Browsing by Subject "Fractions"
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Item Assessing EC-4 preservice teachers' mathematics knowledge for teaching fractions concepts(Texas A&M University, 2008-10-10) Wright, Kimberly BoddieRecognizing the need for U.S. students' mathematics learning to be built on a solid foundation of conceptual understanding, professional organizations such as the National Council of Teachers of Mathematics (2000) and the Conference Board of the Mathematical Sciences (2001) have called for an increased focus on building conceptual understanding in elementary mathematics in several domains. This study focuses on an exploration of two aspects of Hill, Schilling, and Ball's (2004) mathematics knowledge for teaching: specialized content knowledge (SCK) and knowledge of content and students (KCS) related to fractions concepts, an area that is particularly challenging at the elementary level and builds the foundation for understanding more complex rational number concepts in the middle grades. Eight grades early childhood through four preservice teachers enrolled in a mathematics methods course were asked to create concept maps to describe their knowledge of fractions and interpret student work with fractions. Results showed the preservice teachers to be most familiar with the part-whole representation of fractions. Study participants were least familiar with other fraction representations, including fractions as a ratio, as an operator, as a point on a number line, and as a form of division. The ratio interpretation of a fraction presented the greatest difficulty for study participants when asked to describe student misconceptions and create instructional representations to change students' thinking.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 Teaching fractions to middle-school students struggling in mathematics : an exploratory study(2011-05) Misquitta, Radhika Maria Peter; Rieth, Herbert J.; Garcia, Shernaz B.; Bryant, Diane P.; Dodd, Barbara G.; O'Reilly, Mark F.Fractions are an essential skill for students to master, and one students struggling in mathematics face particular difficulty with (National Mathematics Advisory Panel, 2008; Mazzocco & Devlin, 2008). This study employed the multi-probe multiple baseline design to examine the effectiveness of the concrete-representational-abstract (CRA) approach and explicit teaching practices to teach fraction equivalence to students struggling in mathematics. The study was conducted across four students, and replicated simultaneously across four more. The CRA approach included concrete aids such as fraction circles and fraction strips, representations such as pictures of fraction circles and polygons, and algorithms. Explicit teaching involved following a model-lead-test sequence and included an advanced organizer, corrective feedback and cumulative reviews. Results of this study indicated that the intervention program was effective to improve students‟ performances in fraction equivalence tasks. In particular, the use of vii representations was seen to impact performance and concrete aids alone may not be sufficient to improve performance. With regards types of representational and concrete aids employed, results of this study tended to favor the use of linear versus circular aids. Results indicated that students whose performances tend to vary may not benefit to the same extent as those who have stable profiles. Students who demonstrate variable profiles may require additional practice to master skills being taught. This study also examined transfer of skills to word problems and, results demonstrated that the CRA and explicit teaching approaches were beneficial in helping aiding transfer. Several aspects of the program may have contributed to aiding transfer including, minimal exposure to word problems during intervention, drawing connections between representations and abstract information, and incorporating the fair sharing understanding or quotient interpretation of fractions. This program concluded that students were able to maintain performances over time, and that representations in particular appeared to aid conceptual understanding and promote maintenance of skills.