Mathematics-Writing Performance of Students Experiencing Mathematics Difficulties in China
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| Title: | Mathematics-Writing Performance of Students Experiencing Mathematics Difficulties in China |
|---|---|
| Language: | English |
| Authors: | Xiaonan Han (ORCID |
| Source: | Journal of Learning Disabilities. 2026 59(3):185-201. |
| Availability: | SAGE Publications and Hammill Institute on Disabilities. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: journals@sagepub.com; Web site: https://sagepub.com |
| Peer Reviewed: | Y |
| Page Count: | 17 |
| Publication Date: | 2026 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Elementary Education Grade 6 Intermediate Grades Middle Schools |
| Descriptors: | Foreign Countries, Mathematics Skills, Writing (Composition), Learning Problems, Elementary School Students, Grade 6, Writing Skills, Vocabulary, Computation |
| Geographic Terms: | China |
| DOI: | 10.1177/00222194251391829 |
| ISSN: | 0022-2194 1538-4780 |
| Abstract: | This study aimed to conduct a comprehensive investigation into the mathematics-writing (MW) performance of students with mathematics difficulties (MDs) in China. We compared the performance of students with MD with their typically developing (TD) and high-performing (HP) peers. The analysis was based on a sample of 138 sixth-grade students. Our findings revealed (a) the trend in MW performance followed the hierarchy of mathematics ability levels (HP > TD > MD), whereas all groups displayed similar performance in general writing (HP = TD = MD), (b) although all three groups were able to organize their ideas in general writing, they had difficulty structuring their ideas effectively in MW, and (c) students with MD were less likely to incorporate technical mathematics vocabulary and symbols in their MW; they were also more likely to write incomplete sentences and make punctuation mistakes in their MW. Implications for educational strategies, teaching methodologies, and targeted support interventions are discussed. |
| Abstractor: | As Provided |
| Entry Date: | 2026 |
| Accession Number: | EJ1502797 |
| Database: | ERIC |
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| FullText | Links: – Type: pdflink Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwF-PvMcdkG2eSsMeVB8aRU3AAAA4jCB3wYJKoZIhvcNAQcGoIHRMIHOAgEAMIHIBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDJK6jTtSDRs_L88FOgIBEICBmohGmKhctSMhOqRVbWCbDs1Zlckv_QG2BWdqXvoRaaBv14VPCGmms31QkWDzYMTHkzEd6elEUENowFtVH3wwhZG0KhyITmhIJtcRvHgGmdzm7eQbjRB6jaR5pe7xF-J9zXSjnPOdmX9IPIi58c-PXxSX0YUWAQXAgBjOJiedoHUFwVepwFYvBlBcQZGPFZKL9cxiC2UxezQcLZE= Text: Availability: 1 Value: <anid>AN0192937329;led01may.26;2026Apr14.06:50;v2.2.500</anid> <title id="AN0192937329-1">Mathematics-Writing Performance of Students Experiencing Mathematics Difficulties in China </title> <p>This study aimed to conduct a comprehensive investigation into the mathematics-writing (MW) performance of students with mathematics difficulties (MDs) in China. We compared the performance of students with MD with their typically developing (TD) and high-performing (HP) peers. The analysis was based on a sample of 138 sixth-grade students. Our findings revealed (a) the trend in MW performance followed the hierarchy of mathematics ability levels (HP &gt; TD &gt; MD), whereas all groups displayed similar performance in general writing (HP = TD = MD), (b) although all three groups were able to organize their ideas in general writing, they had difficulty structuring their ideas effectively in MW, and (c) students with MD were less likely to incorporate technical mathematics vocabulary and symbols in their MW; they were also more likely to write incomplete sentences and make punctuation mistakes in their MW. Implications for educational strategies, teaching methodologies, and targeted support interventions are discussed.</p> <p>Keywords: mathematics difficulty; primary school; mathematics writing; China</p> <p>Mathematics-writing (MW) refers to the communication of mathematical ideas in written forms and is recognized as a critical component of students' mathematics learning ([<reflink idref="bib11" id="ref1">11</reflink>]). For example, in mainland China, the Mathematics Curriculum Standards for Compulsory Education ([<reflink idref="bib44" id="ref2">44</reflink>]) emphasizes that "through the language of mathematics, students can describe quantitative relationships and spatial forms concisely and precisely, construct mathematical models to express and solve problems and develop the ability to express and communicate mathematically (p. 6)." The U.S. Common Core State Standards ([<reflink idref="bib15" id="ref3">15</reflink>]) also highlight the importance of students being able to communicate with precision, construct logical arguments, evaluate mathematics reasoning, articulate problem-solving strategies, and utilize clear and appropriate mathematics vocabulary.</p> <p>However, MW poses challenges for many students, particularly those with mathematics difficulties (MDs; [<reflink idref="bib31" id="ref4">31</reflink>]). This challenge stems from the need to not only understand mathematical concepts but also to clearly articulate reasoning and procedures using appropriate mathematics vocabulary in a logical, organized manner ([<reflink idref="bib30" id="ref5">30</reflink>]; [<reflink idref="bib58" id="ref6">58</reflink>]). The clear communication of mathematical ideas is critical because even minor ambiguities in writing can lead to misunderstandings or incorrect interpretations. This highlights the essential role of MW in ensuring students can convey their mathematical thinking accurately and clearly, making it a vital skill for demonstrating their understanding of mathematics ([<reflink idref="bib68" id="ref7">68</reflink>]). Despite much research on students' MW (e.g., [<reflink idref="bib14" id="ref8">14</reflink>]; [<reflink idref="bib20" id="ref9">20</reflink>]; [<reflink idref="bib26" id="ref10">26</reflink>]; [<reflink idref="bib31" id="ref11">31</reflink>]), there is still limited research specifically examining the MW of students with MD. Although some studies have investigated the MW of students with MD ([<reflink idref="bib4" id="ref12">4</reflink>]), none of them have included typically developing (TD) students as a comparison group. As a result, the extent to which students with MD differ from their TD peers in terms of MW remains unclear.</p> <p>In this introduction, we begin by providing a definition of MW and elaborating on the features that can be used to assess students' MW. We then proceed to review recent studies that have examined the MW performance of students with MD.</p> <hd id="AN0192937329-2">Mathematics-writing (MW)</hd> <p>MW can be done in both formal and informal formats ([<reflink idref="bib25" id="ref13">25</reflink>]; [<reflink idref="bib57" id="ref14">57</reflink>]). Informal MW, like writing journals or letters, encourages students to demonstrate their thinking processes and mathematics problem-solving in various ways. Studies suggested such activities improve students' problem-solving skills and vocabulary mastery ([<reflink idref="bib10" id="ref15">10</reflink>]; [<reflink idref="bib21" id="ref16">21</reflink>]). However, informal MW may not adequately prepare students for formal MW and high-stakes exams ([<reflink idref="bib57" id="ref17">57</reflink>]) because it is usually evaluated more holistically or qualitatively, rather than through detailed scoring rubrics like formal writing ([<reflink idref="bib58" id="ref18">58</reflink>]). Informal writing often lacks the structure, precision, and precise mathematics vocabulary that are critical in formal MW. Consequently, students may find it challenging to move from casual explanations of their reasoning to the more rigorous and standardized expressions required in formal assessments.</p> <p>Formal MW, typically found in textbooks and high-stake assessments, is designed to encourage students to communicate mathematics concepts for understanding and evaluation clearly. Tasks in this format often require students to explain their work or analyze whether a hypothetical student's work is correct. Formal writing is characterized by the use of a rubric that assesses both the writing process and their understanding of the involved mathematics concepts ([<reflink idref="bib57" id="ref19">57</reflink>]). This approach helps researchers establish clear criteria for evaluating responses and assessing various features of MW ([<reflink idref="bib48" id="ref20">48</reflink>]).</p> <p>Formal writing can be divided into four categories: exploratory, informative or explanatory, argumentative, and creative ([<reflink idref="bib11" id="ref21">11</reflink>]). Argumentative MW involves students making a claim or argument about a mathematics topic, supported by evidence or logical reasoning ([<reflink idref="bib7" id="ref22">7</reflink>]). In this study, we intentionally employ argumentative MW to engage students and promote a deeper involvement with mathematical reasoning, which is a core feature of mathematics as defined by [<reflink idref="bib49" id="ref23">49</reflink>], p. 59).</p> <hd id="AN0192937329-3">MW Features</hd> <p>Similar to previous research on formal MW, we included organization features, mathematics content, mathematics vocabulary, writing grammar, and clarity and precision as features for assessing MW (see Figures 1 and 2). These features are essential because they provide insight into both the depth of students' understanding and their ability to articulate mathematical concepts, both of which are important for MW ([<reflink idref="bib25" id="ref24">25</reflink>]). To clarify, the features identified in this study apply specifically to formal writing.</p> <p>Graph: Figure 1. Mathematics-Writing Scoring Rubric Used in This Study (Part 1). Note. Shaded areas indicate distinctions between the study's rubric and the comparison rubric, as described in the MW scoring section.</p> <p>Graph: Figure 2. Mathematics-Writing Scoring Rubric Used in This Study (Part 2). Note. Shaded areas indicate distinctions between the study's rubric and the comparison rubric, as described in the MW scoring section.</p> <hd id="AN0192937329-4">Organizational Features</hd> <p>Students approach MW similarly to general writing, starting with an introduction in one or two sentences, providing supporting details and reasoning, and then drawing a conclusion in one or two sentences, which highlights the importance of both the introduction and conclusion, as well as the critical role of paragraph structure and transition words in organization ([<reflink idref="bib35" id="ref25">35</reflink>]). Research in general writing indicates that a well-structured essay, with clear paragraph divisions, helps organize ideas logically, making the text easier for readers to follow and understand ([<reflink idref="bib35" id="ref26">35</reflink>]). This is particularly important in MW, where the logical progression of mathematical reasoning is essential for effectively communicating solutions and arguments ([<reflink idref="bib61" id="ref27">61</reflink>]). In addition, transition words play a key role in guiding the reader through the argument, connecting ideas and ensuring that the flow of reasoning is clear and persuasive ([<reflink idref="bib7" id="ref28">7</reflink>]; [<reflink idref="bib54" id="ref29">54</reflink>]). Well-placed transitions can enhance the readability and coherence of mathematical logical thinking and arguments, helping students articulate their reasoning more effectively. Previous studies have revealed a moderate correlation between general writing ability and MW performance ([<reflink idref="bib57" id="ref30">57</reflink>]).</p> <p> <emph>Argumentative MW</emph> is generally complex in structure. It includes a clear stance, multiple paragraphs for claims or contrary opinions ([<reflink idref="bib17" id="ref31">17</reflink>]), and transitions that emphasize logic and reasoning. Specifically, in the introduction of argumentative MW, the writer usually begins with background information to set the context before clearly stating the main argument part ([<reflink idref="bib18" id="ref32">18</reflink>]). In addition, transition words like <emph>therefore, however, consequently</emph>, and <emph>in contrast</emph> are used to connect ideas and evidence, ensuring the argument is coherent and persuasive.</p> <hd id="AN0192937329-5">Mathematics Content</hd> <p>To provide accurate responses to MW, students need to navigate the mathematics content effectively ([<reflink idref="bib4" id="ref33">4</reflink>]). This feature ensures that the core mathematical concepts and procedures are accurately represented in students' writing. When students assess the work of a hypothetical student, they must be able to verify the accuracy of the solution before crafting their argument ([<reflink idref="bib25" id="ref34">25</reflink>]; [<reflink idref="bib57" id="ref35">57</reflink>]). When providing their own solution, they need to resolve the problem and then clearly outline the steps they took to reach their answer ([<reflink idref="bib31" id="ref36">31</reflink>]). For example, consider a task where students assess the work of a hypothetical student, Alex, who incorrectly calculates the area of a rectangle by adding the length and width, stating that "8 units + 3 units = 11 square units." A student who fully understands the mathematical concepts and procedural knowledge involved would explain that the area should be calculated by multiplying the length and width (8 units × 3 units = 24 square units) and articulate the underlying concept of area. If a student correctly identifies the error and provides the correct calculation but omits an explanation of the underlying concept or makes a minor mistake in the explanation, they might receive fewer points. This mathematics content score thus reflects the depth of the student's understanding and their ability to accurately apply and explain mathematical concepts.</p> <hd id="AN0192937329-6">Mathematics Vocabulary</hd> <p>Mathematics vocabulary encompasses the specific words or phrases frequently encountered by students during mathematical instruction and evaluation, such as <emph>nominator, minus</emph>, and <emph>sixty</emph> ([<reflink idref="bib47" id="ref37">47</reflink>]). Mastery of vocabulary is imperative for students' understanding and progress in mathematics ([<reflink idref="bib36" id="ref38">36</reflink>]; [<reflink idref="bib39" id="ref39">39</reflink>]; [<reflink idref="bib41" id="ref40">41</reflink>]; [<reflink idref="bib52" id="ref41">52</reflink>]; [<reflink idref="bib55" id="ref42">55</reflink>]). In MW, the accurate use of mathematics vocabulary allows students to communicate their understanding clearly and concisely, ensuring that their arguments are both correct and easily understood by others ([<reflink idref="bib2" id="ref43">2</reflink>]; [<reflink idref="bib59" id="ref44">59</reflink>]). Without a strong grasp of mathematics vocabulary, students may struggle to express their ideas accurately, leading to misunderstandings or ambiguities in their writing.</p> <p>In MW, students used different types of mathematics vocabulary and representations ([<reflink idref="bib25" id="ref45">25</reflink>]). [<reflink idref="bib45" id="ref46">45</reflink>] have divided mathematics vocabulary into four categories: technical, subtechnical, general, and symbolic. Technical vocabulary includes vocabulary that is uniquely defined within the realm of mathematics, like <emph>parallelogram</emph>. Subtechnical vocabulary involves vocabulary that carries multiple meanings and is used across various subjects, such as <emph>variable</emph>. General vocabulary consists of words that are commonly utilized in daily life but also carry importance within the realm of mathematics, <emph>line</emph>, for example. Symbolic vocabulary refers to the numerals and symbols that signify particular mathematical ideas, such as the number <emph>5</emph>. This framework has gained broad acceptance in research (e.g., [<reflink idref="bib25" id="ref47">25</reflink>]; [<reflink idref="bib53" id="ref48">53</reflink>]; [<reflink idref="bib56" id="ref49">56</reflink>]). In addition, visuals (like parabolas) are also an important form of mathematics vocabulary ([<reflink idref="bib6" id="ref50">6</reflink>]).</p> <hd id="AN0192937329-7">Writing Grammar</hd> <p>Within the context of MW, grammar plays a crucial role in maintaining clear communication ([<reflink idref="bib32" id="ref51">32</reflink>]), such as reducing the chances of misinterpretation ([<reflink idref="bib43" id="ref52">43</reflink>]). Furthermore, we pay close attention to the correct utilization of numerals and symbols in MW, because they play a critical role in accurately conveying mathematical ideas and relationships. Unlike general writing, where words alone might suffice, MW relies heavily on the precise use of numerals and symbols to represent quantities, operations, and complex concepts succinctly and unambiguously ([<reflink idref="bib65" id="ref53">65</reflink>]). Incorrect or inconsistent use of these elements can lead to misunderstandings, misinterpretations, and errors in mathematical reasoning in MW.</p> <hd id="AN0192937329-8">Clarity and Precision</hd> <p>Clarity and precision are crucial in MW because of their importance in effective communication ([<reflink idref="bib1" id="ref54">1</reflink>]). Clarity ensures that the writing is straightforward and easy to understand, while precision ensures that the mathematical expressions and reasoning are accurate. Students are expected to present their thinking process coherently and systematically, linking concepts and methods in a manner that is easily comprehensible to the readers. The MW typically demands a higher level of logical thinking and argument than general writing ([<reflink idref="bib28" id="ref55">28</reflink>]).</p> <hd id="AN0192937329-9">Mathematics Difficulty</hd> <p>It is clear that MW necessitates the integration of mathematics skills and writing abilities ([<reflink idref="bib57" id="ref56">57</reflink>]). It is not surprising that MW poses challenges for many students ([<reflink idref="bib24" id="ref57">24</reflink>]). According to previous research, students with MD tend to perform below their TD peers across various mathematics skills, including counting ([<reflink idref="bib64" id="ref58">64</reflink>]), arithmetic fluency, computation ([<reflink idref="bib37" id="ref59">37</reflink>]; [<reflink idref="bib67" id="ref60">67</reflink>]), and word-problem solving ([<reflink idref="bib3" id="ref61">3</reflink>]; [<reflink idref="bib14" id="ref62">14</reflink>]). Consequently, students with MD may encounter even greater difficulties when faced with MW. Students with MD are generally characterized by lower mathematics performance, often falling below a specific percentile ([<reflink idref="bib50" id="ref63">50</reflink>]), and they are often diagnosed in the later elementary grades ([<reflink idref="bib51" id="ref64">51</reflink>]).</p> <p>[<reflink idref="bib31" id="ref65">31</reflink>] examined the MW performances of 51 students with MD in fourth and fifth grades. Their findings revealed most students with MD exhibited minimal mathematical reasoning in their written expression, even when they could solve the given problem. For example, over 50% of students correctly solved the fraction problem. However, only one student was able to articulate the computational steps and the rationale for using subtraction and addition in their solution. In addition, these students frequently relied on symbolic (54.4%) and general vocabulary (32.0%) in their writing. In addition to the aforementioned studies that describe students' MW performance, there is also research on interventions aimed at enhancing the MW skills of students with MD ([<reflink idref="bib4" id="ref66">4</reflink>]; [<reflink idref="bib34" id="ref67">34</reflink>]). [<reflink idref="bib34" id="ref68">34</reflink>] implemented an intervention to address students' understandings and misconceptions about fractions through argument writing. This approach led to a significant improvement in the quality of students' MW performance.</p> <p>However, in the limited studies that examined the MW performances of students with MD, none of them included a comparison group of TD students. Therefore, it remains unclear to what extent students with MD lag behind their TD peers and the extent to which additional support is needed for these students. In this study, we included TD students as a comparison group and further examined whether students' MW performance varied based on their mathematics performance levels, which included high-performing (HP) students, TD students, and students with MD. We classified students who scored below the 25th percentile as students with MD, students who scored between the 25th and 75th percentile as TD students, and students who scored above the 75th percentile as HP students. These cutoff points are commonly used in the previous literature ([<reflink idref="bib16" id="ref69">16</reflink>]; [<reflink idref="bib50" id="ref70">50</reflink>]).</p> <hd id="AN0192937329-10">Assess MW Through Fractions</hd> <p>Another area of mathematics that poses difficulties for students with MD is fractions ([<reflink idref="bib12" id="ref71">12</reflink>]; [<reflink idref="bib40" id="ref72">40</reflink>]). One major challenge is understanding the part–whole relationships ([<reflink idref="bib9" id="ref73">9</reflink>]). This conceptual barrier makes it difficult for them to accurately understand and manipulate fractions. Unlike whole numbers, where the magnitude is straightforward, fractions involve two digits that together represent a single value, necessitating a shift in understanding ([<reflink idref="bib22" id="ref74">22</reflink>]; [<reflink idref="bib33" id="ref75">33</reflink>]).</p> <p>Designing MW prompts focused on fractions can yield valuable insights into students' reasoning and problem-solving processes when solving fraction problems. For example, in MW tasks involving fractions, students are required to explain how they interpret and solve problems involving fractional quantities, such as describing processes of finding common denominators, simplifying fractions, or converting between improper fractions and mixed numbers. For students with MD, these tasks can be particularly difficult because of the demand on both deep fraction conception understanding and operation skills and the ability to clearly express the reasoning behind these calculations in written form. Moreover, fractions often involve technical vocabulary and symbolic representations that must be correctly used in writing ([<reflink idref="bib12" id="ref76">12</reflink>]). For example, students need to accurately describe vocabulary like <emph>numerator</emph> and explain concepts such as equivalence or fraction operations in a way that demonstrates their understanding. Therefore, including tasks related to fractions in MW assessments could reveal students' misconceptions about fraction learning and identify areas where they need more instruction.</p> <hd id="AN0192937329-11">The Present Study</hd> <p>This study aims to investigate the MW performance of students with MD in China. First, given that existing research primarily focuses on the MW performance of a full range of students, this study delves into the specific difficulties that students with MD encounter in MW tasks, which aids in understanding the unique challenges that students with MD face in solving mathematics problems and in the written expression of mathematical reasoning. Second, this research introduces TD students as a comparison group when examining the MW performance of students with MD. Such comparisons help to reveal the gaps in MW between students with MD and their TD peers, thereby facilitating more targeted support and interventions for students with MD. Third, this study focuses on a Chinese sample in China, filling a gap in the existing literature that predominantly features samples from Western countries, the United States, for example. Considering that the educational background and learning habits of Chinese students may significantly differ from those of students in other cultural contexts, the findings of this study contribute to a better understanding of Chinese students with MD and provide research outcomes with more targeted and practical application value for mathematics education in China. Our research questions were as follows:</p> <p></p> <ulist> <item> RQ1. Do the MW features (i.e., organizational features, mathematics content, mathematics vocabulary, writing grammar, and clarity and precision) students include vary based on students' mathematics ability levels (i.e., MD, TD, and HP students)? How do these features manifest on MW differ from those on general writing? Furthermore, how do students with different mathematics ability levels use mathematics vocabulary in their MW?</item> <p></p> <item> RQ2. How do students with MD perform on various MW features (organizational features, mathematics content, mathematics vocabulary, writing grammar, and clarity and precision)?</item> </ulist> <hd id="AN0192937329-12">Method</hd> <p></p> <hd id="AN0192937329-13">Participants</hd> <p>The research included 138 students in the sixth grade, distributed across three different classes within a second-band school situated in Northern China. School classification is typically based on multiple factors such as teaching quality, student graduation rates, and educational resources. The second-band schools generally have a good reputation locally but do not possess the resources and academic achievements that top-band schools have. As a result, we regard the chosen school as representative of the educational conditions prevalent in the area. The participants included 79 males and 59 females, with an average age of 12.31 years old (<emph>SD</emph> = 0.43). All the students were briefed about the aims of the research before their involvement. Informed consent was acquired from the parents of the students, assuring that the students could opt out of the research at any point without facing any adverse effects. Table 1 displays demographic information.</p> <p>Table 1. Demographics and Descriptive Data by Difficulty Category for Study on Mathematics-Writing.</p> <p>Graph</p> <p> <ephtml> &lt;table&gt;&lt;colgroup&gt;&lt;col align="left" /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;/colgroup&gt;&lt;thead&gt;&lt;tr&gt;&lt;th align="center"&gt;Items&lt;/th&gt;&lt;th align="center" colspan="2"&gt;HP(&lt;italic&gt;n&lt;/italic&gt; = 35)&lt;/th&gt;&lt;th align="center" colspan="2"&gt;TD(&lt;italic&gt;n&lt;/italic&gt; = 103)&lt;/th&gt;&lt;th align="center" colspan="2"&gt;MD(&lt;italic&gt;n&lt;/italic&gt; = 35)&lt;/th&gt;&lt;/tr&gt;&lt;/thead&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Variable&lt;/td&gt;&lt;td&gt;&lt;italic&gt;n&lt;/italic&gt;&lt;/td&gt;&lt;td&gt;(%)&lt;/td&gt;&lt;td&gt;&lt;italic&gt;n&lt;/italic&gt;&lt;/td&gt;&lt;td&gt;(%)&lt;/td&gt;&lt;td&gt;&lt;italic&gt;n&lt;/italic&gt;&lt;/td&gt;&lt;td&gt;(%)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Female&lt;/td&gt;&lt;td&gt;15&lt;/td&gt;&lt;td&gt;(10.9%)&lt;/td&gt;&lt;td&gt;45&lt;/td&gt;&lt;td&gt;(32.6%)&lt;/td&gt;&lt;td&gt;6&lt;/td&gt;&lt;td&gt;(4.3%)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Male&lt;/td&gt;&lt;td&gt;20&lt;/td&gt;&lt;td&gt;(14.5%)&lt;/td&gt;&lt;td&gt;58&lt;/td&gt;&lt;td&gt;(42.0%)&lt;/td&gt;&lt;td&gt;29&lt;/td&gt;&lt;td&gt;(21.0%)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td /&gt;&lt;td&gt;M&lt;/td&gt;&lt;td&gt;&lt;italic&gt;SD&lt;/italic&gt;&lt;/td&gt;&lt;td&gt;M&lt;/td&gt;&lt;td&gt;&lt;italic&gt;SD&lt;/italic&gt;&lt;/td&gt;&lt;td&gt;M&lt;/td&gt;&lt;td&gt;&lt;italic&gt;SD&lt;/italic&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;WRAT&lt;/td&gt;&lt;td&gt;38.3&lt;/td&gt;&lt;td&gt;0.4&lt;/td&gt;&lt;td&gt;36.5&lt;/td&gt;&lt;td&gt;1.6&lt;/td&gt;&lt;td&gt;28.7&lt;/td&gt;&lt;td&gt;4.2&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <p>1 <emph>Note.</emph> MD = Mathematics difficulty; HP = High performance; TD = typically developing; WRAT = Wide Range Achievement Test ([<reflink idref="bib69" id="ref77">69</reflink>]).</p> <p>In this study, students who scored at or below the 25th percentile on the screening test, a commonly used cutoff point in MD research as indicated by previous studies ([<reflink idref="bib16" id="ref78">16</reflink>]; [<reflink idref="bib50" id="ref79">50</reflink>]), were classified as students experiencing MD. The HP students were identified using the 75th percentile, in line with previous research (e.g., [<reflink idref="bib16" id="ref80">16</reflink>]). In sum, we screened students using the Wide Range Achievement Test-4 (WRAT-4; [<reflink idref="bib69" id="ref81">69</reflink>]) and categorized the students into three groups: students with MD (below the 25th percentile), TD students (between the 25th and 75th percentile), and HP students (above the 75th percentile). Chi-square and analysis of variance (ANOVA) tests revealed no significant differences in sex, χ<sups>2</sups>(<reflink idref="bib2" id="ref82">2</reflink>, _I_N_i_ = 138) = 1.24, <emph>p</emph> =.537, and age, <emph>F</emph>(<reflink idref="bib2" id="ref83">2</reflink>, 138) = 1.08, <emph>p</emph> =.342, across the three groups, indicating balanced baseline characteristics. In addition, given the lack of evidence from prior studies suggesting meaningful effects of sex or age on MW performance ([<reflink idref="bib5" id="ref84">5</reflink>]; [<reflink idref="bib25" id="ref85">25</reflink>]; [<reflink idref="bib29" id="ref86">29</reflink>]; [<reflink idref="bib58" id="ref87">58</reflink>]), these variables were not included as covariates in subsequent analyses.</p> <hd id="AN0192937329-14">Measures</hd> <p>All 138 students completed three measures: general writing, mathematics computation, and MW. Data collection occurred at the end of the sixth grade. To ensure reliability, two experienced scorers, who were familiar with the Wechsler Individual Achievement Test–Third Edition (WIAT-III) rubric, independently scored 100% of the assessments.</p> <hd id="AN0192937329-15">General Writing</hd> <p>For general writing, we gathered their writing samples from the midterm examination. They were given a 40-min time limit to compose a narrative essay titled "My Wish," in which they were instructed to express their wish and provide explanations for it. Our evaluation protocol was based on a modified scoring rubric from the WIAT-III (Psychological Corp., 2009), which accounted for elements such as introduction, conclusion, number of paragraphs, and number of transition words. The scoring criteria include evaluating the introduction and conclusion (up to 2 points each), number of paragraphs (0–5 points), and transition words. Each distinct transition word following punctuation (e.g., first, so) earns between 0 and 5 points. A paragraph required a minimum of two punctuation marks and was demarcated through line spacing or indentation. In addition, we summed the overall word count in compliance with the guidelines set by the WIAT-III. The inter-rater reliability, determined by the percentage of agreement, was 92%. All discrepancies were ultimately resolved.</p> <hd id="AN0192937329-16">Mathematics Computation</hd> <p>To evaluate the mathematical computation skills of students, we employed the Mathematics Computation subtest from the WRAT-4 ([<reflink idref="bib69" id="ref88">69</reflink>]). The WRAT-4 Computation subtest was chosen as a screening measure for students of different abilities because of its strong predictive power for overall mathematics ability ([<reflink idref="bib33" id="ref89">33</reflink>]).</p> <p>The test was administered in a whole-class setting. Students were asked to solve 40 computation problems of escalating difficulty in 15 minutes. For each correct response, participants received one point, with the maximum possible score being 40. The Cronbach's alpha is.74 based on our sample. The inter-rater reliability was 100%.</p> <hd id="AN0192937329-17">MW</hd> <p>Our MW measure consists of two prompts, each presenting students with a fraction problem and a hypothetical student's solution. Students must evaluate the given solution, determine whether the answer is correct or incorrect, and justify their judgment with a clear explanation. If the solution is incorrect, students are required to critique the reasoning behind the mistake, identify the error, and construct a well-supported mathematical argument using appropriate reasoning and evidence. This process actively engages students in argumentative MW by requiring them to evaluate, justify, and critique mathematical reasoning rather than simply explain a mistake.</p> <p>For the first problem (MW-1), students were presented with a multistep problem that was solved by a hypothetical student named "Xiao Ming" in four steps (see Figure 3). In Step A, Xiao Ming tried to determine a common denominator via addition, an approach that was wrong since multiplication is the correct method. Step B was executed correctly, although an error was made in step C during the process of adding fractions with the same denominators. Xiao Ming incorrectly summed both the numerators and denominators. Finally, in Step D, it was necessary to convert the resulting improper fraction into its simplest form by dividing both the numerator and denominator by their greatest common factor.</p> <p>Graph: Figure 3. Mathematics-Writing Task 1. Note. The upper side contains the original Chinese versions of MW task's question, the lower side shows the English translations, and below the question are lines provided for students to write their answers. Due to the page limit, we have removed the horizontal space for students to write their responses to the task.</p> <p>In MW-2, we provided a hypothetical student (Tian Tian)'s answer to a problem in five steps (see Figure 4). In Step A, the correct operation that should be applied by the students is division. They need to divide the amount of water used (200 L) by the remaining water level (which is a fraction of the full tank) to determine the tank's volume. The computations in Steps B and C were accurately performed. However, in Step D, there was an error in the multiplication of an integer and a fraction. Tian Tian incorrectly simplified the integer and the numerator of the fraction, whereas he should have multiplied the integer and the numerator of the fraction. In Step E, the result was an improper fraction that had not been simplified. The numerator and the denominator of the fraction should be divided by their common factor to reduce the fraction to its simplest form. The Cronbach's alpha was.85 based on our sample.</p> <p>Graph: Figure 4. Mathematics-Writing Task 2. Note. The upper side contains the original Chinese versions of MW task's question, the lower side shows the English translations, and below the question are lines provided for students to write their answers. Due to the page limit, we have removed the horizontal space for students to write their responses to the task.</p> <p>At the top of the answer sheet, the question is outlined along with detailed instructions to make certain that students grasp the expectations. Beneath each question, there's a provided horizontal space for students to write their responses. Furthermore, a separate boxed area is included on the page's right-hand side for students to write down their calculation steps (see Figures 3 and 4).</p> <hd id="AN0192937329-18">MW Scoring</hd> <p>The evaluation framework we used is a modified version of the one initially devised by [<reflink idref="bib4" id="ref90">4</reflink>], with additional refinements focused on mathematics content and organizational features. Figure 1 highlights the differences between our rubric and theirs, with the distinctions shaded for clarity. To ensure accurate scoring of mathematics content, we have provided a more detailed breakdown for each step, accounting for identifying the error, explaining the reasons for errors and writing the correct answer. Please refer to Supplemental Figures S1 and S2 for detailed scoring rubrics of mathematics content for MW-1 and MW-2. The final score was determined by adding up the scores from each step and converting them into percentages, which corresponded to a specific score. For instance, a score that exceeds 80% of the total would result in a five-point award, while scores between 60% and 80% would yield four points. As we assessed each step for mathematics content, we recorded instances of mathematics vocabulary used in students' explanations, noting each term only once per student. It is important to note that the recording of the mathematics vocabulary did not impact the scoring on mathematics vocabulary. These enhancements contribute to a more nuanced and precise analysis, improving our ability to gauge students' comprehension and use of mathematics concepts.</p> <p>In terms of organizational features, we have divided this category into five dimensions: introduction, conclusion, number of paragraphs, transitions, and number of words. This division was aimed at providing a more detailed assessment while also allowing for a more straightforward comparison with general writing. By applying this method, we can more accurately evaluate students' MW, enabling us to draw clearer conclusions. The inter-rater reliability was 90% for the MW measure.</p> <hd id="AN0192937329-19">Coding</hd> <p>We counted the mathematics vocabulary used by students, categorizing them into four types: technical vocabulary (i.e., <emph>denominator, multiplication</emph>), subtechnical vocabulary (i.e., <emph>total, difference</emph>), general vocabulary (i.e., <emph>line, right</emph>), and symbolic vocabulary (number, symbol, word, i.e., <emph>twenty, five</emph>). Vocabulary was coded as written if a word or any of its variations appeared in the response (i.e., <emph>add</emph> and <emph>addition</emph> both coded as <emph>add</emph>). In addition, misspelled words were still credited if they were recognizable (i.e., <emph>ad</emph> coded as <emph>add</emph>).</p> <hd id="AN0192937329-20">Data Analysis</hd> <p>For the first question, we conducted multivariate analysis of variance (MANOVA) using IBM SPSS version 24 to examine the feature differences in MW and general writing. The between-subjects factor was sample status (MD vs. TD vs. HP). To compare students' MW performance, the within-subjects factor consisted of five MW features: mathematics content, mathematics vocabulary, writing grammar, clarity and precision, and organizational features including number of words, introduction, conclusion, number of paragraphs, and transition words. Post hoc comparisons were subsequently performed to further discern specific differences between the groups on general writing in terms of organizational features. We also recorded the number of instances of each mathematics vocabulary and calculated the average frequency of use of the vocabulary by each student. Due to our small and unequal sample sizes, we used Hedge's <emph>g</emph> to calculate the effect sizes ([<reflink idref="bib27" id="ref91">27</reflink>]). For the second question, we summarized students' performance on MW features using means and standard deviations (<emph>SDs</emph>). The means reported represent the average of the two MW measures.</p> <hd id="AN0192937329-21">Results</hd> <p>As a preliminary analysis, we conducted multiple regression to examine the relative roles of general writing ability and mathematics competence in MW performance. The results showed that mathematics competence demonstrated a significant positive association with MW performance for MD (β = 0.349) and TD students (β = 0.399). However, for HP students, mathematics competence exhibited a significant negative association with MW performance (β = −0.465). In contrast, general writing ability did not demonstrate a significant association with MW performance in any group.</p> <hd id="AN0192937329-22">Variations in MW Based on Students' Mathematics Ability Levels</hd> <p></p> <hd id="AN0192937329-23">Patterns Observed in MW</hd> <p>Table 2 presents students' performance on various MW features based on their mathematics ability level, with the MANOVA revealing significant differences across several features: mathematics content, <emph>F</emph>(<reflink idref="bib2" id="ref92">2</reflink>, 135) = 12.75, <emph>p</emph> &lt;.001, mathematics vocabulary, <emph>F</emph>(<reflink idref="bib2" id="ref93">2</reflink>, 135) = 19.82, <emph>p</emph> &lt;.001, writing grammar, <emph>F</emph>(<reflink idref="bib2" id="ref94">2</reflink>, 135) = 13.04, <emph>p</emph> &lt;.001, and clarity and precision, <emph>F</emph>(<reflink idref="bib2" id="ref95">2</reflink>, 135) = 11.82, <emph>p</emph> &lt;.001. Within organizational features, significant differences were also observed for the number of words, <emph>F</emph>(<reflink idref="bib2" id="ref96">2</reflink>, 135) = 16.72, <emph>p</emph> &lt;.001, and transitions, <emph>F</emph>(<reflink idref="bib2" id="ref97">2</reflink>, 135) = 5.45, <emph>p</emph> =.005. Post hoc comparisons revealed that the HP students performed significantly better than the TD students, and the TD students significantly outperformed students with MD except for transitions and paragraphs (see Table 3). Both the HP and TD students significantly outperformed the MD group regarding transitions (<emph>g</emph> = 0.84 for HP and <emph>g</emph> = 0.48 for TD) and paragraphs (<emph>g</emph> = 0.56 for HP and <emph>g</emph> = 0.54 for TD). However, no significant difference was found between the HP and TD students for either transitions (<emph>g</emph> = 0.29) or paragraphs (<emph>g</emph> = 0.15). However, it is important to note that these patterns do not apply to the introduction and conclusion sections because students from all groups rarely included these sections in their responses. In addition, we have included worked examples from each MW task to further illustrate the performance differences across the MD, TD, and HP students (please refer to Supplemental Figures S3 to S8).</p> <p>Table 2. Performance on Mathematics-Writing Features by Mathematics Ability Level.</p> <p>Graph</p> <p> <ephtml> &lt;table&gt;&lt;colgroup&gt;&lt;col align="left" /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;/colgroup&gt;&lt;thead&gt;&lt;tr&gt;&lt;th align="left"&gt;Features&lt;/th&gt;&lt;th align="center"&gt;HP&lt;italic&gt;M&lt;/italic&gt; (&lt;italic&gt;SD&lt;/italic&gt;)&lt;/th&gt;&lt;th align="center"&gt;TD&lt;italic&gt;M&lt;/italic&gt; (&lt;italic&gt;SD&lt;/italic&gt;)&lt;/th&gt;&lt;th align="center"&gt;MD&lt;italic&gt;M&lt;/italic&gt; (&lt;italic&gt;SD&lt;/italic&gt;)&lt;/th&gt;&lt;th align="center"&gt;HP &amp; TD&lt;italic&gt;M&lt;/italic&gt; (&lt;italic&gt;SD&lt;/italic&gt;)&lt;/th&gt;&lt;/tr&gt;&lt;/thead&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Mathematics content&lt;/td&gt;&lt;td&gt;5.16 (2.03)&lt;/td&gt;&lt;td&gt;4.20 (1.79)&lt;/td&gt;&lt;td&gt;2.91 (1.94)&lt;/td&gt;&lt;td&gt;3.18 (1.41)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;MV&lt;/td&gt;&lt;td&gt;3.63 (1.07)&lt;/td&gt;&lt;td&gt;3.01 (1.15)&lt;/td&gt;&lt;td&gt;1.97 (1.08)&lt;/td&gt;&lt;td&gt;3.19 (1.04)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td colspan="5"&gt;Organizational&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Words&lt;/td&gt;&lt;td&gt;67.47 (28.98)&lt;/td&gt;&lt;td&gt;51.38 (25.99)&lt;/td&gt;&lt;td&gt;2.94 (1.08)&lt;/td&gt;&lt;td&gt;141.07 (21.58)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Introduction&lt;/td&gt;&lt;td&gt;0.01 (0.08)&lt;/td&gt;&lt;td&gt;0.00 (0.05)&lt;/td&gt;&lt;td&gt;2.69 (1.08)&lt;/td&gt;&lt;td&gt;0.99 (0.90)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Conclusion&lt;/td&gt;&lt;td&gt;0.00 (0.00)&lt;/td&gt;&lt;td&gt;0.00 (0.00)&lt;/td&gt;&lt;td&gt;0.40 (0.50)&lt;/td&gt;&lt;td&gt;0.05 (0.04)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Paragraphs&lt;/td&gt;&lt;td&gt;4.26 (0.57)&lt;/td&gt;&lt;td&gt;4.15 (0.78)&lt;/td&gt;&lt;td&gt;0.29 (0.33)&lt;/td&gt;&lt;td&gt;0.00 (0.00)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Transitions&lt;/td&gt;&lt;td&gt;0.40 (0.47)&lt;/td&gt;&lt;td&gt;0.27 (0.42)&lt;/td&gt;&lt;td&gt;0.09 (0.23)&lt;/td&gt;&lt;td&gt;0.29 (0.33)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Writing grammar&lt;/td&gt;&lt;td&gt;3.03 (1.14)&lt;/td&gt;&lt;td&gt;2.43 (1.17)&lt;/td&gt;&lt;td&gt;1.67 (0.90)&lt;/td&gt;&lt;td&gt;2.94 (1.08)&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Clarity and precision&lt;/td&gt;&lt;td&gt;2.97 (1.21)&lt;/td&gt;&lt;td&gt;2.36 (1.20)&lt;/td&gt;&lt;td&gt;1.64 (0.89)&lt;/td&gt;&lt;td&gt;2.69 (1.08)&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <p>2 <emph>Note.</emph> HP = high performance; TD = typically developing; MD = mathematics difficulty; MV = mathematics vocabulary.</p> <p>Table 3. Effect Sizes for Mathematics-Writing Features Comparisons Across Groups with Post Hoc Analysis and Hedges' g.</p> <p>Graph</p> <p> <ephtml> &lt;table&gt;&lt;colgroup&gt;&lt;col align="left" /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;/colgroup&gt;&lt;thead&gt;&lt;tr&gt;&lt;th /&gt;&lt;th align="center" colspan="2"&gt;HP versus&lt;/th&gt;&lt;th align="center"&gt;TD versus&lt;/th&gt;&lt;th align="center" rowspan="2"&gt;Pattern&lt;/th&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th align="left"&gt;Features&lt;/th&gt;&lt;th align="center"&gt;TD&lt;/th&gt;&lt;th align="center"&gt;MD&lt;/th&gt;&lt;th align="center"&gt;MD&lt;/th&gt;&lt;/tr&gt;&lt;/thead&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Mathematics content&lt;/td&gt;&lt;td&gt;0.51&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;1.12&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;0.70&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;HP &amp;#62; TD &amp;#62; MD&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Mathematics vocabulary&lt;/td&gt;&lt;td&gt;0.54&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;1.52&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;0.91&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;HP &amp;#62; TD &amp;#62; MD&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td colspan="5"&gt;Organizational&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Words&lt;/td&gt;&lt;td&gt;0.60&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;1.34&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;0.78&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;HP &amp;#62; TD &amp;#62; MD&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Introduction&lt;/td&gt;&lt;td&gt;0.15&lt;/td&gt;&lt;td&gt;0.24&lt;/td&gt;&lt;td&gt;0.11&lt;/td&gt;&lt;td /&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Conclusion&lt;/td&gt;&lt;td&gt;0.00&lt;/td&gt;&lt;td&gt;0.00&lt;/td&gt;&lt;td&gt;0.00&lt;/td&gt;&lt;td /&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Paragraphs&lt;/td&gt;&lt;td&gt;0.15&lt;/td&gt;&lt;td&gt;0.56&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;0.54&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;HP = TD &amp;#62; MD&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt; Transitions&lt;/td&gt;&lt;td&gt;0.29&lt;/td&gt;&lt;td&gt;0.84&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;0.48&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;HP = TD &amp;#62; MD&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Writing grammar&lt;/td&gt;&lt;td&gt;0.51&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;1.31&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;0.68&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;HP &amp;#62; TD &amp;#62; MD&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Clarity and precision&lt;/td&gt;&lt;td&gt;0.51&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;1.24&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;0.63&lt;xref ref-type="table-fn" rid="tfn4"&gt;&amp;#42;&amp;#42;&amp;#42;&lt;/xref&gt;&lt;/td&gt;&lt;td&gt;HP &amp;#62; TD &amp;#62; MD&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <ulist> <item>3 <emph>Note</emph>. HP = high performance; TD = typically developing; MD = mathematics difficulty.</item> <item>4 <emph>p</emph> &lt;.001.</item> </ulist> <hd id="AN0192937329-24">Patterns Observed in General Writing and Mathematics Vocabulary Usage</hd> <p>To gain a more comprehensive understanding of the MW performance of students with MD, we conducted an additional analysis focusing on their performance in general writing skills. The results are presented in Table 4. Surprisingly, we found no significant differences in performance among HP, TD students, and students with MD across all organizational features, which was inconsistent with the trend of MW (HP &gt; TD &gt; MD).</p> <p>Table 4. Descriptive Statistics and MANOVA Results for General Writing Across Groups.</p> <p>Graph</p> <p> <ephtml> &lt;table&gt;&lt;colgroup&gt;&lt;col align="left" /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;col align="char" char="." /&gt;&lt;/colgroup&gt;&lt;thead&gt;&lt;tr&gt;&lt;th /&gt;&lt;th align="center"&gt;HP&lt;/th&gt;&lt;th align="center"&gt;TD&lt;/th&gt;&lt;th align="center"&gt;MD&lt;/th&gt;&lt;th align="center" rowspan="2"&gt;&lt;italic&gt;df&lt;/italic&gt;&lt;/th&gt;&lt;th align="center" rowspan="2"&gt;&lt;italic&gt;p&lt;/italic&gt;&lt;/th&gt;&lt;/tr&gt;&lt;tr&gt;&lt;th align="center"&gt;Features&lt;/th&gt;&lt;th align="center"&gt;&lt;italic&gt;M&lt;/italic&gt; (&lt;italic&gt;SD&lt;/italic&gt;)&lt;/th&gt;&lt;th align="center"&gt;&lt;italic&gt;M&lt;/italic&gt; (&lt;italic&gt;SD&lt;/italic&gt;)&lt;/th&gt;&lt;th align="center"&gt;&lt;italic&gt;M&lt;/italic&gt; (&lt;italic&gt;SD&lt;/italic&gt;)&lt;/th&gt;&lt;/tr&gt;&lt;/thead&gt;&lt;tbody&gt;&lt;tr&gt;&lt;td&gt;Words&lt;/td&gt;&lt;td&gt;195.32 (199.14)&lt;/td&gt;&lt;td&gt;173.64 (192.41)&lt;/td&gt;&lt;td&gt;212.06 (192.78)&lt;/td&gt;&lt;td&gt;0.56&lt;/td&gt;&lt;td&gt;.572&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Introduction&lt;/td&gt;&lt;td&gt;0.71 (0.94)&lt;/td&gt;&lt;td&gt;0.57 (0.85)&lt;/td&gt;&lt;td&gt;0.80 (0.96)&lt;/td&gt;&lt;td&gt;0.92&lt;/td&gt;&lt;td&gt;.400&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Conclusion&lt;/td&gt;&lt;td&gt;0.65 (1.07)&lt;/td&gt;&lt;td&gt;0.58 (1.08)&lt;/td&gt;&lt;td&gt;0.69 (0.93)&lt;/td&gt;&lt;td&gt;0.14&lt;/td&gt;&lt;td&gt;.871&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Paragraphs&lt;/td&gt;&lt;td&gt;4.03 (1.09)&lt;/td&gt;&lt;td&gt;3.98 (1.10)&lt;/td&gt;&lt;td&gt;4.23 (1.35)&lt;/td&gt;&lt;td&gt;0.60&lt;/td&gt;&lt;td&gt;.549&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;Transitions&lt;/td&gt;&lt;td&gt;1.27 (1.97)&lt;/td&gt;&lt;td&gt;1.30 (1.89)&lt;/td&gt;&lt;td&gt;1.40 (1.87)&lt;/td&gt;&lt;td&gt;0.05&lt;/td&gt;&lt;td&gt;.955&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt; </ephtml> </p> <p>5 <emph>Note</emph>. HP = high performance; TD = typically developing; MD = mathematics difficulty.</p> <p>The utilization of mathematics vocabulary in MW is presented in Supplemental Tables S1 and S2. In general, the usage frequency of technical, general, and symbolic (number) vocabularies followed the trend of HP &gt; TD &gt; MD. However, there were a few exceptions such as in general vocabulary, where the usage frequency of <emph>error</emph> was relatively same among all three groups, with TD slightly higher than HP and MD. Regarding subtechnical vocabulary usage, there were not much differences, with HP being marginally higher (HP &gt; TD = MD). About symbolic (symbol) vocabulary, HP and TD students tended to use them at similar rates, while MD frequency was slightly lower (HP = TD &gt; MD). For symbolic (word) vocabulary, usage frequency was generally low across all groups.</p> <hd id="AN0192937329-25">MW Performance of Students with Mathematics Difficulty</hd> <p>Now, it is evident that students with MD exhibited poorer performance in MW compared to the HP and TD students. In this section, we detail their performance across various MW features. To illustrate the challenges faced by students with MD, we present descriptive information from the other two groups for comparison (see Table 2). Please note that the total score for each feature was 5. In terms of mathematics content, students with MD had a limited understanding of mathematics concepts and procedures involved in the MW problems. In contrast, the statistics of the other two groups showed a general understanding of the problems and the ability to solve them. However, they encountered certain difficulties in comprehensively covering and deeply analyzing all aspects of the problems.</p> <p>For mathematics vocabulary, compared to students with MD, the other two groups showed they were able to correctly use mathematics vocabulary in most circumstances, demonstrating a more sophisticated understanding of the meanings of these terms. Specifically, students with MD faced challenges in using technical mathematics vocabulary (e.g., <emph>common denominator</emph>). Yet, students with MD often relied on general vocabulary like <emph>more</emph> or <emph>less</emph> (e.g., <ephtml> &lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt; </ephtml> is more than <ephtml> &lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt; </ephtml> )—this pattern less pronounced in other students' writing. Students with MD frequently used symbolic number vocabulary (e.g., <emph>24</emph>), with over half of them incorporating these terms in their MW. However, other students not only used symbolic numbers but also frequently included symbols such as <emph>+</emph>.</p> <p>Regarding writing grammar, students with MD were proved to make multiple grammatical errors in their MW responses, which adversely affected the readability of their texts. The statistics of the other two groups indicated, although there were some grammatical errors, most of the sentences were fluent. Compared to the other two groups, students with MD were more likely to write incomplete sentences (e.g., lacking a subject) and make punctuation errors, which led to less clear mathematical reasoning. For example, students with MD wrote incomplete sentences like "is <ephtml> &lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;14&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;24&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt; </ephtml> not <ephtml> &lt;math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mrow&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mrow&gt;&lt;mn&gt;12&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/math&gt; </ephtml> ." In addition, they frequently omitted proper punctuation marks, like periods, which further affected clarity, such as "add top and bottom." While other students made punctuation errors, their sentence structures were generally more complex. For instance, they wrote "The result needs to be simplified, still have a common factor, 4, so, 4 should be divided."</p> <p>Regarding clarity and precision, students with MD lacked clarity and precision in explaining mathematical procedures and concepts. Their MW lacked the necessary level of detail and elaboration, making it difficult for readers to understand their ideas. Conversely, the other two groups generally exhibited better clarity and precision when explaining procedures and concepts. However, they still fell short in terms of depth and completeness in their detailed explanations.</p> <p>In terms of organizational features, students with MD struggled with structuring their writing, producing fewer paragraphs, and using very few transition words, which hindered their ability to effectively connect ideas. In contrast, the HP and TD students wrote more paragraphs and used slightly more transition words, suggesting that their writing was somewhat more organized, although still limited in linking ideas coherently. It is worth noting that neither students with MD nor the other groups included an introduction or conclusion in their MW, further indicating challenges in overall organization and coherence. In addition, students' representations came to our attention during scoring—none of the students included pictures in their MW.</p> <p>Overall, students with MD need improvement across various dimensions. Large <emph>SD</emph>s in features like mathematics content and mathematics vocabulary indicated variability in performance, with some students experiencing MD achieving high scores while others performed poorly. In contrast, smaller <emph>SD</emph>s in transition words and grammar indicated more consistent weaknesses among students with MD.</p> <hd id="AN0192937329-26">Discussion</hd> <p>In this study, our focus was on investigating the MW performance of students who experienced MD. We divided students into three distinct groups based on their mathematics performance: MD (below the 25th percentile), TD (between the 25th and 75th percentiles), and HP (above the 75th percentile) students. Our findings revealed that (a) the trend in MW performance followed the hierarchy of mathematics ability levels (HP &gt; TD &gt; MD), which differed from the trend observed in general writing (MD = TD = HP); (b) although all three groups exhibited capacities to organize their general writing, they faced difficulties organizing their thoughts in MW; (c) students with MD demonstrated less likelihood to use technical mathematics vocabulary and mathematics symbols in their MW; and (d) students with MD were more prone to writing incomplete sentences and making punctuation errors in MW.</p> <hd id="AN0192937329-27">MW Performance and Mathematics Ability Levels</hd> <p>Our findings revealed a consistent pattern in MW performance, with the HP students consistently surpassing the TD students, which in turn outperformed students with MD. However, it is important to note that this trend pattern was not observed in general writing, as all three groups performed similarly in organizational features. Although students with higher mathematics competence generally perform better in MW, the relationship between mathematics competencies and MW is not strictly linear. Strong mathematical knowledge alone does not guarantee success in all features of MW. Even HP students may struggle with organizing and articulating their mathematical reasoning in writing, highlighting the complexity of MW beyond mere mathematical proficiency.</p> <p>Unlike general writing, where all student groups performed similarly in organizational features, MW performance was clearly stratified by mathematical ability. Students with MD demonstrated the lowest MW performance despite their general writing proficiency, reinforcing the idea that MW relies more on domain-specific mathematical knowledge than on broader writing skills. This aligns with [<reflink idref="bib42" id="ref98">42</reflink>] findings that limited domain knowledge hampers content creation and academic specificity in writing.</p> <p>Notably, organizational challenges in MW persisted across all ability levels. The HP students, despite excelling in computation and procedural fluency, struggled to explicitly document their reasoning ([<reflink idref="bib67" id="ref99">67</reflink>]), likely due to the internalization of problem-solving processes. This led to a negative association between mathematics competence and MW performance among HP students. In addition, their limited use of mathematics vocabulary suggests an implicit understanding of concepts that they assume do not require explicit articulation.</p> <p>Previous research has documented common challenges in MW (e.g., [<reflink idref="bib25" id="ref100">25</reflink>]), but these studies did not differentiate students based on their mathematical abilities. Our findings extend this understanding by highlighting persistent organizational difficulties in MW across different ability levels, even among students with strong foundational mathematical knowledge. Moreover, our results suggest an important distinction: while mathematical vocabulary supports problem-solving and reasoning, its underuse in MW may hinder students from clearly conveying their mathematical thinking, particularly among HP students ([<reflink idref="bib52" id="ref101">52</reflink>]).</p> <hd id="AN0192937329-28">Different Trends Observed in General Writing</hd> <p>Our finding that the trend in MW performance aligned with the hierarchy of mathematics ability levels (HP &gt; TD &gt; MD), differing from the trend observed in general writing (MD = TD = HP), is in line with previous findings indicating that the relationship between MW and mathematics knowledge may be stronger than that between MW and general writing ([<reflink idref="bib25" id="ref102">25</reflink>]). This is not surprising because MW requires students to have solid content-area knowledge to accurately demonstrate mathematical thinking in written expressions.</p> <p>This finding underscores the significance of background knowledge for content-area literacy ([<reflink idref="bib8" id="ref103">8</reflink>]). In content-area reading, background knowledge is vital for understanding and interpreting texts within specialized fields ([<reflink idref="bib63" id="ref104">63</reflink>]). Similarly, in MW, comprehension and mastery of mathematics knowledge are crucial for organizing and articulating mathematical reasoning. Therefore, we can deduce that the lack of mathematics knowledge in students with MD might affect their capability in MW. Similarly, [<reflink idref="bib31" id="ref105">31</reflink>] found students with learning disabilities are less likely to be correct when working with fractions and decimals, reflecting deficits in their conceptual understanding of rational numbers, which is part of content-area knowledge. When students have a limited understanding of specific mathematical content, they not only have difficulty producing correct mathematical answers when writing but also have difficulty clearly expressing their mathematical reasoning process even when the answers are correct. So, educators should focus on developing students' content-area knowledge and guide them in applying this knowledge to MW, which will improve students' MW skills as well as promote their overall development in the field of mathematics.</p> <hd id="AN0192937329-29">Mathematics Vocabulary Used in MW</hd> <p>Our findings revealed notable differences in the use of various types of mathematics vocabulary among MD, TD, and HP students, highlighting the intricate relationship between mathematics vocabulary and mathematics competence. Notably, in some categories, HP students showed vocabulary usage patterns similar to those of TD students, suggesting that higher mathematics competence does not always correlate with more advanced vocabulary use.</p> <p>The frequency of technical vocabulary—terms specific to mathematics (e.g., <emph>least common denominator</emph>)—followed the trend HP &gt; TD &gt; MD. This pattern reflects the advantages HP students have in mathematical language and the challenges faced by students with MD ([<reflink idref="bib41" id="ref106">41</reflink>]). The ability to understand and use technical vocabulary plays a crucial role in mathematical competence, as it facilitates precise communication of concepts, enhances problem-solving efficiency, and strengthens reasoning skills. Conversely, students with weaker mathematical competence may struggle with these terms, leading to difficulties in both comprehension and MW performance.</p> <p>Regarding symbolic vocabulary (e.g., <emph>5</emph>), HP and TD students used them at comparable rates, while MD students used them slightly less (HP = TD &gt; MD). This trend suggests that MDs may impact students' ability to integrate symbolic representations into their MW, although to a lesser extent than technical vocabulary. Since mathematical symbols serve as a concise and universally understood way to represent relationships, expressions, and operations, a limited ability to use them effectively may hinder problem representation and solution clarity.</p> <p>In addition, when examining general vocabulary (words with everyday significance that also have mathematical meaning, such as <emph>right</emph>), we found that all three groups exhibited similar frequencies, with TD students using them slightly more than HP and MD students. This finding underscores the non-linear relationship between mathematics competence and vocabulary use. While HP students demonstrated strong command of technical terms, their use of general vocabulary did not surpass that of TD students. We speculated that this might be due to HP students' reliance on symbolic reasoning and mental calculations, leading to fewer written justifications and less structured MW. In this process, technical vocabulary tends to take precedence over general vocabulary, which is often used for explanations and reasoning. Moreover, general vocabulary is not explicitly reinforced in mathematics instruction, which may explain why even HP students struggle to use these words effectively in MW.</p> <hd id="AN0192937329-30">The MW Performance of Students with Mathematics Difficulty</hd> <p>Our findings revealed that students with MD encountered challenges across all MW features, aligning with previous studies ([<reflink idref="bib4" id="ref107">4</reflink>]; [<reflink idref="bib31" id="ref108">31</reflink>]). What distinguishes our study from earlier research is that we not only included students with MD but also quantified the extent of the difference between students with MD and their counterparts. Our results revealed that in mathematics vocabulary, the effect sizes of MD versus TD and HP were 0.91 and 1.52, respectively, indicating large differences. For mathematics content, number of words, writing grammar, clarity, and precision, medium effect sizes were observed. However, paragraphs and transitions demonstrated small effect sizes. The largest difference between students with MD and their counterparts was observed in mathematics vocabulary. Students with MD encountered challenges in utilizing mathematics vocabulary, impacting their comprehension of mathematical concepts, problem-solving abilities, and accurate expression of mathematical ideas ([<reflink idref="bib25" id="ref109">25</reflink>]; [<reflink idref="bib55" id="ref110">55</reflink>]; [<reflink idref="bib60" id="ref111">60</reflink>]). Specifically, students with MD frequently used symbolic numbers and general vocabulary in their MW, which aligns with the results from [<reflink idref="bib4" id="ref112">4</reflink>]. This suggests that they depended on basic numerical concepts and preferred to express mathematical ideas in simpler, more accessible terms. This tendency to use general mathematics vocabulary may indicate underlying challenges in dealing with more complex mathematical notation and concepts.</p> <p>In addition to overall difficulty in MW, we also observed smaller <emph>SD</emph>s in certain MW features for students with MD, including transition words, grammar, and clarity. This finding suggests that students with MD demonstrated a universal difficulty with these MW features, with limited variation in their performance. Specifically, students with MD consistently struggled with the use of transition words, adherence to grammatical rules, and clear expression in writing. Furthermore, their challenges in producing complete sentences and correctly using punctuation marks indicate that they may struggle with fundamental aspects of mathematical communication, resulting in incomplete expressions of their understanding. Identifying such consistent and widespread challenges underscores the importance for educators and researchers to better understand the specific needs of students with MD in MW. It highlights the necessity of targeted interventions and support tailored to address these specific difficulties. For example, revising MW using structured planning tools, such as graphic organizers, has proven effective in helping students with MD organize their thoughts and improve the coherence of their writing ([<reflink idref="bib46" id="ref113">46</reflink>]).</p> <p>Another observation we have when inspecting the MW of students with MD is students with MD may be less likely to include pictures in their MW. Consistent with the work of [<reflink idref="bib4" id="ref114">4</reflink>], our findings also revealed that none of the students with MD included pictures either integrated into or accompanying their written responses. However, there were also previous studies indicating students sometimes supplemented their written responses with pictures ([<reflink idref="bib25" id="ref115">25</reflink>]; [<reflink idref="bib31" id="ref116">31</reflink>]). We can speculate whether students embedding pictures in MW is influenced by mathematics ability levels. It is possible that students with MD may face particular difficulties that make them less likely to use visual aids, such as pictures, when expressing mathematical ideas.</p> <hd id="AN0192937329-31">Limitations and Future Research</hd> <p>This study has several limitations. First, the study employed a quantitative approach, which may not fully capture the multi-dimensional characteristics of MW performance in students with MD. While quantitative data provide valuable insights, it may overlook the nuanced and complex nature of students' writing processes and the challenges they face.</p> <p>Second, the sample was drawn from a limited geographic area, which may not fully capture the diversity of educational contexts and student experiences. As a result, the findings may not be generalizable to a broader population of students across different regions or school settings.</p> <p>Third, we used a researcher-developed MW measure. Although these measures were designed to align with the study's objectives, their researcher-developed nature could limit the generalizability of the findings. Furthermore, the reliability of these measures, while partially validated within the context of this study, may not be as robust as that of standardized assessments. Also, regarding the scoring, while we intended to refine the traditional 5-point scoring system (as seen in studies by [<reflink idref="bib4" id="ref117">4</reflink>]; [<reflink idref="bib25" id="ref118">25</reflink>]), the conversion of continuous scoring to a previous rank order using thresholds (e.g., 80%, 60%) as dividing points has resulted in a loss of information. The conversion method we used may not have clearly distinguished the subtle variations in student understanding, particularly around the critical 80% threshold. Another point is that the tasks given to students resembled a fill-in-the-blank format designed to encourage them to address each step rather than leave any sections blank. We also did not explicitly prompt them to include comprehensive organizational elements such as an introduction or conclusion in their MW. As a result, the assessment of students' organizational skills may not fully capture their ability to structure MW.</p> <p>Future research should consider addressing these limitations to provide a more comprehensive understanding of MW. Specifically, future research should adopt both qualitative and quantitative research methods, to gain a more holistic understanding of the MW performance of students with MD. For example, research could employ interviews to learn more about the specific difficulties students encounter in MW and collect in-depth qualitative data by observing and recording their processes of expressing mathematical ideas.</p> <p>In addition, there is a need for the development and validation of more widely accepted and standardized measures to assess MW, including the development of a more precise and operationally clear scoring system that better captures the range of student abilities. Such tools would enhance the reliability and generalizability of research findings across different studies and populations.</p> <p>Finally, future research should investigate the impact of the MW task format on students' performance in MW, particularly regarding the inclusion of elements like introductions and conclusions. Specifically, studies could examine the different formats of MW, such as using bullet points or full paragraphs.</p> <hd id="AN0192937329-32">Implications</hd> <p>Our findings have several implications for theory and practice. First, it is crucial to have a strong grasp of mathematics content knowledge when it comes to MW ([<reflink idref="bib23" id="ref119">23</reflink>]; [<reflink idref="bib38" id="ref120">38</reflink>]; [<reflink idref="bib66" id="ref121">66</reflink>]). When teaching MW, educators should focus on assessing and equipping students with the necessary mathematical knowledge for writing ([<reflink idref="bib42" id="ref122">42</reflink>]), particularly for those experiencing MD. Before introducing explicit instruction on MW or evaluating students' MW skills, it is crucial to initially assess students' understanding of relevant mathematics knowledge, particularly for those with MD who may lack fundamental mathematics knowledge. Students need a solid foundation in mathematical concepts before they can effectively engage in MW instruction or assessment.</p> <p>Second, educators should provide clear instruction on MW structure and logical organization ([<reflink idref="bib19" id="ref123">19</reflink>]). This is crucial because students of varying mathematical abilities often struggle with organizing their writing. Even HP students may require specific support. With specific instruction, students can enhance their overall writing organizational skills and learn how to construct logical and coherent mathematical arguments ([<reflink idref="bib13" id="ref124">13</reflink>]). This includes creating clear introductions, conclusions, and smooth transitions.</p> <p>Third, considering the variations in the application of different types of mathematics vocabulary in MW, educators should tailor their guidance on utilizing mathematics vocabulary in MW to suit students' mathematics ability levels. For example, it is important to provide additional support to assist students with MD in overcoming difficulties related to incorporating technical and symbolic vocabulary in their MW. Compared to their peers, students with MD demonstrate less frequent use of such vocabulary, indicating potential obstacles in effectively incorporating these terms into their written work ([<reflink idref="bib4" id="ref125">4</reflink>]).</p> <p>Finally, our findings suggest that the relationship between MW and mathematics competence may not be linear. The HP students do not always excel in mathematics vocabulary use and MW organization. For instance, as revealed by the worked examples (please refer to Supplemental Figures S7 and S8), some HP students displayed less structured organizational patterns (e.g., absent introductions or conclusions) and lacked precise vocabulary (e.g., <emph>equivalent</emph>). These patterns were observed even when students showed correct procedural understanding or effectively identified hypothetical errors.</p> <p>This observation reflects a recurring pattern in our data: a proficiency–expression mismatch, in which students with high mathematics competence did not consistently demonstrate parallel strength in articulating their reasoning through writing. The dissociation between procedural success and written clarity suggests that MW development does not automatically follow from mathematical proficiency. Instead, once students reach a certain threshold of mathematical understanding, further improvement in MW appears to depend on additional instruction targeting the articulation and structure of reasoning. This highlights the need for explicit support in mathematical communication, even for HP students, to ensure that their written reasoning reflects the full depth and clarity of their conceptual understanding.</p> <hd id="AN0192937329-33">Conclusion</hd> <p>In conclusion, this study highlights the differences in MW performance among students with varying levels of mathematics abilities. The results indicate a clear hierarchy in MW performance, with HP students outperforming both TD and MD students. Although all groups could organize general writing, they struggled with structuring their thoughts in MW. Notably, students with MD were less likely to use technical vocabulary and symbols, and they tended to write incomplete sentences and make punctuation errors more frequently. 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Wide range achievement test (4th ed.). Lutz, FL: Psychological Assessment Resources.</bibtext> </blist> </ref> <ref id="AN0192937329-36"> <title> Footnotes </title> <blist> <bibtext> Xiaonan Han, Mathematics Learning Disabilities, Mathematics Learning at Elementary Schools, Mathematics Teacher Education. Xin Lin, Mathematics Learning Disabilities, Cognitive and Academic Correlates of Mathematics Learning, Intensive Intervention in Mathematics, Meta-Analysis.</bibtext> </blist> <blist> <bibtext> The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.</bibtext> </blist> <blist> <bibtext> Asia-Pacific Academy of Economics and Management (Ref No. APAEM/SG/0005/2025).</bibtext> </blist> <blist> <bibtext> Xiaonan Han</bibtext> </blist> <blist> <bibtext>Graph</bibtext> </blist> <blist> <bibtext>https://orcid.org/0009-0003-8949-1212 Xin Lin</bibtext> </blist> <blist> <bibtext>Graph https://orcid.org/0000-0002-8077-5134</bibtext> </blist> <blist> <bibtext> Supplemental material is available at https://doi.org/10.1177/00222194251391829</bibtext> </blist> </ref> <aug> <p>By Xiaonan Han and Xin Lin</p> <p>Reported by Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib11" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib44" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib15" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib31" firstref="ref4"></nolink> <nolink nlid="nl5" bibid="bib30" firstref="ref5"></nolink> <nolink nlid="nl6" bibid="bib58" firstref="ref6"></nolink> <nolink nlid="nl7" bibid="bib68" firstref="ref7"></nolink> <nolink nlid="nl8" bibid="bib14" firstref="ref8"></nolink> <nolink nlid="nl9" bibid="bib20" firstref="ref9"></nolink> <nolink nlid="nl10" bibid="bib26" firstref="ref10"></nolink> <nolink nlid="nl11" bibid="bib25" firstref="ref13"></nolink> <nolink nlid="nl12" bibid="bib57" firstref="ref14"></nolink> <nolink nlid="nl13" bibid="bib10" firstref="ref15"></nolink> <nolink nlid="nl14" bibid="bib21" firstref="ref16"></nolink> <nolink nlid="nl15" bibid="bib48" firstref="ref20"></nolink> <nolink nlid="nl16" bibid="bib49" firstref="ref23"></nolink> <nolink nlid="nl17" bibid="bib35" firstref="ref25"></nolink> <nolink nlid="nl18" bibid="bib61" firstref="ref27"></nolink> <nolink nlid="nl19" bibid="bib54" firstref="ref29"></nolink> <nolink nlid="nl20" bibid="bib17" firstref="ref31"></nolink> <nolink nlid="nl21" bibid="bib18" firstref="ref32"></nolink> <nolink nlid="nl22" bibid="bib47" firstref="ref37"></nolink> <nolink nlid="nl23" bibid="bib36" firstref="ref38"></nolink> <nolink nlid="nl24" bibid="bib39" firstref="ref39"></nolink> <nolink nlid="nl25" bibid="bib41" firstref="ref40"></nolink> <nolink nlid="nl26" bibid="bib52" firstref="ref41"></nolink> <nolink nlid="nl27" bibid="bib55" firstref="ref42"></nolink> <nolink nlid="nl28" bibid="bib59" firstref="ref44"></nolink> <nolink nlid="nl29" bibid="bib45" firstref="ref46"></nolink> <nolink nlid="nl30" bibid="bib53" firstref="ref48"></nolink> <nolink nlid="nl31" bibid="bib56" firstref="ref49"></nolink> <nolink nlid="nl32" bibid="bib32" firstref="ref51"></nolink> <nolink nlid="nl33" bibid="bib43" firstref="ref52"></nolink> <nolink nlid="nl34" bibid="bib65" firstref="ref53"></nolink> <nolink nlid="nl35" bibid="bib28" firstref="ref55"></nolink> <nolink nlid="nl36" bibid="bib24" firstref="ref57"></nolink> <nolink nlid="nl37" bibid="bib64" firstref="ref58"></nolink> <nolink nlid="nl38" bibid="bib37" firstref="ref59"></nolink> <nolink nlid="nl39" bibid="bib67" firstref="ref60"></nolink> <nolink nlid="nl40" bibid="bib50" firstref="ref63"></nolink> <nolink nlid="nl41" bibid="bib51" firstref="ref64"></nolink> <nolink nlid="nl42" bibid="bib34" firstref="ref67"></nolink> <nolink nlid="nl43" bibid="bib16" firstref="ref69"></nolink> <nolink nlid="nl44" bibid="bib12" firstref="ref71"></nolink> <nolink nlid="nl45" bibid="bib40" firstref="ref72"></nolink> <nolink nlid="nl46" bibid="bib22" firstref="ref74"></nolink> <nolink nlid="nl47" bibid="bib33" firstref="ref75"></nolink> <nolink nlid="nl48" bibid="bib69" firstref="ref77"></nolink> <nolink nlid="nl49" bibid="bib29" firstref="ref86"></nolink> <nolink nlid="nl50" bibid="bib27" firstref="ref91"></nolink> <nolink nlid="nl51" bibid="bib42" firstref="ref98"></nolink> <nolink nlid="nl52" bibid="bib63" firstref="ref104"></nolink> <nolink nlid="nl53" bibid="bib60" firstref="ref111"></nolink> <nolink nlid="nl54" bibid="bib46" firstref="ref113"></nolink> <nolink nlid="nl55" bibid="bib23" firstref="ref119"></nolink> <nolink nlid="nl56" bibid="bib38" firstref="ref120"></nolink> <nolink nlid="nl57" bibid="bib66" firstref="ref121"></nolink> <nolink nlid="nl58" bibid="bib19" firstref="ref123"></nolink> <nolink nlid="nl59" bibid="bib13" firstref="ref124"></nolink> |
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| Header | DbId: eric DbLabel: ERIC An: EJ1502797 AccessLevel: 3 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Mathematics-Writing Performance of Students Experiencing Mathematics Difficulties in China – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Xiaonan+Han%22">Xiaonan Han</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0003-8949-1212">0009-0003-8949-1212</externalLink>)<br /><searchLink fieldCode="AR" term="%22Xin+Lin%22">Xin Lin</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-8077-5134">0000-0002-8077-5134</externalLink>) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22Journal+of+Learning+Disabilities%22"><i>Journal of Learning Disabilities</i></searchLink>. 2026 59(3):185-201. – Name: Avail Label: Availability Group: Avail Data: SAGE Publications and Hammill Institute on Disabilities. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: journals@sagepub.com; Web site: https://sagepub.com – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: Y – Name: Pages Label: Page Count Group: Src Data: 17 – Name: DatePubCY Label: Publication Date Group: Date Data: 2026 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Journal Articles<br />Reports - Research – Name: Audience Label: Education Level Group: Audnce Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+6%22">Grade 6</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink> – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Writing+%28Composition%29%22">Writing (Composition)</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Problems%22">Learning Problems</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+6%22">Grade 6</searchLink><br /><searchLink fieldCode="DE" term="%22Writing+Skills%22">Writing Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Vocabulary%22">Vocabulary</searchLink><br /><searchLink fieldCode="DE" term="%22Computation%22">Computation</searchLink> – Name: Subject Label: Geographic Terms Group: Su Data: <searchLink fieldCode="DE" term="%22China%22">China</searchLink> – Name: DOI Label: DOI Group: ID Data: 10.1177/00222194251391829 – Name: ISSN Label: ISSN Group: ISSN Data: 0022-2194<br />1538-4780 – Name: Abstract Label: Abstract Group: Ab Data: This study aimed to conduct a comprehensive investigation into the mathematics-writing (MW) performance of students with mathematics difficulties (MDs) in China. We compared the performance of students with MD with their typically developing (TD) and high-performing (HP) peers. The analysis was based on a sample of 138 sixth-grade students. Our findings revealed (a) the trend in MW performance followed the hierarchy of mathematics ability levels (HP > TD > MD), whereas all groups displayed similar performance in general writing (HP = TD = MD), (b) although all three groups were able to organize their ideas in general writing, they had difficulty structuring their ideas effectively in MW, and (c) students with MD were less likely to incorporate technical mathematics vocabulary and symbols in their MW; they were also more likely to write incomplete sentences and make punctuation mistakes in their MW. Implications for educational strategies, teaching methodologies, and targeted support interventions are discussed. – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: DateEntry Label: Entry Date Group: Date Data: 2026 – Name: AN Label: Accession Number Group: ID Data: EJ1502797 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1177/00222194251391829 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 185 Subjects: – SubjectFull: Foreign Countries Type: general – SubjectFull: Mathematics Skills Type: general – SubjectFull: Writing (Composition) Type: general – SubjectFull: Learning Problems Type: general – SubjectFull: Elementary School Students Type: general – SubjectFull: Grade 6 Type: general – SubjectFull: Writing Skills Type: general – SubjectFull: Vocabulary Type: general – SubjectFull: Computation Type: general – SubjectFull: China Type: general Titles: – TitleFull: Mathematics-Writing Performance of Students Experiencing Mathematics Difficulties in China Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Xiaonan Han – PersonEntity: Name: NameFull: Xin Lin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0022-2194 – Type: issn-electronic Value: 1538-4780 Numbering: – Type: volume Value: 59 – Type: issue Value: 3 Titles: – TitleFull: Journal of Learning Disabilities Type: main |
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