A schema-based instruction allows students to approach a mathematics problem by focusing on the underlying semantic or problem structure, thus facilitating conceptual understanding and adequate skills. The purpose of this study was to examine the effectiveness of schema-based intervention on the mathematical word problem solving skills of middle school students with learning disabilities in grades 6 and 7. A nonconcurrent multiple baseline design was used for the study. Four middle school students with learning disabilities participated in pre-experimental (i.e., introduction, screening test, and Mathematics Interest Inventory sessions) and experimental (i.e., baseline, intervention, post-intervention test with generalization test, and maintenance test) sessions over a 13-week period. Participants were randomly assigned to a priori baseline durations (i.e., 6, 9, 12, 17 days) (Watson & Workman, 1981). During the intervention phase, students received 12 sessions of individual 30-35 minute schema-based intervention for 6 days (i.e., 2 sessions per day). Students participated in guided and independent practice and were encouraged to ask questions as they worked to master the material taught in each intervention session. During the postintervention phase, the four students’ accuracy performance was evaluated by six untimed achievement or generalization tests. The achievement and generalization tests contained a total of 10 one-step multiplication and division word problems. All of the students achieved scores greater than a pre-determined criterion level of 70% accuracy on the six consecutive tests. Two weeks after termination of the post intervention phase, each student’s accuracy performance on the achievement and generalization tests was examined during the follow-up maintenance phase. Findings revealed that the four students’ performance substantially improved after they received the intervention. All four students achieved scores that exceeded the criterion level (70% accuracy) on the achievement tests during the post intervention phase. These findings provide empirical evidence that schema-based intervention is effective in teaching middle school students with learning disabilities to solve multiplication and division word problems. Limitations of the research and implications for practice and future research are discussed. / text

This study aims at answering questions pertaining to the performance of bilingual Arab-American students on solving word problems written in their home and school languages: (1) Does the language in which a word problem is stated have an effect on the performance of the bilingual Arab-American students?; (2) Do Arab-American students with higher levels of Arabic proficiency perform better in either or both versions of the word problems?; and (3) What are some common differences and similarities in the problem solving processes of Arab-American students as they solve problems in English or Arabic? The study used both quantitative and qualitative methods to analyze these questions. A total of 173 students from a full-time Islamic school participated in this study: 56 students in fifth grade, 56 students in sixth grade, and 61 students in seventh grade. All students were asked to solve two sets of ten word problems each. The students were randomly assigned to one of four groups. Results showed that Arab-American students performed significantly better in the English version of the word problems. Arab-American students with higher levels of Arabic proficiency performed better in the Arabic version of the word problems. Students' standardized scores on mathematics problem solving was a significant factor in explaining variances in student performance on both language versions of both sets of word problems. While students' standardized scores on reading comprehension was a significant factor in predicting the students' performance on the English version of the word problems, students' final average in the Arabic subject was a significant factor in predicting students' performance on the Arabic version of the word problems. Differences and similarities emerged in the problem solving processes of Arab-American students solving the word problems in either English or Arabic. Some students found statements involving double comparisons, problems with hidden information, and problems that required multi-step solutions or thinking backwards to be problematic in both language versions of the problems. Difficult vocabulary was especially problematic for students when solving the Arabic version of the word problems.

Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics that call for an inquiry learning model (NCTM, 2000). Unfortunately, this model may not be sufficient to meet the needs of students with disabilities. Researchers are currently looking at what elements will assist students with disabilities to learn mathematics both conceptually and procedurally. Explicit direct instruction, modeling, guided and independent practice, and providing advanced organizers have been found to help students with disabilities to be successful. Results indicated that students with mild disabilities were able to use the strategy independently to accurately solve the training word problems using division or multiplication. Also, students were able to generalize both the strategy use as well as the word problem accuracy to the measurement of area problems. Additionally, two of the three students continued to use the strategy appropriately to accurately solve word problems in the 6-week follow-up phase. Suggestions for future studies are provided as well as educational implications. / by Mary R. Taber. / Thesis (Ed.D.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

This study identified factors related to solving mathematical word problems and then examined the differences in characteristics between students with low achievement in mathematics who were likely to have a learning disability and students with low achievement in mathematics who were unlikely to have a learning disability. Factoral analysis identified two significant factors: abstract thinking and long term retrieval from memory. Results indicated qualitative differences between sixth grade students with achievement in mathematics at or below the 25th percentile with indications of learning disabilities (MLD) and students with achievement in mathematics at or below the 25th percentile without an indication of a learning disability (Low Math/NLD). The Learning Disabilities Diagnostic Inventory, which measures intrinsic processing disorders indicative of learning disabilities, was used to differentiate between students with MLD (n = 13) and students with Low Math/NLD (n = 16). The Woodcock-Johnson III Tests of Achievement, Clinical Evaluation of Language Fundamentals-Fourth Edition, and the Informal Mathematics Assessment (IFA) were used to compare the two groups. In contrast to students with MLD, students with Low Math/NLD had a higher mathematical performance and had more difficulties with math fluency. When solving mathematics word problems on the IFA, a test composed of word problems, student interview, and error analysis, students with Low Math/NLD had more correct answers, more computational errors, and fewer translation errors than students with MLD did. Students with MLD had conceptual difficulties in the areas of analyzing, reasoning, and abstract thinking.

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Includes bibliographical references (leaves 83-98). Issued in print and online. Available via ProQuest Digital Dissertations.

The main aim of my thesis is the investigation and description of students' strategies for solving word problems at basic schools. The thesis is divided into theoretical and practical part. The first part describes the types of word problems at the basic school, pupils? and teaching strategies. There are also explained meaning of terms algorithms and didactic contract. There is also own confrontation of textbooks which are used at secondary schools. The theoretical part is formed the experiment that was performed at the second stage of a basic school in two parallel classes. In the experiment there were entered three types of identical tests for solving word problems. There is judged pupils? improvement, using different strategies and effect of algorithms and didactic contract. In conclusion there are summarized results and knowledge from the experiment.

The theoretical part of the diploma thesis contains didactic analysis of word problems, that is the definition of a word problem, classification of word problems from various perspectives and methods of solving word problems, according to czech specialists in didactics of mathematics. The second part describes the teaching of mathematics at the secondary Waldorf schools with an emphasis on teaching in main lesson blocks. The core of the work lies in the experimental part which consists of two sections. The first section describes the preparation, implementation and evaluation of educational experiments on the subject of word problems. The educational experiment was conducted in the first class of the Waldorf lyceum in Prague in the academic year 2014/2015. All days of the main lesson block are described. Part of the reflection of the teacher and an observer who participated in the entire main lesson block is the part of thesis. The practical part continues with the pupil's solving strategies analysis. Pupils wrote a didactic test with word problems once before the teaching experiment and once after it. The analysis of each problem is following, in which the interesting phenomena that emerged in the pupils' solutions are explored. The conclusion summarises the main points of the research conducted...

The No Child Left Behind Act and National Council of Teachers of Mathematics' Principles and Standards both had a significant impact on the format and content of the Texas Assessment of Knowledge and Skills (TAKS) math test. Content analysis of the 2004 TAKS eighth grade math test identified the prevalence of linguistic complexity, mathematical rigor, and visual presentation factors and explored their relationship to student success on individual test items. Variables to be studied were identified through a review of literature in the area of reading comprehension of math word problems. Sixteen variables of linguistic complexity that have been significantly correlated with student math test performance were selected. Four variables of visual presentation were identified and ten variables of mathematical rigor. An additional five variables of mathematical rigor emerged from preliminary study of the 2003 TAKS math test. Of the 35 individual variables, only four reached a significant level of correlation with the percent of students correctly answering a given test item. The number of digits presented in the problem statement and number of known quantities both exhibited a significant positive correlation with the dependent variable. The number of times a student had to perform a multiplication operation had a significant negative correlation with the percent of correct responses, as did the total number of operations required. Stepwise regression of these four variables revealed total number of operations and known quantities to be the best combination of predictors of correct responses. When grouped in categories by problem type and compared, items involving mathematical reasoning but no mathematical operations had a significantly higher percentage of correct responses than those requiring at least one operation. Further categorization revealed problems involving applications only (without computation) associated with the highest levels of correct responses, followed by those involving only computation. Items requiring both applications and computations had a significantly lower percent of correct responses.

MEDSED / Department of Maths, Science and Technology Education

The state of Maryland has implemented the Common Core State Standards for Mathematics (CCSSM) operations & algebraic thinking and number & operations-fractions with emphasis on students in Grades K-5 acquiring the ability to solve word problems for state and curriculum math assessments. However, since the implementation of CCSSM, 30% of elementary students in a Maryland school district have demonstrated underachievement (basic or below basic level) on problem-solving sections of the state and school standardized tests. This qualitative case study, guided by Polya's model of the four phases of mathematical problem-solving, was conducted to address this problem. The research questions addressed teachers' perceptions of how they teach underachieving students' word problem-solving skills, how prepared they feel, the challenges they experience when teaching word problem-solving skills, and the resources for instructing underachieving students on mathematical word problem-solving. Semi-structured interviews were conducted with 8 certified elementary classroom teachers. Data from the teacher interviews were analyzed using pattern coding and thematic analysis. The findings indicated that teachers are not fully prepared to teach the CCSSM, teachers need assistance in creating standards-based detailed lesson plans, and teachers need help with the development of pedagogical strategies that enhance students' math vocabulary. Findings may lead to positive social change by informing the design of professional development and increasing the number of students who achieve proficiency in mathematical word problem-solving.