Browsing by Subject "Word problems"
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Item Effects of a web-based strategic, interactive computer application (fun fraction) on the performance of middle school students with learning disabilities in solving word problems with fractions and multiplication(2013-08) Shin, Mikyung, 1980-; Bryant, Diane PedrottyThe purpose of this study was to investigate the effects of a web-based strategic, interactive computer application (Fun Fraction) on the ability of middle school students with LD, who have mathematics goals on their IEPs, to solve word problems with fractions and multiplication including two factors of a whole number (less than or equal to 4) and proper fractions. A multiple-probe single case research design across subjects was applied for the study. Three middle school students with learning disabilities participated in baseline, intervention, and maintenance test sessions over a 13-week period. Findings showed that there was an experimental effect for all three students, tested on their instructional probes; students' performance improved from baseline to intervention phases after receiving instruction through Fun Fraction. John and Alec reached the mastery level of 80% on two of the three review days. The level of change from baseline to intervention phases ranged from 28.67% to 68.89%. Even through there was no immediacy effect for John, the trend of his data (10.33) revealed a substantial growth in general. Additionally, the percentage of data showing improvement between baseline and intervention phases was 70% for Tiffany, 56% for John, and 100% for Alec. In particular, the improvement trend of Alec's data was statistically significant (Tau[subscript novlap] = 1, p < .05, CI 90% = .341<>1.659). All of them reached 80% accuracy percentage on their one-time maintenance tests. Regarding the three problem types of combine, partition, and compare for each representation and equation question, students struggled the most with combine representation questions and showed relatively better competence in compare equation questions. A learning-related social validity questionnaire and usability questionnaire indicated that students liked learning through Fun Fraction and recognized well the useful interaction design features embedded in Fun Fraction. Cognitive and metacognitive strategy questionnaires also indicated that students liked the represent strategy that allowed students to manipulate the rectangular area model, and students expressed positive views on the thinking process through metacognitive strategies embedded in Fun Fraction.Item Effects of rephrasing word problems on sixth-grade ESL and native English-speaking students' mathematics performance and attitudes(Texas Tech University, 1998-12) Tan, JiangOne hundred and four sixth-grade students, 52 native English-speaking and 52 English as a Second Language (ESL) students, participated in this experimental study. The purpose of the study was to investigate the effects of native language and rephrasing of mathematics word-problems on their performance on mathematics word-problem solving and attitude toward mathematical tasks. It was predicted that rephrasing mathematics wordproblems, by replacing low-frequency vocabularies and restructuring complex sentences to make the problems easy to understand, would positively affect students' performance on the problems and change their attitude toward mathematical tasks. It was also predicted that the enhancing effects of rephrasing of word-problems would be more profound among ESL students than native-English-speaking students. The enhancing effect of rephrasing, as predicted, was evidenced in the study in which students working with the revised version of the mathematics word-problems outperformed those who working with the original version of problems drawn from mathematics textbooks. As revealed in the result of the study, the native Englishspeaking students performed better than the ESL students on the mathematics test. Not supported by the study, however, the interaction effect between native language and rephrasing of word-problems that rephrasing should have had a stronger effect on ESL students than it did for the native English-speaking students. Opposite to the prediction, native English-speaking students working with the revised version of the test performed significantly better than control group students working with the original version. Although ESL students working with the revised version of the test had better score than those working on the original version, they did not perform significantly better than the other group. The pattern of the difference was explained in terms of anguage proficiency of Englishspeaking and ESL students. It was postulated that the rephrasing of the word-problems did not reduce the language difficulty level that was appropriate to some ESL students, especially those who were at the beginning level of a ESL program, but rephrasing benefited native English speaking students who had problems understanding original mathematics word-problems. This explanation implies that extra attention should be given to students' language proficiency in future research.Item The effects of schema-based intervention on the mathematical word problem solving skills of middle school students with learning disabilities(2009-08) Na, Kyong-Eun; Bryant, Diane PedrottyA 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.Item 'Playing the game' of story problems : situated cognition in algebra problem solving(2010-12) Walkington, Candace Ann; Petrosino, Anthony J. (Anthony Joseph), 1961-; Carmona-Dominguez, Guadalupe; Marshall, Jill; Walker, Mary; Greeno, JimThe importance of mathematics instruction including "real life" contexts relevant to students’ lives and experiences is widely acknowledged (Common Core State Standards Initiative, 2010; National Council of Teachers of Mathematics, 2000; 2006; 2009), however questions about why contextualized mathematics is beneficial and how different types of contextualization impact problem solving have yet to be fully addressed by research. Common justifications for contextualized mathematics include the idea that relevant contexts may help students to apply what they learn in school to out-of-school situations, and that relevant contexts may scaffold learning by providing a bridge between what students understand and the content they are trying to learn. The present study investigates these justifications, as well as students' beliefs and problem-solving methods, using story problems on linear functions. A situated cognition theoretical framework (Greeno, 2006) is used to interpret student behavior in the complex, social system of "school mathematics." In a series of interviews, students from a low-performing urban school were presented with algebra problems. Some problems were personalized to the ways in which they described using mathematics in their everyday lives, while others were normal story problems, story problems with equations, or abstract symbolic equations. Results showed that students rarely explicitly used situational knowledge when solving story problems, had consistent issues with verbal interpretation of stories, and engaged in non-coordinative reasoning where they bypassed the intermediate step of understanding the given situation before trying to solve the problem. After completing most of Algebra I, students still had considerable difficulty with symbolic representations, and struggled to coordinate formal and informal mathematical reasoning. Problems with the same mathematical structure with different amounts of verbal and symbolic support elicited different strategies from students, with personalized problems having high response rates and high use of informal strategies. This suggests that students can use sophisticated, situation-based reasoning on contextualized problems, and that different problem framings may scaffold learning. However, results also demonstrated that the culture of schooling, and story problems as an artifact of this culture, undermines many of the justifications for contextualizing mathematics, and that students need more authentic ways to develop their mathematical reasoning.