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Computer-Assisted Instruction (CAI) offers the potential to deliver cognitive and meta-cognitive strategies in mathematical word problem-solving for students with mathematics difficulties. However, there is a lack of commercially available CAI programs with cognitive and meta-cognitive strategies for mathematical word problemsolving that pay particular attention to the critical design features for students with mathematics difficulties. Therefore, empirical evidence regarding the effects of CAI program with cognitive and meta-cognitive strategies on the word problem-solving of students with mathematics difficulties has not been found. Considering the imperative need for a CAI program with cognitive and metacognitive strategies for students with mathematics difficulties, an interactive multimedia software, ‘Math Explorer,’ was designed, developed, and implemented to teach one-step addition and subtraction word problem-solving skills to students with mathematics difficulties. Math Explorer incorporates: (a) four-step cognitive strategies and corresponding three-step meta-cognitive strategies adapted from the research on cognitive and meta-cognitive strategies, and (b) instruction, interface, and interaction design features of CAI identified as crucial for successful delivery of cognitive and metacognitive strategies for students with mathematics difficulties. The purpose of this study was to investigate the effectiveness of Math Explorer, which was designed to be a potential tool to deliver cognitive and meta-cognitive strategy instruction in one-step addition and subtraction word problem-solving. Three research questions guided this study: (a) To what extent does the use of Math Explorer affect the accuracy performance of students with mathematics difficulties in grades 2-3 on computer-based tasks with one-step addition and subtraction word problem-solving?, (b) To what extent does the use of Math Explorer generalize to the accuracy performance of students with mathematics difficulties in grades 2-3 on paper/pencil-based tasks with one-step addition and subtraction word problem-solving?, and (c) To what extent does the use of Math Explorer maintain the accuracy performance of students with mathematics difficulties in grades 2-3 on computer- and paper/pencilbased tasks with one-step addition and subtraction word problem-solving? A multiple probe across subjects design was used for the study. Four students with mathematics difficulties participated in the pre-experimental (i.e., introduction; screening test; and computer training I) and experimental (i.e., baseline, computer training II, intervention, and follow-up) sessions over an 18-week period. Each week of the intervention phase, the students received an individual 20- to 30-minute Math Explorer intervention, at most, five days. After each intervention, they took the 10-minute computer- or paper/pencil-based tests developed by the researcher. The intervention phase for each student lasted five to seven weeks. Two weeks after termination of the intervention phase, their accuracy performance on the computer- and paper/pencil-based tests were examined during the follow-up phases. The findings of the study revealed that all four of the students were able to use the cognitive and meta-cognitive strategies to solve the addition and subtraction word problems and improved their accuracy performance on the computer-based tests. Their improved accuracy performance found on the computer-based tests was successfully transferred to the paper/pencil-based tests. About two weeks after termination of the intervention phase, except for one student who had many absences and behavioral problems during the extended intervention phase, the three students successfully maintained their improved accuracy performance during the follow-up phase. Taken together, the findings of the study clearly provide evidence that Math Explorer is an effective method for teaching one-step addition and subtraction word problem-solving skills to students with mathematics difficulties and suggest that the instruction, interface, and interaction design features of CAI program is carefully designed to produce successful mathematical performance of students with mathematics difficulties. Limitations of the research and implications for practice and future research were discussed. / text

This multiple case study investigated pedagogical differences and similarities among practices used to teach word problems in private schools of Turkey and the United States, the factors impacting teachers’ instructional decisions, and their approaches to teaching word problems as well as the role of culture in teaching and learning word problems. Quantitative survey data were collected from 28 Turkish and 27 U.S. high school mathematics teachers from private or independent schools. The survey investigated teachers’ background information, resources used, and their use of teaching practices (teacher-centered, student-centered, concrete-visualizing, analytical) and types of word problems (true or practice-oriented) as well as their thoughts about the structure of word problems. Qualitative data were collected through classroom observations, videotaping, and focus-group interviews from four ninth grade algebra teachers in Turkey and the United States. Qualitative data helped the researcher expand upon the quantitative findings and examine how word problems actually were being taught in the classroom, the factors impacting teachers’ instruction and approaches to teaching word problems, and participants’ reflections on their own practices as well as on their international partners’ word problems instruction. The findings indicated no significant difference for most survey items, but descriptive statistical analysis revealed that Turkish survey participants incorporated teacher-centered, concrete-visualizing practices, and practice-oriented word problems more often in their instruction, while U.S. survey participants frequently used student centered, concrete-visualizing practices, and true problems. Qualitative findings pointed out what specific teaching practices were evident in the classrooms observed and videotaped in Turkey and the United States. While Turkish teachers thought the university entrance examination and national curriculum had the biggest impact on their teaching, U.S. teachers found school environment (traditional versus progressive) and student perception of word problems as influential on their instruction. The role of culture on teaching and learning word problems was observed in regard to teacher centered versus student-centered instruction, teacher versus student role, and student engagement. Study findings also indicated that cross-examination of teaching promotes teachers’ reflection on their own practices and, thus, should be encouraged and promoted across STEM disciplines and throughout a teaching career. Implications and recommendations for future research, curriculum developers, and mathematics teachers are discussed. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

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.

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.

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.

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.

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-05-12T19:25:53Z No. of bitstreams: 1 TeseACCC.pdf: 4747832 bytes, checksum: ed3a10dc96079c2721ac8f1679c11377 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-18T20:31:02Z (GMT) No. of bitstreams: 1 TeseACCC.pdf: 4747832 bytes, checksum: ed3a10dc96079c2721ac8f1679c11377 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-05-18T20:31:09Z (GMT) No. of bitstreams: 1 TeseACCC.pdf: 4747832 bytes, checksum: ed3a10dc96079c2721ac8f1679c11377 (MD5) / Made available in DSpace on 2017-05-23T19:17:56Z (GMT). No. of bitstreams: 1 TeseACCC.pdf: 4747832 bytes, checksum: ed3a10dc96079c2721ac8f1679c11377 (MD5) Previous issue date: 2016-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / To Study is a class of behavior as complex as relevant in modern society, and such as, should be taught to children and teenagers in order to promote adequate repertoires for this process to occur effectively and autonomously. Studies developed with the objective of training educators to promote appropriate behavior studies indicate the importance of this kind of initiative; access opportunities of this kind, however, is limited to subjects participating in these studies. Based on the teaching programming as established procedure for the preparation of appropriate teaching conditions, and self-preparation as a comprehensively way provide adult education, this study aimed to develop a program to self-prepare of parents and teachers as promoting agents of appropriate behaviors of studies of children and examining the process of development of educational programs itself in terms of favoring and adverse conditions of using represented technology. The development of the program involved: preparation of an teaching program for teacher training (Step I), integration of teacher’s program with one for the preparation of parents, previously produced by other programmer (Step II) and the project writing of the unified program to training parents and teachers (Step III). In terms of the unified program, four terminals objectives were proposed, 22 intermediate objectives of more generic level described in the form of behavioral relations and 731 in more specific levels, corresponding to expressed behavioral relationships synthetically. These objectives were sequenced and arranged in order to compose a 14 modules program, structured in units developed from a regular standard structural and graphic with teaching conditions that promote active participation of learners in each unit, requirements are made in small steps or stages of learning, informative consequences on performance for each evaluation activity (immediate feedback), and considering potential characteristics of learners (whose initial repertoire was defined in the program preparation process). The produced material shall become accessible to the population that may need it through publication and available for review through systematic and controlled applications. With regard to the program preparation process, it was possible to identify conditions that interfered both positively and negatively in the process (programmer's repertoire, access to experts on the subject, self-correcting condition of the program among others) and highlight measures taken in relation to variables that negatively influenced the process, as well needs for further study, process improvement and subsidies for it uses, given its relevance as a tool to produce more effective and socially relevant teaching-learning processes. / Estudar é uma classe de comportamentos tão complexa quanto relevante na sociedade moderna, e como tal deve ser ensinada a crianças e jovens de modo a promover repertórios adequados para que este processo ocorra de modo eficaz e autônomo. Estudos desenvolvidos com o objetivo de capacitar agentes educativos ao promover comportamentos adequados de estudo indicam a relevância deste tipo de iniciativa; o acesso a oportunidades deste tipo, contudo, é limitado a indivíduos que participam destes estudos. Tendo por base a programação de ensino como procedimento consagrado para a elaboração de condições de ensino adequadas, e a autoinstrução como forma abrangente de proporcionar formação de adultos, este estudo teve como objetivos desenvolver um programa para autopreparo de pais e professores como agentes de promoção de comportamentos adequados de estudos de crianças e examinar o próprio processo de elaboração de programas de ensino em termos de condições favorecedoras e desfavorecedoras da utilização da tecnologia que ela representa. O desenvolvimento do programa implicou no preparo de um programa de ensino para capacitação de professores (Etapa I), integração deste programa com um destinado ao preparo de pais elaborado previamente por outra programadora (Etapa II) e a redação do material do programa unificado para capacitar pais e professores (Etapa III). Em termos do programa unificado, foram propostos quatro objetivos terminais, 22 objetivos intermediários de nível mais gerais descritos na forma de relações comportamentais e 731 em níveis mais específicos, correspondentes a relações comportamentais expressas de forma sintética. Estes objetivos foram sequenciados e organizados de modo a compor um programa constituído de 14 módulos, estruturados em unidades desenvolvidas a partir de um padrão estrutural e gráfico comum, com condições de ensino que promovem participação ativa dos aprendizes em cada unidade, exigências feitas em pequenos passos ou etapas da aprendizagem, consequências informativas sobre o desempenho para cada atividade avaliativa (feedback imediato), e levando em conta características potenciais dos aprendizes (cujo repertório de entrada foi definido no processo de elaboração do programa). O material produzido deverá se tornar acessível à população que dele possa necessitar por meio de publicação e disponível para avaliação por meio de aplicações sistematizadas e controladas. Em relação ao processo de elaboração do programa, foi possível identificar condições que interferiram tanto positiva quanto negativamente no processo (repertório do programador, acesso a especialistas sobre a temática, condição autocorretiva do programa, entre outras) e evidenciar providências tomadas em relação a variáveis que influenciaram negativamente o processo, bem como necessidades de estudo adicional e aprimoramento do processo e de subsídios para sua utilização, dada sua relevância como ferramenta para produzir processos de ensino-aprendizagem mais eficazes e socialmente relevantes.

The study explored factors that affect academic achievements in Grade 6 mathematics classrooms in a case of solving word problems. It investigated empirically the causes and perceptions that lead to difficulties in solving word problems and eventually identified strategies for teaching them. The constructivist philosophy was adopted. The study used the mixed-method design with quantitative data complementing the qualitative information. In gathering data, a word problem task, questionnaires, a class observation schedule, face-to-face and focus group interviews were used, focusing on SFS (pseudo) school learners and their teachers as a convenient sample. Data analysis was done in an integrated fashion where concurrent triangulation was followed. The statistics results illustrate that factors such as English language proficiency adversely affect the academic achievements of Grade 6 learners when solving word problems. Reading instructions aloud repeatedly and explaining key mathematical concepts have emerged as key strategies in understanding and solving word problems in mathematics. / Inclusive Education / M. Ed. (Inclusive Education)

South African learners struggle to achieve in both international and national Mathematics assessments. This has inevitably become a serious concern to many South Africans and people in the education arena. An algebraic word problem holds high preference among the topics and determines success in Mathematics, yet it remains a challenge to learners. Previous studies show there is a connection between learners’ low performance in Mathematics and errors they commit. In addition, others relate this low performance to English language inproficiency. This has encouraged the researcher to investigate the errors Grade 11 learners make when they solve algebraic word problems. The researcher used a sequential explanatory mixed approach to investigate Grade 11 learners from Gauteng, South Africa when they solve algebraic word problems. Accordingly, a convenient sampling helped to select three schools, and purposive sampling to choose the learners. In this study, the researcher employed a quantitative analysis by conducting a test named MSWPT with 150 learners. In addition, the researcher used qualitative analyses by conducting the Newman (1977) interview format with 8 learners to find out areas where errors are made and what kind of errors they are. Findings discovered that 90 learners demonstrated unfitness due to poor linguistic proficiency, while the remaining 60 learners fall into three main categories, namely those who benefitted from researcher unpacking of meaning; those who lack transition skills from arithmetic to algebra; and those who lack comprehension and calculation knowledge. Conclusively, the researcher found linguistic, comprehension, semantic and calculation errors. The reasons learners make these errors are due to (i) a lack of sufficient proficiency in English and algebraic terminology (ii) the gap between arithmetic and algebra. / Institute for Science and Technology Education (ISTE) / M. Sc. (Mathematic Science Education)