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Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities...
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Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties

A special issue of Education Sciences (ISSN 2227-7102). This special issue belongs to the section "Special and Inclusive Education".

Deadline for manuscript submissions: closed (31 October 2025) | Viewed by 19214

Special Issue Editor

Prof. Dr. Yan Ping Xin

E-Mail Website
Guest Editor
Department of Educational Studies, Purdue University, West Lafayette, IN, USA
Interests: mathematics problem solving; students with learning disabilities and difficulties; intervention strategies; computer-assisted instruction

Special Issue Information

Dear Colleagues,

Early school mathematics is the foundation for the future success of advanced mathematics and other gatekeeper courses in secondary settings, leading to various educational and occupational opportunities. However, about 86% of students with disabilities performed below the proficiency level in the 4th grade, and 94% performed below proficiency at the 8th grade level (NAEP, 2023). How do we help at-risk students early on so they are not further falling behind?   

In this Special Issue, we invite researchers and practitioners to report empirical studies that examine the effect of innovative intervention/instructional strategies or programs that (a) address students’ conceptual understanding in learning mathematics, (b) teach mathematical big ideas to promote generalization, (c) explore the impact of problem posing on advancing students’ mathematical problem-solving abilities/skills, (d) take advantages of AI technology to analyze students learning process providing diagnostic information that can guide instructional decision making and planning. 

In sum, this Special Issue will collect cutting-edge knowledge in examining the effect of mathematics intervention programs in real education settings and the use of AI in education assessment and/or intervention pertinent to mathematics learning of K-12 students with learning disabilities or difficulties in mathematics (LDM). Possible topics include but are not limited to:

  • Empirical research to evaluate the effect of innovative intervention strategies or programs for teaching mathematics to students with LDM in real classrooms or school settings.
  • Empirical research to evaluate the impact of intervention/programs to promote the implementation of evidence-based practice in real classroom settings.
  • Empirical research or literature synthesis pertinent to the use of AI in analyses of mathematical learning process providing diagnostic information to facilitate instructional planning and decision makings.

Prof. Dr. Yan Ping Xin
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a double-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Education Sciences is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematics
  • problem solving
  • problem posing
  • conceptual understanding
  • artificial intelligence
  • learning disabilities
  • at risk
  • K-12 students

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Published Papers (9 papers)

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Research

Jump to: Review, Other

28 pages, 5083 KB  
Article
Optimizing Assessment Thresholds of a Computer Gaming Intervention for Students with or at Risk for Mathematics Learning Disabilities: Accuracy and Response Time Trade-Offs
by Sam Choo, Jechun An, Nancy Nelson and Derek Kosty
Educ. Sci. 2025, 15(12), 1660; https://doi.org/10.3390/educsci15121660 - 9 Dec 2025
Viewed by 773
Abstract
Students with mathematics learning disabilities often have difficulties in adding whole numbers. Such difficulties are evident in both response time and accuracy, but the relationship between accuracy and response time requires further consideration, especially in the context of technology-based interventions and assessments. In [...] Read more.
Students with mathematics learning disabilities often have difficulties in adding whole numbers. Such difficulties are evident in both response time and accuracy, but the relationship between accuracy and response time requires further consideration, especially in the context of technology-based interventions and assessments. In this article, we apply a novel approach using the drift-diffusion model to examine potential trade-offs and find balanced performance points that account for both accuracy and response time, using data from an efficacy trial of a mathematics technology gaming intervention for first-grade students with or at risk for learning disabilities. Results indicate that accuracy tends to increase as response time decreases, but only to a certain point. Practical implications include that educators should consider both accuracy and response time to intensify and individualize their instruction and take student background (i.e., gender, special education status, and English language status) into account. We suggest that developing technology-based mathematics interventions and assessments requires careful design and configuration to balance accuracy and response time, thereby enabling adaptive performance thresholds for better understanding and supporting student learning in early mathematical fluency. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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17 pages, 1860 KB  
Article
Visual Translator: Bridging Students’ Handwritten Solutions and Automatic Diagnosis of Students’ Use of Number Lines to Represent Fractions
by Dake Zhang, Zhizhi Wang, Min Li and Yuhan Tao
Educ. Sci. 2025, 15(12), 1638; https://doi.org/10.3390/educsci15121638 - 5 Dec 2025
Viewed by 708
Abstract
The latest AI advancements have provided opportunities for developing automated scoring and diagnosis systems that interpret and evaluate students’ written solutions and assist teachers’ grading and evaluation, yet computer vision still represents a technical challenge in detecting and describing the numerical values and [...] Read more.
The latest AI advancements have provided opportunities for developing automated scoring and diagnosis systems that interpret and evaluate students’ written solutions and assist teachers’ grading and evaluation, yet computer vision still represents a technical challenge in detecting and describing the numerical values and spatial locations of key elements in students’ hand-written solutions to mathematics tasks. This study reports the development and evaluation of an AI-based platform, called Visual Translator (VT), that automatically detects and describes the key visual information which is essential to the next step of auto-grading and diagnosis. The VT was trained with a private dataset of students’ handwritten solution images. Human-experts annotated the key elements in students’ solution images to build ground truth. We evaluated the VT performance by comparing the fraction value identification accuracy and location detection accuracy between VT and available LLMs against human expert annotations. Results suggested that VT surpassed GPT and Grok in fraction value identification, and also outperformed Geimini, the only LLM that supports image segmentation, in location detection. This model serves as the first step to reach the ultimate goal for classifying problem-solving strategies and error types in students’ handwritten solutions. Implications for computer vision research, auto-grading and diagnosis in K12 mathematics education are discussed. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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27 pages, 915 KB  
Article
Fostering Reflection and Attention to Enhance Struggling Students’ Mathematical Problem Solving—A Case Study
by Tikva Ovadiya
Educ. Sci. 2025, 15(11), 1538; https://doi.org/10.3390/educsci15111538 - 14 Nov 2025
Viewed by 2126
Abstract
Research has shown that attention plays a crucial role in developing mathematical problem-solving skills, particularly for students who struggle with non-routine tasks. Even basic operations require shifts in attention, underscoring the deep connection between attention and mathematical cognition. Attentional strategies are observable and [...] Read more.
Research has shown that attention plays a crucial role in developing mathematical problem-solving skills, particularly for students who struggle with non-routine tasks. Even basic operations require shifts in attention, underscoring the deep connection between attention and mathematical cognition. Attentional strategies are observable and can be developed with targeted scaffolding. This study aimed to enhance high school students’ attentional engagement in problem-solving through a structured intervention. Over an academic year, twelve struggling students in Grades 11 and 12 participated in three one-on-one sessions with a researcher, receiving focused instruction. These sessions encouraged reflection and attention by using the “CCRSRC” model: Connections (identifying similarity connections among the problems presented); Choice (the student deciding which problem to solve); Reflection (explaining the choice); Solving (an attempt is made); Repetition (repeating steps 1–4 as often as wished); and Choice (to end the repetition and move on). Mason’s theory of shifts of attention was used to examine learners’ attentional development. This article provides a detailed analysis of one intervention case, offering insight into how CCRSRC actions serve as catalysts for fostering learner attention. In addition to describing and characterizing a single case, the article summarizes the attention data of all learners involved in the individual intervention. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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32 pages, 7537 KB  
Article
A Follow-Up on the Development of Problem-Solving Strategies in a Student with Autism
by Irene Polo-Blanco, María-José González-López and Raúl Fernández-Cobos
Educ. Sci. 2025, 15(10), 1359; https://doi.org/10.3390/educsci15101359 - 13 Oct 2025
Cited by 1 | Viewed by 1476
Abstract
Students with autism spectrum disorder (ASD) often face difficulties in solving arithmetic word problems, particularly in transitioning from informal counting strategies to more efficient methods based on number facts and formal operations. This study examined the development of problem-solving strategies in a single [...] Read more.
Students with autism spectrum disorder (ASD) often face difficulties in solving arithmetic word problems, particularly in transitioning from informal counting strategies to more efficient methods based on number facts and formal operations. This study examined the development of problem-solving strategies in a single student with ASD and intellectual disability across two sequential single-case experiments using multiple baseline designs. Study 1 (age 13 years 9 months; 17 sessions) employed Modified Schema-Based Instruction (MSBI) to teach addition and subtraction change problems, while Study 2 (age 14 years 10 months; 18 sessions) utilized the Conceptual Model-based Problem Solving (COMPS) approach for multiplication and division equal-group problems. Success was defined as both correctness of the response and correctly identifying the required operation. Results indicated that the student’s performance improved in all problem types in both studies, with maintenance observed 8 weeks after Study 1 and 5 weeks after Study 2. Instruction effects generalized to two-step addition and subtraction problems in Study 1, and to two-step addition and multiplication problems in Study 2. The findings indicate that both MSBI and COMPS facilitated the student’s shift from informal strategies to efficient operation-based problem solving. Implications for practice include the need for individualized reinforcements, careful adaptation of instruction, and providing teachers with a variety of problems and knowledge of these teaching methods to support students with ASD in developing advanced problem-solving skills. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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19 pages, 1666 KB  
Article
Examining Fraction Performance and Learning Trajectories in Students with Learning Disabilities: Effects of Whole-Class Intervention
by Jessica H. Hunt, Michelle Taub, Matthew Marino and Kenneth Holman
Educ. Sci. 2025, 15(9), 1234; https://doi.org/10.3390/educsci15091234 - 17 Sep 2025
Cited by 2 | Viewed by 2134
Abstract
Digital game-based interventions have shown promise in improving STEM engagement and conceptual understanding among elementary students. This study focuses on how a game-enhanced, whole-class mathematics intervention influences the fraction performance and conceptual development of students with learning disabilities (LDs). Using a triangulated mixed [...] Read more.
Digital game-based interventions have shown promise in improving STEM engagement and conceptual understanding among elementary students. This study focuses on how a game-enhanced, whole-class mathematics intervention influences the fraction performance and conceptual development of students with learning disabilities (LDs). Using a triangulated mixed methods design, we analyzed pre- and post-intervention data from students in intervention and comparison classrooms. Students participating in the game-based instruction demonstrated medium, positive gains in both performance and conceptual reasoning, in contrast to declines observed in the comparison group. The findings illustrate how equitable design principles can support mathematical growth among students with LDs, with implications for research and practice. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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20 pages, 1873 KB  
Article
Exploring the Effects of a Problem-Posing Intervention with Students at Risk for Mathematics and Writing Difficulties
by Jing Wang, Pamela Shanahan Bazis and Qingli Lei
Educ. Sci. 2025, 15(6), 780; https://doi.org/10.3390/educsci15060780 - 19 Jun 2025
Cited by 1 | Viewed by 2827
Abstract
Word problem posing is a critical component of student mathematics learning. This study examined the effects of a problem-posing intervention designed to improve mathematics performance and sentence-writing conventions. Using a multiple baseline across participants design, three third-grade students with mathematics and writing difficulties [...] Read more.
Word problem posing is a critical component of student mathematics learning. This study examined the effects of a problem-posing intervention designed to improve mathematics performance and sentence-writing conventions. Using a multiple baseline across participants design, three third-grade students with mathematics and writing difficulties received one-on-one intervention delivered after school at a university reading center. Data were collected from baseline, intervention, and maintenance phases. Visual analysis and Tau-U statistical analysis indicated that all three students showed improvements in problem solving, problem posing, total words written, words spelled correctly, and correct writing sequence. Post-intervention data suggested that students maintained the improvement over baseline. Discussion and implications for future practice and research were provided. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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Review

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23 pages, 1284 KB  
Review
Mathematics Teachers’ Pedagogical Content Knowledge in Strengthening Conceptual Understanding in Students with Learning Disabilities: A Practice-Based Conceptual Synthesis
by Friggita Johnson and Finita G. Roy
Educ. Sci. 2026, 16(2), 176; https://doi.org/10.3390/educsci16020176 - 23 Jan 2026
Viewed by 1146
Abstract
Students with learning disabilities (LD) often struggle to develop deep, transferable conceptual understanding in mathematics due to cognitive and processing challenges, underscoring the relevance of instruction grounded in strong teacher pedagogical content knowledge (PCK). This issue is critical given widening post-pandemic achievement gaps [...] Read more.
Students with learning disabilities (LD) often struggle to develop deep, transferable conceptual understanding in mathematics due to cognitive and processing challenges, underscoring the relevance of instruction grounded in strong teacher pedagogical content knowledge (PCK). This issue is critical given widening post-pandemic achievement gaps and increased expectations for conceptual understanding in inclusive classrooms. Although many studies document effective mathematics interventions for students with LD, relatively few examine how teachers’ PCK functions in these classrooms. In contrast, general education research highlights the importance of PCK for conceptual learning. This manuscript bridges these studies by examining how insights from broader PCK research may inform instruction for students with LD. This manuscript presents a practice-based conceptual synthesis of research on mathematics teachers’ PCK, integrating findings from special education and mathematics intervention literature with classroom vignettes and practitioner examples. The synthesis highlights how core PCK components—content knowledge, understanding of student thinking and misconceptions, and instructional strategies—may support early conceptual understanding in students with LD, emphasizing multiple representations, error analysis, and routines that promote generalization through distributed practice. Implications for practice, professional development, and future research are discussed, offering practice-informed pathways to support inclusive mathematics instruction for students with LD. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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19 pages, 830 KB  
Review
Conceptual Model-Based Problem Solving: An Evidence-Based Review for Students Who Are Struggling in Mathematics
by Yan Ping Xin, Yichen Wang, Busra Yilmaz Yenioglu and Lejia Yu
Educ. Sci. 2025, 15(12), 1664; https://doi.org/10.3390/educsci15121664 - 10 Dec 2025
Cited by 1 | Viewed by 1514
Abstract
Over the past decade, the mathematical performance of at-risk students has not improved and has, in fact, declined since 2020. Conceptual Model-Based Problem-Solving (COMPS) strategies have been studied by researchers in and outside of the U.S. To date, there is no systematic review [...] Read more.
Over the past decade, the mathematical performance of at-risk students has not improved and has, in fact, declined since 2020. Conceptual Model-Based Problem-Solving (COMPS) strategies have been studied by researchers in and outside of the U.S. To date, there is no systematic review evaluating this body of research. The purpose of this study was to conduct a systematic review evaluating the quality and evidence base of research studies that utilized COMPS strategies in helping students learn mathematics. A total of 20 studies involving students with disabilities or learning difficulties in mathematics, with grade levels ranging from third to eighth grade, were included in this review. We used Council for Exceptional Children quality indicators and What Works Clearinghouse standards to evaluate the methodology rigor of this body of research and determine the evidence base of the COMPS strategies. The results of this systematic review of the evidence base indicate that COMPS is an evidence-based practice particularly based on the single-case design studies identified in this review. Implications for future research and practices are discussed in the context of paradigm shifts in mathematics teaching and learning. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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Other

Jump to: Research, Review

16 pages, 1752 KB  
Systematic Review
A Meta-Analysis of Technology-Based Word-Problem Interventions for Students with Disabilities
by Soo Jung Kim and Yan Ping Xin
Educ. Sci. 2024, 14(12), 1372; https://doi.org/10.3390/educsci14121372 - 13 Dec 2024
Cited by 4 | Viewed by 4874
Abstract
The aim of this meta-analysis was to investigate the effect of technology-based interventions on mathematical word problem solving for students with disabilities. This study also assessed the quality of research based on What Works Clearinghouse (WWC) design standards. A total of 21 studies [...] Read more.
The aim of this meta-analysis was to investigate the effect of technology-based interventions on mathematical word problem solving for students with disabilities. This study also assessed the quality of research based on What Works Clearinghouse (WWC) design standards. A total of 21 studies were included in the analysis. This study computed an overall effect and analyzed moderators of group design studies (Hedges’ g) and single-case design studies (between-case standardized mean difference) in the same analyses. The results show that the overall effect of technology-based interventions on word problems across 21 studies was large (Hedges’ g = 1.18, 95% CI = 0.84, 1.52). Additionally, the studies meeting WWC design standards demonstrated significantly greater effects. The moderator analyses indicated that certain study characteristics, such as publication years, settings, intervention agents, technology devices and types, and mathematics topics moderated the effects of interventions. The four studies that evaluated the generalization effect of the intervention using distal standardized assessments showed a near moderate effect (Hedges’ g = 0.49, 95% CI = 0.09, 0.9). Implications for future research and practice are discussed. Full article
(This article belongs to the Special Issue Conceptual Understanding in Mathematics: Focusing on Students with Learning Disabilities or Difficulties)
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