The purpose of this study was to evaluate the effects of specialized skill instruction on the ability of sixth-grade students to solve mathematics word problems. Subjects were 578 sixth graders from eight elementary schools. Researcher-developed materials were used based on seven identified content strands. Specific sections of a widely used achievement test were used to identify ability groups in both reading and mathematics and served as the pretest and posttest measures.

In three experiments, I first examined the correlation between the presence of transformation of stimulus function (TSF) across computation and the presence of TSF across saying and writing for spelling words, and then tested the effects of the establishment of TSF across saying and writing on the establishment of TSF across math operants. Eight middle school students with learning disabilities participated in experiments I and II. All participants demonstrated reader/writer and math skills such as textual responding and using counting strategies to solve one-step word problems. Four of the eight participants also demonstrated TSF across saying and writing for spelling. The dependent variables of Experiment I were the accuracy and fluency of solving word problems after receiving fluency training on math facts, as well as the number of counting strategies used when solving word problems. Results showed that all participants with TSF across saying and writing for spelling demonstrated significant increases in both their accuracy and fluency when responding to word problems (i.e., ES = 1) whereas participants who did not demonstrate TSF across saying and writing for spelling demonstrated minimal gain from accuracy and fluency training of math facts (i.e., mean ES = 0.3). Experiment II tested the effects of fluency and accuracy training of word problems on the accurate and fluent responding to math facts and other math operants. Results showed that accuracy and fluency training had large effects on all participants (i.e., ES = 1). Participants who did not demonstrate TSF also demonstrated larger improvement (i.e., ES > 0.67) compared to Experiment I. The results of Experiments I and II demonstrated an association between TSF across math operants and TSF across saying and writing for spelling. Experiment III further tested for a functional relation by examining the effects of the establishment of TSF across saying and writing for spelling on the establishment of TSF across math operants with three of the participants who did not demonstrate TSF across saying and writing for spelling in the first two experiments. Upon establishment of TSF across saying and writing for spelling words, all three participants demonstrated TSF across math operants (i.e., increased accuracy and fluency of word problems, extinction of counting strategies). The results of the three experiments suggest the importance of teaching math as a verbal behavior, more specifically, as a speaker-as-own-listener behavior instead of as visual match-to-sample repertoires. Future replication of the procedure is needed to extend the external validity of the current experiments.

The purpose of this action research study was to evaluate my own practice of teaching writing word problems with fraction subtraction and fraction multiplication using appropriate context. I wanted to see how focusing my instruction on the use of the area model and manipulatives could develop students’ understanding of fractions when writing word problems. I chose this topic because Florida has adopted the Common Core State Standards and will be implementing them in the coming years. These standards encourage the development of deeper understanding of mathematics, including fractions. I hoped this research would give my students the opportunity to make sense of fraction subtraction and fraction multiplication word problems on a deeper level, while giving me insight into my own practice in teaching context within word problems. Through this study, I learned that my students continued to switch the context of subtraction with multiplication within word problems. Students did make clear gains in their writing of fraction subtraction and fraction multiplication word problems. Although there is a limited amount of research on students mixing their context within fraction word problems, this study offers additional insight into a teacher’s practice with writing fraction 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.

Arts-Across-the-Curriculum is gaining popularity in the field of education as arts programs are being cut from schools and teachers looks for ways to incorporate art in their classroom. Most of these teachers have minimal formal arts training, but recognize the importance of introducing their students to various fine arts disciplines. These educators seek opportunities to learn new ways to bring arts to their students and may bring teaching artists into their classrooms to teach students or teachers. The clear connection between drama and the core subjects of history and literature allow teaching artists to easily create units utilizing both curriculum areas. Mathematics does not present clear connections to drama and the prevalence of mathematics anxiety, especially in the arts, prevents connections from being made. As an educator, theatre artist and lover of mathematics, Arts-Across-the-Curriculum provides me a opportunity to meld these together as a way to help young people find excitement in their education. Partnering with a fourth grade teacher, I developed a unit of lesson plans using playwriting as a way to understand word problems that was user-friendly for a teacher with no arts training. The Dramath Unit was integrated into the class as part of regular curriculum taught by the participating classroom teacher. Based on feedback from the participating teacher, I revised the unit for future use.

Submitted in fulfillment of the requirements of the Degree of Master of Technology: Language Practice, Durban University of Technology, 2011. / The abolition of apartheid in South Africa in the late 1980s and the advent of democracy in 1994 resulted in dramatic changes in the education system. Of great significance to this study is the freedom African parents were allowed in choosing the medium of instruction to be used at schools. Surprisingly African parents encouraged their children to study through the medium of English mainly due to the education and employment opportunities English will provide them in the future (Mda, 1997). Now, seventeen years into democracy, English as a national language and the preferred medium of instruction has been blamed for poor results among ESL learners (Moreosole, 1998). Taylor, Muller and Vinjevold (2003: 54) point out that the difficulties associated with studying in a language other than one’s home language are more pronounced in mathematics, a subject which is strongly dependent on technical language proficiency. A section in the Grade 8 mathematics syllabus that is generally problematic for ESL learners is that of word problems (Wetzel, 2008). This is because ESL learners lack the language and reading skills needed to comprehend word problems, and the listening skills required to understand the educator’s explanation of the solution (Crandall, Dale, Rhodes and Spanos, 1985). To address the aims and objectives of this study, relevant literature was reviewed and various teaching strategies were examined to determine which strategies may be most effective in helping ESL learners solve word problems. Grounded within the Constructivist Learning Theory, this study was based on Vygotsky’s zone of proximal development and Bruner’s concept of scaffolding. Using a mixed methods approach, this study investigated problems that mathematics educators and ESL learners experience in the teaching and learning of word problems through the medium of English, and also identified strategies that mathematics educators use to teach word problems to ESL learners. iv Analysis of the educator questionnaire and the focus group interviews with learners revealed that ESL learners are experiencing difficulty solving word problems in English and educators are, to a large extent, adapting their teaching strategies when teaching them. The data also indicated that groupwork was considered by the majority of educators to be the most suitable method in the teaching of word problems to ESL learners, but sadly this method was used less frequently compared to whole class discussion and individual work due to discipline problems, the educators’ inability to handle group dynamics and the tendency for learners not to contribute to the group discussion. The findings also suggest that it is necessary for the educator to use a variety of teaching strategies to ensure that ESL learners enjoy success in mathematics. Based on the findings, this study makes recommendations regarding the teaching and learning of word problems and the use of adapted teaching strategies to foster active participation in lessons and group discussions, thereby increasing learner confidence and aiding in the understanding of English terminology used in mathematics word problems.

A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand, Johannesburg. December 2014. / The National Curriculum and Assessment Policy Statement document (CAPS) (Department of Basic Education, 2012: 4) outlines some of the salient skills related to the modelling of word problems that Mathematics learners are expected to acquire during the course of their learning. One such critical skill is the learners' ability to represent and describe situations in algebraic language, formulae and expressions. In line with this broad objective, the present study investigated learners' linguistic knowledge and skills in translating from word to linear algebraic representations. Particularly focussing on errors learners made during the translation process, a class of 40 Grade 11 learners at one school in Gauteng West District were selected and given a written test on word problems. To gain access to learner misunderstandings leading to the observed errors and their sources, five learners were selected for interviews that were audio recorded. A Mixed-method Sequential Explanatory Design was used in the study. The major finding of this present study was that learners committed more semantic errors than syntactic and schematic errors suggesting that they (learners) had challenges in understanding the language used in the word problems. The major sources of semantic errors were found to be learners' lack of vocabulary knowledge, inexperience in interacting with expository text structures and their lack of syntax awareness. In addition to the above finding, learners exhibited limited metacognitive skills essential in word problem solving as well as their inability to reflect on the appropriateness of their written algebraic representations for all categories of word problems. The study concludes by providing recommendations on how errors committed in word problem solving can be attended to

Specific to the recommendation of the National Council of Teachers of Mathematics (1980) to identify and analyze problem solving strategies and the settings in which the development of these strategies could be optimized, this study is a compilation of three case studies which describe what elementary school children say and do when solving verbal mathematics problems in small groups. Persuant to this goal, three four-member groups were selected and asked to reach a consensus within each group on the solution to a variety of routine and non-routine problems. In this relatively unstructured setting, transcriptions of verbal interactions, written records of all computations, and observer notes were compiled for each group. The resulting identification and description of the problem solving behaviors which occurred were analyzed in terms of two broad interactive functions by which children seek to understand verbal problems: the construction of mental representations or physical displays of the problems and the evaluations of these constructions. Representations, in this perspective, are constructed at two levels: a contextual level at which the problem situation is linguistically interpreted and a structural level at which a statement of a problem underlying mathematical structure is defined. Evaluations also occur which allow group members to monitor their understanding and direct the course of the problem solving effort. The findings indicate that intermediate aged children when solving problems in small groups display general patterns of behavior. These patterns of behavior include: the manner in which the groups approach and effectively isolate the contextual elements of a verbal problem, the propensity of groups to change the mode in which a problem is represented by utilizing manipulatives, diagrams, tables and other physical displays, and the manner in which groups monitor the course of problem solving and reach consensuses on solution proposals. Within this general pattern, however, specific subject and task variables characterize individual groups, affecting both the group interaction and the incidence of specific problem solving behaviors. These findings suggest practical classroom applications for group problem solving formats in the elementary school classroom. Additional research, however, must provide the link between group problem solving and individual performance.