., a response was recorded within three MAD of their median response time) on at least 2/3 of trials in order to be included in further analysis. Eleven participants in the relational thinking Level 1 task, three participants in the relational thinking Level 2 task, and five participants in the fraction comparison task did not have enough valid trials and were excluded. All data were analyzed in R. We used the lmerTest package (Kuznetsova et al., [<reflink idref="bib46" id="ref111">46</reflink>]) to conduct mixed‐effects models and compared successive models using the Anova function from the base stats package (R CoreTeam, [<reflink idref="bib60" id="ref112">60</reflink>]). We used the Raincloud package (Allen et al., [<reflink idref="bib2" id="ref113">2</reflink>]) to visualize group performance.</p> <hd id="AN0162916547-13">RESULTS</hd> <p></p> <hd id="AN0162916547-14">Relational thinking task performance</hd> <p>The first series of analyses examined performance on each level of the relational thinking task. Overall, all grade levels performed above chance on Level 1 (see Table 3 for a summary of performance on the relational thinking and math tasks). A logistic mixed‐effects model predicting trial accuracy with grade, semester in which testing occurred, and number of previous testing sessions as fixed effects and school and participant as random effects revealed that accuracy increased with grade level (β = 0.15, <emph>SE</emph> = 0.07, <emph>p</emph> < 0.001; Figure 2). A similar linear model predicting response times (RTs) also showed RTs became faster as function of grade level (β = −32.77, <emph>SE</emph> = 26.16, <emph>p</emph> < 0.001; Figure 2). These results suggest that relational thinking continues to improve throughout elementary and middle school.</p> <p>3 TABLE Average performance by grade on the relational thinking task Levels 1 and 2, math fluency, and fraction comparison tasks (mean score and range for each assessment)</p> <p> <ephtml> <table><thead><tr><th /><th align="left">Grade 4</th><th align="left">Grade 6</th><th align="left">Grade 8</th></tr></thead><tbody><tr><td>Relational thinking level 1 accuracy (% correct)</td><td>68 (5, 100)</td><td>76 (23, 100)</td><td>79 (30, 100)</td></tr><tr><td>Relational thinking level 1 RT (ms) on correct trials</td><td>1,719 (420, 2,796)</td><td>1,651 (356, 2,536)</td><td>1,453 (488, 2,515)</td></tr><tr><td>Relational thinking level 2 accuracy (% correct)</td><td>67 (39, 87)</td><td>69 (32, 95)</td><td>73 (35, 100)</td></tr><tr><td>Relational thinking level 2 RT (ms) on correct trials</td><td>1,869 (461, 3,109)</td><td>1,880 (466, 3,488)</td><td>1,770 (434, 3,016)</td></tr><tr><td>Math fluency raw score</td><td>45 (17, 77)</td><td>53 (31, 76)</td><td>56 (0, 88)</td></tr><tr><td>Fraction comparison accuracy (% correct)</td><td>71 (18, 100)</td><td>83 (21, 100)</td><td>83 (27, 100)</td></tr></tbody></table> </ephtml> </p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01may23/desc13320-fig-0002.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="desc13320-fig-0002.jpg" title="2 Accuracy and response time distributions by grade for Level 1 of the relational thinking task" /> </p> <p></p> <p>Next, we examined the data from Level 2. Only participants who achieved at least 75% accuracy on Level 1 moved onto Level 2. By this criterion, 75/243 4th graders (31%), 145/270 6th graders (54%), and 266/431 8th graders (62%) moved onto Level 2. A chi‐squared test for trend in proportions indicated that the proportion of participants advancing to Level 2 increased with grade (χ<sups>2</sups> = 55.82, <emph>p</emph> < 0.001). Similar grade‐wise developmental trends were found for Level 2 performance. A logistic mixed‐effects model predicting trial accuracy with grade, semester in which testing occurred, and number of gameplays as fixed effects and school, and participant as random effects revealed that accuracy increased with grade level (β = 0.07, <emph>SE</emph> = 0.02, <emph>p</emph> < 0.001; Figure 3). A similar linear model predicting RTs, however, found that participants did not become significantly faster with grade (β = −47.61, <emph>SE</emph> = 58.8, <emph>p</emph> = 0.42; Figure 3). These analyses demonstrate that, overall, both the simpler and more complex forms of relational thinking assessed by our task continue to show developmental improvements through the end of middle school.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01may23/desc13320-fig-0003.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="desc13320-fig-0003.jpg" title="3 Accuracy and response time distributions by grade for Level 2 of the relational thinking task" /> </p> <p></p> <hd id="AN0162916547-17">Relations between relational thinking and EFs</hd> <p>In the next series of analyses, we investigated how the EF measures relate to accuracy on Level 1 of the relational thinking task in each grade. We used data from only Level 1 in these—and all subsequent—analyses because it enabled us to include a larger proportion of our sample, particularly for the 4th grade students. Another good reason for limiting subsequent analyses to Level 1 is that we assume it places fewer demands on other EFs than Level 2.</p> <p>As shown in Figure 4, accuracy on the relational thinking task is significantly correlated with all three of the EF composites and task switching in 4th grade, correlated with working memory and task switching in 6th grade, and correlated with working memory, interference resolution, and task switching in 8th grade. Notably, the correlations between relational thinking and each of the canonical EF measures were relatively weak at all grades (<emph>r</emph>‐values ranging from 0.05 to 0.27; median <emph>r</emph>‐value: 0.16); in fact, they were generally lower than the correlations among the canonical EF measures themselves (<emph>r</emph>‐values from 0.17 to 0.31; median: 0.25).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01may23/desc13320-fig-0004.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="desc13320-fig-0004.jpg" title="4 Pearson correlation coefficients for pairwise comparisons between all variables of interest for each grade. * p < 0.05, ** p < 0.01; *** p < 0.001; p‐values are not corrected for multiple comparisons" /> </p> <p></p> <p>Next, for each grade, we tested whether relational thinking can be predicted based on the EF composite and task switch scores. We compared linear mixed effects models that predicted relational thinking based on the semester in which participants were tested and the number of times they had completed the relational thinking task, as well as a random effect of school (Model 1), to a model that additionally included the EF composite and task switch scores (Model 2). If the model including EFs was the superior model, as indicated by an ANOVA test, we then examined the coefficients of each EF score.</p> <p>In each cohort, the model containing the EF scores (Model 2) was superior to the model without these scores (4th grade: χ<sups>2</sups> = 12.97, <emph>p</emph> < 0.001; 6th grade: χ<sups>2</sups> = 12.06, <emph>p</emph> < 0.001; 8th grade: χ<sups>2</sups> = 29.87, <emph>p</emph> < 0.001; Tables 4–6). However, different EF measures were predictive of relational thinking at each grade level. In 4th grade, no EF measure individually predicted unique variance. In 6th grade, working memory was the only significant predictor; in 8th grade, task switching was the only significant predictor. Thus, although relational thinking is correlated with other EF measures in this dataset, the relation between these different metrics of cognitive functioning is not stable over time and is relatively weak – certainly no higher than the relations among the canonical EF measures.</p> <p>4 TABLE Model coefficients for models predicting 4th grade relational thinking scores from EF scores</p> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>0.560003 [0.21, 0.91]</td><td>0.380004 [0.02, 0.73]</td></tr><tr><td>3 Previous sessions</td><td>−0.01 [−0.86, 0.84]</td><td>−0.23 [−1.07, 0.61]</td></tr><tr><td>Semester</td><td>−0.15 [−0.49, 0.18]</td><td>−0.13 [−0.45, 0.19]</td></tr><tr><td>Response inhibition</td><td /><td>0.12 [−0.12, 0.37]</td></tr><tr><td>Interference resolution</td><td /><td>0.06 [−0.17, 0.29]</td></tr><tr><td>Working memory</td><td /><td>0.17 [−0.01, 0.36]</td></tr><tr><td>Task switching</td><td /><td>0.13 [−0.03, 0.29]</td></tr><tr><td>N</td><td>188</td><td>188</td></tr><tr><td>N (school)</td><td>7</td><td>7</td></tr><tr><td>AIC</td><td>536.72</td><td>543.36</td></tr><tr><td>BIC</td><td>556.14</td><td>575.73</td></tr><tr><td>R<sup>2</sup></td><td>0.10</td><td>0.14</td></tr></tbody></table> </ephtml> </p> <ulist> <item>2 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>3 *** <emph>p</emph> < 0.001.</item> <item>4 ** <emph>p</emph> < 0.01.</item> <item>5 * <emph>p</emph> < 0.05.</item> <item>6 Previous sessions: the number of times the tests had previously been administered to a participant; Semester: fall or spring; N: number of participants; N (school): number of schools.</item> <item>5 TABLE Model coefficients for models predicting 6th grade relational thinking scores from EF scores</item> </ulist> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>0.09 [−0.22, 0.39]</td><td>0.10 [−0.22, 0.41]</td></tr><tr><td>Semester</td><td>−0.13 [−0.40, 0.15]</td><td>−0.05 [−0.33, 0.22]</td></tr><tr><td>Response inhibition</td><td /><td>−0.03 [−0.28, 0.21]</td></tr><tr><td>Interference resolution</td><td /><td>0.15 [−0.15, 0.46]</td></tr><tr><td>Working memory</td><td /><td>0.180004 [0.01, 0.36]</td></tr><tr><td>Task switching</td><td /><td>0.14 [0.00, 0.28]</td></tr><tr><td>N</td><td>213</td><td>213</td></tr><tr><td>N (school)</td><td>3</td><td>3</td></tr><tr><td>AIC</td><td>619.92</td><td>626.26</td></tr><tr><td>BIC</td><td>636.73</td><td>656.52</td></tr><tr><td>R<sup>2</sup></td><td>0.02</td><td>0.09</td></tr></tbody></table> </ephtml> </p> <ulist> <item>7 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>8 *** <emph>p</emph> < 0.001.</item> <item>9 ** <emph>p</emph> < 0.01.</item> <item>10 * <emph>p</emph> < 0.05.</item> <item>11 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>12 Semester: fall or spring. N: number of participants. N (school): number of schools.</item> <item>6 TABLE Model coefficients for models predicting 8th grade relational thinking scores from EF scores</item> </ulist> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>0.14 [−0.22, 0.50]</td><td>0.23 [−0.13, 0.58]</td></tr><tr><td>3 Previous sessions</td><td>0.90 [−0.26, 2.06]</td><td>1.04 [−0.09, 2.16]</td></tr><tr><td>Semester</td><td>0.320003 [0.11, 0.52]</td><td>0.220004 [0.02, 0.42]</td></tr><tr><td>Response inhibition</td><td /><td>−0.06 [−0.23, 0.10]</td></tr><tr><td>Interference resolution</td><td /><td>0.12 [−0.07, 0.32]</td></tr><tr><td>Working memory</td><td /><td>0.11 [−0.02, 0.23]</td></tr><tr><td>Task switching</td><td /><td>0.220002 [0.11, 0.33]</td></tr><tr><td>N</td><td>368</td><td>368</td></tr><tr><td>N (school)</td><td>3</td><td>3</td></tr><tr><td>AIC</td><td>1043.54</td><td>1035.63</td></tr><tr><td>BIC</td><td>1066.99</td><td>1074.71</td></tr><tr><td>R<sup>2</sup></td><td>0.08</td><td>0.14</td></tr></tbody></table> </ephtml> </p> <ulist> <item>13 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>14 *** <emph>p</emph> < 0.001.</item> <item>15 ** <emph>p</emph> < 0.01.</item> <item>16 * <emph>p</emph> < 0.05.</item> <item>17 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>18 Semester: fall or spring. N: number of participants. N (school): number of schools.</item> </ulist> <hd id="AN0162916547-19">Relations between cognitive variables and math performance</hd> <p></p> <hd id="AN0162916547-20">Math fluency</hd> <p>Next, we investigated the relative contributions of relational thinking and canonical EFs to students' math fluency scores. In each cohort, we first predicted math fluency scores from a base model consisting of testing semester, the number of times the participant had previously seen the task, and a random effect of school (Model 1). Then we compared the base model to one that additionally included the EF scores as predictors (Model 2) and one that included both the EF scores and relational thinking (Model 3). The model with relational thinking predicted the most variance in each cohort (4th grade: χ<sups>2</sups> = 27.6, <emph>p</emph> < 0.001; 6th grade: χ<sups>2</sups> = 12.26, <emph>p</emph> < 0.001; 8th grade: χ<sups>2</sups> = 9.75, <emph>p</emph> = 0.002; Tables 7–9), and relational thinking was the only predictor that was significant across all three grades in the full model. Therefore, we found that performance on the relational thinking test is a unique predictor of student's math fluency scores after controlling for the variance explained by four metrics of canonical EFs derived from ten EF tasks.</p> <p>7 TABLE Model coefficients for models predicting 4th grade math fluency scores from EF scores and relational thinking</p> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>0.29 [−0.05, 0.64]</td><td>0.09 [−0.26, 0.44]</td><td>−0.04 [−0.37, 0.29]</td></tr><tr><td>3 Previous sessions</td><td>0.57 [−0.26, 1.40]</td><td>0.33 [−0.49, 1.14]</td><td>0.44 [−0.32, 1.21]</td></tr><tr><td>Semester</td><td>0.22 [−0.16, 0.60]</td><td>0.27 [−0.11, 0.64]</td><td>0.30 [−0.05, 0.64]</td></tr><tr><td>Response inhibition</td><td /><td>0.04 [−0.20, 0.28]</td><td>0.00 [−0.22, 0.22]</td></tr><tr><td>Interference resolution</td><td /><td>−0.03 [−0.25, 0.20]</td><td>−0.04 [−0.25, 0.16]</td></tr><tr><td>Working memory</td><td /><td>0.13 [−0.05, 0.30]</td><td>0.07 [−0.10, 0.23]</td></tr><tr><td>Task switching</td><td /><td>0.210003 [0.06, 0.37]</td><td>0.160004 [0.02, 0.31]</td></tr><tr><td>Relational thinking</td><td /><td /><td>0.360002 [0.22, 0.49]</td></tr><tr><td>N</td><td>187</td><td>187</td><td>187</td></tr><tr><td>N (school)</td><td>7</td><td>7</td><td>7</td></tr><tr><td>AIC</td><td>523.63</td><td>530.15</td><td>509.40</td></tr><tr><td>BIC</td><td>543.02</td><td>562.46</td><td>544.94</td></tr><tr><td>R<sup>2</sup></td><td>0.22</td><td>0.30</td><td>0.36</td></tr></tbody></table> </ephtml> </p> <ulist> <item>19 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>20 *** <emph>p</emph> < 0.001.</item> <item>21 ** <emph>p</emph> < 0.01.</item> <item>22 * <emph>p</emph> < 0.05.</item> <item>23 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>24 Semester: fall or spring. N: number of participants. N (school): number of schools.</item> <item>8 TABLE Model coefficients for models predicting 6th grade math fluency scores from EF scores and relational thinking</item> </ulist> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>−0.16 [−0.46, 0.14]</td><td>−0.09 [−0.39, 0.21]</td><td>−0.13 [−0.42, 0.16]</td></tr><tr><td>Semester</td><td>0.22 [−0.06, 0.49]</td><td>0.310004 [0.06, 0.57]</td><td>0.320004 [0.07, 0.57]</td></tr><tr><td>Response inhibition</td><td /><td>0.19 [−0.04, 0.42]</td><td>0.19 [−0.03, 0.42]</td></tr><tr><td>Interference resolution</td><td /><td>0.370004 [0.09, 0.65]</td><td>0.330004 [0.05, 0.60]</td></tr><tr><td>Working memory</td><td /><td>0.290002 [0.12, 0.45]</td><td>0.250003 [0.08, 0.41]</td></tr><tr><td>Task switching</td><td /><td>0.10 [−0.03, 0.23]</td><td>0.08 [−0.05, 0.20]</td></tr><tr><td>Relational thinking</td><td /><td /><td>0.220002 [0.09, 0.34]</td></tr><tr><td>N</td><td>212</td><td>212</td><td>212</td></tr><tr><td>N (school)</td><td>3</td><td>3</td><td>3</td></tr><tr><td>AIC</td><td>612.50</td><td>595.61</td><td>589.90</td></tr><tr><td>BIC</td><td>629.28</td><td>625.82</td><td>623.47</td></tr><tr><td>R<sup>2</sup></td><td>0.03</td><td>0.22</td><td>0.24</td></tr></tbody></table> </ephtml> </p> <ulist> <item>25 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>26 *** <emph>p</emph> < 0.001.</item> <item>27 ** <emph>p</emph> < 0.01.</item> <item>28 * <emph>p</emph> < 0.05.</item> <item>29 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>30 Semester: fall or spring. N: number of participants. N (school): number of schools.</item> <item>9 TABLE Model coefficients for models predicting 8th grade math fluency scores from EF scores and relational thinking</item> </ulist> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>−0.02 [−0.38, 0.33]</td><td>0.05 [−0.29, 0.40]</td><td>0.02 [−0.32, 0.36]</td></tr><tr><td>3 Previous sessions</td><td>−0.01 [−1.14, 1.13]</td><td>0.15 [−0.93, 1.24]</td><td>−0.00 [−1.08, 1.08]</td></tr><tr><td>Semester</td><td>0.540002 [0.34, 0.73]</td><td>0.420002 [0.23, 0.61]</td><td>0.390002 [0.20, 0.58]</td></tr><tr><td>Response inhibition</td><td /><td>−0.03 [−0.19, 0.14]</td><td>−0.02 [−0.18, 0.14]</td></tr><tr><td>Interference resolution</td><td /><td>0.190004 [0.00, 0.38]</td><td>0.17 [−0.01, 0.36]</td></tr><tr><td>Working memory</td><td /><td>0.200003 [0.07, 0.32]</td><td>0.180003 [0.06, 0.30]</td></tr><tr><td>Task switching</td><td /><td>0.180003 [0.07, 0.28]</td><td>0.140003 [0.04, 0.25]</td></tr><tr><td>Relational thinking</td><td /><td /><td>0.150003 [0.06, 0.25]</td></tr><tr><td>N</td><td>368</td><td>368</td><td>368</td></tr><tr><td>N (school)</td><td>3</td><td>3</td><td>3</td></tr><tr><td>AIC</td><td>1028.47</td><td>1010.67</td><td>1007.49</td></tr><tr><td>BIC</td><td>1051.92</td><td>1049.75</td><td>1050.48</td></tr><tr><td>R<sup>2</sup></td><td>0.12</td><td>0.21</td><td>0.22</td></tr></tbody></table> </ephtml> </p> <ulist> <item>31 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>32 *** <emph>p</emph> < 0.001.</item> <item>33 ** <emph>p</emph> < 0.01.</item> <item>34 * <emph>p</emph> < 0.05.</item> <item>35 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>36 Semester: fall or spring. N: number of participants. N (school): number of schools.</item> </ulist> <hd id="AN0162916547-21">Fraction comparison</hd> <p>In the final series of analyses, we investigated the role of relational thinking on students' fraction comparison task performance. In particular, we asked whether relational thinking would predict additional variance in fraction performance after accounting for math fluency and canonical EFs. Note that in these models we did not include the random effect of school because the models failed to converge. Including school as a fixed effect did not improve the model fits, so this variable was excluded altogether. We began with a base model that predicted fraction performance from math fluency scores, testing semester, and the number of previous testing sessions (Model 1). We then compared the base model to one that additionally included the EF scores (Model 2), and then one that included both EF scores and relational thinking (Model 3). For all grades, the model with relational thinking predicted the most variance in fraction scores (4th grade: <emph>F</emph> = 7.446, <emph>p</emph> = 0.007; 6th grade: <emph>F</emph> = 13.4, <emph>p</emph> < 0.001; 8th grade: <emph>F</emph> = 34.89, <emph>p</emph> < 0.001; Tables 10–12), and relational thinking was the only significant domain‐general cognitive predictor in the full model for all three grades. These results demonstrate that relational thinking predicts additional unique variance in student's fraction scores, above and beyond the contributions of EFs and math fluency.</p> <p>10 TABLE Model coefficients for models predicting 4th grade fraction scores from math fluency, EF scores, and relational thinking</p> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>0.21 [−0.12, 0.54]</td><td>0.09 [−0.25, 0.43]</td><td>0.03 [−0.31, 0.36]</td></tr><tr><td>3 Previous sessions</td><td>0.38 [−0.42, 1.17]</td><td>0.20 [−0.60, 1.00]</td><td>0.27 [−0.52, 1.05]</td></tr><tr><td>Semester</td><td>0.13 [−0.14, 0.40]</td><td>0.16 [−0.11, 0.43]</td><td>0.18 [−0.08, 0.45]</td></tr><tr><td>Math fluency</td><td>0.410002 [0.27, 0.54]</td><td>0.360002 [0.22, 0.50]</td><td>0.280002 [0.13, 0.43]</td></tr><tr><td>Response inhibition</td><td /><td>0.03 [−0.20, 0.26]</td><td>0.01 [−0.22, 0.24]</td></tr><tr><td>Interference resolution</td><td /><td>−0.04 [−0.26, 0.19]</td><td>−0.05 [−0.26, 0.17]</td></tr><tr><td>Working memory</td><td /><td>0.16 [−0.03, 0.34]</td><td>0.13 [−0.05, 0.31]</td></tr><tr><td>Task switching</td><td /><td>0.15 [−0.00, 0.30]</td><td>0.13 [−0.02, 0.28]</td></tr><tr><td>Relational thinking</td><td /><td /><td>0.210003 [0.06, 0.36]</td></tr><tr><td>N</td><td>185</td><td>185</td><td>185</td></tr><tr><td>R<sup>2</sup></td><td>0.19</td><td>0.23</td><td>0.26</td></tr></tbody></table> </ephtml> </p> <ulist> <item>37 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>38 *** <emph>p</emph> < 0.001.</item> <item>39 ** <emph>p</emph> < 0.01.</item> <item>40 * <emph>p</emph> < 0.05.</item> <item>41 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>42 Semester: fall or spring. N: number of participants.</item> <item>11 TABLE Model coefficients for models predicting 6th grade fraction scores from math fluency, EF scores, and relational thinking</item> </ulist> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>−0.02 [−0.28, 0.25]</td><td>0.01 [−0.25, 0.28]</td><td>−0.00 [−0.26, 0.25]</td></tr><tr><td>Semester</td><td>−0.12 [−0.38, 0.14]</td><td>−0.11 [−0.37, 0.15]</td><td>−0.08 [−0.33, 0.17]</td></tr><tr><td>Math fluency</td><td>0.430002 [0.31, 0.56]</td><td>0.400002 [0.26, 0.53]</td><td>0.340002 [0.20, 0.47]</td></tr><tr><td>Response inhibition</td><td /><td>0.280004 [0.05, 0.52]</td><td>0.300003 [0.08, 0.53]</td></tr><tr><td>Interference resolution</td><td /><td>0.02 [−0.27, 0.30]</td><td>0.01 [−0.27, 0.28]</td></tr><tr><td>Working memory</td><td /><td>0.03 [−0.14, 0.20]</td><td>0.00 [−0.16, 0.17]</td></tr><tr><td>Task switching</td><td /><td>−0.04 [−0.18, 0.09]</td><td>−0.07 [−0.20, 0.06]</td></tr><tr><td>Relational thinking</td><td /><td /><td>0.230002 [0.11, 0.36]</td></tr><tr><td>N</td><td>211</td><td>211</td><td>211</td></tr><tr><td>R<sup>2</sup></td><td>0.18</td><td>0.21</td><td>0.26</td></tr></tbody></table> </ephtml> </p> <ulist> <item>43 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>44 *** <emph>p</emph> < 0.001.</item> <item>45 ** <emph>p</emph> < 0.01.</item> <item>46 * <emph>p</emph> < 0.05.</item> <item>47 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>48 Semester: fall or spring. N: number of participants.</item> <item>12 TABLE Model coefficients for models predicting 8th grade fraction scores from math fluency, EF scores, and relational thinking</item> </ulist> <p> <ephtml> <table><thead><tr><th /><th align="left">Model 1</th><th align="left">Model 2</th><th align="left">Model 3</th></tr></thead><tbody><tr><td>2 Previous sessions</td><td>0.470003 [0.13, 0.81]</td><td>0.510003 [0.17, 0.85]</td><td>0.440003 [0.12, 0.77]</td></tr><tr><td>3 Previous sessions</td><td>0.71 [−0.36, 1.78]</td><td>0.78 [−0.29, 1.86]</td><td>0.47 [−0.56, 1.50]</td></tr><tr><td>Semester</td><td>0.11 [−0.08, 0.30]</td><td>0.08 [−0.11, 0.27]</td><td>0.06 [−0.13, 0.24]</td></tr><tr><td>Math fluency</td><td>0.410002 [0.31, 0.50]</td><td>0.370002 [0.26, 0.47]</td><td>0.310002 [0.21, 0.41]</td></tr><tr><td>Response inhibition</td><td /><td>−0.02 [−0.18, 0.14]</td><td>−0.01 [−0.16, 0.15]</td></tr><tr><td>Interference resolution</td><td /><td>0.06 [−0.13, 0.25]</td><td>0.04 [−0.14, 0.21]</td></tr><tr><td>Working memory</td><td /><td>0.07 [−0.06, 0.19]</td><td>0.05 [−0.07, 0.17]</td></tr><tr><td>Task switch</td><td /><td>0.10 [−0.00, 0.21]</td><td>0.05 [−0.06, 0.15]</td></tr><tr><td>Relational thinking</td><td /><td /><td>0.280002 [0.19, 0.38]</td></tr><tr><td>N</td><td>366</td><td>366</td><td>366</td></tr><tr><td>R<sup>2</sup></td><td>0.20</td><td>0.21</td><td>0.28</td></tr></tbody></table> </ephtml> </p> <ulist> <item>49 <emph>Note</emph>: All continuous predictors are mean‐centered and scaled by 1 standard deviation. Beta coefficients are standardized, and bracketed values indicate 95% confidence intervals.</item> <item>50 *** <emph>p</emph> < 0.001.</item> <item>51 ** <emph>p</emph> < 0.01.</item> <item>52 * <emph>p</emph> < 0.05.</item> <item>53 Previous sessions: the number of times the tests had previously been administered to a participant.</item> <item>54 Semester: fall or spring. N: number of participants.</item> </ulist> <hd id="AN0162916547-22">DISCUSSION</hd> <p>The primary aims of the present study were to delineate the development of relational thinking skills and to investigate whether relational thinking is a separable cognitive skill from the canonical EFs that contribute unique variance to students' math achievement. We assessed a large sample of elementary and middle school students on a newly developed tablet‐based assessment battery that included ten standard tests of EF, a relational thinking task, a math fluency task, and a fraction comparison task.</p> <p>Our relational thinking task contained two levels: children needed to determine whether the two pairs of shapes matched along a single dimension (Level 1) or two dimensions (Level 2). Performance on both task levels captured developmental improvements in relational thinking skills throughout elementary and middle school. We also found that performance on Level 1 of the task was significantly correlated with EFs, particularly working memory and task switching. However, relational thinking was a significant predictor of math achievement after accounting for the variance explained by EFs. This was true both for math fluency—which tests student's speeded ability to solve arithmetic, multiplication, and division problems—and fraction comparison. Furthermore, relational thinking was a significant predictor of fraction comparison performance even when math fluency, a domain‐specific measure, was taken into account. These findings suggest that relational thinking is a distinct cognitive process that supports math performance in school‐aged children over and above canonical EFs.</p> <p>In prior work, it has been difficult to disentangle the influence of EFs and relational thinking because many standard assessments of reasoning are relatively complex and tax multiple abilities at once. However, the relational thinking task used here—particularly Level 1—was designed to minimize demands on EFs and other cognitive skills. By explicitly stating the different rule types prior to starting the game and by providing only two answer choices for each trial, Level 1 of the task focuses on children's ability to abstract a common relation between exemplars. Level 2, in which participants needed to identify matches in two dimensions rather than one, required participants to resolve increased relational complexity (Halford et al., [<reflink idref="bib37" id="ref114">37</reflink>]) and represent hierarchical rule structures (Bunge & Zelazo, [<reflink idref="bib9" id="ref115">9</reflink>]). However, it also presumably increased demands on canonical EFs, as participants had to override the previously learned rules of Level 1 (which was always explained and performed first). Critically, only data from the cleaner measure of relational thinking, Level 1, were included in the analyses examining relations with EFs and with math achievement.</p> <p>To address the question of whether relational thinking is a distinct ability from the canonical EFs, we assessed which EF scores predicted performance on Level 1 of the relational thinking task, as well as how these scores related to children's math fluency and fraction comprehension performance. Consistent with previous studies that have documented relations between reasoning tasks that tap relational thinking and EFs (e.g., Fry & Hale, [<reflink idref="bib29" id="ref116">29</reflink>]; Richland & Burchinal, [<reflink idref="bib63" id="ref117">63</reflink>]; Richland et al., [<reflink idref="bib66" id="ref118">66</reflink>]; Starr et al., [<reflink idref="bib74" id="ref119">74</reflink>]; Thibaut & French, [<reflink idref="bib80" id="ref120">80</reflink>]; Thibaut et al., [<reflink idref="bib79" id="ref121">79</reflink>]), relational thinking scores were significantly correlated with EF scores – however, which EF components it correlated with varied as a function of age. Notably, the correlation coefficients for the associations between relational thinking and the canonical EFs tended to be even <emph>lower</emph> than the correlations among the canonical EFs themselves. This result, together with the fact that no single EF factor was a consistent predictor of relational thinking across all age groups, suggests that relational thinking is separable from each of these other EFs.</p> <p>Because EFs are conceptualized as domain‐general cognitive processes that support academic performance, examining whether relational thinking predicts mathematical achievement is a criterion by which to assess whether it should be considered an EF. Indeed, we found that relational thinking and EFs each predicted unique variance in students' math achievement. The connection between EFs and math achievement is well‐documented (see Bull & Lee, [<reflink idref="bib6" id="ref122">6</reflink>]; Cragg & Gilmore, [<reflink idref="bib19" id="ref123">19</reflink>] for reviews). However, individual differences in EFs do not explain all, or even a majority, of the variance in math scores. Here, we found that relational thinking predicted additional variance in math fluency and fraction comparison scores that was not accounted for by canonical EFs. Furthermore, in the case of fraction comparison, relational thinking predicted additional unique variance after accounting for both EFs and math fluency, meaning that the model already contained both domain‐general and domain‐specific predictors before we added in relational thinking. In fact, relational thinking was consistently the strongest domain‐general predictor of math performance, judging from the pairwise correlations and linear regression model coefficients. Therefore, individual differences in students' relational thinking ability are predictive of achievement across multiple types of mathematical thinking.</p> <p>Given the inherently relational nature of many mathematical concepts, it is not surprising that relational thinking contributes to math performance throughout grade school. Our findings are consistent with previous work demonstrating that reasoning relates to math achievement (Fuchs et al., [<reflink idref="bib31" id="ref124">31</reflink>]; Green et al., [<reflink idref="bib35" id="ref125">35</reflink>]; Taub et al., [<reflink idref="bib78" id="ref126">78</reflink>]), and suggest, specifically, that the relational thinking component of reasoning supports mathematical thinking. In addition, our findings add to the growing body of literature that suggests that relational thinking is particularly important for mathematical concepts like fractions and decimals (DeWolf et al., [<reflink idref="bib20" id="ref127">20</reflink>]; Kalra et al., [<reflink idref="bib43" id="ref128">43</reflink>]). For example, Kalra et al. ([<reflink idref="bib43" id="ref129">43</reflink>]) found that relational thinking, as assessed by the Test of Relational Reasoning Jr. (TORR Jr; Jablansky et al., [<reflink idref="bib42" id="ref130">42</reflink>]) predicted fraction knowledge scores in 2nd and 5th graders even when controlling for a variety of domain‐general (e.g., working memory) and domain‐specific (e.g., math fluency) predictors.</p> <p>Fractions are typically students' first exposure to number concepts beyond the natural numbers, and frequently they represent a stumbling block in math curricula (Siegler et al., [<reflink idref="bib71" id="ref131">71</reflink>]). In comparison to the natural numbers, fractions' bipartite structure (<emph>a/b</emph>) increases their relational complexity because students must process the value of each individual component as well as the overall value of the fraction. Instructional techniques that make the relational nature of fractions explicit (i.e., that fractions represent a relation between two numbers) may therefore help students make the conceptual jump from understanding natural numbers to understanding rational numbers (DeWolf et al., [<reflink idref="bib20" id="ref132">20</reflink>]). Indeed, several studies have demonstrated that pedagogical methods that explicitly encourage the use of relational thinking can improve student's ability to learn mathematical concepts (Carpenter et al., [<reflink idref="bib11" id="ref133">11</reflink>]; Kidd et al., [<reflink idref="bib44" id="ref134">44</reflink>]; Mcneil & Alibali, [<reflink idref="bib53" id="ref135">53</reflink>]; Richland et al., [[<reflink idref="bib64" id="ref136">64</reflink>], [<reflink idref="bib67" id="ref137">67</reflink>]]). An important future direction will be to explore how increasing emphasis on relational thinking skills in math classrooms may improve student outcomes (Vendetti et al., [<reflink idref="bib84" id="ref138">84</reflink>]).</p> <p>There is no single criterion of what makes a cognitive ability an EF. Most standard definitions reflect the idea that EFs are mid‐level, domain‐general, effortful cognitive processes that contribute to goal‐directed behavior and support academic achievement. Much of the developmental psychology literature has focused on the three core abilities of inhibition, working memory, and cognitive flexibility (Diamond, [<reflink idref="bib21" id="ref139">21</reflink>]; Lehto et al., [<reflink idref="bib49" id="ref140">49</reflink>]; Miyake et al., [<reflink idref="bib56" id="ref141">56</reflink>]), but these three components are not necessarily exclusive. Furthermore, total independence has never been used as a criterion for considering two putative processes as distinct EFs; in fact, these three canonical EFs have been theorized to support one another (Diamond, [<reflink idref="bib21" id="ref142">21</reflink>]). The present data provide evidence that relational thinking is a mid‐level, domain‐general, effortful cognitive process that is only weakly correlated with the canonical EFs and that is independently related to academic achievement, as measured by two math tests. Therefore, consistent with previous views that relational thinking is central to human cognition (Alexander, [<reflink idref="bib1" id="ref143">1</reflink>]; Cattell, [<reflink idref="bib13" id="ref144">13</reflink>]; Halford et al., [<reflink idref="bib38" id="ref145">38</reflink>]), we argue that relational thinking should be considered among the pantheon of EFs.</p> <p>Our claim is based on analyses of data collected from a large, diverse sample of children in middle childhood who performed the ACE battery of cognitive tasks (Younger et al., [<reflink idref="bib88" id="ref146">88</reflink>]). However, this study is not without limitations. The ACE battery contains ten different cognitive tasks, nine of which were grouped through exploratory factor analysis into three EF composites. Relational thinking, on the other hand, was—along with task switching—measured using a single task. Because completion of the full ACE battery and scholastic assessments was already a multi‐day endeavor, inclusion of additional tasks was not feasible. Importantly, however, the relational thinking task proved sensitive to capturing both developmental improvements and individual differences. An important future direction will be to assess relational thinking with multiple measures (e.g., the Test of Relational Reasoning‐Junior (Jablansky et al., [<reflink idref="bib42" id="ref147">42</reflink>])). In addition, future work exploring the relation between EFs and academic achievement should also assess relational thinking to provide a more comprehensive view of the contributions of domain‐general cognitive abilities.</p> <p>In conclusion, the present work introduces a task that can be used to effectively measure individual differences in relational thinking ability throughout middle childhood. This task specifically focuses on the ability to identify and integrate abstract relations, while minimizing the demands on EFs. Individual differences in relational thinking predicted significant variance in students' math fluency and fraction comparison scores throughout middle childhood, even when variance from other EFs was accounted for. These results support our claim that relational thinking should be considered alongside the canonical EFs as a distinct core cognitive ability that uniquely contributes to academic achievement.</p> <hd id="AN0162916547-23">ACKNOWLEDGMENTS</hd> <p>This research was supported by funding from the National Science Foundation, Science of Learning Collaborative Networks Grant (NSFSLCN‐1540854) awarded to Melina Uncapher and Adam Gazzaley, and co‐PIs Joaquin Anguera, Silvia Bunge, Fumiko Hoeft, Bruce McCandliss, Jyoti Mishra, and Miriam Rosenberg‐Lee (Project iLead Consortium). Ariel Starr was supported by NICHD award F32HD085736. The authors would like to thank the research staff, Jordin Rodondi, Caleb Banks, Zoe D'Esposito, John David Lorentz and the large team of UCSF volunteers as well as the students, teachers, parents, and school and district administrators who made this research program possible. We are also grateful to the team of developers who have made the ACE assessment possible including WoWLabz, Zynga.org, and Rose Feldman, and the programmers that created the aceR processing code, Jose Gallegos and Monica Thieu.</p> <hd id="AN0162916547-24">CONFLICTS OF INTEREST</hd> <p>This study was conducted with approval from the University of California, San Francisco Institutional Review Board. The authors have no conflicts of interest to disclose.</p> <hd id="AN0162916547-25">DATA AVAILABILITY STATEMENT</hd> <p>Data is available from the Project iLead Consortium by request and will be made publicly available 2 years after publication.</p> <ref id="AN0162916547-26"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref26" type="bt">1</bibl> <bibtext> Because the composite EF scores do not preserve subtle difference in factor loadings across the cohorts and time points, we also ran all of the analyses with factor scores instead of composite scores. The main pattern of results remained unchanged. 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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Relational Thinking: An Overlooked Component of Executive Functioning
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Starr%2C+Ariel%22">Starr, Ariel</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-0433-5003">0000-0003-0433-5003</externalLink>)<br /><searchLink fieldCode="AR" term="%22Leib%2C+Elena+R%2E%22">Leib, Elena R.</searchLink><br /><searchLink fieldCode="AR" term="%22Younger%2C+Jessica+W%2E%22">Younger, Jessica W.</searchLink><br /><searchLink fieldCode="AR" term="%22Project+iLead+Consortium%22">Project iLead Consortium</searchLink><br /><searchLink fieldCode="AR" term="%22Uncapher%2C+Melina+R%2E%22">Uncapher, Melina R.</searchLink><br /><searchLink fieldCode="AR" term="%22Bunge%2C+Silvia+A%2E%22">Bunge, Silvia A.</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Developmental+Science%22"><i>Developmental Science</i></searchLink>. May 2023 26(3).
– Name: Avail
  Label: Availability
  Group: Avail
  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
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 18
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2023
– Name: SourceSuprt
  Label: Sponsoring Agency
  Group: SrcSuprt
  Data: Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD) (DHHS/NIH)<br />National Science Foundation (NSF)
– Name: NumberContract
  Label: Contract Number
  Group: NumCntrct
  Data: F32HD085736<br />NSFSLCN1540854
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Junior+High+Schools%22">Junior High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Thinking+Skills%22">Thinking Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Executive+Function%22">Executive Function</searchLink><br /><searchLink fieldCode="DE" term="%22Task+Analysis%22">Task Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Achievement%22">Mathematics Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Middle+School+Students%22">Middle School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Tests%22">Mathematics Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Scores%22">Scores</searchLink><br /><searchLink fieldCode="DE" term="%22Fractions%22">Fractions</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Ability%22">Cognitive Ability</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/desc.13320
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 1363-755X<br />1467-7687
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Relational thinking, the ability to represent abstract, generalizable relations, is a core component of reasoning and human cognition. Relational thinking contributes to fluid reasoning and academic achievement, particularly in the domain of math. However, due to the complex nature of many fluid reasoning tasks, it has been difficult to determine the degree to which relational thinking has a separable role from the cognitive processes collectively known as executive functions (EFs). Here, we used a simplified reasoning task to better understand how relational thinking contributes to math achievement in a large, diverse sample of elementary and middle school students (N = 942). Students also performed a set of ten adaptive EF assessments, as well as tests of math fluency and fraction magnitude comparison. We found that relational thinking was significantly correlated with each of the three EF composite scores previously derived from this dataset, albeit no more strongly than they were with each other. Further, relational thinking predicted unique variance in students' math fluency and fraction magnitude comparison scores over and above the three EF composites. Thus, we propose that relational thinking be considered an EF in its own right as one of the core, mid-level cognitive abilities that supports cognition and goal-directed behavior.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2023
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1372378
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1372378
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  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1111/desc.13320
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
    Subjects:
      – SubjectFull: Thinking Skills
        Type: general
      – SubjectFull: Executive Function
        Type: general
      – SubjectFull: Task Analysis
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Mathematics Achievement
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      – SubjectFull: Elementary School Students
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      – SubjectFull: Middle School Students
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      – SubjectFull: Fractions
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      – SubjectFull: Cognitive Ability
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      – TitleFull: Relational Thinking: An Overlooked Component of Executive Functioning
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