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The article discusses how to enhance word-problem instruction for students experiencing mathematics difficulty (MD) through schema instruction with an attack strategy. It emphasizes the importance of language, calculation, spatial understanding skills, and background knowledge in word-problem solving. The use of schema instruction, paired with supplementary strategies like mathematics language, paraphrasing, gestures, visuals, and organizers, has shown positive outcomes for students with MD. The article provides detailed guidance on implementing these strategies to support students in improving their word-problem-solving skills, especially those with reading or language difficulties. [Extracted from the article]

The National Council of Teachers of Mathematics (NCTM) emphasizes the teaching of "Big Ideas" in mathematics. This study focuses on the part–part–whole (PPW) relationship as a crucial aspect of word problem solving involving addition and subtraction. This study, conducted in the United States, evaluated the effects of conceptual model-based problem-solving (COMPS) with the concrete-representational-abstract (CRA) sequence on teaching addition and subtraction word problem solving to students with autism spectrum disorder (ASD). Using a multiple-probe design across the participants, the researchers examined the impact of the intervention on students' performance across three types of word problems: join-in, take-away, and combine. Results demonstrated significant improvements in students' problem-solving abilities on criterion tests. In addition, students successfully generalized their skills to solve problems with new contexts. The findings of this study provide implications for future research and educational practice. [ABSTRACT FROM AUTHOR]

Researchers established virtual manipulatives as an evidence-based practice for students with intellectual and developmental disabilities (IDD). However, much of the existing research for this population targets middle school students with IDD. This study examined a virtual number line paired with teacher modeling and the system of least prompts to support high school students with IDD in acquiring, maintaining, and generalizing addition and subtraction problems. Through a single case research study with three high school students with IDD, the researchers found a functional relation between the intervention package and student accuracy. Students also became more independent but struggled to maintain their skills when prompting was not provided. Further, the students were unable to generalize the skills of addition and subtraction to real-life scenarios targeting time and money. These findings and their implications for the field of IDD are examined. [ABSTRACT FROM AUTHOR]

Solving word problems is a large part of algebra coursework and statewide testing. However, solving secondary mathematics word problems is difficult for most students and extremely challenging for students with specific learning disabilities (SLD). In recent meta-analyses, two problem solving strategies emerged as effective for secondary students with SLD: Schema-Based Instruction (SBI) and General Heuristics Instruction (GHI). While SBI has been highlighted in recent works, GHI deserves further explanation. In this article, we provide details of GHI and highlight its flexibility and utility using different algebra examples. [ABSTRACT FROM AUTHOR]

This paper studies the effect of implementing a new Arabic language learning software Test Survey for Students (TSFS) developed by the researchers and marketed as brain training software for primary students on language skills using Science, Technology, Arts, and Mathematics (STEAM) subjects. The teaching of Arabic language via computer-assisted language learning (CALL) takes place for the first time in Qatari schools specifically for primary students. The researchers included a theoretical analysis of current trends in CALL and Arabic language skills. Reading skills, learning word and sentence skills, and dictation skills were the three Arabic basic skills tested to measure the effectiveness of developing these skills and improve achievement for third-grade students using CALL in STEAM subjects. Mixed models analyzed using the statistical software for social sciences suggest that teaching Arabic language skills with STEAM topics using educational software is effective and has a promising potential to be extended to the whole of middle east and north Africa region. [ABSTRACT FROM AUTHOR]

This study concerns an intervention incorporating the KNOWS strategy (K—Know, N—Need to know, O—Organize, W—Work, and S—Solution), a mnemonic problem-solving tool to improve students' performance in ratio word problems. Quantitative data through pre- and post-tests were collected from 42 Year 9 students in one of the secondary schools in Brunei Darussalam. Results from a paired-sampled t -test show that the students scored higher in the post-test compared to the pre-test, confirming the effectiveness of the KNOWS intervention in improving students' performance in ratio word problems. Despite the improvement in students' performance, this study highlights some misconceptions and common mistakes of students when solving ratio word problems before and after the KNOWS intervention. It also suggests alternative ways of using the KNOWS strategy as an instructional option to improve students' performance in ratio word problems. [ABSTRACT FROM AUTHOR]

This article presents an adaptation of an arts-based research method usually reserved for child-focused research to examine organizational processes. We developed Draw, Write, Reflect (DWR), advancing a known method, Draw and Write, for investigating phenomena relating to child participants, to explore a new context: adults engaging in academic careers. This article reports on the rationale behind the novel use of this research method, outlines a DWR procedure for future research, and contains reflections of both the researchers and the respondents regarding their experiences participating in DWR. Offering participants a combination of visual and oral methods allowed the researchers to obtain data in a more individualized approach steered by participants' preferences. The multidimensional insights obtained through DWR would not have been attainable through each method on its own. Furthermore, we argue arts-based research can serve as a vehicle for disseminating academic work beyond conventional academe to a growing, nonacademic audience. [ABSTRACT FROM AUTHOR]

Project- or discovery-based learning activities promote curiosity, enjoyment, and interest deriving from the stimulating context in which students operate. Providing a concrete contextualization of laboratory activities could improve student motivation and learning outcomes. In this contribution, a case study related to a workshop on laboratory activities proposed for Engineering Master students is presented, and designed with the aim of developing practical competencies, increasing problem-solving skills, and providing design abilities. Using the facilities available in the Measurements and Control Laboratory, the students, starting from concept knowledge acquired in basic subjects, such as Physics, Chemistry, Mathematics, and Electronics, design and implement their experiments, gaining a deeper understanding of core disciplinary concepts while strengthening soft and teamwork skills. The challenges and possibilities of these self-directed thinking and learning laboratory activities are also discussed. [ABSTRACT FROM AUTHOR]

Although prior research has highlighted the significance of representations for mathematical learning, there is still a lack of research on how students use multimodal external representations (MERs) to solve mathematical tasks in digital game-based learning (DGBL) environments. This exploratory study was to examine the salient patterns problem solvers demonstrated using MERs when they engaged in a single-player, three-dimensional architecture game that requires the acquisition and application of math knowledge and thinking in game-based context problem solving. We recorded and systematically coded the behaviors of using MERs demonstrated by 20 university students during 1.5 hours of gameplay. We conducted both cluster and sequential analyses with a total of 2654 encoded behaviors. The study indicated that the maneuverable visual-spatial representation was most frequently used in the selected architecture game. All of the participants performed a high level of representational transformations, including both treatment and conversion transformations. However, compared to the students in the second cluster who were mostly non-game players, students in the first cluster (composed of mainly experienced video game players) displayed a higher frequency of interacting with various MERs and a more cautious and optimized reflective problem-solving process. [ABSTRACT FROM AUTHOR]

This mixed-methods study focused on advanced student engagement, mathematics competence, and the influence of teachers in classrooms that used 3D printing to teach mathematics. Quantitative methods were used to understand changes in student perceptions of competence, engagement, and feelings regarding group work. Qualitative methods were used to explore teacher self-efficacy in teaching using Prototype Problem Solving and 3D modeling. The results indicated positive changes in student disengagement. It also highlighted the influence of teachers in implementing new pedagogy in the classroom as significant differences were found between groups of students based on school. The teacher participants indicated that in addition to learning how to use 3D modeling and printing in their classrooms, using Prototype Problem Solving Activities and the professional development that they received in this program inspired them to provide more creative opportunities when teaching mathematics in a heterogeneous classroom. [ABSTRACT FROM AUTHOR]

State exams frequently use word problems to measure mathematics performance, making difficulties with word problem solving a barrier for many students with learning disabilities (LD) in mathematics. Based on meta-analytic data for students with LD, five empirically validated word-problem strategies are presented, with components of model-based problem solving (MBPS) highlighted. [ABSTRACT FROM AUTHOR]

The content of noise, vibration, and harshness is an important part of the undergraduate mechanical engineering program education to prepare students ready for their future career, and it has received great attention from educators. Since course content in noise, vibration, and harshness usually requires more mathematical background knowledge and skills such as problem-solving in differential equations and linear algebra, students at the undergraduate level usually experience difficulty in the problem-solving work in noise, vibration, and harshness, though they have already completed the pre-requisite mathematics courses. In this paper, a new schedule and course content design for noise and vibration courses are introduced. By embedding active learning and design during projects, the students were able to obtain a better understanding of the concept of acoustics and vibration, as well as applying the knowledge from lectures to labs so they can connect the learning to real-world applications. Four projects are introduced and explained. To evaluate the effectiveness of the course, student outcomes are assessed and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation. [ABSTRACT FROM AUTHOR]

The Pandemic has required teachers to find ways to provide high-quality instruction in a virtual format. Video-based instruction (VBI) is a version of technology-aided instruction that has been effectively used in classrooms to improve mathematical outcomes for students with disabilities. This manuscript describes how a special education teacher can utilized VBI through free online platforms (i.e., SeeSaw, Loom) to implement a mathematical problem solving instructional strategy (modified schema-based instruction; MSBI) for students with autism spectrum disorder (ASD) while at home. MSBI utilizing VBI has successfully been used by teachers and researchers to improve additive and multiplicative problem solving skills for students with ASD. This manuscript describes how special education teachers can support students and their caregivers by providing high-quality problem solving instruction in a virtual environment. [ABSTRACT FROM AUTHOR]

A large number of students with and without disabilities—including students at-risk—are currently learning online through synchronous and/or asynchronous instruction. As such, it is important for educators to be equipped with evidence-based practices—or at the minimum research-based practices—that can be adapted or modified to teach students online, including the area of mathematics. This article discusses how educators can adapt and implement explicit instruction—an evidence-based practice for teaching students with disabilities in mathematics—to educate students with disabilities and those struggling or at-risk in mathematics within an online environment. In addition, this article presents resources for free and paid technology as well as additional considerations when implementing explicit instruction in an online environment. [ABSTRACT FROM AUTHOR]

This meta-analysis extended the current literature regarding the effects of computer technology (CT) on mathematics achievement, with a particular focus on low-performing students. A total of 45 independent effect sizes extracted from 31 empirical studies based on a total of 2,044 low-performing students in K-12 classrooms were included in this meta-analysis. Consistent with previous reviews, this study suggested a statistically significant and positive effect of CT ( d ¯ = 0.56) on low-performing students' mathematics achievement. Of four CT types, the largest CT effect was found with problem-solving system ( d ¯ = 0.86), followed by tutoring (d ¯ = 0.80), game-based intervention ( d ¯ =.58), and computerized practice ( d ¯ =.23). Furthermore, other moderators were found to explain variation in CT effects on low-performing students' mathematics achievement. Study findings contributed to clarifying the effect of CT for low-performing students' mathematics achievement. Implications for instructional design and practices are also discussed. [ABSTRACT FROM AUTHOR]

Students who demonstrate mathematics difficulties (MDs) in the early grades are at risk of poor educational outcomes. Fortunately, strategic early mathematics intervention programs can improve academic outcomes for students with MDs, and instructional technology has demonstrated promise in delivering targeted and individualized mathematics instruction. However, it is unclear whether instructional technology is effective for all students, and there is a dearth of research on adaptations to technology-based interventions for students with difficulties attending to instruction. To this end, the current study investigated functional relations between the use of targeted instructional cueing and self-regulation support features in an iPad-based mathematics program and improved response accuracy for kindergarten students. Results presented here suggest a functional relation between the provision of instructional cueing and self-regulation support features and improved response accuracy for students who participated in an iPad-based mathematics intervention program. Implications for early mathematics instruction and technology-based intervention development are discussed. [ABSTRACT FROM AUTHOR]

Many secondary students with specific learning disabilities (SLD) struggle with mathematics problem solving. When students with SLD are taught to use effective problem-solving strategies, their ability to solve mathematics word problems improves. The purpose of this article is to provide a guide for secondary teachers to implement self-regulated strategy development (SRSD) to teach mathematics problem-solving strategies to secondary students with SLD. The specific problem-solving strategy described in this article is SOLVE, which stands for Study the problem, Organize the facts, Line up a plan, Verify your plan with action, and Evaluate your results. Both SRSD and SOLVE are described, and an example of one teacher's application of SRSD is shared. When taught concurrently, SRSD and SOLVE can be useful tools to help students with disabilities overcome the challenges of problem-solving in mathematics. [ABSTRACT FROM AUTHOR]

Algebra is considered an important high school course because it is recognized as the gateway to higher mathematics, college opportunities, and well-paying jobs. In the United States, most secondary schools require students to be proficient in algebra to be able to graduate from high school. One major component of algebra is word problem solving, which is used in algebra courses to teach students mathematical modeling and applied problem-solving skills. However, word problem solving is often a significantly challenging area for students with learning disabilities because it involves computing mathematical equations and implementing a myriad of cognitive processes that require conceptual knowledge. Diagrams are considered an effective and powerful visualization strategy because they help students see the hidden mathematical structure of the problem. The use of diagrams is recommended as students work toward more complex math concepts in middle school and high school. [ABSTRACT FROM AUTHOR]

The article offers information on the Specially Designed Instruction (SDI) based on individual needs for secondary co-taught mathematics courses for the student with disabilities. Topics include that students are guaranteed SDI on the basis of their individualized education programs (IEP); and co-teachers combine their expertise in student characteristics, content knowledge and evidence based practices to deliver instruction to address both the general curriculum and the IEP curriculum.

The article talks about the use of schemas approaches to improve the mathematical reasoning and word-problem performance among students with learning disabilities. The topic addressed include details on the information on the illustration of impacts of reliance on key words resulting in incorrect answers.

The article discusses the use of the search, translate, answer, review (STAR) strategy to improve mathematical problem solving abilities of students with emotional and behavioral disorders (EBD). Topics mentioned include the components of the STAR strategy which engage students with cognitive processes required to solve mathematical problem, the strategy's use of mnemonic devices to manage word problems, and the aspects to consider when applying the STAR strategy for students with EBD.

Textbooks are frequently used as a resource to teach children how to solve word problems in mathematics classes. The solving models explicitly proposed by textbooks, and the kind of problems they propose, can therefore have a decisive influence on the way in which students learn to solve them. This paper analyses the extent to which the problem solving models proposed by the books include reasoning as one of the steps needed to solve a problem. To do this, the processes and steps articulated in the models proposed in the books by Anaya, SM and Santillana are categorized according to data, reasoning, choice of operation, strategies, execution of operations, expression of results, checking and inventing. The results indicate that reasoning processes are hardly ever found in the models, especially in lower year courses. It is concluded that mathematical textbooks provide incomplete solving models that fail to promote reasoning. [ABSTRACT FROM AUTHOR]

The focus of the present study was enhancing word problem and calculation achievement in ways that support prealgebraic thinking among second-grade students at risk for mathematics difficulty. Intervention relied on a multitier support system (i.e., responsiveness to intervention, or RTI) in which at-risk students participate in general classroom instruction and receive supplementary small-group tutoring. Participants were 265 students in 110 classrooms in 25 schools. Teachers were randomly assigned to one of three conditions: calculation RTI, word problem RTI, or business-as-usual control. Intervention lasted 17 weeks. Multilevel modeling indicated that calculation RTI improved calculation but not word problem outcomes, word problem RTI enhanced proximal word problem outcomes as well as performance on some calculation outcomes, and word problem RTI provided a stronger route than calculation RTI to prealgebraic knowledge. [ABSTRACT FROM PUBLISHER]

This study examined whether curriculum-based measures (CBMs) of math word-problem contributed unique variance in predictions of performance on high-stakes tests, beyond the contribution of calculation and reading skills. CBMs were administered to a representative sample of 142 third-grade students at three time points. Results indicate that problem-solving CBMs uniquely predicted a problem-solving composite measure and the California Standardized and Reporting test, and were able to discriminate students at risk and not at risk for math difficulties. Implications for practice are discussed. [ABSTRACT FROM PUBLISHER]

Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word problems that employ specific word problem types. The cognitive strategy, Math Scene Investigator (MSI), is an example of a cognitive strategy for word problem solving. The MSI strategy described in this paper is suitable for primary-level students with mathematics difficulties and LD. Instructional steps are provided along with an example of an interactive lesson. [ABSTRACT FROM PUBLISHER]

A visual representation, such as a diagram, can be a powerful strategy for solving mathematical word problems. However, using a representation to solve mathematical word problems is not as simple as it seems! Many students with learning disabilities struggle to use a diagram effectively and efficiently. This article provides a framework for supporting special educators’ use of diagnostic assessment as a means of understanding and identifying areas of need for students with learning disabilities in order to promote diagram proficiency for solving mathematical word problems. [ABSTRACT FROM PUBLISHER]

The purpose of this study was to examine effectiveness of paraphrasing interventions on mathematics word problem-solving accuracy in third grade children ( N = 72) at risk for mathematics disabilities (MD). Three instructional conditions directed students' attention through paraphrasing, via writing, to different propositions within word problems. Students were randomly assigned to one of four intervention conditions: paraphrase question propositions (restate), paraphrase relevant propositions (relevant) and paraphrase all propositions (complete) or an untreated control. A mixed ANCOVA indicated that paraphrasing relevant and complete propositions significantly increased posttest accuracy when compared to the control and restate condition. Results from the study provide support for the effectiveness of paraphrasing interventions that directs students to restate/paraphrase propositions of mathematics word problems relative to the control condition. [ABSTRACT FROM AUTHOR]

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and word problems in the fall and (2) an assessment of prealgebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into one of four difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with prealgebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. [ABSTRACT FROM AUTHOR]

Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had little application to errors in word problems. Using an error analysis approach, this study aimed to investigate in depth the various types and frequency of errors made by students with LD and their AA peers during math problem solving. The resulting similarities and differences between the two groups of students are discussed with insight into underlying cognitive processes, and implications for future research. [ABSTRACT FROM AUTHOR]

This study investigated the role of strategy instruction and cognitive abilities on word problem solving accuracy in children with math difficulties (MD). Elementary school children ( N = 120) with and without MD were randomly assigned to 1 of 4 conditions: general-heuristic (e.g., underline question sentence), visual-schematic presentation (diagrams), general-heuristic + visual-schematic, and an untreated control. When compared to the control condition that included children with MD, an advantage at posttest was found for children with MD for the visual-schematic-alone condition on measures of problem solving and calculation accuracy, whereas all strategy conditions facilitated posttest performance in correctly identifying problem solving components. The results also suggested that strategy conditions drew upon different cognitive resources. The General-heuristic condition drew primarily upon the executive component of working memory (WM), Visual-schematic condition drew upon the visual component of WM and the combined strategies condition drew upon number processing skills. [ABSTRACT FROM AUTHOR]

The article discusses approaches to teaching mathematics to students with learning disabilities, highlighting adherence to the Common Core State Standards (CCSS) for education in the U.S. The author describes how using Math Frame, an organizational system aimed at helping students work through the process of problem solving, can be used to help students with mathematics word problems. Curriculum design based on the Math Frame is discussed and examples of Math Frame worksheets are presented.

English language learners (ELLs) struggle with solving word problems for a number of reasons beyond math procedures or calculation challenges. As a result, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a math comprehension strategy called Dynamic Strategic Math (DSM) on word problem solving for Latino ELLs. The strategy provides performance-contingent feedback based on the student’s reading and language comprehension level. A multiple baseline design was used to assess 6 second-grade Latino ELLs at risk for math failure/math disability. As compared with the baseline phase, DSM increased word problem solving for all the participants. All students’ level of performance was maintained during follow-up sessions. The results suggest the intervention facilitated math problem–solving performance. [ABSTRACT FROM PUBLISHER]

Mathematics continues to be one of the most challenging aspects of the school curriculum for students with learning disabilities. The provision of pedagogically sound foundational computation and word problem instruction in the elementary grades is critical for students to progress through the mathematics curriculum successfully. A multiple-probe-across-participants design was used to investigate the effects of explicit instruction using the concrete-representational-abstract sequence with integrated cognitive strategies to teach five fourth- and fifth-grade students how to subtract when regrouping is required. All five participants benefited from the scripted instructional lessons. Practical implications and suggestions for future research in this area are provided. [ABSTRACT FROM AUTHOR]

The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on measures of addition and word-problem skill, second grade students ( N= 332) were classified in terms of MD status. Then, students were assessed on three early numerical competency measures ( Number Line Estimation, Number Sets Test, and Counting Knowledge) as well as a measure of subtraction. On Number Line Estimation and Number Sets Test, students with CD and those with PD scored comparably, but both outperformed students with CDPD. On Counting Knowledge-Double First, students with CDPD scored lower than the three contrasting groups. On subtraction, students with CD outperformed those with PD, and students with PD and those with CDPD performed comparably. Findings are discussed in terms of differential performance as a function of difficulty status and implications for understanding and teaching subtypes of MD. [ABSTRACT FROM AUTHOR]

Solving word problems is a difficult task for students at-risk for or with learning disabilities (LD). One instructional approach that has emerged as a valid method for helping students at-risk for or with LD to become more proficient at word-problem solving is using schemas. A schema is a framework for solving a problem. With a schema, students are taught to recognize problems as falling within word-problem types and to apply a problem solution method that matches that problem type. This review highlights two schema approaches for second- and third-grade students at-risk for or with LD: schema-based instruction and schema-broadening instruction. A total of 12 schema studies were reviewed and synthesized. Both types of schema approaches enhanced the word-problem skill of students at-risk for or with LD. Based on the review, suggestions are provided for incorporating word-problem instruction using schemas. [ABSTRACT FROM AUTHOR]

The paper presents two studies that analysed whether participants' performance and memory for texts improved when situational information was introduced in arithmetic word problem formulation. To that end, discourse comprehension models served as frame of reference to define situational information. In Study 1, participants' problem solving performance was better when situational information was introduced than when a standard format was used. In Study 2, when problems with relevant situational information with the mathematic schema of the problem were introduced, participants' performance was not only better, they also remembered more information and this was better organised than when irrelevant situational information was included. However, participant's arithmetic competence mediated these results. Taken together, these results support the notion that construction of situation model is an important component for word problem solving. [ABSTRACT FROM AUTHOR]

Studies of mental arithmetic have shown that adults solve simple arithmetic problems by retrieving an answer automatically from a network of stored associations. However, most studies have been limited to single-digit addition and multiplication problems. In this article, we examine whether retrieval is also automatic in the context of more complex arithmetic tasks, such as arithmetic word problems. To test this hypothesis, we used a priming procedure with a target-naming task, in which the primes were the numbers included in two sentences containing the numerical information of an arithmetic word problem (e.g., 3 and 2 in “Joe had 3 marbles. Then Tom gave him 2 marbles”), and the targets were either congruent (e.g., 5) or incongruent (e.g., 8) with the prime. A neutral prime was also used replacing the numbers of the problem by capital letters (e.g., X and Y). Manipulating the relationship between the prime and the target and the duration of time that separates these two events, the overall results revealed shorter times in naming the congruent target than in a neutral condition and longer times in naming the incongruent target, even though mental arithmetic was completely irrelevant to the task. These results support the notion that automaticity of arithmetic-fact retrieval is not limited to simple addition, but it is also possible in other tasks, such as arithmetic word problems, which demand more cognitive resources than single-digit addition. [ABSTRACT FROM AUTHOR]

This study examined whether and, if so, how word-problem features differentially affect problem difficulty as a function of mathematics difficulty (MD) status: no MD (n = 109), MD only (n = 109), or MD in combination with reading difficulties (MDRD; n = 109). The problem features were problem type (total, difference, or change) and position of missing information in the number sentence representing the word problem (first, second, or third position). Students were assessed on 14 word problems near the beginning of third grade. Consistent with the hypothesis that mathematical cognition differs as a function of MD subtype, problem type affected problem difficulty differentially for MDRD versus MD-only students; however, the position of missing information in word problems did not. Implications for MD subtyping and for instruction are discussed. [ABSTRACT FROM AUTHOR]

Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching word problem (WP) story grammar on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or at risk for mathematics disabilities in two urban public elementary schools in the Midwest. An adapted multipleprobe-across-participants design was used to assess the functional relation between the intervention and students' problem-solving performance. The results indicated that conceptual model-based representation prompted by WP story grammar improved students' performance on arithmetic WP solving and promoted prealgebra concept and skill acquisition. The practical implications of integrating algebraic reasoning in elementary mathematics are discussed. [ABSTRACT FROM AUTHOR]

This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits. [ABSTRACT FROM AUTHOR]

This study examined the effectiveness of instruction focused on teaching students with learning disabilities (LD) to solve 1- and 2-step word problems of varying types. Three students with LD in Grade 8 participated in the study. During the treatment, students received instruction in diagram generation and a strategy that incorporates diagrams as a part of the procedure to solve word problems. The results indicated that all students improved in the number of diagrams they used and in their ability to generate diagrams. Their word problem solving performance increased. Moreover, the students generated and used diagrams to solve other types of problems. Overall, the students were very satisfied with the instruction and would continue to use the diagrams and the strategy to solve word problems in other classroom settings. [ABSTRACT FROM AUTHOR]

Background/Context: The theoretical framework of the paper comes from research on problem solving, considered by many to be the essence of mathematics; research on the importance of oral language in learning mathematics; and on the importance of the teacher as the primary instrument of learning mathematics for most students. As a nation, we are not doing well enough in teaching our students mathematics, and need to look to new perspectives about why this is happening. Purpose: This paper looks at a promising tool for enabling students who are not skilled readers to approach problem solving tasks. But in sharing its usefulness with teachers in professional development, the instrument uncovered specific and serious gaps in teacher content knowledge. Group discussion, using the protocol helped to clarify some of those gaps. Setting: All three problem-probing sessions occurred during professional development activities for New York City Public School mathematics teacher leaders. The facilitator was Academic Director of a New Visions for Public Schools' Middle School Mathematics Standards project, (MS)2, funded by. NSF. The sessions were part of a variety of ongoing professional development activities, and occurred during the third year of a five year study. Therefore, the 12 to 20 participants of each session, though different from each other, all knew the facilitator. Research Design: The research design was qualitative. Teachers were presented with a written problem and directed not to solve it. The discourse that followed flowed of its own accord, with participants speaking as they thought and responded to the facilitator and/or the other participants. Records of speakers' words were transcribed in one case hand, and in two other cases by audio tapes. The discourse was then analyzed by the researcher from two perspectives: what mathematical misconceptions mere revealed and how the talk helped to clarify them. Conclusions/recommendations: From preliminary, explorations, the protocol seems an accessible and effective instrument for decoding and analyzing mathematics word problems by teachers who were not able to approach such tasks before. Also suggested was its potential value as an assessment instrument for teachers' content knowledge. Further study is needed to determine what kinds of in-class supports teachers need to internalize the process and use this instrument on a regular basis with their students. Background/Context: A of the literature demonstrates that schools are frequently called upon to improve, by developing high levels of teacher collaboration. At the same time, there a paucity of research investigating the extent to which teachers' collaborative school improvement practices are related to student achievement. Purpose: The purpose of study to was to review the literature and empirically test the relationship between a theoretically driven measure of teacher collaboration for school improvement and student achievement. Setting: The data for this study were drawn from students and teachers in a large urban school district located in the midwestern United States. Population: The population for this study came from the elementary schools in one large midwestern school district. Survey data were drawn from a sample of 47 elementary schools with 452 teachers and 2,536 fourth-grade students. Research Design: Hierarchical linear modeling (HLM) was the primary analytic method. Survey data were collected approximately 2 months before students took the mandatory state assessments, which provided the scale scores that served as dependent variables in this research. HLM accounted for the nested nature of the data (students nested in schools).… [ABSTRACT FROM AUTHOR]

Mathematics and word problem solving are basic tools employed in the schooling of advanced societies and their learning involves various cognitive processes. The present paper reviews theoretical models and empirical studies that explain how the application of knowledge about the real world, acquired during subjects' lives, mediates in problem solving. For this purpose, first, different types of mathematical word problems are described; second, cognitive theoretical models that justify the need of applying knowledge about the real world in order to generate a situation model for children to successfully solve word problems are described; third, empirical studies that have shown the validity of these theoretical models are analysed and their results discussed with a view to improving student performance. Finally, general conclusions obtained from the review are put forth and some educational implications based on these conclusions are presented. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve arithmetic word problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. In addition, this effect was more marked in the case of children who had poorer mathematical skills and in the case of more difficult problems. We argue that this pattern of results is compatible only with the situation or mental model theory, and not with the schema theory. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate students' use of visual imagery and its relationship to spatial visualization ability while solving mathematical word problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N = 66) participated in this study. Students were assessed on measures of mathematical problem solving, visual imagery representation, and spatial visualization ability. The results indicated that gifted students performed better on both spatial visualization measures than students with LD and average-achieving students. Use of visual images was positively correlated with higher mathematical word problem-solving performance. Furthermore, the use of schematic imagery was significantly and positively correlated with higher performance on each spatial visualization measure; conversely, it was negatively correlated with the use of pictorial images. [ABSTRACT FROM AUTHOR]

This study was designed to determine a word problem difficulty classification in children with arithmetic learning disabilities (ALD; n = 104) in comparison with typically achieving students (n = 44). We tested variables such as (a) semantic structure (Change, Combine, Compare, and Equalize), (b) operation (subtraction and addition), and (c) position of the unknown quantity in the problem. Facet theory with multidimensional scaling techniques (MINISSA) was used to analyze the underlying dimensions in the responses of each group of participants. Our results indicate that although the word problem difficulty classifications for the 2 groups of children were different, the position of the unknown quantity had a greater influence on the level of difficulty of story problems than other variables. The noncanonical problems—specifically, those with the unknown term in the first place—although difficult for both groups of children, were the most difficult problems for children with ALD. [ABSTRACT FROM AUTHOR]

The present study assesses the characteristics of addition and subtraction word problems from three representative Spanish Primary Education textbook series. The analysis undertaken is based on three variables: a) the semantic structure of the problems; b) the degree of "challenge" underlying these problems; and c) the situational context depicted in the problems. The results showed that textbooks problems have a highly stereotyped nature. Thus, from the viewpoint of its semantic structure, the simplest problems to solve were also the most numerous. Problems posing a challenge are few and tend to be formulated in very standard settings. The study's implications are discussed in terms of the role of word problems in textbooks. [ABSTRACT FROM AUTHOR]

This study (N = 48) examined the relationship between preservice secondary teachers' subject-matter expertise in mathematics and their judgments of students' algebra problem-solving difficulty. As predicted by the "expert blind spot" hypothesis, participants with more advanced mathematics education, regardless of their program affiliation or teaching plans, were more likely to view symbolic reasoning and mastery of equations as a necessary prerequisite for word equations and story problem solving. This view is in contrast with students' actual performance patterns. An examination across several subject areas, including mathematics, science, and language arts, suggests a common pattern. This article considers bow teachers' developmental views may influence classroom practice and professional development, and calls into question policies that seek to streamline the licensure process of new teachers on the basis of their subject-matter expertise. [ABSTRACT FROM AUTHOR]

El presente trabajo ha sido desarrollado para analizar la importancia del conocimiento conceptual en la resolución de problemas aritméticos con estructura aditiva. Para ello, y partiendo de un modelo explicativo de los procesos y estrategias implicados en la tarea de resolver problemas, hemos estudiado la influencia del conocimiento conceptual en el propio contexto de resolución de problemas a partir de la idea de resistencia a la instrucción, es decir, a partir de la cantidad de ayuda que un alumno /a necesita para resolver la tarea. Los resultados muestran una relación entre el conocimiento conceptual y la resolución de problemas, aunque la mayor influencia se observa fundamentalmente en los problemas más complejos, aquellos que necesitan de conocimientos numéricos más avanzados. Los resultados son interpretados desde la importancia de la resolución de problemas en el proceso de enseñanza y aprendizaje de la aritmética. The present study has been designed to analyse the role of conceptual knowledge in solving addition and subtraction word problems. For this purpose--and based on an explanatory model of the processes and strategies involved in problem solving--we have studied the influence of conceptual knowledge within the context of solving arithmetic word problems. The approach adopted is based on the notion of resistance to instruction; that is, of the quantity of help that a pupil needs to solve a task. The results show a relationship between conceptual knowledge and solving arithmetic word problems. However, a greater influence is observed in the most complex problems: those that require more advanced numerical knowledge. The implications of these results are related directly to arithmetic teaching and learning process. [ABSTRACT FROM AUTHOR]