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The Use of an Intelligent Tutoring Program to Promote Independent Problem-Solving Skills of Students with Learning Disabilities or Difficulties

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Title: The Use of an Intelligent Tutoring Program to Promote Independent Problem-Solving Skills of Students with Learning Disabilities or Difficulties
Language: English
Authors: Xuan Yang (ORCID 0000-0002-6218-8331), Yan Ping Xin (ORCID 0000-0002-0035-9203)
Source: Learning Disability Quarterly. 2026 49(2):98-111.
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: 14
Publication Date: 2026
Sponsoring Agency: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
Contract Number: 080500689
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Grade 4
Intermediate Grades
Descriptors: Intelligent Tutoring Systems, Problem Solving, Students with Disabilities, Learning Disabilities, Learning Problems, Word Problems (Mathematics), Mathematics Instruction, Program Effectiveness, Computer Managed Instruction, Elementary School Students, Grade 4
DOI: 10.1177/07319487261423553
ISSN: 0731-9487
2168-376X
Abstract: Educational laws and current standards emphasize fostering conceptual understanding in problem-solving, as well as cultivating higher-order thinking and reasoning skills, with the ultimate goal of developing independent mathematical thinkers. The purpose of this study, conducted at a Midwest U.S. elementary school, was to explore the impact of the Please Go Bring Me-COnceptual Model-based Problem-Solving intelligent tutor on word problem-solving skills and multiplicative concept development of students with learning disabilities or difficulties in mathematics. The multiple-probe across-participants design was used to explore the functional relationship between the intervention program and students' problem-solving skills and the development of conceptual knowledge. Concept development was measured by the levels of independence in solving problems provided by the intelligent tutor. Results showed that the tutoring system was effective in promoting students' critical thinking and word problem-solving performance. It seems that features, such as the guided discovery strategy embedded in the tutoring system may have contributed to students' development as an independent problem solver.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1501922
Database: ERIC
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  Value: <anid>AN0192656044;dyw01may.26;2026Apr02.02:27;v2.2.500</anid> <title id="AN0192656044-1">The Use of an Intelligent Tutoring Program to Promote Independent Problem-Solving Skills of Students With Learning Disabilities or Difficulties </title> <p>Educational laws and current standards emphasize fostering conceptual understanding in problem-solving, as well as cultivating higher-order thinking and reasoning skills, with the ultimate goal of developing independent mathematical thinkers. The purpose of this study, conducted at a Midwest U.S. elementary school, was to explore the impact of the Please Go Bring Me-COnceptual Model-based Problem-Solving intelligent tutor on word problem-solving skills and multiplicative concept development of students with learning disabilities or difficulties in mathematics. The multiple-probe across-participants design was used to explore the functional relationship between the intervention program and students' problem-solving skills and the development of conceptual knowledge. Concept development was measured by the levels of independence in solving problems provided by the intelligent tutor. Results showed that the tutoring system was effective in promoting students' critical thinking and word problem-solving performance. It seems that features, such as the guided discovery strategy embedded in the tutoring system may have contributed to students' development as an independent problem solver.</p> <p>Keywords: word problem-solving; intelligent tutor; independent problem solver; conceptual knowledge</p> <p>According to [<reflink idref="bib17" id="ref1">17</reflink>], more than 15% of public-school students in the United States received special education services. Among this group, the learning disabilities were the most common category, accounting for 32%, or about 2.3million students. The 2022 National Assessment of Educational Progress (NAEP) data reveal that fourth-grade students with learning disabilities or difficulties in mathematics (LDM) experience a greater achievement decline in mathematics proficiency compared with their average or high performing peers. Compared with 2022, the most recent 2024 NAEP data show that math scores in grade four increased by two points nationally, largely driven by higher-performing students. However, there were no significant changes during the same period for lower performing students at the 10th and 25th percentiles. Data from the NAEP further indicate that schools may be facing challenges in meeting the objectives of Every Student Succeeds Act ([<reflink idref="bib7" id="ref2">7</reflink>]), which emphasize promoting equitable access to high-quality mathematics education, including conceptual understanding for all students, particularly those with LDM. Specifically, the Common Core State Standards for Mathematics ([<reflink idref="bib2" id="ref3">2</reflink>]) highlight the critical role of word problem-solving in promoting higher-order thinking and reasoning skills throughout elementary mathematics education. These high expectations pose significant challenges for general and special educators in promoting overall student learning and achievement ([<reflink idref="bib38" id="ref4">38</reflink>]).</p> <p>Mathematical problem-solving has been recognized as a critical component in enhancing students' ability to construct a conceptual understanding of fundamental mathematical ideas and procedures ([<reflink idref="bib1" id="ref5">1</reflink>]). In addition, it nurtures logical reasoning skills, which are essential for achieving success in diverse mathematical tasks like estimation, word problem-solving, and computational exercises ([<reflink idref="bib31" id="ref6">31</reflink>]). Solving mathematical word problems requires a variety of skills, including reading and comprehending linguistically presented problems, developing a conceptual understanding of the problem context, generating appropriate mathematical equations, performing computational procedures, and determining the final answers ([<reflink idref="bib3" id="ref7">3</reflink>]; [<reflink idref="bib24" id="ref8">24</reflink>]). As such, word problem-solving has become a growing focus in mathematics curricula and instruction. However, students with learning and mathematical disabilities (LMD) continue to face substantial challenges in solving mathematical word problems due to difficulties in cognitive and metacognitive strategies, as well as in mathematical reasoning ([<reflink idref="bib10" id="ref9">10</reflink>]; [<reflink idref="bib15" id="ref10">15</reflink>]). This status quo is further exacerbated by the ongoing, widespread and persistent shortage of special education teachers, as reported by the National Center for Education Statistics in 2022. This issue has worsened in the post-pandemic era, threatening the quality of educational services available to these students ([<reflink idref="bib5" id="ref11">5</reflink>]; [<reflink idref="bib16" id="ref12">16</reflink>]).</p> <p>Given the extensive challenges students with LDM encounter when solving word problems, there is a growing need to identify effective interventions that align with the Common Core's focus on fostering higher-order thinking and ensuring equitable access to academic standards for every student. To this end, computer-assisted instruction (CAI) presents a promising solution to address both the diverse learning needs in inclusive classrooms and the challenges posed by limited human resources in special education. Computer-assisted instruction, which involves the use of computers to deliver educational content and support learning ([<reflink idref="bib6" id="ref13">6</reflink>]), has been widely recognized as an effective approach to enhance engagement and academic performance among students with LDM ([<reflink idref="bib23" id="ref14">23</reflink>]). For instance, [<reflink idref="bib12" id="ref15">12</reflink>] synthesized the effect of CAI on mathematics word problem-solving performance of students with LDM. The results indicated that CAI showed overall positive effects in promoting word problem-solving performance of students with LDM with a large effect size (<emph>g</emph> = 0.77). Furthermore, when the CAI emphasized model-based problem-solving, it resulted in an even larger effect size (<emph>g</emph> = 1.42). With different levels of sophistication, CAI features individualized interaction, immediate feedback, adjustable pacing, and delivery of student-adaptive instruction designed to meet each student's unique learning needs ([<reflink idref="bib12" id="ref16">12</reflink>], [<reflink idref="bib13" id="ref17">13</reflink>]).</p> <p>A growing body of literature demonstrates the positive effects of CAI on word problem-solving for students with LDM. [<reflink idref="bib24" id="ref18">24</reflink>] investigated the effects of a multi-component CAI program "Fun Fraction" on middle school students with mathematics learning disabilities. The program was developed to enhance students' conceptual understanding and problem-solving performance in fraction word problems by integrating cognitive and metacognitive strategies, virtual manipulatives, and explicit, systematic instruction. The instructional framework incorporated the cognitive problem-solving steps—read, restate, represent, and answer—while embedding metacognitive support at each stage through self-instruction prompts (e.g., "I will read the problem" or "I will read it again if I don't understand") and self-monitoring questions (e.g., "Have I understood the problem and can now move forward?"). Results indicated that the CAI program incorporating these cognitive and metacognitive strategies had a positive impact on improving students' ability to solve fraction word problems.</p> <p>[<reflink idref="bib34" id="ref19">34</reflink>] used a group design to investigate the effects of a CAI program "model-based problem-solving" (MBPS) that focuses on nurturing students' additive reasoning and problem-solving. The MBPS CAI program consisted of two key components: module A emphasizes the development of foundational mathematical concepts, such as composing and decomposing numbers and understanding the idea of composite units (CUs). Modules B and C engage students in representing and solving various additive word problems using the COnceptual Model-based Problem-Solving (COMPS, [<reflink idref="bib33" id="ref20">33</reflink>]) strategy, which emphasizes students' representation of mathematical relationships extracted from the word problem story in the part-part-whole model equations. A total of 17 third graders with LDM participated in the study. Based on the level of support needed, nine students were assigned to the MBPS CAI condition, and eight students were assigned to the business-as-usual (BAU) condition. Both conditions received regular mathematics instruction plus response to intervention remediation during each school day. Students in MBPS condition worked "one-on-one" with the MBPS computer tutor for a total of 18 sessions, while BAU group worked on solving similar math problems with participating schoolteachers for the same amount of time. It was reported that teachers often prompted students to draw pictures to support their understanding of word problems; and they also taught students to use the "keyword" strategy to help with the operation sign in the math sentence. The results showed students in the MBPS group performed better than those in the BAU group who received the standard "business as usual" intervention from their teachers.</p> <p>[<reflink idref="bib37" id="ref21">37</reflink>] conducted a small-scale randomized controlled trial (RCT) study with 19 students to compare the effect of a web-based Please Go Bring Me-COnceptual Model-based Problem-Solving (PGBM-COMPS) intelligent tutor with the BAU condition on multiplicative mathematics problem-solving and reasoning of students with LDM. Results indicated that, for both the problem-solving and reasoning measures, although both groups improved their performance from pre- to post-test, the improvement rate of the students in the PGBM-COMPS group was much greater than that of the BAU group (ES = 1.99 on a researcher-developed problem-solving measure). Furthermore, there were significant group differences on a distal measure, and the Stanford Achievement Test (SAT-10, [<reflink idref="bib19" id="ref22">19</reflink>]). The pre–post gain score effect size was 1.23 favoring the PGBM-COMPS condition.</p> <hd id="AN0192656044-2">Theoretical Framework</hd> <p>The PGBM-COMPS intelligent tutor was the product of a National Science Foundation (NSF) supported project ([<reflink idref="bib36" id="ref23">36</reflink>]). The PGBM-COMPS computer tutor draws on three research-based frameworks: a constructivist view of learning from mathematics education ([<reflink idref="bib26" id="ref24">26</reflink>]), data (or statistical) learning from computer sciences, and the COMPS ([<reflink idref="bib33" id="ref25">33</reflink>]) that generalizes word-problem underlying structures from special education. The constructivist view of learning integrates the concept of guided discovery learning with principles from cognitive instructional design ([<reflink idref="bib14" id="ref26">14</reflink>]). Different from pure discovery learning in which the teachers provide little or no guidance to the students, guided discovery learning requires teachers to provide hints, direction, coaching, feedback and modeling to guide students as they explore solutions for a problem ([<reflink idref="bib14" id="ref27">14</reflink>]). Rooted in guided learning theory, the PGBM-COMPS tutor adopted a student-adaptive teaching approach ([<reflink idref="bib25" id="ref28">25</reflink>]), which foster the development in critical thinking and multiplicative reasoning, eventually supporting students in becoming independent thinkers and problem solvers.</p> <p>The PGBM-COMPS intelligent tutor used in Xin et al.'s (2017) study includes two parts: (a) the "Please Go and Bring for me..." turn-taking game for promoting students' construction of multiplicative double counting (MDC)—one of the fundamental ideas in multiplicative reasoning and (b) the COMPS program that was designed to advance students to the abstract level of thinking and mathematical model-based problem-solving. In the PGBM game, the student is directed to a box of Unifix cubes to build and return with a tower consisting of a specified number of cubes (e.g., a tower with three cubes in each). After two to nine "trips" for bringing same-size towers, the "bringer" is asked "How many towers (i.e., # of Composite Unit [CU]) did you bring?"; "How many cubes are in each tower?" (i.e., unit rate, UR); "How many cubes (1's) are there in all?"; and "How did you figure out that answer?" These four key questions were designed to promote students reflection on the activity sequence: (a) <emph>first</emph> building each tower (i.e., producing a CU from one), (b) iterating that CU several times (e.g., the students were sent to build the same sized tower, say a tower with <emph>three cubes in each</emph>, five times, and bring it back to the same station), <emph>then</emph> they were asked to figure out the total number of cubes (i.e., the ones) in all towers that they brought to the station. Through playing this PGBM game, the students were guided to reflect on the activity with an intention to separate the CU (three cubes-per-tower, the unit rate) from the number of composite unit (five towers of three cubes each), leading to the distribution (coordination) of those two unit types to produce a third CU (the product, or 15 ones) ([<reflink idref="bib30" id="ref29">30</reflink>]).</p> <p>The COMPS part of the program advances students to an abstract level of problem-solving that is accomplished by problem representation in model equations based on students' understanding of <emph>mathematical relations</emph> between the quantities, rather than "keyword" comprehension and/or translations (e.g., words, such as "together' or "total" were translated into a plus sign for solving the problem).</p> <hd id="AN0192656044-3">Purpose and Research Questions</hd> <p>This study was conducted within the larger context of an NSF-funded project ([<reflink idref="bib36" id="ref30">36</reflink>]) with a goal to nurture multiplicative reasoning, create and field test an intelligent tutor PGBM-COMPS to address the skill deficit and immediate needs of elementary students with LDM in meeting the Common Core State Standards for Mathematics—particularly in the area of multiplicative word problem-solving. Given the large effect from the PGBM-COMPS program on both the research-developed dependent measure as well as the far transfer measure (SAT-10), further investigation is needed to examine how participating students' progress toward becoming independent problem solvers through their interactions with the intelligent tutor. As such, the purpose of this study was to examine the impact of the PGBM-COMPS intelligent tutoring system on the development of multiplicative concept and problem-solving of students with LDM. Students' growth in concept development was measured by their levels of independence (LoI) in solving various multiplicative problems, provided by the intelligent tutor, that were dynamically adapted to students' conceptual profiles. The specific research questions are as follows:</p> <p></p> <ulist> <item> <bold> Research Question 1 (RQ1): </bold> What is the functional relationship between the PGBM-COMPS intelligent tutor and students' multiplicative problem-solving performance?</item> <p></p> <item> <bold> Research Question 2 (RQ2): </bold> What are the effects of PGBM-COMPS intelligent tutor program on participating students' LoI in solving various multiplicative word problems?</item> </ulist> <hd id="AN0192656044-4">Method</hd> <p></p> <hd id="AN0192656044-5">Participants and Setting</hd> <p>Institutional Review Board's approval was received from the university and school district prior to recruitment. The study was conducted in a mid-western elementary school in the United States. Participants were recommended by the participating schools based on their substantial challenges in learning mathematics. Five students were recommended to the research team by the participating school because they were struggling with solving multiplicative word problems. Students had to meet the following criteria to be eligible for the study: (a) scored below the 30th percentile on the <emph>Mathematics Problem-Solving</emph> sub-test of the SAT-10, (b) scored at or below 60% accuracy on a researcher-developed multiplicative reasoning (MR) test, (c) had parent permission to participate, and (d) assented to participate. Students were excluded if they had diagnoses of emotional disturbance and/or exhibited challenging behaviors, or if they had difficulties comprehending the English language. Three students met the inclusion criteria and participated in the study. Table 1 presents demographic information of the students.</p> <p>Table 1. Demographics for Student Participants in Study on Use of an Intelligent Tutoring Program.</p> <p>Graph</p> <p> <ephtml> <table><colgroup><col align="left" /><col align="char" char="." /><col align="char" char="." /><col align="char" char="." /></colgroup><thead><tr><th align="center">Variable</th><th align="center">Travis</th><th align="center">Jim</th><th align="center">Jose</th></tr></thead><tbody><tr><td>Gender</td><td>Male</td><td>Male</td><td>Male</td></tr><tr><td>Ethnicity</td><td>Caucasian</td><td>African-American</td><td>Hispanic</td></tr><tr><td>Age</td><td>10</td><td>10</td><td>10</td></tr><tr><td>Grade</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Free/reduced-price lunch</td><td>Free</td><td>Free</td><td>Free</td></tr><tr><td>SES</td><td>Low</td><td>Low</td><td>Low</td></tr><tr><td>Years in special education</td><td>3 (LD)</td><td>2 (LD)</td><td>1</td></tr><tr><td>Learning support classroom placement</td><td>Math</td><td>Math</td><td>Math</td></tr><tr><td>Percentage of time in general education class</td><td>40-80%</td><td>40-80%</td><td>40-80%</td></tr><tr><td>IQ</td><td>OLSAT</td><td>OLSAT</td><td>OLSAT</td></tr><tr><td> Full scale</td><td>82</td><td>87</td><td>89</td></tr><tr><td> Verbal</td><td>78</td><td>83</td><td>92</td></tr><tr><td> Performance (non-verbal)</td><td>86</td><td>97</td><td>87</td></tr><tr><td>SAT-10 (percentile)</td><td>8th</td><td>15th</td><td>26th</td></tr></tbody></table> </ephtml> </p> <p>1 <emph>Note</emph>. LD = learning disabilities; SES = social economic status; OLSAT = Otis–Lennon School Ability Test ([<reflink idref="bib18" id="ref31">18</reflink>]); SAT = Stanford Achievement Test (SAT-10, Pearson Inc., 2004).</p> <p>All instruction sessions and assessments were conducted in the school's computer lab during the after-school program Monday through Friday from 2:45 to 3:30 p.m. throughout the semester. During the intervention phase, the intelligent tutoring system provided adaptive instruction based on individual student performance. As a result, Travis, Jim and Jose completed 23, 26, and 18 sessions, respectively. The computer lab was equipped with around 20 computers, tables, chairs and a big bookshelf with books. Each computer was equipped with a headset and a mouse. A webcam and screen recording software were installed on each student's computer to capture both the computer screen and students' actions during the problem-solving process for future analyses. To ensure security, all video recordings were stored on an encrypted storage device, which was physically secured in a locked cabinet within a controlled-access university office. Researchers supervised the intervention sessions on site, addressing any computer/technical glitches and redirecting students to the designated module as needed.</p> <hd id="AN0192656044-6">Dependent Measures</hd> <p>The PGBM-COMPS intelligent tutor was designed to adapt instruction based on students' problem-solving performance, promote students' conceptual understanding and facilitate independent reasoning. Consequently, the primary dependent measure was students' LoI in solving problems when interacting with the intelligent tutor. The PGBM-COMPS intelligent tutor enabled researchers to collect real-time data on students' concept development as they interacted with the tutoring program. Concept development was measured through the LoI, which tracked students' problem-solving processes while engaging with tasks embedded in the intelligent tutor. The LoI was measured by the frequency of prompts delivered by the tutor to guide students toward reaching correct solutions, with fewer prompts indicating greater student independence. For instance, when students were asked to solve this problem "I have 28 cubes under the cover. How many towers of 7 can I make of these before I run out of cubes?" If the students were unable to answer the question, the intelligent tutor would ask the student "please make a tower of 7" (first prompt). After students did it, the tutor would ask the student "Now do you know the answer to the problem?" If the students were unable to generate the correct answer, then the tutor would ask the students to make another tower of 7 (second prompt). After students made another tower of 7 (now the students had made two towers of 7), the tutor would ask the same question again "Now do you know the answer to the problem?" (i.e., How many towers of 7 can I make of a total of 28 cubes before I run out of cubes?). If the students were able to give a correct answer to the problem, then the number of prompts given by the tutor is two. However, if students still gave an incorrect answer or no answers, then the tutor would continue the prompt: "please make a tower of 7..." This prompting process continued until students were able to generate an answer. It should be noted the prompts were different based on the nature of the tasks that the intelligent tutor presenting to the student (for more information about the six schemes involved in the PGBM platform games, see [<reflink idref="bib29" id="ref32">29</reflink>]). As such, unlike conventional test-based dependent measures, the LoI is a process measure collected and generated by the intelligent tutor, based on the number of prompts rendered to each individual student during their interaction with the tutoring program.</p> <p>The secondary measure was a researcher-developed MR criterion test ([<reflink idref="bib29" id="ref33">29</reflink>]) and its alternative forms that were administered during baseline, intervention, and posttest. The MR criterion test consisted of 10 various multiplicative problems that were designed to assess the concepts of MDC (two items), same unit coordination (one item), unit differentiation and selection (UDS, one item), mixed unit coordination (MUC, one item), quotative division (QD, three items), and partitive division (PD, two items). The alternative forms contained the same text items; however, the sequence of the items was randomized. The MR test items were informed by scholarly literature in mathematics and special education and were further refined through collaboration with mathematics education researchers and practitioners. During the development of the MR assessment, the test items were sent out to experts in the field for feedback and input. The MR test was finalized incorporating feedback and input from experts in the field of mathematics education, special education ([<reflink idref="bib37" id="ref34">37</reflink>], [<reflink idref="bib35" id="ref35">35</reflink>]). Pearson's correlation coefficient for the test–retest reliability of the MR test was.89 and the internal consistency was.86 ([<reflink idref="bib37" id="ref36">37</reflink>]). Table 2 presents the sample MR problems. Students' performance on the LoI was continuously monitored by the intelligent tutor during the intervention, and their performance on the MR test was assessed upon completion of each module.</p> <p>Table 2. Sample Tasks Included in the Multiplicative Reasoning (MR) Test ([<reflink idref="bib29" id="ref37">29</reflink>]).</p> <p>Graph</p> <p> <ephtml> <table><colgroup><col align="left" /><col align="char" char="." /></colgroup><thead><tr><th align="center">Problem type</th><th align="center">Sample problem situations</th></tr></thead><tbody><tr><td>Multiplicative double counting</td><td>Pretend that you have made many towers, each made of 7 cubes. How many cubes are in every tower? Your Answer: _____________How many cubes are in the first 4 towers? Your Answer: _____________So we can count those by seven, "7, 14, 21, 28..." Do you think you will say the number 70 if you continue counting cubes in the towers? Your Answer: _______Why?__________Do you think you will say the number 84 if you continue counting cubes in the towers? Your Answer:_______ Why?_________________________</td></tr><tr><td>Same unit coordination</td><td>Rachael has built 13 towers with two cubes in each. Mary has built seven towers with 4 cubes in each. Who has more towers, Rachael or Mary? Your Answer: _____________ How many more towers does she have?________</td></tr><tr><td>Unit differentiation and selection</td><td>Tom's father bought six pizzas. Each pizza had four slices. Tom's mother bought a few more pizzas. Then, there were nine pizzas. How many more slices did Toms' mother bring?</td></tr><tr><td>Mixed unit coordination</td><td>Maria made birthday bags. She wants each bag to have six candies. After making three bags, she still had 12 candies left. How many bags will she have altogether after putting these 12 candies in bags?</td></tr><tr><td>Quotative division</td><td>There are 28 students in Ms. Franklin's class. During reading, she puts all students in groups of 4. She asked a student (Steve): "How many groups will I make?" Steve said: "32. Because 28 + 4 is 32.″ Do you think that Steve is correct? Your Answer: __________Why?________________</td></tr><tr><td>Partitive division</td><td>Grandma baked 27 cookies. She has three grandchildren: Manuel, Erika, and Anna. She gave all cookies to the children, and each grandchild received the same number of cookies. How many cookies did each grandchild get?</td></tr></tbody></table> </ephtml> </p> <hd id="AN0192656044-7">Data Scoring</hd> <p></p> <hd id="AN0192656044-8">Levels of Independence</hd> <p>To determine the LoI, researchers extracted, coded and analyzed each student's problem-solving data recorded by the software. If a student solved a problem correctly without any prompts, the LoI score was 100%; if one prompt was required, then the LoI score was 80%; if two prompts were required, the score was 60%; if three prompts were required, the score was 40%; and if four or more prompts were required, the score was 20%; If the student failed to solve the problem after four or more prompts, a score of 0 was assigned. A rubric (see Table 3) was developed to ensure accurate scoring.</p> <p>Table 3. Scoring Rubric for Level of Independence (LoI).</p> <p>Graph</p> <p> <ephtml> <table><colgroup><col align="left" /><col align="char" char="." /></colgroup><thead><tr><th align="center">Number of prompts provided by the intelligent tutor</th><th align="center">LoI scores (%)</th></tr></thead><tbody><tr><td>0</td><td>100</td></tr><tr><td>1</td><td>80</td></tr><tr><td>2</td><td>60</td></tr><tr><td>3</td><td>40</td></tr><tr><td>Four or more prompts</td><td>20</td></tr><tr><td>Failed to solve the problem correctly after 4 or more prompts</td><td>0</td></tr></tbody></table> </ephtml> </p> <hd id="AN0192656044-9">Problem-Solving Accuracy</hd> <p>To determine the accuracy of students' problem-solving performance on the MR tests, the total points earned were divided by the total possible points to calculate the percentage of correctly solved problems for each test. Each problem on the tests was worth two points, so the total possible score for each test was 20 points. A rubric (see Table 4) was developed to ensure accurate scoring. If a student wrote the correct final answer or provided the correct answer along with the problem-solving process, two points were awarded. If a student demonstrated correct reasoning but did not arrive at the correct answer, or if the correct answer was reached through incorrect reasoning, one point was awarded. Students were awarded zero points if they either provided an incorrect answer without explanation or demonstrated both incorrect reasoning and an incorrect answer.</p> <p>Table 4. Multiplicative Reasoning (MR) Test Scoring Rubric.</p> <p>Graph</p> <p> <ephtml> <table><colgroup><col align="left" /><col align="char" char="." /></colgroup><thead><tr><th align="left" colspan="2">Sample question 1: after an art class, there were 78 crayons out on the tables. There are six boxes for the crayons. Ms. Brown puts the same number of crayons in each box. How many crayons would she put in each box?</th></tr></thead><tbody><tr><td>2 points</td><td>(1) The student wrote the correct number as the answer, e.g., "13"(2) The student wrote the correct answer and provided correct problem-solving process (no matter what strategy was used), such as (a) "78÷6= 13" or (b) "6 × 13 =78"</td></tr><tr><td>1 point</td><td>(1) The student provided a problem-solving process that reflected the correct understanding and reasoning but ended up with an incorrect answer or no answer, e.g., "78÷6=12 or 78÷6"(2) The student had the correct number as the answer, but the math sentence was incorrect, e.g., "78 × 6", so 13"(3) If there were two questions within a problem, each sub-question was worth 1 point</td></tr><tr><td>0 points</td><td>(1) Both the problem-solving process and the answer were incorrect, e.g., "78 × 6 =468".(2) Only an incorrect number (e.g., "468") or nothing was written as the answer</td></tr></tbody></table> </ephtml> </p> <hd id="AN0192656044-10">Design</hd> <p>An adapted multiple-probe design ([<reflink idref="bib9" id="ref38">9</reflink>]) across participants was used to evaluate the potential functional relationship between the intervention and students' problem-solving accuracy on the MR test. According to [<reflink idref="bib9" id="ref39">9</reflink>], it can be advantageous for researchers to choose a design in which "multiple baseline and probe procedures are combined into a 'multiple-probe' technique," so that intermittent probes can be utilized to provide "an alternative to continuous assessment" (p. 189). Consequently, an adapted multiple-probe design was selected to avoid probing every session, thereby preventing the continuous assessment of skills that students have not yet learned. The study design included a baseline phase in which students completed the MR test. During the intervention phase, students received adaptive instruction through the tutoring program and were assessed on their LoI while solving problems presented by the system. Their problem-solving processes were automatically recorded by the software for subsequent analysis. In addition, students were assessed using MR tests and its alternative/equivalent forms. Following the intervention, a posttest phase was conducted during which students completed the same tests administered at baseline.</p> <hd id="AN0192656044-11">Procedure</hd> <p>All three students completed one MR test during the baseline. The intervention was introduced to each of the students in a staggered fashion. Following module A instruction, one MR criterion test was administered for monitoring students' overall progress before Module B took place. The same sequence was followed by all three students as they went through all of the five modules. Posttests were given following all modules' instruction. Each student worked individually on a desktop computer to interact with the intelligent tutoring system throughout the intervention, four times per week in sessions lasting approximately 20 to 25 minutes. Researchers were doctoral students in the area of special education and had experience implementing computer-assisted intervention with students with LDM. They monitored all the intervention sessions. Their roles included administering pre–post assessments, fixing technical issues from computer, recording computer screens, and guiding students to the appropriate sessions of the tutoring program after interruption. Calculators were permitted throughout the experiment to accommodate students' deficits with computational skills. Blank sheet of papers and pencils were also provided in case students need to draw or write something down when working with the intelligent tutor.</p> <hd id="AN0192656044-12">Intervention</hd> <p>The PGBM-COMPS program comprises five modules (A, B, C, D, and E). Module A focuses on MDC. When working with MDC tasks (e.g., PGBM seven towers with three cubes in each [7T3]; how many cubes in all?), students explicitly keep track of two quantities while counting two number sequences. Module B involves tasks to develop skills in UDS and MUC. During the MUC task, students are required to identify which unit to operate on, ones or CUs, and coordinate with the two units (i.e., CU and ones), and then segment the ones into CUs. Unit differentiation and selection tasks (e.g., 7T3 + six cubes; how many cubes in all) and MUC tasks (6T3 + 12 cubes = ? T3) develop students' sense on which <emph>unit</emph> they are operating, whether it is the number of cubes (the ones) or number of towers (the CU). Module C presents QD tasks where students solve the problems through either mDC or segmenting cubes into equal-sized groups for solutions. Module D deals with PD problems. The program presents concrete models that demonstrate the concept of equally distributing 1s to the given number of CUs for solution. In each of the above modules, concrete modeling (e.g., with cubes/towers context) were always connected to mathematical symbols and expression to facilitate concept symbol coordination. Module E engages students in representing and solving multiplicative word problems in various contexts involving large quantities using the mathematical model equation (e.g., unit rate [number of items in each unit] × number of units = product, [<reflink idref="bib33" id="ref40">33</reflink>]). The intelligent tutor was designed to promote students' mathematical thinking and problem-solving skills by providing individualized instructions and prompts. Students' forming of the math sentence including decision-making on the operation sign were determined by the model equation. For instance, if one of the factors (either the unit rate or the number of units) is the unknown quantity, dividing the <emph>product</emph> by the given factor would give the answer to the unknown quantity or the unknown factor. In each module (except for B), the PGBM platform game and the COMPS model-based instruction go hand in hand to facilitate students' mathematical concept development and generalized problem-solving skills. In general, the intelligent tutoring program promoted students to move to the next module based on their previous performance. In particular, the tutoring system applied a criterion of "three consecutive correct answers" to promote students from one module to next one.</p> <hd id="AN0192656044-13">Levels of Support</hd> <p>The PGBM-COMPS tutoring system adaptively provides differentiated tiers of prompts based on students' real-time performance, with the number of prompts required by individual learners reflecting their progression toward independence in achieving problem-solving mastery. The prompting system is grounded in [<reflink idref="bib32" id="ref41">32</reflink>] Zone of proximal development (ZPD) and cognitive load theory ([<reflink idref="bib27" id="ref42">27</reflink>]). Within the ZPD paradigm, prompts function as adaptive scaffolds tailored to learners' developing abilities. The tutoring system adopts a three-tiered scaffolding sequence, in which the Tier 1 prompts are minimally intrusive to encourage self-correction, while subsequent tiers progressively increase support. For instance, after an initial incorrect answer, the system provides a generic prompt "Try again." Students are then given a second opportunity to solve the problem without additional guidance, encouraging them to re-examine their work, identify errors, and revise their strategy independently.</p> <p>The Tier 2 prompts provide guided scaffolding. The system directs students' attention to the critical components of the problem and supports their transition from concrete or semi-concrete representations to abstract thinking. For example, in module A, to solve the problem "7 towers with 5 cubes in each. How many cubes are there in all?" Initially, students are prompted to bring the first tower of five cubes and then are asked the same question again. If they fail to answer correctly, they are prompted to bring the second tower of five cubes and to answer the same question again. If incorrect once again, the system prompts students to bring the remaining 6 towers and then find the total number of cubes. The system provides graduated layers of support to guide students in reasoning through the problem-solving process.</p> <p>Finally, the Tier 3 prompts provide explicit modeling of the problem-solving process. For instance, in module B, when solving the problem "Tom has a collection of 4 towers with 5 cubes in each. John has a collection of 4 towers with 10 cubes in each. How many more cubes does John have than Tom?" While the Tier 2 prompts provide hints to start with finding the total number of cubes in each collection using virtual cubes and then finding the difference between the two collections, the Tier 3 prompts provide explicit, step-by-step modeling of the entire problem-solving process. The explicit demonstrations do not simply provide answers, they aim to make the reasoning process explicit to students through decomposing problems, visualizing relationships, and explaining reasoning. In module C, when solving this problem "There is a total of 12 cubes. If we make towers with 3 cubes in each, how many towers would we have built?" The Tier 3 prompts provide explicit instruction by first building four towers with three cubes in each. When building the first tower, the system places number "1" underneath the tower to indicate it is the first tower and puts number "3" on top of the tower to show the number of cubes used. When building the second tower, the system places number "2" underneath the tower and puts the number "6" on top of it to indicate the number of cubes used so far. This continues for the remaining towers in the same way. Through this process, students monitor two number sequences: the number of cubes used (<reflink idref="bib3" id="ref43">3</reflink>, 6, 9, 12) and the number of towers built (<reflink idref="bib1" id="ref44">1</reflink>, 2, 3, 4), which leads to the solution: "We would have built 4 towers."</p> <hd id="AN0192656044-14">Interrater Reliability</hd> <p></p> <hd id="AN0192656044-15">MR Test</hd> <p>The researcher scored the copied version of each test using an answer key and the aforementioned rubrics. A research assistant (RA) in special education who was blind to the purpose of the study independently re-scored 30% of the copied version of test items. The interrater reliability was calculated by dividing the number of agreements by the sum of agreements and disagreements and multiplied by 100%. The interrater reliability was 100% for each of the student's MR problem-solving test scores.</p> <hd id="AN0192656044-16">Levels of Independence</hd> <p>The first author served as the primary observer in data collection on LoI. Interobserver agreement (IOA) data were collected by a trained secondary observer for each student. The secondary observer was an undergraduate student who was trained by the researcher on the LoI coding procedures through two 20-minute training sessions. To complete the training, the secondary observer was required to research 80% agreement with the primary observer in the independent coding of a student's LoI. The second observer independently coded at least seven sessions across the five modules for each student (at least three sessions in module A, two sessions in module B, and one session in each of the following modules), which represented 35% (eight sessions) of the total sessions for Travis, 31% (eight sessions) for Jim, and 39% (seven sessions) for Jose. Interobserver agreement was calculated by dividing the number of point-by-point agreements by the sum of point-by-point agreements and disagreements and multiplied by 100. The IOA was 100% for each student.</p> <hd id="AN0192656044-17">Treatment Fidelity</hd> <p>The PGBM-COMPS intelligent tutor served as the primary role in delivering the intervention. The intervention for each student was prescribed by the intelligent tutor, and students were required to follow the sequence of the five modules to proceed with the intervention. Students' progress and performance data were automatically documented by the tutoring system. Given that (a) the students were required to complete each intervention task in pre-determined order delivered by the intelligent tutor, (b) the intelligent tutor used computer log data to capture student's mouse clicks or response input, for instance, for monitoring students' engagement and learning progress, and (c) the computer program consistently enforced the dosage and sequence of instructional modules, we deemed that the implementation fidelity was ensured. That is, each student completed the intervention program as designed.</p> <hd id="AN0192656044-18">Data Analysis</hd> <p>Visual analysis was used as the primary method to determine whether a functional relation existed between the independent and dependent variables ([<reflink idref="bib11" id="ref45">11</reflink>]). For visual analysis, the level, trend, variability, immediacy of effect, overlap were evaluated ([<reflink idref="bib4" id="ref46">4</reflink>]). In addition, the percentage of non-overlapping data (PND) was used to calculate the treatment effect of the intervention. Percentage of non-overlapping data is most commonly used treatment effect index in single-subject studies ([<reflink idref="bib8" id="ref47">8</reflink>]). It is calculated by dividing the number of intervention data points that exceed the highest baseline data point in the expected direction by the total number of data points in the intervention phase ([<reflink idref="bib22" id="ref48">22</reflink>]).</p> <hd id="AN0192656044-19">Results</hd> <p>Figure 1 presents students' performance in solving word problems on the MR tests. Figure 2 illustrates students' growth in multiplicative concept development as measured by the LoI. The results indicate students improved their performance on the MR test and gained various LoI as they progressed through the modules in the system.</p> <p>Graph: Figure 1. Percentage of Correct Responses on the Multiplicative Reasoning (MR) Test During the Baseline, Intervention, and Post-test Phases for the Three Students</p> <p>Graph: Figure 2. Levels of Independence in Solving Multiplicative Problems: Data From Three Students</p> <hd id="AN0192656044-20">Baseline Performance</hd> <p>During baseline phase, the mean performance on the MR criterion test was 0% correct for Travis, 41% correct for Jim and 25% correct for Jose. Across the three students, the baseline performance was relatively stable and low, indicating the need for intervention.</p> <hd id="AN0192656044-21">Intervention Effect</hd> <p></p> <hd id="AN0192656044-22">Travis: (a) MR Test</hd> <p>Travis's performance increased from 0% during baseline to 15% in module A, 80% in module B, 90% in module C, and reached 100% in both modules D and E. His median score was 90% and the PND was 100%. Travis's data showed a strong upward trend with a low degree of variability. The immediate improvement at the start of the intervention phase indicated a strong immediacy of effect. <emph>(b) Levels of Independence</emph>: In module A, Travis had a mean LoI of 90.5% (median = 89%). His performance remained consistently above 85% across sessions, beginning at 92.5% in the first session, peaking at 100% in the fifth session, and ending the module with 85%. In module B, Travis had a mean LoI of 68.2% (median=67.6%). His LoI was 85.8% in the first session, dropped to 28.6% when the MUC component was first introduced in the fourth session. However, his LoI gradually increased, finishing with a final LoI of 100%. Travis maintained a high LoI in both modules C and D, with mean LoI of 95% (median = 95%) and 95.9% (median = 97.6%), respectively, consistently staying above 90% throughout both modules. In module E, Travis maintained a 100% LoI throughout all sessions.</p> <hd id="AN0192656044-23">Jim: (a) MR test</hd> <p>Jim's performance increased from 40% in baseline to 70% in module A and 60% in module B. Jim achieved 100% in module C and maintained his high performance 100% in both module D and E. His median score was 100% and the PND was 100%. Overall, Jim's problem-solving performance during the intervention showed a moderate upward trend with a moderate degree of variability. <emph>(b) Level of Independence.</emph> In module A, Jim had a mean LoI of 83.4% (median = 92%). He began the module with an LoI of 86% in the first session, peaked at 100% in the second session. His LoI demonstrated various level of independence for the following sessions and finally reached to 96%. In module B, Jim had a mean LoI of 79.72% (median = 78%). His LoI was 64% in the first session, gradually increased to 93.3% at the end of this module. In module C, Jim had a mean LoI of 77% (median = 94%). He started the module with the LoI of 100%, but it dropped sharply to 20% in the second session. However, his LoI rebounded to above 90% in the following sessions. In module D, he achieved a mean LoI of 91.25% (median = 97.5%), with two sessions at 100%, one session at 70% and one session at 95%. In module E, he had a mean LoI of 85% (median = 85%) with all sessions above 80%.</p> <hd id="AN0192656044-24">Jose: (a) MR test</hd> <p>Jose increased his performance from 30% in baseline to 70%, 80%, 70%, 100%, and 75% in modules A, B, C, D, and E, respectively. His median score was 75% and the PND was 100% correct. Jose's problem-solving performance showed a moderate upward trend with a moderate degree of variability. (b) <emph>Levels of Independence.</emph> In module A, Jose had a mean LoI of 64.5% (median = 65%). He began the module with an LoI of 20% in the first session, and gradually increased to 100% at the end of the module. In module B, Jose had a mean LoI of 34% (median = 30%). His LoI was 20% at the first session and gradually increased to 46% at the end of the session. In module C, Jose had a mean LoI of 63.9 (median = 65%). His LoI was between 53.3% and 73.3% during this module. In module D, Jose had a mean LoI of 84.4% (median = 84.4%) with all sessions above 80%. As Jose's computer experienced a malfunction toward the end of module E, his LoI data for this module was not recorded.</p> <hd id="AN0192656044-25">Post-Test</hd> <p>All students maintained high levels of accuracy of MR tests, with average scores of 90% for Travis, 100% for Jim and 90% for Jose. These results indicated that all students' performance was maintained even after the withdrawal of instruction from the intelligent tutor.</p> <hd id="AN0192656044-26">Discussion</hd> <p></p> <hd id="AN0192656044-27">Effects on Word Problem-Solving and Mathematical Reasoning</hd> <p>Overall, the intelligent tutoring system, grounded in guided discovery learning theory, demonstrated promise in improving multiplicative problem-solving performance for students with LDM. Based on a visual analysis of the data presented in Figure 1, there is an immediate change in level of performance on MR test once the intelligent tutoring intervention was introduced to each of the students following the baseline. The data path during the intervention phase showed an upward or elevated steady trend, which indicated an enhanced performance. In addition, there was no overlapping of data points between the baseline and intervention phases across all three students on their problem-solving performance, which indicated a strong treatment effect (PND was 100%, [<reflink idref="bib21" id="ref49">21</reflink>]). Results from MR tests demonstrated that each module of the intelligent tutoring program effectively enhanced multiplicative reasoning and problem-solving skills among students with LDM. The consistent improvements observed across modules highlight the program's effectiveness in strengthening students' foundational mathematical skills.</p> <p>Students' enhanced mathematics performance may be attributed to the specific design features of the PGBM-COMPS tutoring system. First, the tutoring system provided three levels of differentiated prompts with interactive feedback and corrective guidance in response to errors. This design facilitated real-time learning from mistakes. Second, the multiple levels of prompts served as an adaptive scaffolding by breaking down complex problems into manageable steps and guiding students through the reasoning process, thus supporting the construction of the mathematical concept. This scaffolding was particularly beneficial for students who initially struggled with identifying the relevant unit of operation. Travis for instance, relied heavily on Tier 2 and Tier 3 prompts during the UDS tasks, suggesting that explicit guidance in directing attention to the coordination between CU and ones was critical for solving this type of problems. Third, the non-judgment feedback provided by the system might have reduced students' anxiety and made the learning experience less intimidating. For example, when students mapped the information in a word problem to a diagram equation incorrectly, the system provided them opportunities to try again. Fourth, the integration of virtual manipulatives with visual and auditory supports aligned with the principles of universal design for learning by providing multiple means of representation. These design features might have reduced comprehension barriers for students with LDM by helping them visualize abstract multiplicative relationships and stay focused on relevant aspects of the tasks leading to correct solution ([<reflink idref="bib20" id="ref50">20</reflink>]). Finally, the system allowed students to learn at their own pace, providing individualized support based on real-time performance. The combination of these features made the learning experience more engaging and accessible for students with LDM.</p> <hd id="AN0192656044-28">Effects on Multiplicative Concept Development and Level of Independence</hd> <p>The findings seemed to indicate that each student reached various LoI across five different modules. Overall, students' LoI increased across most modules, indicating that the guided discovery learning-based tutoring system supported students with LMD in developing multiplicative reasoning and becoming progressively more independent in solving mathematical word problems. The intelligent tutoring program has a focus on nurturing conceptual understanding, promoting students' construction of mathematical ideas and engaging students in the problem-solving process through guided instruction and heuristic prompting. This approach makes the underlying mathematical reasoning explicit, ultimately supporting students in becoming independent thinkers in mathematical problem-solving. As students interacted with the intelligent tutor, they required progressively fewer prompts or supports as they gradually learned to apply problem-solving skills independently. In addition, the tutoring system allows students to learn at their own pace, revisit prompt, and reflect on errors without social stigma, which, to some extent, fosters their mathematical self-efficacy. Moreover, students' growing independence was also reflected in their willingness to attempt more challenging problems. As they gained confidence in their learning, they were less likely to give up whenever they faced with difficulties. Instead, they actively sought solutions. The program utilized the computer's adaptability to simulate concrete (e.g., unifix cubes) and figurative (e.g., fingers and pictures) representations, facilitating students' transition to the symbolic or abstract representations (mathematical models). This process promoted generalized problem-solving skills, supporting students in becoming more successful independent problem solvers.</p> <p>However, it seems there were some variations in students' LoI across some modules. In particular, Travis and Jose seemed to require substantial amount of prompting to solve problems in UDS tasks in module B, suggesting difficulties in choosing the correct unit for operation—whether to operate on the CU (e.g., number of towers) or the ones (e.g., number of cubes). During UDS tasks, students were required to distinguish between ones and CUs, flexibly shift attention between the two unit levels, and coordinate operations across these units. For example, given the problem "Each tower has 6 cubes. If there are 5 towers, how many cubes are there in all?," a student with weak working memory might focus on the number of towers (<reflink idref="bib5" id="ref51">5</reflink>) and forget the CU (six cubes per tower). They may answer "5" instead of "30" because they lose track of the relationship between towers and cubes. These demands are particularly challenging for students with LDM, due to well-documented limitations in working memory capacity and increased cognitive load during multi-step reasoning tasks (e.g., [<reflink idref="bib28" id="ref52">28</reflink>]; [<reflink idref="bib39" id="ref53">39</reflink>]). Compared with the initial CU identification tasks in module A, the UDS tasks imposed greater cognitive load and heavier working memory demands, which may help explain the greater variability observed in students' LoI data during this module. Therefore, additional scaffolding may be needed to support students' success with these tasks. Specifically, the tutoring system could incorporate enhanced visual cues (e.g., distinct colors for ones vs CUs), break tasks into smaller, more manageable steps to reduce cognitive load, and provide intermediate prompts that explicitly guide students' attention during unit shifts.</p> <hd id="AN0192656044-29">Limitations and Future Research</hd> <p>This study has several limitations. First, it only involved a small sample size of three students. Future studies should consider including more students or employ a group design to enhance the external validity of the study. Second, due to the limited number of the intervention sessions available during the school day, it was difficult for students to achieve mastery of the tasks in some modules before moving on to the next phase. Future studies may consider providing enough time for students to explore the program in each module and make sure students get the mastery level before moving on to the next module. Third, occasionally, the intelligent tutoring program encountered technical issues, such as screen freezing and login failure, which may have interrupted students' learning to some extent. Future studies may examine the effect of the intelligent tutor that is free of bugs.</p> <hd id="AN0192656044-30">Implications for Practice</hd> <p>The study supported the use of the COMPS intelligent tutor to teach fourth-grade students with LDM to solve word problems by developing conceptual understanding and representing problem information using mathematical model equations. The results of the study suggested that the guided discovery-based intelligent tutoring system may serve as an effective supplement to traditional mathematics instruction. Considering the challenge students with LDM experience in solving word problems, the heuristic prompting provided by the system may serve as an important scaffold. This scaffolding supported students' learning processes and contributed to the development of greater independence in mathematical problem-solving. In addition, the system's adaptability ensures students receive the right level of support at the right time, accelerating their journey toward independent mathematical reasoning. The effectiveness of the tutoring system highlights its potential as an effective tool for differentiated instruction. Given the serious shortage of effective tools to support teachers working with students with LDM ([<reflink idref="bib34" id="ref54">34</reflink>]), the COMPS intelligent tutor may be used as a tool in the classroom to facilitate students' mathematical reasoning and concept development, and help students with LDM gradually become independent in problem-solving and boost their confidence in learning mathematics.</p> <hd id="AN0192656044-31">Conclusion</hd> <p>By integrating guided discovery learning with interactive instruction using virtual manipulatives, the PGBM-COMPS intelligent tutor in this study seemed to foster students' multiplicative reasoning and independent problem-solving skills, align with the emphasis of the Common Core State Standards. 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Sage.</bibtext> </blist> </ref> <ref id="AN0192656044-33"> <title> Footnotes </title> <blist> <bibtext> Xuan Yang</bibtext> </blist> <blist> <bibtext>Graph</bibtext> </blist> <blist> <bibtext>https://orcid.org/0000-0002-6218-8331 Yan Ping Xin</bibtext> </blist> <blist> <bibtext>Graph https://orcid.org/0000-0002-0035-9203</bibtext> </blist> <blist> <bibtext> This research was supported by U.S. NSF (DRL #080500689) awarded to Purdue University (PI: Yan Ping Xin). The opinions expressed do not necessarily reflect the views of the Foundation. Xuan Yang was funded by the Humanities and Social Science Fund of Ministry of Education of China (grant number: 22YJC880101) for their contributions to the manuscript preparation.</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> </ref> <aug> <p>By Xuan Yang and Yan Ping Xin</p> <p>Reported by Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib17" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib38" firstref="ref4"></nolink> <nolink nlid="nl3" bibid="bib31" firstref="ref6"></nolink> <nolink nlid="nl4" bibid="bib24" firstref="ref8"></nolink> <nolink nlid="nl5" bibid="bib10" firstref="ref9"></nolink> <nolink nlid="nl6" bibid="bib15" firstref="ref10"></nolink> <nolink nlid="nl7" bibid="bib16" firstref="ref12"></nolink> <nolink nlid="nl8" bibid="bib23" firstref="ref14"></nolink> <nolink nlid="nl9" bibid="bib12" firstref="ref15"></nolink> <nolink nlid="nl10" bibid="bib13" firstref="ref17"></nolink> <nolink nlid="nl11" bibid="bib34" firstref="ref19"></nolink> <nolink nlid="nl12" bibid="bib33" firstref="ref20"></nolink> <nolink nlid="nl13" bibid="bib37" firstref="ref21"></nolink> <nolink nlid="nl14" bibid="bib19" firstref="ref22"></nolink> <nolink nlid="nl15" bibid="bib36" firstref="ref23"></nolink> <nolink nlid="nl16" bibid="bib26" firstref="ref24"></nolink> <nolink nlid="nl17" bibid="bib14" firstref="ref26"></nolink> <nolink nlid="nl18" bibid="bib25" firstref="ref28"></nolink> <nolink nlid="nl19" bibid="bib30" firstref="ref29"></nolink> <nolink nlid="nl20" bibid="bib18" firstref="ref31"></nolink> <nolink nlid="nl21" bibid="bib29" firstref="ref32"></nolink> <nolink nlid="nl22" bibid="bib35" firstref="ref35"></nolink> <nolink nlid="nl23" bibid="bib32" firstref="ref41"></nolink> <nolink nlid="nl24" bibid="bib27" firstref="ref42"></nolink> <nolink nlid="nl25" bibid="bib11" firstref="ref45"></nolink> <nolink nlid="nl26" bibid="bib22" firstref="ref48"></nolink> <nolink nlid="nl27" bibid="bib21" firstref="ref49"></nolink> <nolink nlid="nl28" bibid="bib20" firstref="ref50"></nolink> <nolink nlid="nl29" bibid="bib28" firstref="ref52"></nolink> <nolink nlid="nl30" bibid="bib39" firstref="ref53"></nolink>
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  Group: Ti
  Data: The Use of an Intelligent Tutoring Program to Promote Independent Problem-Solving Skills of Students with Learning Disabilities or Difficulties
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  Data: English
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  Data: <searchLink fieldCode="AR" term="%22Xuan+Yang%22">Xuan Yang</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-6218-8331">0000-0002-6218-8331</externalLink>)<br /><searchLink fieldCode="AR" term="%22Yan+Ping+Xin%22">Yan Ping Xin</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-0035-9203">0000-0002-0035-9203</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22Learning+Disability+Quarterly%22"><i>Learning Disability Quarterly</i></searchLink>. 2026 49(2):98-111.
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  Label: Availability
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  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
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  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 14
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2026
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  Label: Sponsoring Agency
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  Data: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
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  Label: Contract Number
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  Data: 080500689
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  Data: Journal Articles<br />Reports - Research
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  Label: Education Level
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  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+4%22">Grade 4</searchLink><br /><searchLink fieldCode="EL" term="%22Intermediate+Grades%22">Intermediate Grades</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Intelligent+Tutoring+Systems%22">Intelligent Tutoring Systems</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Students+with+Disabilities%22">Students with Disabilities</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Disabilities%22">Learning Disabilities</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Problems%22">Learning Problems</searchLink><br /><searchLink fieldCode="DE" term="%22Word+Problems+%28Mathematics%29%22">Word Problems (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Program+Effectiveness%22">Program Effectiveness</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Managed+Instruction%22">Computer Managed Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+4%22">Grade 4</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1177/07319487261423553
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  Data: 0731-9487<br />2168-376X
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  Label: Abstract
  Group: Ab
  Data: Educational laws and current standards emphasize fostering conceptual understanding in problem-solving, as well as cultivating higher-order thinking and reasoning skills, with the ultimate goal of developing independent mathematical thinkers. The purpose of this study, conducted at a Midwest U.S. elementary school, was to explore the impact of the Please Go Bring Me-COnceptual Model-based Problem-Solving intelligent tutor on word problem-solving skills and multiplicative concept development of students with learning disabilities or difficulties in mathematics. The multiple-probe across-participants design was used to explore the functional relationship between the intervention program and students' problem-solving skills and the development of conceptual knowledge. Concept development was measured by the levels of independence in solving problems provided by the intelligent tutor. Results showed that the tutoring system was effective in promoting students' critical thinking and word problem-solving performance. It seems that features, such as the guided discovery strategy embedded in the tutoring system may have contributed to students' development as an independent problem solver.
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  Data: 2026
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  Data: EJ1501922
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        Value: 10.1177/07319487261423553
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        PageCount: 14
        StartPage: 98
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        Type: general
      – SubjectFull: Problem Solving
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      – SubjectFull: Students with Disabilities
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      – SubjectFull: Learning Disabilities
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      – SubjectFull: Learning Problems
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      – SubjectFull: Word Problems (Mathematics)
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      – SubjectFull: Mathematics Instruction
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      – SubjectFull: Program Effectiveness
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      – SubjectFull: Computer Managed Instruction
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      – SubjectFull: Elementary School Students
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      – SubjectFull: Grade 4
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      – TitleFull: The Use of an Intelligent Tutoring Program to Promote Independent Problem-Solving Skills of Students with Learning Disabilities or Difficulties
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