How Prior Knowledge, Gesture Instruction, and Interference after Instruction Interact to Influence Learning of Mathematical Equivalence
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| Title: | How Prior Knowledge, Gesture Instruction, and Interference after Instruction Interact to Influence Learning of Mathematical Equivalence |
|---|---|
| Language: | English |
| Authors: | Susan Wagner Cook, Elle M. D. Wernette, Madison Valentine, Mary Aldugom, Todd Pruner, Kimberly M. Fenn |
| Source: | Cognitive Science. 2024 48(2). |
| 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: | 30 |
| Publication Date: | 2024 |
| Sponsoring Agency: | National Science Foundation (NSF) |
| Contract Number: | 1561182 1561122 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Early Childhood Education Elementary Education Grade 2 Primary Education Grade 3 |
| Descriptors: | Prior Learning, Nonverbal Communication, Grade 2, Grade 3, Elementary School Students, Mathematics Instruction, Video Technology, Problem Solving, Instructional Effectiveness, Interference (Learning) |
| DOI: | 10.1111/cogs.13412 |
| ISSN: | 0364-0213 1551-6709 |
| Abstract: | Although children learn more when teachers gesture, it is not clear "how" gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly resistant to interference. We investigated this possibility in a classroom study with 402 second- and third-grade children. Participants received classroom-level instruction in mathematical equivalence using videos with or without accompanying gesture. After instruction, children solved problems that were either visually similar to the problems that were taught, and consistent with an operational interpretation of the equal sign (interference), or visually distinct from equivalence problems and without an equal sign (control) in order to assess the role of gesture in resisting interference after learning. Gesture facilitated learning, but the effects of gesture and interference varied depending on type of problem being solved and the strategies that children used to solve problems prior to instruction. Some children benefitted from gesture, while others did not. These findings have implications for understanding the mechanisms underlying the beneficial effect of gesture on mathematical learning, revealing that gesture does not work via a general mechanism like enhancing attention or engagement that would apply to children with all forms of prior knowledge. |
| Abstractor: | As Provided |
| Notes: | https://osf.io/pcn5j |
| Entry Date: | 2024 |
| Accession Number: | EJ1418270 |
| Database: | ERIC |
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| FullText | Links: – Type: pdflink Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwHAzyXSNAHGNyN_X16DXTY6AAAA4zCB4AYJKoZIhvcNAQcGoIHSMIHPAgEAMIHJBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDHgYlhMt8W29fSjGXwIBEICBm1ejjcp8c2aOQHNaSOD7fcbU8Y6_Rvo75MHE-fpGlWnuK2wPE5Yjk48CNpDSxzlqhFd_FCO2V6kBKklpmQPGTGbL0_ZqA1CpMFWZFxh_oJK8JwIpHnP8dWRUrxjPemPl0kI4AE5m2aal7q9oZRvGKDCv8kEYvs4_XOUN8RbzcUe_nIBaTc-ZiyXe0N7fjMDebbX6hAUKCDlE4i3k Text: Availability: 1 Value: <anid>AN0175674256;cgn01feb.24;2024Feb28.06:02;v2.2.500</anid> <title id="AN0175674256-1">How Prior Knowledge, Gesture Instruction, and Interference After Instruction Interact to Influence Learning of Mathematical Equivalence </title> <p>Although children learn more when teachers gesture, it is not clear how gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly resistant to interference. We investigated this possibility in a classroom study with 402 second‐ and third‐grade children. Participants received classroom‐level instruction in mathematical equivalence using videos with or without accompanying gesture. After instruction, children solved problems that were either visually similar to the problems that were taught, and consistent with an operational interpretation of the equal sign (interference), or visually distinct from equivalence problems and without an equal sign (control) in order to assess the role of gesture in resisting interference after learning. Gesture facilitated learning, but the effects of gesture and interference varied depending on type of problem being solved and the strategies that children used to solve problems prior to instruction. Some children benefitted from gesture, while others did not. These findings have implications for understanding the mechanisms underlying the beneficial effect of gesture on mathematical learning, revealing that gesture does not work via a general mechanism like enhancing attention or engagement that would apply to children with all forms of prior knowledge.</p> <p>Keywords: Gesture; Math; Learning; Mathematical learning; Conceptual change; Memory consolidation</p> <hd id="AN0175674256-2">Introduction</hd> <p>When children learn math, they often develop misconceptions about fundamental concepts. For example, young children overwhelmingly tend to adopt an operational understanding of the equal sign, in which they view the equal sign as a symbol to add everything up or to write down their answer. This operational understanding is consistent with many of the curricular materials they encounter (McNeil &amp; Alibali, [<reflink idref="bib59" id="ref1">59</reflink>]; McNeil et al., [<reflink idref="bib60" id="ref2">60</reflink>]). However, to be successful in algebra, children need to develop a relational understanding of the equal sign, in which they view the equal sign as a symbol indicating that the two sides of the equation are equal (Kieran, [<reflink idref="bib44" id="ref3">44</reflink>]). A relational understanding of the equal sign is important in predicting later math achievement (Byrd, McNeil, Chesney, &amp; Matthews, [<reflink idref="bib11" id="ref4">11</reflink>]; Matthews &amp; Fuchs, [<reflink idref="bib53" id="ref5">53</reflink>]).</p> <p>Misconceptions are problematic because they can interfere with subsequent learning (McNeil, [<reflink idref="bib57" id="ref6">57</reflink>]). Children will fall behind if they fail to abandon incorrect knowledge in favor of new representations (Booth, McGinn, Barbieri, &amp; Young, [<reflink idref="bib10" id="ref7">10</reflink>]). To understand and support knowledge change in mathematics and other domains, we need to not only understand how children acquire new knowledge, but also how children acquire new knowledge in the face of misconceptions. Understanding how children successfully overcome their misconceptions of mathematical equivalence may be helpful in revealing approaches to help children overcome inappropriate prior knowledge for other concepts and in other domains (Barbieri, Miller‐Cotto, &amp; Booth, [<reflink idref="bib7" id="ref8">7</reflink>]).</p> <hd id="AN0175674256-3">Hand gesture and learning of mathematical equivalence</hd> <p>One instructional tool that improves learning of mathematical equivalence is incorporating supportive <emph>hand gestures</emph> into instruction (e.g., Cook, Duffy, &amp; Fenn, [<reflink idref="bib21" id="ref9">21</reflink>]). Instruction with gesture improves learning of a variety of mathematical and scientific concepts (Cook, [<reflink idref="bib19" id="ref10">19</reflink>]; Cook et al., [<reflink idref="bib21" id="ref11">21</reflink>]; Goldin‐Meadow &amp; Alibali, [<reflink idref="bib28" id="ref12">28</reflink>]; Goldin‐Meadow, Kim, &amp; Singer, [<reflink idref="bib29" id="ref13">29</reflink>]; Kang, Hallman, Son, &amp; Black, [<reflink idref="bib43" id="ref14">43</reflink>]; Li, Wang, Mayer, &amp; Liu, [<reflink idref="bib50" id="ref15">50</reflink>]; Ping &amp; Goldin‐Meadow, [<reflink idref="bib65" id="ref16">65</reflink>]; Sauter, Uttal, Alman, Goldin‐Meadow, &amp; Levine, [<reflink idref="bib69" id="ref17">69</reflink>]). In mathematical equivalence, incorporating gesture into instruction enhances learning while also supporting transfer to novel problems (Cook et al., [<reflink idref="bib21" id="ref18">21</reflink>]). Gesture also helps learners consolidate their learning and maintain new knowledge over time (Cook, Mitchell, &amp; Goldin‐Meadow, [<reflink idref="bib23" id="ref19">23</reflink>]; Cook, Yip, &amp; Goldin‐Meadow, [<reflink idref="bib24" id="ref20">24</reflink>]). Children who either produce gesture during learning or simply perceive an instructor gesturing during instruction show improved performance on subsequent tests compared with children who do not see or produce gestures (Congdon et al., [<reflink idref="bib16" id="ref21">16</reflink>], Cook et al., [<reflink idref="bib21" id="ref22">21</reflink>]).</p> <p>Importantly, the mechanism by which gestures support learning is not well‐established. Here, we test the hypothesis that hand gestures help learners acquire memory representations that are resistant to interference from prior misconceptions.</p> <hd id="AN0175674256-4">Mechanisms underlying the beneficial effect of gesture on learners</hd> <p>Although there is substantial work identifying benefits associated with learning by observing hand gestures, the mechanisms underlying such effects have not been elucidated (Cook, [<reflink idref="bib20" id="ref23">20</reflink>]). Instead, there are multiple general mechanisms by which seeing gesture has been hypothesized to promote learning. Gestures are complex and multidimensional representations that occur in the context of spoken language and various dimensions of gesture could support learning in myriad ways. For example, gestures have been postulated to promote learning because they are embodied representations (Gordon &amp; Ramani, [<reflink idref="bib30" id="ref24">30</reflink>]; Macedonia, [<reflink idref="bib51" id="ref25">51</reflink>]) and because they are spatial and motoric representations (Kita, Alibali, &amp; Chu, [<reflink idref="bib45" id="ref26">45</reflink>]). Gesture could also support learning indirectly, by facilitating processing of the accompanying speech (Holle et al., [<reflink idref="bib38" id="ref27">38</reflink>]; Hubbard, Wilson, Callan, &amp; Dapretto, [<reflink idref="bib40" id="ref28">40</reflink>]), disambiguating the accompanying speech (Holle &amp; Gunter, [<reflink idref="bib37" id="ref29">37</reflink>]), or increasing comprehension of the accompanying speech (Novack &amp; Goldin‐Meadow, [<reflink idref="bib63" id="ref30">63</reflink>]).</p> <p>Together, gesture and speech form a multimodal signal, and multimodal presentation of information is thought to enhance learning in a variety of ways. As a multimodal signal, gestures may increase attention and engagement during learning (Bahrick &amp; Lickliter, [<reflink idref="bib5" id="ref31">5</reflink>], Bahrick &amp; Lickliter, 2002, Bahrick &amp; Lickliter, [<reflink idref="bib6" id="ref32">6</reflink>]) or might improve access to memory representations via dual codes or change the neural representations underlying learning (Mathias &amp; von Kriegstein, [<reflink idref="bib52" id="ref33">52</reflink>]). It is also possible that gestures may help learners appropriately encode information (Yeo et al., [<reflink idref="bib76" id="ref34">76</reflink>]).</p> <p>Studies of gesture and learning have often failed to discriminate among potential mechanisms by which gesture might be supporting learning. Moreover, these mechanisms are not mutually exclusive. Given the diversity of mechanisms supporting learning and memory in human information processing, it is unlikely that there is a single mechanism by which gesture supports learning across domains of knowledge, specific concepts, or even across individual learners. Focusing only on whether gestures help learning is unlikely to reveal exactly <emph>how</emph> gesture supports learning, as tasks, spoken instructions, and gestures simultaneously vary along multiple dimensions.</p> <p>An alternative approach is to use our understanding of how knowledge changes in a particular task to inform our investigation into how gesture might support learning in a particular task. Here, we considered the task of mathematical equivalence. Gesture has been well‐established to support learning in this domain (Cook et al., [<reflink idref="bib23" id="ref35">23</reflink>]; Novack et al., [<reflink idref="bib62" id="ref36">62</reflink>]; Singer &amp; Goldin‐Meadow, [<reflink idref="bib70" id="ref37">70</reflink>]). Moreover, children's knowledge change in the domain of mathematical equivalence has been well‐studied (Baroody &amp; Ginsburg, [<reflink idref="bib8" id="ref38">8</reflink>]; Kieren, [<reflink idref="bib44" id="ref39">44</reflink>]; McNeil, [[<reflink idref="bib56" id="ref40">56</reflink>]]; Rittle‐Johnson &amp; Alibali, [<reflink idref="bib67" id="ref41">67</reflink>]).</p> <hd id="AN0175674256-5">Proactive interference and learning of mathematical equivalence</hd> <p>Children often arrive at instruction in mathematical equivalence with an incorrect conceptualization of the equal sign, which interferes with their ability to acquire a correct representation (McNeil, [[<reflink idref="bib56" id="ref42">56</reflink>]]). Children's misunderstanding of the equal sign comes from their vast experience solving simple addition problems, where the equal sign comes directly before the answer (e.g., 4 + 3 = _, 4 + 3 + 8 = ___). Children typically practice many simple arithmetic problems in early elementary school, with the consequence that, over time, they develop a misconception that the equal sign indicates an operation, rather than a relation (McNeil, [[<reflink idref="bib55" id="ref43">55</reflink>]], [<reflink idref="bib57" id="ref44">57</reflink>]). Children often come to believe that the equal sign means "put your answer down" or "add up all the numbers" (Baroody &amp; Ginsburg, [<reflink idref="bib8" id="ref45">8</reflink>]; Kieren, [<reflink idref="bib44" id="ref46">44</reflink>]). This misconception causes difficulty with problems where the relational interpretation of the equal sign is necessary. Both children and adults are impaired in equivalence problem solving if they are exposed to many problems with the equal sign coming immediately before the answer (Chesney &amp; McNeil, [<reflink idref="bib12" id="ref47">12</reflink>]; McNeil, [<reflink idref="bib56" id="ref48">56</reflink>]; McNeil, Rittle‐Johnson, Hattikudur, &amp; Petersen, [<reflink idref="bib61" id="ref49">61</reflink>]) or if the operational pattern of combining elements is activated prior to solving problems (Crooks &amp; Alibali, [<reflink idref="bib25" id="ref50">25</reflink>]).</p> <p>In addition, even children who manage to acquire new knowledge of the equal sign after instruction may be at risk of forgetting this new knowledge because of proactive interference from this misconception (Cook et al., [<reflink idref="bib23" id="ref51">23</reflink>]). Because gesture promotes learning, generalization, and retention of mathematical equivalence, a domain where children arrive at learning with a robust misperception and are thus susceptible to interference, we hypothesized that one mechanism by which gesture might facilitate learning of mathematical equivalence is by creating memory representations that are less susceptible to interference in memory. If so, learners should be less susceptible to proactive interference after learning mathematical equivalence with gesture compared to learning without gesture.</p> <hd id="AN0175674256-6">Proactive interference and hand gesture</hd> <p>Hand gesture might provide a helpful tool for supporting learners in situations where interference from prior knowledge is likely. Gestures typically provide a semantically congruent representation in a second modality and providing information across modalities has been shown to improve subsequent memory (Heikkilä et al., [<reflink idref="bib34" id="ref52">34</reflink>]), including in school‐age children (Heikkilä &amp; Tippana, [<reflink idref="bib35" id="ref53">35</reflink>]). Gestures have also been shown to support generalization (Cook et al., [<reflink idref="bib21" id="ref54">21</reflink>]), and memory representations that support generalization often work via mechanisms that also support resisting interference (Herszage &amp; Censor, [<reflink idref="bib36" id="ref55">36</reflink>]). Finally, gestures support appropriate encoding of information from the environment (Yeo et al., [<reflink idref="bib76" id="ref56">76</reflink>]), which might also serve to reduce interference from prior misconceptions if prior knowledge influences encoding of information from the environment.</p> <p>To test the potential role of gesture in reducing interference after learning of mathematical equivalence, we provided children with instruction on mathematical equivalence in their regular classrooms. Some classrooms received instruction that included gestures, and some classrooms received instruction that did not include gestures. Immediately after learning, some children in each classroom completed basic arithmetic problems designed to interfere with their learning and others completed a control task requiring identical operations on structurally dissimilar problems. Children were tested immediately after the interference task and again 24 h later.</p> <p>We expected that exposing children to problems with the equal sign immediately before the answer would disrupt retention of a newly acquired relational understanding of equivalence, because performing problems with the equal sign immediately before the answer during instruction has been shown to impair equivalence performance in both children and adults (Chesney &amp; McNeil, [<reflink idref="bib12" id="ref57">12</reflink>]; Crooks &amp; Alibali, [<reflink idref="bib25" id="ref58">25</reflink>]; McNeil, [<reflink idref="bib56" id="ref59">56</reflink>]; McNeil et al., [<reflink idref="bib61" id="ref60">61</reflink>]). We additionally expected that exposure to addition problems with the equal sign immediately before the answer would be more disruptive for children who had learned without gesture compared with children who had learned with gesture, based on the finding that gesture can support learning and retention of equivalence knowledge. Thus, we predicted that the difference in performance between children who solved interfering problems and control problems would be smaller for children who learned with gesture than those who learned without gesture.</p> <hd id="AN0175674256-7">Prior knowledge and hand gesture</hd> <p>Given that the goal of exposing children to problems with the equal sign immediately before the answer is to reactivate prior knowledge, the effects of the interference manipulation might depend on the specifics of children's prior knowledge. Prior work in other tasks suggests that the beneficial effect of gesture varies according to children's knowledge prior to instruction (e.g., Congdon, Kwon, &amp; Levine, [<reflink idref="bib17" id="ref61">17</reflink>]; Guarino &amp; Wakefield, [<reflink idref="bib32" id="ref62">32</reflink>]; Wakefield &amp; James, [<reflink idref="bib72" id="ref63">72</reflink>]). We wondered whether learners who use different strategies prior to instruction might show differences in how they respond to instruction and interference (as in Congdon et al., [<reflink idref="bib17" id="ref64">17</reflink>]). Children who use different strategies to solve equivalence problems show differences in how they reconstruct problems (McNeil &amp; Alibali, [<reflink idref="bib58" id="ref65">58</reflink>]) and in their endorsement of an operational definition of the equal sign (Knuth, Stephens, McNeil, &amp; Alibali, [<reflink idref="bib46" id="ref66">46</reflink>]). Accordingly, we thought that strategy use prior to instruction might affect how learners respond to gesture during instruction and interference after instruction. Children who tend to solve equivalence problems by adding up all of the numbers in the problem are more likely to make conceptual errors when reconstructing problems (McNeil &amp; Alibali, [<reflink idref="bib58" id="ref67">58</reflink>]). As conceptual errors are consistent with addition problems with the equal sign immediately before the answer, we wondered whether children who use this strategy might be particularly helped by gesture or especially susceptible to interference. Thus, we also explored whether the effect of gesture varied based on children's problem‐solving strategies prior to instruction, and whether differences in performance between children who solved interfering problems and control problems might also vary according to the problem‐solving strategies children used prior to instruction.</p> <hd id="AN0175674256-8">Method</hd> <p></p> <hd id="AN0175674256-9">Participants</hd> <p>Target sample size was estimated using simulations. Because instruction was randomized at the classroom level, the crucial variable for determining power was the number of recruited classrooms rather than the number of students in each classroom. To detect estimated effects, we planned to recruit 32 classrooms into our study.</p> <p>We recruited 659 second‐ and third‐grade students (318 female; 319 male; 22 unknown gender) from 33 classrooms in eight different elementary schools in Michigan using procedures approved by the Michigan State University Institutional Review Board. This experiment was conducted on a classroom‐wide level and all students in each classroom participated in the instruction and assessments. We used an opt‐out consent procedure for inclusion in the study. Information and consent forms were distributed to parents approximately 2 weeks before data collection and parents were asked to return the forms if they did not want their child's data to be included in the analysis. Before beginning procedures in each classroom, children provided verbal assent to confirm their voluntary participation in data analysis; one child declined to participate in the study. Teachers also provided consent. After data collection, data were destroyed for any child whose parents indicated that they did not want their child's data to be included in the study, and for the child who declined to provide assent to participate.</p> <p>We used weighted averages of the demographic data for each of the sampled schools to estimate the demographics of our sample. Most (82.3%) of the students from the sampled population qualified for a free or reduced‐price lunch based on average household income (range: 78.5–90.5%). The sampled population averaged 27.3% Caucasian (range: 25–35.4%), 37.2% African American (range: 30.1–39.3%), 18.5% Hispanic (range: 15.2–19.4%), 5.9% Asian/Pacific (range: 5.0–6.2%), 0.5% American Indian (range: 0.3–0.5%), and 10.6% multiracial (range: 9.6–13.9%).</p> <hd id="AN0175674256-10">Excluded participants</hd> <p></p> <hd id="AN0175674256-11">Schools and classrooms</hd> <p>Data from one school (<emph>n</emph> = 108, five classrooms) were excluded from all analyses because gesture instruction was mistakenly confounded with grade rather than counterbalanced by grade, due to experimenter error. Coincidentally, the school was also the only school sampled from a district with higher average socioeconomic status (SES) than the other schools in the sample.</p> <p>Data from two additional classrooms were also excluded from some of our analyses. For analyses including effects of interference, we excluded one classroom because all children who met our inclusion criteria (solving all pretest problems incorrectly, <emph>n</emph> = 10) were in the same interference condition; thus, we were not able to estimate a random classroom effect for these children. Finally, for analyses including grade as a factor, we excluded children from a mixed grade classroom (<emph>n</emph> = 17).</p> <hd id="AN0175674256-12">Individual exclusions</hd> <p>Children were individually excluded for a variety of reasons. For our planned analysis, we excluded children who answered at least one pretest question correctly (<emph>n</emph> = 118), because these children have at least some knowledge of equivalence prior to instruction. This criterion for exclusion was determined a priori and is consistent with our prior research (Cook et al., [<reflink idref="bib21" id="ref68">21</reflink>]). Finally, we excluded children who were missing data from the training or testing on Day 1 (<emph>n</emph> = 5). Children who did not complete some or all assessments on the second day were included in the analysis as our analytic approach is robust to missing data.</p> <p>After all exclusions, the sample used to test the main hypothesis was comprised of 412 children from 28 classrooms (196 female, 198 male, 18 without gender information; <emph>M<subs>age</subs></emph> = 8.37 years, <emph>SD<subs>age</subs></emph> = 0.74; 210 second graders (14 classrooms), 190 third graders (13 classrooms), and 12 children from a mixed second/third‐grade classroom. The sample used to test exploratory hypotheses about prior knowledge consisted of 400 children from 27 classrooms (194 female, 190 male, 16 without gender information; <emph>M<subs>age</subs></emph> = 8.35 years, <emph>SD<subs>age</subs></emph> = 0.74; 210 second graders (14 classrooms), 190 third graders (13 classrooms).</p> <hd id="AN0175674256-13">Design</hd> <p>This study had two sessions separated by approximately 24 h. On the first day, children completed a pretest in mathematical equivalence and then watched video instruction (Gesture or No Gesture) on how to solve equivalence problems. They solved a practice problem after each of four instructional videos. After this instruction, children solved problems that were either structurally similar (Interference) or structurally dissimilar (Control) to the equivalence problems for which they had received instruction. Finally, children completed an equivalence problem‐solving posttest and a transfer problem‐solving test.</p> <p>Approximately 24 h later, children completed a second equivalence problem‐solving posttest, a true‐false test, and a short answer test designed to assess their conceptual understanding of the equal sign. All materials can be found in Appendix A.</p> <p>Classrooms were randomly assigned to one of two Instruction conditions—Gesture and No Gesture. To control for variance across schools, within each school, Instruction condition was counterbalanced across classrooms of the same grade level. Finally, within classrooms, individual children were randomly assigned to a Similarity condition in which they solved either similar (Interference) or dissimilar (Control) problems after instruction. Half of the children in each classroom received workbook packets from each Similarity condition. Assignment to a Similarity condition was done without regard to children's consent status or pretest performance, and so the final sample was not perfectly balanced in each classroom.</p> <hd id="AN0175674256-14">Procedure</hd> <p></p> <hd id="AN0175674256-15">Pretest</hd> <p>Children first provided their name, age in years, the month they were born, and their gender. Children then solved two equivalence problems with equivalent addends, with the blank varying in position across the two problems (e.g., 5 + 7 + 3 = 5 + __ and 5 + 7 + 3 = __ + 3. See Appendix A for all materials). These problems were used to eliminate children with prior knowledge of the instructed concept and also formed the basis of our exploratory analysis of the role of children's prior knowledge.</p> <hd id="AN0175674256-16">Training</hd> <p>We created eight training videos (four for each condition) that described how to solve mathematical equivalence problems. The videos were each approximately 1 min long (<emph>M<subs>time</subs></emph> = 1:08 min, range: 1:07−1:09). In each video, a female instructor stands to the viewer's right of a monitor displaying an equivalence problem that does not have an answer in the blank. All problems included equivalent addends matching in position across the equal sign (e.g., 5 + 7 + 2 = 5 + __, where 5 is in the same position on both sides of the problem). The blank was always to the right of the equal sign. There were two problems where the blank was on the right side of the plus sign and two problems where the blank was on the left side of the plus sign. Both the equivalence problem and the instructor were in direct view of the camera throughout the video (Figure 1).</p> <p>In each video, the instructor explains that the sum on the right side of the equal sign should be the same as that on the left side of the equal sign. For example, in one training video, she explains how to solve the problem "4 + 6 + 2 = 4 + ___" by saying:</p> <p>"Remember, the equal sign means that the total amount on the left side must be the same as the right side. This will help us figure out what goes inside the blank. Let's figure out how to do this. Four plus six equals 10, 10 plus two equals 12, and what number plus four also equals 12? Four plus eight equals 12. You know you have the wrong answer if the amount on the right side of the equal sign is different than the amount on the left side of the equal sign. You know you have the right answer when the two sides are the same amount, which is 12 and 12. So, one side is equal to the other side."</p> <p>This same script was delivered in each of the videos with the only difference being the specific numbers in each of the problems and whether the video included gesture or not. In the videos with gesture, the instructor used deictic pointing gestures to indicate specific numbers in the equation as they are mentioned and representational gestures with the hands sweeping underneath the equation to emphasize the two sides of the equation when talking about the sides of the equation. In the videos without gesture, the instructor's hands rested at her side throughout the video.</p> <p>The gesture and no gesture explanations were individually recorded, and then carefully edited so they matched for prosody, speaking rate, instructor location, body position, and eye gaze, as can be seen in Fig. 1. To match the videos, we first selected similar takes for each pair of videos by listening to simultaneously presented audio from takes of the gesture and no gesture videos and watching overlapping videos. We chose the takes that were perceived to be highly similar across both modalities. Then, the video and the audio of each pair of videos (Gesture and No Gesture) were layered into a single project in Final Cut Pro for editing. We then identified silences that occurred at the same point in both videos. These were usually pauses between clauses. Then, we altered the timing of the silent portion of the No Gesture videos by speeding up or slowing down the silent portion of the video so that the timing of the spoken explanation of the No Gesture video exactly matched the timing of the Gesture video. Then, specific portions of the Gesture condition audio and corresponding video were edited in the same way to match the No Gesture condition. We chose to consistently edit the No Gesture files first to decrease the necessity of adjusting the timing of any of the gestures. After the audio and video were matched, the video and audio for all videos were enhanced to remove artifacts and increase clarity. Apart from the timing adjustments, identical audio and visual enhancement was applied to all eight videos. Thus, the two sets of videos were constructed to vary only in whether they contained gesture.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/CGN/01feb24/cogs13412-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="cogs13412-fig-0001.jpg" title="1 Schematic depiction of the experimental procedure. Classrooms were randomly assigned to Instructional conditions (Gesture or No Gesture) and students in each classroom were randomly assigned to Similarity conditions (Interference or Control)." /> </p> <p></p> <p>In each classroom, students watched either four Gesture videos or four No Gesture videos during instruction. After watching each instructional video, students solved one practice problem on a worksheet. All practice problems had equivalent addends and matched in the location of the blank with the problem in the immediately prior instructional video. The problems were all unique and did not appear in the pretest or in the training videos (or in any of the posttests). Students were not provided with any feedback or assistance while solving these problems.</p> <hd id="AN0175674256-18">Similarity</hd> <p>Following instruction and practice, students solved four standard addition problems with three numbers. As depicted in Fig. 1, these problems were either presented horizontally, so they were visually and structurally like the equivalence problems from the instructional videos (Interference) or presented vertically so they were visually and structurally unlike the equivalence problems used in the instruction (Control). Participants were randomly assigned to a Similarity condition (Interference or Control) such that roughly half of the students in each classroom received each condition.</p> <p>The problems in the Interference Condition were intended to interfere with the equivalence training by activating the idea that the equal sign means "put your answer down." These problems had the equal sign immediately before an answer blank. Prior work has shown that after solving several problems in this format, even adults show impaired performance on equivalence problems with multiple addends on both sides of the equal sign (Chesney, McNeil, Brockmole, &amp; Kelley, [<reflink idref="bib13" id="ref69">13</reflink>]; McNeil, [<reflink idref="bib56" id="ref70">56</reflink>]; McNeil et al., [<reflink idref="bib61" id="ref71">61</reflink>]). The problems in the Control Condition contained the same numbers and, therefore, required the same computations as the interference problems. Importantly, the control problems were oriented vertically, containing an equal bar rather than an equal sign. These problems should be less likely to activate specific knowledge of the equal sign. They were designed to control for both the act of problem solving after instruction and for the difficulty of the specific mathematical operations required.</p> <hd id="AN0175674256-19">Session one tests</hd> <p>After Instruction and Similarity, children completed two tests. For each problem on each test, the student needed to provide a numeric response. The first was a posttest that contained eight equivalence problems with equivalent addends matching in position across the equal sign, like those used during pretest and instruction. All problems were unique and did not appear in any of the other training or test materials. The second test was a transfer test that contained four equivalence problems with nonequivalent addends (e.g., 5 + 7 + 3 = _ + 4). These problems were intended to assess near transfer. Although these problems can be solved with the same strategy as that taught during instruction, the visual format of the problems is distinct so that some transfer is necessary. This session took approximately 25−35 min.</p> <hd id="AN0175674256-20">Session two tests</hd> <p>Approximately 24 h later, researchers returned to students' classrooms and administered four additional tests: a second equivalence posttest, a test of conceptual understanding of the equal sign, a test of configural understanding of the sides of an equation, and a test of definitional understanding of the equal sign (Appendix A). These conceptual, configural, and definitional tests were adapted from prior work (e.g., Rittle‐Johnson, Siegler, &amp; Alibali, [<reflink idref="bib68" id="ref72">68</reflink>]).</p> <p>The second equivalence test consisted of eight additional equivalence problems with equivalent addends matching in position across the equal sign, like those completed in the posttest in session one. Again, for each problem, the student needed to provide a numeric response. These problems were unique and did not appear in any of the other training or test materials. The conceptual test consisted of eight true/false problems. In these problems, children were instructed to assess already‐solved problems (e.g., "7 = 7" or "7 = 4 + 5") to indicate whether they believed each mathematical statement was right or wrong. Children circled "R" if they thought the problem was right and "W" if they thought the problem was wrong.[<reflink idref="bib1" id="ref73">1</reflink>] The configural test asked children to examine one problem: 5 + 4 + 8 = 9 + 8 and then "circle one side of the equation." Children were reminded that they were not required to solve the problem, only draw a circle.</p> <p>Finally, children were presented with two free‐response questions, which tested definitional understanding of the equal sign. Both questions were asked about a problem depicted at the top of the page: "3 + 4 = 7" with an arrow pointing directly at the equal sign from below. The first problem stated that the arrow was pointing to the equal sign and then asked, "What does the equal sign mean?" Children were instructed to write in their own words what they believed the equal sign means, and after, were asked, "Can the equal sign mean anything else? Please explain." This allowed students two opportunities to exhibit explicit knowledge of the equal sign. Session two lasted approximately 20 min. During all phases of the experiment, children remained in their assigned seats within their regular classroom.</p> <hd id="AN0175674256-21">Results</hd> <p>We used R to analyze the data (version 4.0.2, R Core Team, [<reflink idref="bib66" id="ref74">66</reflink>]). We used the tidyverse (version 2.0.0, Wickham, François, Henry &amp; Müller, [<reflink idref="bib74" id="ref75">74</reflink>]) package for data manipulation, cleaning, and visualization. Statistical analysis was completed with lme4 (version 1.1.34, Bates, Maechler, Bolker &amp; Walker, [<reflink idref="bib9" id="ref76">9</reflink>]) and contrasts were calculated with emmeans (version 1.7.2, Lenth, [<reflink idref="bib49" id="ref77">49</reflink>]).</p> <hd id="AN0175674256-22">Excluded variables</hd> <p>Performance was very poor (7% correct across the sample) on the written free response questions assessing definitional understanding of equivalence. Many children did not respond, and many responses were difficult to interpret due to variation in children's handwriting and spelling abilities. Accordingly, we eliminated this test from our analyses. This decision was made after we started to analyze the data; we did not establish criteria for removing measures from consideration prior to analysis.</p> <hd id="AN0175674256-23">Demographic variables</hd> <p>To investigate the relationship between demographic variables and learning, we used a logistic mixed‐effects regression model including Gender, Age, Grade, and School. We predicted the log odds of correctly solving each problem (Performance) from a model with main effects of the demographic variables of interest (Gender, Age, Grade, School) while controlling for Test (five levels: Day 1 Equivalence, Day 1 Transfer, Day 2 Equivalence, Day 2 Conceptual True/False, Day 2 Configural). We expected performance to vary according to the different problem types on each test, especially since the True/False questions have a chance level performance of 50%. We also included random intercepts for participants and for items (individual problems). We did not include the mixed grade classroom in models when we included Grade as a factor. Because classroom was confounded with instructional condition in our design, we did not include classroom as a demographic factor. Participants with missing gender were not included in any analyses that included gender as a factor.</p> <hd id="AN0175674256-24">Gender</hd> <p>There was no evidence for an effect of Gender on Performance (b = 0.03, z = 0.15, <emph>p</emph> =.88.</p> <hd id="AN0175674256-25">Grade</hd> <p>There was a significant positive effect of Grade on Performance, with third graders performing better than second graders (b = 1.31, z = 5.23, <emph>p</emph> &lt;.0001).</p> <hd id="AN0175674256-26">Age</hd> <p>There was a significant negative effect of Age on Performance, with older children performing worse than younger children (b = −0.38, z = −2.26, <emph>p</emph> =.024), contrary to expectations. However, there was also a high correlation between Grade and Age (<emph>r</emph><sups>2</sups> =.62), and so this unexpected effect might have been the result of multicollinearity between age and grade. Accordingly, we considered a subsequent demographic model without Grade. In this model, there was a positive, nonsignificant effect of Age on Performance (b = 0.17, z = 1.21, <emph>p</emph> =.23), as expected, and the effects of Gender and School were similar to the effects seen in the main demographic model.</p> <hd id="AN0175674256-27">School</hd> <p>We computed pairwise contrasts for the seven included schools in the full demographic model with the Tukey correction for multiple comparisons. There were significant differences across schools. Students in three of the schools performed significantly better than students in the lowest performing school (<emph>p</emph>'s &lt;.016), and students in one of the schools performed marginally better than students in the lowest performing school (<emph>p</emph> =.12). Students in two schools were no different than students in the lowest performing school (<emph>p's</emph> &gt;.23). There were no other trends toward differences in performance across schools in our study (all <emph>p'</emph>s &gt;.23).</p> <hd id="AN0175674256-28">Planned analyses</hd> <p>We planned to test our primary hypothesis with a logistic mixed‐effects regression model predicting the log odds of correctly solving each problem from an interaction between Instruction condition, Similarity condition, and Test. We also planned random intercepts for participants, who were nested within random classrooms, and items. Due to an oversight, we failed to finalize and submit our preregistration prior to beginning data analysis.</p> <p>Our model predicted the log odds of solving each problem correctly from the three‐way interaction between Instruction (two levels: Gesture, No Gesture), Similarity (two levels: Interference, Control), and Test (five levels: Day 1 Equivalence, Day 1 Near Transfer, Day 2 Equivalence, Day 2 Conceptual True/False, Day 2 Configural), as well as all lower‐level interactions. All factors were effect coded. We included random intercepts for participants, nested within classrooms, and random intercepts for problem.</p> <p>We predicted a three‐way interaction between Instruction, Similarity, and Test. To assess whether the three‐way interaction improved model fit, we compared the planned model to an identical model containing only two‐way interactions. Contrary to our hypothesis, the three‐way interaction between Instruction, Similarity, and Test did not significantly improve model fit (χ<sups>2</sups>(<reflink idref="bib4" id="ref78">4</reflink>) = 3.49, <emph>p</emph> =.48). Moreover, when we used contrasts to directly compare the difference between the similarity conditions for gesture and no gesture on each test, there were no significant contrasts (all <emph>p</emph>'s &gt;.25).</p> <p>We then compared the model with two‐way interactions to a model containing only main effects. The model with two‐way interactions provided a significantly better fit to the data (χ<sups>2</sups>(<reflink idref="bib9" id="ref79">9</reflink>) = 26.20, <emph>p</emph> =.0019). To examine the two‐way interactions, we calculated contrasts for each combination of our factors individually, that is, for the difference between Similarity conditions (Control – Interference) at each level of Instruction, the difference between Similarity conditions (Control – Interference) sat each level of Test, and the difference between Instruction conditions (Gesture – No Gesture) at each level of Test with the Tukey correction for multiple comparisons within each set of contrasts. Because we used a logistic regression model, all estimates for contrasts were calculated on the log odds ratio scale. For Similarity by Instruction, there was no evidence for an effect of Similarity in either Instruction Condition (Gesture: estimate = 0.05, z = 0.22, <emph>p</emph> =.821; No Gesture: estimate = 0.26, z = 0.96 <emph>p</emph> =.34). For Similarity by Test, there was a marginal benefit to solving Interference problems compared with Control problems on the Day 2 Equivalence problems (estimate = 0.35, z = 1.76, <emph>p</emph> =.08). There was no evidence for an effect on any other Test (Day 1 Equivalence: estimate = 0.08, z = 0.42, <emph>p</emph> =.67; Day 1 Near Transfer: estimate = −0.14, z = −0.61, <emph>p</emph> =.54; Day 2 Conceptual: b = 0.05, z = 0.24, <emph>p</emph> =.81; Day 2 Sides: estimate = 0.44, z = 1.4, <emph>p</emph> =.16). For Instruction by Test, there were nonsignificant trends toward positive effects of Gesture on Day 1 Equivalence (estimate = 0.5, z = 1.55, <emph>p</emph> =.12), Day 1 Near Transfer (estimate = −0.57, z = −1.67, <emph>p</emph> =.10), Day 2 Equivalence (estimate = 0.56, z = 1.74, <emph>p</emph> =.082), and Day 2 Configural (estimate = 0.57, z = 1.39, <emph>p</emph> =.16) problems. However, there was no evidence for a benefit of Gesture on Day 2 Conceptual problems (estimate = 0.06, z = 0.18, <emph>p</emph> =.86). Thus, the analysis of performance revealed trends for gesture to be associated with improved performance on all tests except for the Day 2 Conceptual problems (see Fig. 2). However, there was no evidence that gesture improved the ability to resist interference from solving similar problems after instruction or that solving similar problems after instruction interfered with performance for any type of problem, contrary to our predictions.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/CGN/01feb24/cogs13412-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="cogs13412-fig-0002.jpg" title="2 Estimated means for participants receiving Gesture and No Gesture Instruction for each of the Tests. Estimates were calculated using the model with two‐way interactions between Instruction, Similarity, and Test. The points depict the estimated proportion correct, and the lines represent the standard error of the estimate." /> </p> <p></p> <hd id="AN0175674256-30">Interference manipulation check</hd> <p>Given that we did not see any effects of interference in our model, we decided to directly compare performance during training with performance on the equivalence posttest as a test of our manipulation. We expected performance to decline from training to posttest as during the training children are solving problem immediately after receiving training on a structurally identical problem, and so the basic calculations are likely primed, artificially inflating performance. Our model predicted the log odds of solving each problem correctly from the three‐way interaction between Instruction (two levels: Gesture, No Gesture), Similarity (two levels: Interference, Control), and Test (two levels: Training, Day 1 Equivalence), as well as all lower‐level interactions. We also included School and Grade as control variables. All factors were effect coded. We included random intercepts for participants, nested within classrooms, and random intercepts for problem. We used contrasts to estimate the decline in performance (Training – Posttest) for each combination of Instruction and Interference and compared these contrasts to test whether this decline varied across our experimental factors. Because we used a logistic regression model, all estimates for contrasts were calculated on the log odds ratio scale. There was no evidence that the decline in performance was larger in the Interference group than the Control group, for participants who received Gesture Instruction (<emph>p</emph> =.80) or for participants who received No Gesture instruction (<emph>p</emph> =.15). If anything, the pattern of performance was most consistent with a lack of a decline in performance after solving Interference problems in the No Gesture Condition and a decline in all other groups (Fig. S1).</p> <hd id="AN0175674256-31">Exploratory analyses</hd> <p></p> <hd id="AN0175674256-32">Demographic factors</hd> <p>We next considered a model controlling for demographic factors that were related to performance. We added School and Grade as control factors to the originally planned model and compared this model to the planned model that did not include School and Grade. Both models excluded the combined second/third‐grade classroom. The model including demographic factors provided a significantly better fit to the data (χ<sups>2</sups>(<reflink idref="bib7" id="ref80">7</reflink>) = 28.80, <emph>p</emph> &lt;.001). We compared this model to simpler models and again found that the model with three‐way interactions was not significantly better than a model with only two‐way interactions (χ<sups>2</sups>(<reflink idref="bib4" id="ref81">4</reflink>) = 3.91, <emph>p</emph> =.42), while the model with only two‐way interactions was a significantly better fit than a model that only included main effects (χ<sups>2</sups>(<reflink idref="bib9" id="ref82">9</reflink>) = 20.53, <emph>p</emph> =.015). We again calculated contrasts and found a pattern of results that was nearly identical to the previously reported model that did not control for demographic factors. However, in this analysis, there were significant effects of gesture on Day 1 Equivalence (.40, z = 2.00, <emph>p</emph> =.045), Day 1 Near Transfer (.46, z = 1.98, <emph>p</emph> =.047), and Day 2 Equivalence (.46, z = 2.25, <emph>p</emph> =.024). Moreover, the trend for improved performance on Day 2 Equivalence problems after solving Interference problems was no longer significant (.29, z = 1.47, <emph>p</emph> =.14).</p> <hd id="AN0175674256-33">Factor analysis</hd> <p>Given that performance on the three problem‐solving tests showed similar patterns across our analyses, we next considered whether performance on the posttests was appropriately characterized according to our design, which included five separate tests of performance. We used a principal components analysis to assess the number of factors underlying performance across the five posttests. This analysis suggested that there were only two factors underlying performance. Inspection of the factors revealed that one factor was made up of all equation‐solving questions (posttest and transfer) and the second factor was made up of most of the questions from the conceptual test. There was one question from the conceptual test (7 = 7) that was negatively loaded for the conceptual factor and positively weighted for the equation‐solving factor, although more weakly than the other items. This item also had the lowest performance of all conceptual items (52% correct). The configural item testing understanding of sides loaded with the equation‐solving factor, although more weakly than the other items. Based on these patterns, we recoded the problems from all tests into a Problem Type variable with two levels, Equation‐solving problems (24 questions which required numeric responses) and Conceptual problems (seven questions which required right/wrong judgments). We excluded the negatively loaded conceptual item and the configural item from further analysis.</p> <p>We then reran our model with demographic factors with Problem Type. Again, the model with two‐way interactions provided the best fit to the data (Supplementary Material). Moreover, when we compared this model to a model that did not include the Similarity factor, there was no evidence that including similarity improved model fit (χ<sups>2</sups>(<reflink idref="bib3" id="ref83">3</reflink>) = 0.36, <emph>p</emph> =.95). In the final model, there was an interaction between Problem Type and Instruction. Post hoc contrasts revealed that, for Conceptual problems, there was no difference in performance between the Gesture and No Gesture instructional conditions (estimate = 0.0055, z =.023, <emph>p</emph> =.98), while for Equation‐solving problems, students who received instruction with Gesture performed significantly better than students who received instruction with No Gesture (estimate =.51, z = 2.23, <emph>p</emph> =.026, see Fig. 3).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/CGN/01feb24/cogs13412-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="cogs13412-fig-0003.jpg" title="3 Estimated means for children receiving Gesture and No Gesture Instruction for each of the Problem Types. Estimates were calculated using the model with two‐way interactions between Instruction, Similarity, and Problem Type. The points depict the estimated proportion correct, and the lines represent the standard error of the estimate." /> </p> <p></p> <hd id="AN0175674256-35">Prior knowledge</hd> <p>We expected that the Similarity manipulation would influence children's learning by reactivating incorrect prior knowledge. However, although all included children solved the pretest problems incorrectly, children used various incorrect strategies when solving the pretest problems. If the Similarity manipulation works by reactivating knowledge that children have prior to instruction, then the effect of Similarity might be expected to vary according to the strategies that children use prior to instruction. Accordingly, we explored whether there were differential effects of Similarity and Instruction depending on the specific problem‐solving strategies that children used on the pretest.</p> <p>As established in prior work (Perry, Breckinridge Church, &amp; Goldin‐Meadow, [<reflink idref="bib64" id="ref84">64</reflink>]; Hornberg, Wang &amp; McNeil, 2018), we used the solutions that children provided to the two pretest problems to infer the strategy that they were using to solve equivalence problems prior to instruction. In order to increase the number of children who could be included in this analysis, for the pretest problem that did not include a 2, we included answers that were 1 away from an answer to indicate use of that strategy.</p> <p>Two clear, large clusters of consistent strategy use were prevalent in our data set, the Add‐All‐Numbers strategy (AA) and the Add‐to‐Blank strategy (AB). In the Add‐All‐Numbers strategy (<emph>n</emph> = 104), children add all the numbers that they see in the problem. We considered children to use this strategy if they did this consistently for both pretest problems. In the Add‐to‐Blank strategy (<emph>n</emph> = 112), children add all the numbers to up to the answer blank in the problem, ignoring any numbers after the answer blank. We categorized children as using the Add‐to‐Blank strategy if they did this for both pretest problems. For example, for the problem 5 + 7 + 2 = __ + 2, if a child used the Add‐All‐Numbers strategy, they would indicate that the answer was 16. In contrast, if the child used the Add‐to‐Blank strategy, they would indicate that the answer was 14. There was, therefore, a one‐to‐one mapping between children's responses on the pretest and strategy categorization. There were also many children who provided answers that did not show a consistent strategy across the two pretest problems (<emph>n</emph> = 167). These children were categorized as "Inconsistent." Children in these three groups likely vary in how they conceptualize the problem. In the Add‐All‐Numbers strategy, children are demonstrating attention to the numbers in the problem but show no evidence of attending to the symbols in the problem or the structure of the problem. In contrast, in the Add‐to‐Blank strategy, children are sensitive to the location of the blank, indicating some attention to the structure of the problem. Other work has shown that children who use an Add‐All‐Numbers strategy may be less likely to accurately encode the structure of the equation compared with children who are using other strategies, including other incorrect strategies (McNeil &amp; Alibali, [<reflink idref="bib58" id="ref85">58</reflink>]). Because the children in these three groups were distributed across the 27 classrooms in the study, these children were randomly assigned to Instructional and Similarity conditions by our experimental design, providing a quasi‐experimental test of the effect of prior knowledge on performance. Accordingly, we analyzed whether pretest strategy interacted with instruction and similarity. Our model included demographic factors School and Grade as control variables and a four‐way interaction between Pretest Strategy (AA, AB, Inconsistent), Instruction, Similarity, and Problem Type. We compared this model to a model with only three‐way interactions and found that the more complex model provided a significantly better fit to the data (χ<sups>2</sups>(<reflink idref="bib4" id="ref86">4</reflink>) = 43.2, <emph>p</emph> &lt;.000001).</p> <p>To interpret the four‐way interaction (Fig. 4), we used contrasts to estimate the size of the difference between Similarity conditions (Control – Interference) across all combinations of Instruction, Problem Type, and Pretest Strategy. We then compared these contrasts to test whether this difference varied across Pretest Strategy groups by Instruction and Problem Type, with the Tukey adjustment for comparing a family of estimates. Because we used a logistic regression model, all estimates for contrasts were calculated on the log odds ratio scale. There was one significant contrast, and one trend. The effect of Similarity varied according to children's prior knowledge and type of instruction (see Fig. 4). When solving Equation‐Solving problems after receiving No Gesture Instruction, children who had used the Add‐All‐the‐Numbers (AA) strategy prior to instruction performed better after solving Control problems compared with Interference problems (estimate = 0.89) compared with children who had solved problems using Inconsistent strategies prior to instruction, who performed better after solving Interference problems compared with Control problems (estimate = −1.15, <emph>p</emph> =.027, Fig. 4, top left panel). A trend emerged when comparing the groups that used the Add‐All‐the‐Numbers (AA) and Add‐to‐Blank (AB) strategies prior to instruction. When solving Equation‐Solving problems after receiving No Gesture Instruction, the AA group performed better after solving Control problems compared with Interference problems (estimate = 0.89) compared to the AB group, who tended to performed better after solving Interference problems compared with Control problems (estimate = −0.79, <emph>p</emph> =.098, Fig. 4, top left panel). There was no other evidence for differential effects of Similarity across pretest strategy groups for any combination of problem type and Instruction (all <emph>p</emph>'s &gt;.30). Thus, there was some evidence that solving Interference problems after instruction negatively influenced Equation Solving relative to solving Control problems, but this pattern was only seen for children who had used the Add‐All‐the‐Numbers strategy prior to instruction and who had received No Gesture Instruction compared to children who had used the Add‐to‐Blank strategy and who had also received.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/CGN/01feb24/cogs13412-fig-0004.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="cogs13412-fig-0004.jpg" title="4 Estimated means for children receiving Control and Interference problems for both Instructional Conditions and Problem Types. Estimates were calculated using the model with two‐way interactions between Instruction, Similarity, and Problem Type. The points depict the estimated proportion correct, and the bars represent the standard error of the estimate." /> </p> <p></p> <p>We additionally used contrasts to compare the size of the difference between Instructional conditions (Gesture – No Gesture) across all combinations of Similarity, Problem Type, and Pretest Strategy. We then compared these contrasts to test whether this difference varied across Pretest Strategy groups by Instruction and Problem Type, with the Tukey adjustment for comparing a family of estimates. There were three significant contrasts, and one contrast with <emph>p</emph> =.11 (see Fig. 5). When solving Equation‐Solving problems after receiving Interference Problems after instruction, children in the AA group showed better performance in the Gesture condition relative to the No Gesture condition (estimate = 1.44) compared with children in the AB group (estimate = −.64, <emph>p</emph> =.018, Fig. 5, lower left panel). When solving Equation‐Solving problems after receiving Interference Problems after instruction, the AA group also showed a trend for a greater difference between the Gesture and No Gesture conditions compared with children who had solved problems using Inconsistent strategies (estimate =.046, <emph>p</emph> =.11, Fig. 5, lower left panel). When solving Conceptual problems after receiving Control Problems after instruction, children in the AA group also showed a greater difference between the Gesture and No Gesture conditions (estimate = 2.27) compared with children in the AB group (estimate = −.55, <emph>p</emph> =.003, Fig. 5, top right panel) or the Inconsistent group (estimate =.09, <emph>p</emph> =.018, Fig. 5, top right panel). There were no other significant contrasts (all <emph>p</emph>'s &gt;.27). Thus, it appeared that children who has used the Add‐All‐the‐Numbers strategy prior to instruction showed the largest difference between the Gesture Instruction and No Gesture instruction compared to children who had used the Add‐to‐Blank or Inconsistent strategies prior to instruction.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/CGN/01feb24/cogs13412-fig-0005.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="cogs13412-fig-0005.jpg" title="5 Estimated means for children receiving Gesture and No Gesture Instruction for each of the Similarity Conditions and Problem Types. Estimates were calculated using the model with two‐way interactions between Instruction, Similarity, and Problem Type. The points depict the estimated proportion correct, and the bars represent the standard error of the estimate." /> </p> <p></p> <hd id="AN0175674256-38">Discussion</hd> <p>Here, we attempted to understand the effect of gesture on learning by providing children with instruction that either did or did not include hand gesture and then interfering with children's learning by experimentally manipulating their postinstruction problem‐solving experience. After instruction, some children solved problems that were structurally similar to those used during instruction. These problems were expected to interfere with learning. Others solved problems that were dissimilar from those used during instruction that were not expected to interfere with learning. Consistent with prior work, there was a benefit associated with including gesture in instruction. However, our postinstructional manipulation did not successfully interfere with children's learning. Exploratory analyses suggested that the benefit of gesture was specific to performance on equation‐solving problems and was not present for conceptual problems and that children were differentially affected by instruction and interference, depending on the type of problem being solved and their strategy use prior to instruction.</p> <p>This work presents a large study investigating the beneficial effect of gesture on children's learning in a classroom context using random assignment. Although the results are largely consistent with prior studies demonstrating beneficial effects of gesture on learning, findings also suggest some caveats to the claim that gesture is a beneficial tool for supporting learning. The beneficial effect of gesture was not as large or as robust as that seen in prior work using individual tutorials (e.g., Cook et al., [<reflink idref="bib23" id="ref87">23</reflink>]; Koumoutsakis, Church, Alibali, Singer, &amp; Ayman‐Nolley, [<reflink idref="bib47" id="ref88">47</reflink>]; Wakefield, Novack, Congdon, Franconeri, &amp; Goldin‐Meadow, [<reflink idref="bib73" id="ref89">73</reflink>]) and was not observed when children were solving conceptual problems. It is not surprising to find that effects that are seen in more controlled environments are less robust when data are collected in more naturalistic contexts or with more diverse samples. However, it is also the case that the specifics of the materials and the instructional delivery, children's prior knowledge, and other aspects of the experimental context all vary considerably across studies and may underlie variations in patterns of performance.</p> <p>We did not find evidence that our interference manipulation consistently disrupted problem solving. This is inconsistent with prior work showing that these types of problems interfere with mathematical equivalence problem solving in both children and adults (Chesney &amp; McNeil, [<reflink idref="bib12" id="ref90">12</reflink>]; Crooks &amp; Alibali, [<reflink idref="bib25" id="ref91">25</reflink>]; McNeil, [<reflink idref="bib56" id="ref92">56</reflink>]; McNeil et al., [<reflink idref="bib61" id="ref93">61</reflink>]). Although our interference problems varied in their visual similarity to the instructed problems, unlike prior work, both the interference problems and the control problems used in this study required students to perform addition and may have activated similar problem‐solving schemas. Future work should investigate a wider variety of interference tasks, including tasks which vary in both visual similarity and in the similarity of the required mathematical operations to understand the potentially complex relation between prior knowledge, instruction, and interference.</p> <hd id="AN0175674256-39">The role of prior knowledge in learning</hd> <p>Many experimental studies of learning focus on tasks for which learners have little or no specific prior knowledge of the to‐be‐learned content, where learners can build new knowledge without replacing or overwriting previously learned material (Anderson, [<reflink idref="bib4" id="ref94">4</reflink>]). For example, learners who are acquiring foreign language vocabulary need to create associations between new words and concepts but do not typically have to overcome large numbers of previously established associations between the new words and other concepts. Indeed, building new associations is known to be difficult when there are previous associations in one's native language that are not consistent with the to‐be‐learned association (Frantzen, [<reflink idref="bib26" id="ref95">26</reflink>]). Importantly, instructional practices and principles developed in contexts where learners do not have specific prior knowledge of the to‐be‐learned material may not be effective when ported to learning environments where learners have considerable prior knowledge.</p> <p>It is striking that children in our study did not consistently benefit from gesture, in a task where gesture has previously been shown to be helpful. Instead, the benefits of instruction with gesture depended on the prior knowledge of the children receiving the instruction and on the type of problem being solved after instruction. A similar pattern has been reported for children participating in a lesson about measurement (Congdon et al., [<reflink idref="bib17" id="ref96">17</reflink>]). It is likely that the specific characteristics of both the spoken instruction and the accompanying gesture influence which children are likely to benefit from instruction (Kutaka et al., 2023). Similarly, the negative effects of our interference manipulation did not uniformly affect the children in this study. There was some suggestion that the interference manipulation may have specifically disrupted performance for children who received No Gesture Instruction and had solved problems using the Add‐All‐the‐Numbers strategy prior to instruction compared with learners who had Inconsistent problem solving prior to instruction. This pattern is consistent with our original hypothesis but suggests a less general effect of interference than originally postulated.</p> <p>This pattern of results is consistent with other work indicating that learning involves a complex interplay between prior knowledge and characteristics of instruction, and that prior knowledge and instruction interact (see Congdon &amp; Goldin‐Meadow, [<reflink idref="bib18" id="ref97">18</reflink>]). For example, in the expertise reversal effect, instructional techniques that support learning for novices do not work for individuals with more knowledge, which has been observed in both children (Congdon et al., [<reflink idref="bib17" id="ref98">17</reflink>]; Homer &amp; Plass, [<reflink idref="bib39" id="ref99">39</reflink>]) and adults (Kalyuga, Ayres, Chandler, &amp; Sweller, [<reflink idref="bib42" id="ref100">42</reflink>]). Experts sometimes do not benefit from additional visual support such as pictures or dynamic visualizations, while novices often require this additional visual support (Kalyuga, [<reflink idref="bib41" id="ref101">41</reflink>]). A related pattern of performance is also seen when examining how feedback influences mathematical learning. Feedback can impair learning for individuals with some knowledge but facilitate learning for those without prior knowledge (Fyfe &amp; Rittle‐Johnson, [<reflink idref="bib27" id="ref102">27</reflink>]).</p> <p>However, because the pattern of findings supporting the differential effects of gesture and interference depending on prior knowledge were based on exploratory analyses, additional research will be necessary to confirm this pattern. If the effects of observing gesture on learning vary across individuals depending on their prior knowledge, then understanding the mechanisms by which gesture influences learning will require studies with samples that are large enough to unpack these patterns.</p> <hd id="AN0175674256-40">Mechanisms by which gesture influences learning</hd> <p>The findings reported here provide some insight into mechanisms by which observing gesture may support learning. The fact that observing gesture differentially influenced learning depending on prior knowledge rules out more general mechanisms by which gesture has been postulated to support learning, such as increasing attention and engagement (Valenzeno, Alibali, &amp; Klatzky, [<reflink idref="bib71" id="ref103">71</reflink>]) or by providing an embodied conceptual representation (Gordon &amp; Ramani, [<reflink idref="bib30" id="ref104">30</reflink>]; Macedonia, [<reflink idref="bib51" id="ref105">51</reflink>]). If observing gesture facilitated learning by simply increasing overall attention or engagement during instruction or by providing an especially accessible format of information representation, we would expect observing gesture to benefit learners regardless of prior knowledge. These findings are also not consistent with accounts that suggest that gesture might engage or enhance specific memory mechanisms in support of learning (Cook et al., [<reflink idref="bib24" id="ref106">24</reflink>]), which would also be expected to be helpful for all learners. The fact that observing gesture benefitted some learners but did not benefit others suggests that the mechanisms by which gesture supports learning are not equally effective for all learners (Congdon &amp; Goldin‐Meadow, [<reflink idref="bib18" id="ref107">18</reflink>]).</p> <p>Because children who solved problems using the Add‐All‐the‐Numbers strategy showed the most consistent evidence of benefitting from instruction with gesture, observing gesture may have been helpful in supporting a piece of the correct understanding that children who solved problems using the Add‐All‐the‐Numbers strategy are missing. One possibility is that gesture may help children to appropriately encode the equation. Children who use an Add‐All‐Numbers strategy have greater difficulty encoding the structure of the equation in comparison with children who use other strategies (McNeil &amp; Alibali, [<reflink idref="bib58" id="ref108">58</reflink>]). When asked to reproduce equations after viewing them, these children often fail to include the equal sign, or place the equal sign in an incorrect location at the end of the problem and before an answer blank. If gesture supports effective encoding, then gesture should be most helpful for those children who are having difficulty with appropriate encoding. Indeed, other work has shown that gesture may be an effective tool for supporting encoding (Yeo et al., [<reflink idref="bib76" id="ref109">76</reflink>]), and that supporting encoding can support knowledge change (Alibali et al., [<reflink idref="bib2" id="ref110">2</reflink>]). Together, these findings suggest that changing the way children encode information is a potential mechanism that might explain the difference in the effect of gesture seen here. If this account is correct, then we would expect measures of encoding to predict sensitivity to gesture in instruction above and beyond pretest strategy use. Future work can test this hypothesis.</p> <p>Another possibility is that gesture is supporting learning by disambiguating the meaning of the instructor's spoken message. For this account to be consistent with the data reported here, we would have to postulate that children's ability to understand the instructor's spoken message depends on their prior knowledge. Given the role of prior knowledge in language comprehension more generally (e.g., McNamara &amp; Kintsch, 1996), this seems likely. Children who are solving the problem using the Add‐All‐the‐Numbers strategy may fail to correctly understand the instructor's use of the terms "equal sign" or "side" during instruction. Gesture may be one approach that helps children link mathematical vocabulary to mathematical notation in support of learning (Alibali et al., [<reflink idref="bib3" id="ref111">3</reflink>]), but other manipulations might also serve a similar function.</p> <hd id="AN0175674256-41">Comparisons with previously reported findings on the role of gesture in learning</hd> <p>Our study varied in design from prior work investigating the effect of observing gesture on learning mathematical equivalence in some important ways. First, instruction was administered in classrooms via controlled video (similar to prior work in Piagetian conservation, Church, Ayman‐Nolley, &amp; Mahootian, [<reflink idref="bib14" id="ref112">14</reflink>]). There were benefits associated with observing instruction with gesture; however, these benefits were not robust. Although children who learned with gesture tended to numerically outperform those who learned without gesture on all three equation‐solving tasks (Day 1 Equivalence, Day 1 Near Transfer, Day 2 Equivalence), in our planned analysis, we did not find strong statistical support for an effect of gesture. In addition, the size of the observed effect of gesture was smaller than the effect seen in our prior work using a similar paradigm (e.g., Cook et al., [<reflink idref="bib21" id="ref113">21</reflink>]; Cook, Friedman, Duggan, Cui, &amp; Popescu, [<reflink idref="bib22" id="ref114">22</reflink>]), and was limited to equation‐solving problems in our exploratory analysis. However, because we implemented instructions at the classroom level, and we included classroom as a random effect in our analysis, this study was somewhat limited by design in being able to statistically detect effects of instruction. Instead, the study was designed and powered to detect interactions between instruction with gesture and the type of problems solved after instruction, which were implemented at the individual level.</p> <p>Second, our use of an opt‐out consent procedure makes it likely that this sample is representative of urban school children in the United States, compared with studies using laboratory samples or opt‐in consent procedures that are only able to include children whose parents can bring them to the lab or who successfully return permission slips. If research on gesture is going to improve learning in classrooms, researchers need to test gestures in classroom environments using diverse samples (e.g., Church et al., [<reflink idref="bib14" id="ref115">14</reflink>]).</p> <p>Third, our video instructions were longer and more detailed than those often used in similar experimental work (e.g., Cook et al., [<reflink idref="bib21" id="ref116">21</reflink>]). We explained the correct strategy and indicated how to test whether an answer was correct or not. These instructions may be more like classroom instruction compared to instructions used in previous experimental studies of how gesture influences learning, which are often very short, with limited verbal and gestural content. Effects of gesture may be greater when the available information is limited (Aldugom &amp; Cook, 2022).</p> <p>Fourth, the instructions controlled several factors with high precision. We went beyond simply ensuring that instructions were highly similar across conditions and instead used a meticulous video editing process to ensure that the instructor's body position, eye gaze, and prosody were identical across conditions. This allows us to be more certain that the findings reported are entirely due to gesture and not due to other differences across videos.</p> <hd id="AN0175674256-42">Strengths and limitations</hd> <p>One strength of this study is that it is likely to have strong external validity. Our sample size was large, and our study was implemented in classrooms. We also conducted our study in a location with a diverse participant population and used an opt‐out consent procedure. Furthermore, we randomized our intervention within this diverse sample. Also, as previously mentioned, our videos were carefully edited to ensure that the only difference between instructional conditions was the use of hand gesture.</p> <p>This study also has some limitations. Although these data provide empirical support for the claim that the effects of instruction with gesture may vary according to students' prior knowledge (as in Congdon et al., [<reflink idref="bib17" id="ref117">17</reflink>]), this conclusion is based on exploratory analyses. These findings should be replicated in a confirmatory design and could also be explored in archival data sets to assess whether there is additional evidence to support the findings reported here. It would also be helpful to include more fine‐grained assessment of children's knowledge prior to instruction, as this could provide further insight into underlying mechanisms by which gesture supports learning.</p> <p>One additional limitation is that while we studied a concept that is important for children's subsequent development in mathematics, these results may not reflect learning of other concepts or learning in other domains. This work should be extended to other mathematical concepts and other domains. Unpacking the relation between characteristics of learners and characteristics of the instructions from which they benefit can provide insight into the learning process that can be used to deliver personalized, multimodal, instruction to learners across domains.</p> <hd id="AN0175674256-43">Future directions and conclusions</hd> <p>In this study, we aimed to understand the mechanisms underlying learning with gesture by interfering with learning. We predicted that interference would not impair learning if instruction included gesture but would negatively impact learning if instruction did not include gesture. Although these predictions were not realized in the data, our exploratory analyses revealed differences in the benefit of gesture and the impairment of interference on learning, based on children's prior knowledge. This reveals a complex relationship between prior knowledge and interventions to improve learning (Congdon et al., [<reflink idref="bib17" id="ref118">17</reflink>], Greve, Cooper, Tibon, &amp; Henson, [<reflink idref="bib31" id="ref119">31</reflink>]; Hambrick &amp; Engle, [<reflink idref="bib33" id="ref120">33</reflink>]; Witherby &amp; Carpenter, [<reflink idref="bib75" id="ref121">75</reflink>]). Because pretest accuracy did not differ between children who were differentially influenced by gesture, these data also reveal that basic performance may not be an appropriate indicator of prior knowledge. Instead, assessments of prior knowledge may need to go beyond simple performance measures to assess the way that students approach problem solving. For example, children who produce gesture‐speech mismatches in the domain of mathematical equivalence have been shown to be especially likely to learn from instruction (Perry et al., [<reflink idref="bib64" id="ref122">64</reflink>]); these children may respond differently to various forms of instruction compared with children who do not produce gesture‐speech mismatches. Future work should probe other problem‐solving strategies and design interventions based on these strategies.</p> <p>This research also suggests that a thorough understanding of the relationship between prior knowledge and instruction may increase the efficacy of interventions designed to optimize learning. Although preliminary, it suggests that failing to consider students' prior knowledge may lead to the development of interventions that work for children with prevalent forms of knowledge, but these interventions may be less effective or ineffective for children with less prevalent forms of knowledge. Targeting students' prior knowledge may, therefore, increase the efficacy of instruction.</p> <hd id="AN0175674256-44">Acknowledgments</hd> <p>This paper is dedicated to the memory of Ryan Glenn Duffy. We thank Andrew Mistak and Jeffrey Shymanski for help with stimulus creation, and Michelle Stepan, Alison Day, Kelsey Pagorek, Nataly Dawood, Islam Said, Sundeep Dhanjal, Virginia Smith, Parul Gupta, and Sravya Mallajosyula for help with data collection. This work is supported by the National Science Foundation Grant Nos 1561182 and 1561122, to the first and last authors, respectively. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.</p> <hd id="AN0175674256-45">Open Research Badges</hd> <p>This article has earned Open Data badges and Open Materials badges. Data and materials are available at https://osf.io/pcn5j/.</p> <hd id="AN0175674256-46">A Appendix Test and training equivalence problems</hd> <p>Day 1 Assessments</p> <p></p> <p> <ephtml> &lt;table&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Pretest&lt;/td&gt;&lt;td&gt;Training&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;6 + 3 + 8 = 6 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td&gt;3 + 2 + 7 = &amp;#95;&amp;#95; + 7&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;5 + 7 + 2 = &amp;#95;&amp;#95; + 2&lt;/td&gt;&lt;td&gt;7 + 5 + 8 = &amp;#95;&amp;#95; + 8&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td /&gt;&lt;td&gt;3 + 8 + 7 = 3 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td /&gt;&lt;td&gt;4 + 9 + 8 = 4 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;p&gt;Addition problems&lt;/p&gt;&lt;p&gt;(&lt;italic&gt;Contol condition&lt;/italic&gt;)&lt;/p&gt;&lt;/td&gt;&lt;td&gt;Addition problems (&lt;italic&gt;Interference condition&lt;/italic&gt;)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;p&gt;&lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics xmlns=""&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mspace width="0.28em" /&gt;&lt;annotation encoding="application/x-tex"&gt;$\frac{{ \def\eqcellsep{&amp;}\begin{array}{@{}*{2}{c}@{}} \;&amp;4\\ \;&amp;7\\ + &amp;9 \end{array} }}{\;}$&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/p&gt;&lt;/td&gt;&lt;td&gt;4 + 7 + 9 = &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;p&gt;&lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics xmlns=""&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mspace width="0.28em" /&gt;&lt;annotation encoding="application/x-tex"&gt;$\frac{{ \def\eqcellsep{&amp;}\begin{array}{@{}*{2}{c}@{}} \;&amp;8\\ \;&amp;3\\ + &amp;5 \end{array} }}{\;}$&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/p&gt;&lt;/td&gt;&lt;td&gt;8 + 3 + 5 = &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;p&gt;&lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics xmlns=""&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mspace width="0.28em" /&gt;&lt;annotation encoding="application/x-tex"&gt;$\frac{{ \def\eqcellsep{&amp;}\begin{array}{@{}*{2}{c}@{}} \;&amp;6\\ \;&amp;2\\ + &amp;4 \end{array} }}{\;}$&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/p&gt;&lt;/td&gt;&lt;td&gt;6 + 2 + 4 = &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;p&gt;&lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics xmlns=""&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mspace width="0.28em" /&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mspace width="0.28em" /&gt;&lt;annotation encoding="application/x-tex"&gt;$\frac{{ \def\eqcellsep{&amp;}\begin{array}{@{}*{2}{c}@{}} \;&amp;7\\ \;&amp;5\\ + &amp;6 \end{array} }}{\;}$&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/p&gt;&lt;/td&gt;&lt;td&gt;7 + 5 + 6 = &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Posttest&lt;/td&gt;&lt;td&gt;Transfer test&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;8 + 3 + 4 = &amp;#95;&amp;#95; + 4&lt;/td&gt;&lt;td&gt;9 + 4 + 7 = &amp;#95;&amp;#95; + 6&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;3 + 2 + 6 = 3 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td&gt;4 + 2 + 5 = 3 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;7 + 2 + 6 = 7 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td&gt;8 + 6 + 3 = 7 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;6 + 8 + 7 = &amp;#95;&amp;#95; + 7&lt;/td&gt;&lt;td&gt;3 + 8 + 5 = &amp;#95;&amp;#95; + 4&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2 + 6 + 3 = 2 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td /&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;5 + 4 + 8 = &amp;#95;&amp;#95; + 8&lt;/td&gt;&lt;td /&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;3 + 7 + 6 = 3 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td /&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;9 + 7 + 2 = &amp;#95;&amp;#95; + 2&lt;/td&gt;&lt;td /&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <p>Day 2 Assessments</p> <p></p> <p> <ephtml> &lt;table&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Posttest&lt;/td&gt;&lt;td&gt;Conceptual test&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;6 + 2 + 5 = 6 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td&gt;7 = 4 + 5&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;4 + 8 + 3 = 4 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td&gt;6 = 4 + 2&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;3 + 9 + 4 = &amp;#95;&amp;#95; + 4&lt;/td&gt;&lt;td&gt;7 = 7&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;7 + 4 + 2 = &amp;#95;&amp;#95; + 2&lt;/td&gt;&lt;td&gt;8 = 5 + 3&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2 + 7 + 6 = 2 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td&gt;9 = 6 + 2&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;5 + 6 + 3 = 5 + &amp;#95;&amp;#95;&lt;/td&gt;&lt;td&gt;6 = 6 + 0&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;9 + 4 + 3 = &amp;#95;&amp;#95; + 3&lt;/td&gt;&lt;td&gt;7 + 6 = 6 + 6 + 1&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;8 + 7 + 6 = &amp;#95;&amp;#95; + 6&lt;/td&gt;&lt;td&gt;13 + 16 = 16 + 13&lt;/td&gt;&lt;td&gt;R W&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Test of understanding of side&lt;/td&gt;&lt;td&gt;Test of conceptual understanding of the equal sign&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;&lt;p&gt;Circle one side of the equation:&lt;/p&gt;&lt;p&gt;5 + 4 + 8 = 9 + 8&lt;/p&gt;&lt;/td&gt;&lt;td&gt;&lt;p&gt;The following questions are about this statement: 3 + 4 = 7&lt;/p&gt;&lt;p&gt;&lt;bold&gt;&amp;#8593;&lt;/bold&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td /&gt;&lt;td&gt;The arrow above points to an equal sign. What does the equal sign mean?&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td /&gt;&lt;td&gt;Can the equal sign mean anything else? Please explain.&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/CGN/01feb24/cogs13412-fig-0006.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="cogs13412-fig-0006.jpg" title="A1 An example of (a) Gesture and (b) No Gesture instructional training videos taken from the same timepoint. Each classroom was randomly assigned to an Instructional condition before the first session." /> </p> <p></p> <ref id="AN0175674256-48"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref73" type="bt">1</bibl> <bibtext> To avoid confusion between right and wrong due to the silent /w/, we piloted our procedure with TRUE and FALSE, but these were difficult for the children in our sample and led to confusion in the classroom. Performance on the conceptual problems was well above chance in our sample (.66 correct), suggesting that children generally understood the task. Moreover, there were clear instructions on the page ("Please look at each problem and decide whether the problem is right or wrong. Circle R for Right and W for Wrong."). However, it is possible that individual children confused the meaning of the responses or failed to understand the task, reducing performance in this task.</bibtext> </blist> </ref> <ref id="AN0175674256-49"> <title> References </title> <blist> <bibtext> Aldugom, M., &amp; Cook, S. W. (2022). Does the amount of instruction influence the benefit of learning with gesture? Paper presented at the International Society for Gesture Studies. Chicago, IL.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref110" type="bt">2</bibl> <bibtext> Alibali, M. W., Crooks, N. M., &amp; McNeil, N. M. (2018). Perceptual support promotes strategy generation: Evidence from equation solving. British Journal of Developmental Psychology, 36 (2), 153 – 168.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref83" type="bt">3</bibl> <bibtext> Alibali, M. W., Nathan, M. J., Wolfgram, M. S., Church, R. B., Jacobs, S. A., Johnson Martinez, C., &amp; Knuth, E. J. (2014). How teachers link ideas in mathematics instruction using speech and gesture: A corpus analysis. Cognition and instruction, 32 (1), 65 – 100.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref78" type="bt">4</bibl> <bibtext> Anderson, J. R. (1987). Methodologies for studying human knowledge. Behavioral and Brain Sciences, 10 (3), 467 – 477.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref31" type="bt">5</bibl> <bibtext> Bahrick, L. E., &amp; Lickliter, R. (2000). Intersensory redundancy guides attentional selectivity and perceptual learning in infancy. Developmental Psychology, 36 (2), 190 – 201. https://doi.org/10.1037/0012‐1649.36.2.190</bibtext> </blist> <blist> <bibl id="bib6" idref="ref32" type="bt">6</bibl> <bibtext> Bahrick, L. E., &amp; Lickliter, R. (2014). Learning to Attend Selectively: The Dual Role of Intersensory Redundancy. Current Directions in Psychological Science, 23 (6), 414 – 420. https://doi.org/10.1177/0963721414549187</bibtext> </blist> <blist> <bibl id="bib7" idref="ref8" type="bt">7</bibl> <bibtext> Barbieri, C. A., Miller‐Cotto, D., &amp; Booth, J. L. (2019). Lessening the Load of Misconceptions: Design‐Based Principles for Algebra Learning. Journal of the Learning Sciences, 28 (3), 381 – 417. https://doi.org/10.1080/10508406.2019.1573428</bibtext> </blist> <blist> <bibl id="bib8" idref="ref38" type="bt">8</bibl> <bibtext> Baroody, A. J., &amp; Ginsburg, H. P. (1983). The effects of instruction on children's understanding of the "equals" sign. The Elementary School Journal, 84 (2), 199 – 212</bibtext> </blist> <blist> <bibl id="bib9" idref="ref76" type="bt">9</bibl> <bibtext> Bates, D., Mächler, M., Bolker, B., &amp; Walker, S. (2015). Fitting Linear Mixed‐Effects Models Using lme4. Journal of Statistical Software, 67 (1), 1 – 48. https://doi.org/10.18637/jss.v067.i01</bibtext> </blist> <blist> <bibtext> Booth, J. L., McGinn, K. M., Barbieri, C., &amp; Young, L. K. (2017). Misconceptions and learning algebra. In S. Stewart (Ed.), And the rest is just algebra (pp. 63 – 78). Springer International Publishing</bibtext> </blist> <blist> <bibtext> Byrd, C. E., McNeil, N. M., Chesney, D. L., &amp; Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to children's learning of early algebra. Learning and Individual Differences, 38, 61 – 67.</bibtext> </blist> <blist> <bibtext> Chesney, D. L., &amp; McNeil, N. M. (2014). Activation of operational thinking during arithmetic practice hinders learning and transfer. Journal of Problem Solving, 7 (1), 24 – 35.</bibtext> </blist> <blist> <bibtext> Chesney, D. L., McNeil, N. M., Brockmole, J. R., &amp; Kelley, K. (2013). An eye for relations: Eye‐tracking indicates long‐term negative effects of operational thinking on understanding of math equivalence. Memory &amp; Cognition, 41 (7), 1079 – 1095.</bibtext> </blist> <blist> <bibtext> Church, R. B., Ayman‐Nolley, S., &amp; Mahootian, S. (2004). The role of gesture in bilingual education: Does gesture enhance learning? International Journal of Bilingual Education and Bilingualism, 7 (4), 303 – 319.</bibtext> </blist> <blist> <bibtext> Clements, D. H., Sarama, J., Baroody, A. J., Kutaka, T. S., Chernyavskiy, P., Joswick, C., ... &amp; Joseph, E. (2021). Comparing the efficacy of early arithmetic instruction based on a learning trajectory and teaching‐to‐a‐target. Journal of Educational Psychology, 113 (7), 1323.</bibtext> </blist> <blist> <bibtext> Congdon, E. L., Novack, M. A., Brooks, N., Hemani‐Lopez, N., O'Keefe, L., &amp; Goldin‐Meadow, S. (2017). Better together: Simultaneous presentation of speech and gesture in math instruction supports generalization and retention. Learning and Instruction, 50, 65 – 74.</bibtext> </blist> <blist> <bibtext> Congdon, E. L., Kwon, M. K., &amp; Levine, S. C. (2018). Learning to measure through action and gesture: Children's prior knowledge matters. Cognition, 180, 182 – 190.</bibtext> </blist> <blist> <bibtext> Congdon, E. L., &amp; Goldin‐Meadow, S. (2021). Mechanisms of embodied learning through gestures and actions: Lessons from development. In M. D. Robinson &amp; L. E. Thomas (Eds.), Handbook of embodied psychology: Thinking, feeling, and acting (pp. 527 – 546).</bibtext> </blist> <blist> <bibtext> Cook, S. W. (2011). Abstract thinking in space and time: Using gesture to learn math. Cognition, Brain, Behavior, 15, 553 – 570.</bibtext> </blist> <blist> <bibtext> Cook, S. W. (2018). Enhancing learning with hand gestures: Potential mechanisms. In Psychology of learning and motivation (Vol. 69, pp. 107 – 133). Academic Press.</bibtext> </blist> <blist> <bibtext> Cook, S. W., Duffy, R. G., &amp; Fenn, K. M. (2013). Consolidation and transfer of learning after observing hand gesture. Child Development, 84 (6), 1863 – 1871.</bibtext> </blist> <blist> <bibtext> Cook, S. W., Friedman, H. S., Duggan, K. A., Cui, J., &amp; Popescu, V. (2017). Hand gesture and mathematics learning: Lessons from an Avatar. Cognitive Science, 41 (2), 518 – 535.</bibtext> </blist> <blist> <bibtext> Cook, S. W., Mitchell, Z., &amp; Goldin‐Meadow, S. (2008). Gesturing makes learning last. Cognition, 106, 1047 – 1058.</bibtext> </blist> <blist> <bibtext> Cook, S. W., Yip, T. K., &amp; Goldin‐Meadow, S. (2010). Gesturing makes memories that last. Journal of Memory and Language, 63 (4), 465 – 475.</bibtext> </blist> <blist> <bibtext> Crooks, N. M., &amp; Alibali, M. W. (2013). Noticing relevant problem features: Activating prior knowledge affects problem solving by guiding encoding. Frontiers in Psychology, 4, 884.</bibtext> </blist> <blist> <bibtext> Frantzen, D. (1998). Intrinsic and extrinsic factors that contribute to the difficulty of learning false cognates. Foreign Language Annals, 31 (2), 243 – 254.</bibtext> </blist> <blist> <bibtext> Fyfe, E. R., &amp; Rittle‐Johnson, B. (2016). Feedback both helps and hinders learning: The causal role of prior knowledge. Journal of Educational Psychology, 108 (1), 82 – 97.</bibtext> </blist> <blist> <bibtext> Goldin‐Meadow, S., &amp; Alibali, M. W. (2013). Gesture's role in speaking, learning, and creating language. Annual Review of Psychology, 64, 257 – 283.</bibtext> </blist> <blist> <bibtext> Goldin‐Meadow, S., Kim, S., &amp; Singer, M. (1999). What the teacher's hands tell the student's mind about math Journal of Educational Psychology, 91, 720 – 730.</bibtext> </blist> <blist> <bibtext> Gordon, R., &amp; Ramani, G. B. (2021). Integrating embodied cognition and information processing: A combined model of the role of gesture in children's mathematical environments. Frontiers in Psychology, 12, 650286.</bibtext> </blist> <blist> <bibtext> Greve, A., Cooper, E., Tibon, R., &amp; Henson, R. N. (2019). Knowledge is power: Prior knowledge aids memory for both congruent and incongruent events, but in different ways. Journal of Experimental Psychology: General, 148 (2), 325 – 341.</bibtext> </blist> <blist> <bibtext> Guarino, K. F., &amp; Wakefield, E. M. (2020). Teaching Analogical Reasoning With Co‐speech Gesture Shows Children Where to Look, but Only Boosts Learning for Some. Front Psychol. 11, 575628. https://doi.org/10.3389/fpsyg.2020.575628. PMID: 33071916; PMCID: PMC7538547.</bibtext> </blist> <blist> <bibtext> Hambrick, D. Z., &amp; Engle, R. W. (2002). Effects of domain knowledge, working memory capacity, and age on cognitive performance: An investigation of the knowledge‐is‐power hypothesis. Cognitive Psychology, 44 (4), 339 – 387.</bibtext> </blist> <blist> <bibtext> Heikkilä, J., Alho, K., Hyvönen, H., &amp; Tiippana, K. (2015). Audiovisual semantic congruency during encoding enhances memory performance. Experimental Psychology, 62, 123 – 130.</bibtext> </blist> <blist> <bibtext> Heikkilä, J., &amp; Tiippana, K. (2016). School‐aged children can benefit from audiovisual semantic congruency during memory encoding. Experimental brain research, 234, 1199 – 1207.</bibtext> </blist> <blist> <bibtext> Herszage, J., &amp; Censor, N. (2018). Modulation of learning and memory: A shared framework for interference and generalization. Neuroscience, 392, 270 – 280.</bibtext> </blist> <blist> <bibtext> Holle, H., &amp; Gunter, T. C. (2007). The role of iconic gestures in speech disambiguation: ERP evidence. Journal of Cognitive Neuroscience, 19 (7), 1175 – 1192. https://doi.org/10.1162/jocn.2007.19.7.1175</bibtext> </blist> <blist> <bibtext> Holle, H., Obermeier, C., Schmidt‐Kassow, M., Friederici, A. D., Ward, J., &amp; Gunter, T. C. (2012). Gesture facilitates the syntactic analysis of speech. Frontiers in Psychology, 3, 74.</bibtext> </blist> <blist> <bibtext> Homer, B. D., &amp; Plass, J. L. (2010). Expertise reversal for iconic representations in science visualizations. Instructional Science, 38 (3), 259 – 276.</bibtext> </blist> <blist> <bibtext> Hubbard, A. L., Wilson, S. M., Callan, D. E., &amp; Dapretto, M. (2009). Giving speech a hand: Gesture modulates activity in auditory cortex during speech perception. Human Brain Mapping, 30 (3), 1028 – 1037.</bibtext> </blist> <blist> <bibtext> Kalyuga, S. (2007). Expertise reversal effect and its implications for learner‐tailored instruction. Educational Psychology Review, 19 (4), 509 – 539.</bibtext> </blist> <blist> <bibtext> Kalyuga, S., Ayres, P., Chandler, P., &amp; Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38 (1), 23 – 31.</bibtext> </blist> <blist> <bibtext> Kang, S., Hallman, G. L., Son, L. K., &amp; Black, J. B. (2013). The different benefits from different gestures in understanding a concept. Journal of Science Education and Technology, 22 (6), 825 – 837.</bibtext> </blist> <blist> <bibtext> Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317 – 326.</bibtext> </blist> <blist> <bibtext> Kita, S., Alibali, M. W., &amp; Chu, M. (2017). How do gestures influence thinking and speaking? The gesture‐for‐conceptualization hypothesis. Psychological Review, 124 (3), 245.</bibtext> </blist> <blist> <bibtext> Knuth, E. J., Stephens, A. C., McNeil, N. M., &amp; Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37 (4), 297 – 312.</bibtext> </blist> <blist> <bibtext> Koumoutsakis, T., Church, R. B., Alibali, M. W., Singer, M., &amp; Ayman‐Nolley, S. (2016). Gesture in instruction: Evidence from live and video lessons. Journal of Nonverbal Behavior, 40, 301 – 315.</bibtext> </blist> <blist> <bibtext> Kutaka, T. S., Chernyavskiy, P., Sarama, J., &amp; Clements, D. H. (2023). Ordinal models to analyze strategy sophistication: Evidence from a learning trajectory efficacy study. Journal of School Psychology, 97, 77 – 100.</bibtext> </blist> <blist> <bibtext> Lenth, R. V. (2022). Emmeans: Estimated marginal means, aka least‐squares means. https://CRAN.R‐project.org/package=emmeans</bibtext> </blist> <blist> <bibtext> Li, W., Wang, F., Mayer, R. E., &amp; Liu, H. (2019). Getting the point: Which kinds of gestures by pedagogical agents improve multimedia learning? Journal of Educational Psychology, 111 (8), 1382 – 1395.</bibtext> </blist> <blist> <bibtext> Macedonia, M. (2014). Bringing back the body into the mind: Gestures enhance word learning in foreign language. Frontiers in Psychology, 5, 1467.</bibtext> </blist> <blist> <bibtext> Mathias, B., &amp; von Kriegstein, K. (2023). Enriched learning: behavior, brain, and computation. Trends in Cognitive Sciences.</bibtext> </blist> <blist> <bibtext> Matthews, P. G., &amp; Fuchs, L. S. (2020). Keys to the gate? Equal sign knowledge at second grade predicts fourth‐grade algebra competence. Child Development, 91 (1), E14 – E28.</bibtext> </blist> <blist> <bibtext> McNamara, D. S., &amp; Kintsch, W. (1996) Learning from texts: Effects of prior knowledge and text coherence, Discourse Processes, 22 (3), 247 – 288, https://doi.org/10.1080/01638539609544975</bibtext> </blist> <blist> <bibtext> McNeil, N. M. (2007). U‐shaped development in math: 7‐Year‐olds outperform 9‐year‐olds on equivalence problems. Developmental Psychology, 43 (3), 687 – 695.</bibtext> </blist> <blist> <bibtext> McNeil, N. M. (2008). Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can hinder learninger of mathematical equivalence. Child Development, 79, 1524 – 1537.</bibtext> </blist> <blist> <bibtext> McNeil, N. M. (2014). A "change‐resistance" account of children's difficulties understanding mathematical equivalence. Child Development Perspectives, 8, 42 – 47.</bibtext> </blist> <blist> <bibtext> McNeil, N. M., &amp; Alibali, M. W. (2004). You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science, 28 (3), 451 – 466. https://doi.org/10.1016/j.cogsci.2003.11.002</bibtext> </blist> <blist> <bibtext> McNeil, N. M., &amp; Alibali, M. W. (2005). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development, 6 (2), 285 – 306.</bibtext> </blist> <blist> <bibtext> McNeil, N. M., Grandau, L., Knuth, E. J., Alibali, M. W., Stephens, A. C., Hattikudur, S., &amp; Krill, D. E. (2006). Middle‐school students' understanding of the equal sign: The books they read can't help. Cognition and Instruction, 24 (3), 367 – 385.</bibtext> </blist> <blist> <bibtext> McNeil, N. M., Rittle‐Johnson, B., Hattikudur, S., &amp; Petersen, L. A. (2010). Continuity in representation between children and adults: Arithmetic knowledge hinders undergraduates' algebraic problem solving. Journal of Cognition and Development, 11 (4), 437 – 457.</bibtext> </blist> <blist> <bibtext> Novack, M. A., Congdon, E. L., Hemani‐Lopez N., &amp; Goldin‐Meadow S. (2014). From action to abstraction: using the hands to learn math. Psychol Sci, 25 (4): 903 ‐ 910. https://doi.org/10.1177/0956797613518351.</bibtext> </blist> <blist> <bibtext> Novack, M., &amp; Goldin‐Meadow, S. (2015). Learning from gesture: How our hands change our minds. Educational Psychology Review, 27, 405 – 412.</bibtext> </blist> <blist> <bibtext> Perry, M., Breckinridge Church, R., &amp; Goldin‐Meadow, S. (1988). Transitional knowledge in the acquisition of concepts. Cognitive Development, 3 (4), 359 – 400.</bibtext> </blist> <blist> <bibtext> Ping, R. M., &amp; Goldin‐Meadow, S. (2008). Hands in the air: Using ungrounded iconic gestures to teach children conservation of quantity. Developmental Psychology, 44, 1277 – 1287.</bibtext> </blist> <blist> <bibtext> R Core Team. (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R‐project.org/.</bibtext> </blist> <blist> <bibtext> Rittle‐Johnson, B., &amp; Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91 (1), 175 – 189. https://doi.org/10.1037/0022‐0663.91.1.175</bibtext> </blist> <blist> <bibtext> Rittle‐Johnson, B., Siegler, R. S., &amp; Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93 (2), 346 – 362.</bibtext> </blist> <blist> <bibtext> Sauter, M., Uttal, D. H., Alman, A. S., Goldin‐Meadow, S., &amp; Levine, S. C. (2012). Learning what children know about space from looking at their hands: The added value of gesture in spatial communication. Journal of Experimental Child Psychology, 111 (4), 587 – 606.</bibtext> </blist> <blist> <bibtext> Singer, M. A., &amp; Goldin‐Meadow, S. (2005). Children learn when their teacher's gestures and speech differ. Psychological Science, 16 (2), 85 – 89.</bibtext> </blist> <blist> <bibtext> Valenzeno, L., Alibali, M. W., &amp; Klatzky, R. (2003). Teachers' gestures facilitate students' learning: A lesson in symmetry. Contemporary Educational Psychology, 28 (2), 187 – 204.</bibtext> </blist> <blist> <bibtext> Wakefield, E. M., &amp; James, K. H. (2015). Effects of learning with gesture on children's understanding of a new language concept. Developmental Psychology, 51 (8), 1105 – 1114. https://doi.org/10.1037/a003947</bibtext> </blist> <blist> <bibtext> Wakefield, E., Novack, M. A., Congdon, E. L., Franconeri, S., &amp; Goldin‐Meadow, S. (2018). Gesture helps learners learn, but not merely by guiding their visual attention. Developmental Science, 21 (6), e12664.</bibtext> </blist> <blist> <bibtext> Wickham, H., François, R., Henry, L., &amp; Müller, K. (2020) Dplyr: A Grammar of Data Manipulation. R Package Version 0.8.4. https://CRAN.R‐project.org/package=dplyr</bibtext> </blist> <blist> <bibtext> Witherby, A. E., &amp; Carpenter, S. K. (2022). The rich‐get‐richer effect: Prior knowledge predicts new learning of domain‐relevant information. Journal of Experimental Psychology: Learning, Memory, and Cognition, 48 (4), 483 – 498. https://doi.org/10.1037/xlm0000996</bibtext> </blist> <blist> <bibtext> Yeo, A., Cook, S. W., Nathan, M. J., Popescu, V., &amp; Alibali, M. W. (2018). Instructor gesture improves encoding of mathematical representations. In Proceedings of the 40th Annual Conference of the Cognitive Science Society.</bibtext> </blist> </ref> <aug> <p>By Susan Wagner Cook; Elle M. D. Wernette; Madison Valentine; Mary Aldugom; Todd Pruner and Kimberly M. Fenn</p> <p>Reported by Author; Author; Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib59" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib60" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib44" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib11" firstref="ref4"></nolink> <nolink nlid="nl5" bibid="bib53" firstref="ref5"></nolink> <nolink nlid="nl6" bibid="bib57" firstref="ref6"></nolink> <nolink nlid="nl7" bibid="bib10" firstref="ref7"></nolink> <nolink nlid="nl8" bibid="bib21" firstref="ref9"></nolink> <nolink nlid="nl9" bibid="bib19" firstref="ref10"></nolink> <nolink nlid="nl10" bibid="bib28" firstref="ref12"></nolink> <nolink nlid="nl11" bibid="bib29" firstref="ref13"></nolink> <nolink nlid="nl12" bibid="bib43" firstref="ref14"></nolink> <nolink nlid="nl13" bibid="bib50" firstref="ref15"></nolink> <nolink nlid="nl14" bibid="bib65" firstref="ref16"></nolink> <nolink nlid="nl15" bibid="bib69" firstref="ref17"></nolink> <nolink nlid="nl16" bibid="bib23" firstref="ref19"></nolink> <nolink nlid="nl17" bibid="bib24" firstref="ref20"></nolink> <nolink nlid="nl18" bibid="bib16" firstref="ref21"></nolink> <nolink nlid="nl19" bibid="bib20" firstref="ref23"></nolink> <nolink nlid="nl20" bibid="bib30" firstref="ref24"></nolink> <nolink nlid="nl21" bibid="bib51" firstref="ref25"></nolink> <nolink nlid="nl22" bibid="bib45" firstref="ref26"></nolink> <nolink nlid="nl23" bibid="bib38" firstref="ref27"></nolink> <nolink nlid="nl24" bibid="bib40" firstref="ref28"></nolink> <nolink nlid="nl25" bibid="bib37" firstref="ref29"></nolink> <nolink nlid="nl26" bibid="bib63" firstref="ref30"></nolink> <nolink nlid="nl27" bibid="bib52" firstref="ref33"></nolink> <nolink nlid="nl28" bibid="bib76" firstref="ref34"></nolink> <nolink nlid="nl29" bibid="bib62" firstref="ref36"></nolink> <nolink nlid="nl30" bibid="bib70" firstref="ref37"></nolink> <nolink nlid="nl31" bibid="bib56" firstref="ref40"></nolink> <nolink nlid="nl32" bibid="bib67" firstref="ref41"></nolink> <nolink nlid="nl33" bibid="bib55" firstref="ref43"></nolink> <nolink nlid="nl34" bibid="bib12" firstref="ref47"></nolink> <nolink nlid="nl35" bibid="bib61" firstref="ref49"></nolink> <nolink nlid="nl36" bibid="bib25" firstref="ref50"></nolink> <nolink nlid="nl37" bibid="bib34" firstref="ref52"></nolink> <nolink nlid="nl38" bibid="bib35" firstref="ref53"></nolink> <nolink nlid="nl39" bibid="bib36" firstref="ref55"></nolink> <nolink nlid="nl40" bibid="bib17" firstref="ref61"></nolink> <nolink nlid="nl41" bibid="bib32" firstref="ref62"></nolink> <nolink nlid="nl42" bibid="bib72" firstref="ref63"></nolink> <nolink nlid="nl43" bibid="bib58" firstref="ref65"></nolink> <nolink nlid="nl44" bibid="bib46" firstref="ref66"></nolink> <nolink nlid="nl45" bibid="bib13" firstref="ref69"></nolink> <nolink nlid="nl46" bibid="bib68" firstref="ref72"></nolink> <nolink nlid="nl47" bibid="bib66" firstref="ref74"></nolink> <nolink nlid="nl48" bibid="bib74" firstref="ref75"></nolink> <nolink nlid="nl49" bibid="bib49" firstref="ref77"></nolink> <nolink nlid="nl50" bibid="bib64" firstref="ref84"></nolink> <nolink nlid="nl51" bibid="bib47" firstref="ref88"></nolink> <nolink nlid="nl52" bibid="bib73" firstref="ref89"></nolink> <nolink nlid="nl53" bibid="bib26" firstref="ref95"></nolink> <nolink nlid="nl54" bibid="bib18" firstref="ref97"></nolink> <nolink nlid="nl55" bibid="bib39" firstref="ref99"></nolink> <nolink nlid="nl56" bibid="bib42" firstref="ref100"></nolink> <nolink nlid="nl57" bibid="bib41" firstref="ref101"></nolink> <nolink nlid="nl58" bibid="bib27" firstref="ref102"></nolink> <nolink nlid="nl59" bibid="bib71" firstref="ref103"></nolink> <nolink nlid="nl60" bibid="bib14" firstref="ref112"></nolink> <nolink nlid="nl61" bibid="bib22" firstref="ref114"></nolink> <nolink nlid="nl62" bibid="bib31" firstref="ref119"></nolink> <nolink nlid="nl63" bibid="bib33" firstref="ref120"></nolink> <nolink nlid="nl64" bibid="bib75" firstref="ref121"></nolink> |
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| Items | – Name: Title Label: Title Group: Ti Data: How Prior Knowledge, Gesture Instruction, and Interference after Instruction Interact to Influence Learning of Mathematical Equivalence – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Susan+Wagner+Cook%22">Susan Wagner Cook</searchLink><br /><searchLink fieldCode="AR" term="%22Elle+M%2E+D%2E+Wernette%22">Elle M. D. Wernette</searchLink><br /><searchLink fieldCode="AR" term="%22Madison+Valentine%22">Madison Valentine</searchLink><br /><searchLink fieldCode="AR" term="%22Mary+Aldugom%22">Mary Aldugom</searchLink><br /><searchLink fieldCode="AR" term="%22Todd+Pruner%22">Todd Pruner</searchLink><br /><searchLink fieldCode="AR" term="%22Kimberly+M%2E+Fenn%22">Kimberly M. Fenn</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22Cognitive+Science%22"><i>Cognitive Science</i></searchLink>. 2024 48(2). – 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: 30 – Name: DatePubCY Label: Publication Date Group: Date Data: 2024 – Name: SourceSuprt Label: Sponsoring Agency Group: SrcSuprt Data: National Science Foundation (NSF) – Name: NumberContract Label: Contract Number Group: NumCntrct Data: 1561182<br />1561122 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Journal Articles<br />Reports - Research – Name: Audience Label: Education Level Group: Audnce Data: <searchLink fieldCode="EL" term="%22Early+Childhood+Education%22">Early Childhood Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+2%22">Grade 2</searchLink><br /><searchLink fieldCode="EL" term="%22Primary+Education%22">Primary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+3%22">Grade 3</searchLink> – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Prior+Learning%22">Prior Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Nonverbal+Communication%22">Nonverbal Communication</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+2%22">Grade 2</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+3%22">Grade 3</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Video+Technology%22">Video Technology</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Instructional+Effectiveness%22">Instructional Effectiveness</searchLink><br /><searchLink fieldCode="DE" term="%22Interference+%28Learning%29%22">Interference (Learning)</searchLink> – Name: DOI Label: DOI Group: ID Data: 10.1111/cogs.13412 – Name: ISSN Label: ISSN Group: ISSN Data: 0364-0213<br />1551-6709 – Name: Abstract Label: Abstract Group: Ab Data: Although children learn more when teachers gesture, it is not clear "how" gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly resistant to interference. We investigated this possibility in a classroom study with 402 second- and third-grade children. Participants received classroom-level instruction in mathematical equivalence using videos with or without accompanying gesture. After instruction, children solved problems that were either visually similar to the problems that were taught, and consistent with an operational interpretation of the equal sign (interference), or visually distinct from equivalence problems and without an equal sign (control) in order to assess the role of gesture in resisting interference after learning. Gesture facilitated learning, but the effects of gesture and interference varied depending on type of problem being solved and the strategies that children used to solve problems prior to instruction. Some children benefitted from gesture, while others did not. These findings have implications for understanding the mechanisms underlying the beneficial effect of gesture on mathematical learning, revealing that gesture does not work via a general mechanism like enhancing attention or engagement that would apply to children with all forms of prior knowledge. – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: Note Label: Notes Group: Note Data: https://osf.io/pcn5j – Name: DateEntry Label: Entry Date Group: Date Data: 2024 – Name: AN Label: Accession Number Group: ID Data: EJ1418270 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1418270 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1111/cogs.13412 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 30 Subjects: – SubjectFull: Prior Learning Type: general – SubjectFull: Nonverbal Communication Type: general – SubjectFull: Grade 2 Type: general – SubjectFull: Grade 3 Type: general – SubjectFull: Elementary School Students Type: general – SubjectFull: Mathematics Instruction Type: general – SubjectFull: Video Technology Type: general – SubjectFull: Problem Solving Type: general – SubjectFull: Instructional Effectiveness Type: general – SubjectFull: Interference (Learning) Type: general Titles: – TitleFull: How Prior Knowledge, Gesture Instruction, and Interference after Instruction Interact to Influence Learning of Mathematical Equivalence Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Susan Wagner Cook – PersonEntity: Name: NameFull: Elle M. D. Wernette – PersonEntity: Name: NameFull: Madison Valentine – PersonEntity: Name: NameFull: Mary Aldugom – PersonEntity: Name: NameFull: Todd Pruner – PersonEntity: Name: NameFull: Kimberly M. Fenn IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 0364-0213 – Type: issn-electronic Value: 1551-6709 Numbering: – Type: volume Value: 48 – Type: issue Value: 2 Titles: – TitleFull: Cognitive Science Type: main |
| ResultId | 1 |
