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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

The aim of the thesis is to find out students' reasoning of chosen word problem by using quadratic equation. The work focuses on specific errors end problems reported by students and evaluated by Newman's method of Error Causes for Written Mathematical Tasks. The theoretical work was based on analyse of current mathematical textbooks and comparison with several international pedagogical studies and thesis with similar specialization. Furthermore, a detailed description of methodology and my own research are described in practical part of the thesis. Principle of study was to chose group of the students from two different high schools ( one well know grammar school and one business high school in Prague) and record the process of reasoning the word problem by camera. The concluison is dedicated to proper analyses of mistakes and problems during the student's reasonings. Powered by TCPDF (www.tcpdf.org)

This study concentrated on word problems in Grades Kindergarten-3 and the application of the Standards for Mathematical Practice and the Content Standards. The study also included an analysis of focus, coherence, and rigor in the materials. The textbooks used were among the first editions to be published after the acceptance of the Common Core State Standards in more than 40 states. The study analyzed the presence of the Common Core Standards in each series and how the three textbook series compared to each other in their word problem solving. The correlation of materials in the three textbook series relied on publishers’ descriptions in the Lesson Openers where the usages of the Standards for Mathematical Practice and the Content Standards and the principles of focus, coherence, and rigor are listed. The publishers’ descriptions were analyzed and compared to the individual evaluation criteria. Using an evaluation criterion, the study examined how Standards for Mathematical Practice were implemented in the textbooks. With the exception of a few grades in two textbook series, the texts displayed low percentages in their adherence to the Standards. The textbook series were similar in their development of word problems labeled with Standards for Mathematical Practice and word problems not labeled with the Standards. In this comparison, the only difference between the two types of word problems was in the verbiage. The Content Standards were used to determine the textbook series alignment with the Standards. The three textbook series showed low implementation of word problem Content Standards when compared to the total number of Standards. In two series, only one Content Standard was listed multiple times rather than a combination of comparable Standards. Relying on the publishers’ descriptions, the study showed how publishers implemented focus, coherence, and rigor in their materials. Of the three publishers, one publisher did not list coherence and rigor in its materials. The other two publishers adhered to focus and coherence in most or all of their materials. All of the publishers fell short in the application of rigor in their textbook series.

This study uses a discourse analysis from the perspectives of James Paul Gee (2005; 1999) in order to establish a socio-situated view of why grade 10 students often experience difficulties in representing mathematical word problems into appropriate equations and expressions that enable a solution to the problems. A discursive methodology was used to throw light on the difficulties that students experience that was different from the perspectives adopted previously, viz. from a view of the structure of the problems, from a pedagogic point of view and a cognitive understanding. An initial case study in one school in which four students were selected revealed that a master model existed that students were enacting when doing and talking about their experiences with word problems, viz. that word problems are obfuscatory. This master model rendered the students relatively mathematically helpless within a Discourse of school mathematics word problems. In order to more fully understand these findings an extended study was set up in which the methodology and analytic framework were refined. This extended study saw four students at each of three different sites selected to participate. The findings of this extended study were that the students enacting a situated Discourse model were more enabled within the Discourse of school mathematics word problems, whilst those enacting a deficit Discourse model were either peripheral or outside of that Discourse. This study contributes in that the constructs for the phenomena and the analytic tools within the context of school mathematics needed to be pioneered, adapted and refined over a period of time to address aspects particular to school mathematics. This resulted in a view from a socio-situated perspective which saw a shift in seeing what students do with the problem to what students do in the social setting associated with the problem. From this shift in focus came a new understanding of student difficulties with word problems that gave rise to a sub-Discourse within the Discourse surrounding school mathematics word problems, and students finding themselves in this sub-Discourse becoming marginalised through enacting a deficit Discourse model because they are unable to ascribe to the success model, or situated Discourse model.

This study investigated the effects of a direct instruction program on the ability of elementary school students identified as at risk for math failure to add and subtract numbers with decimals, and complete addition and subtraction word problems with decimals. Direct instruction has previously been shown to increase the math skills of special education and general education students. This study examined the extent to which these students could master these skills in six hours of instruction, with carefully designed sequences of examples and strategy instruction in word problems. The study took place in two elementary schools. The participants were fifth grade students who had received low math scores on a school wide test and placed in a math group accordingly. The students were given a pretest and placed into two different groups, iv based on a stratified random process. The students in the treatment group received six lessons in decimals and word problems. After the six lessons, the groups were given a posttest. Student progress was assessed by comparing the groups on posttest results, comparing the students’ pretest and posttest scores, and using the ANOVA to determine statistical significance. On the posttest, the students in the treatment group scored 35 percentage points higher than the students in the control group – this difference was statistically significant. The increase was largest in their ability to add and subtract decimals, however many of the students also made considerable progress in their ability to solve word problems.

The purpose of this study was to investigate solution strategies that Thai second graders used to solve addition and subtraction word problems. Fifty-eight children participated in this study, 40 children took a written test, and 18 children participated in an interview. In addition, two classrooms were selected for observation, and six second-grade teachers completed a questionnaire regarding their understanding of mathematical problem solving. The results indicated that Thai children in this study were successful in solving addition and subtraction word problems. For addition word problems, the compare problem and the join problem were the easiest problems. The combine problem was moderately difficult. For subtraction word problems, the compare problem and the separate problem were easy while the combine problem was difficult. The join problem was the most difficult subtraction word problem. Since word problems used in this study contained mostly two-digit numbers, Thai children in this study used knowledge such as borrowing, carrying and regrouping to solve two-digit addition and subtraction word problems. Most Thai children in this study used counting strategies with fingers to solve both addition and subtraction word problems. Counting on strategies were most often used for addition word problems and counting up strategies were most often used for subtraction word problems. Counting all strategies were not used by Thai children in this study. Other strategies that were not based on counting strategies were also found. Those strategies were using tallies, using a known number fact, using an invented fingers model, and using a base-ten strategy. The strategies that Thai children used to solve word problems were not different from those used by children in United States and other countries such as Korea. Most children used three basic strategies to solve word problems: counting strategies; using a known number fact; and using a base-ten strategy. However, the base-ten strategy was not usually used by children in United States. The base-ten strategy was used by Thai children in this study and in Asia countries such as Korea. Moreover, the findings showed that Thai children in this study used mostly fingers to represent counting sequences while children in the United States used other physical objects such as cubes and counters. In observing Thai classroom instruction and having Thai teachers complete the questionnaire, the results suggested that Thai teachers in this study viewed problems as routine word problems and viewed problem solving as solving routine word problems. Teachers did not emphasize problem solving, reasoning, and thinking skills. As a result, children developed memorizing skills rather than thinking and reasoning skills. Children had never explored different types of word problems and non-routine problems, so when the children were faced with problems that differed from their school mathematics instruction, for the most part, children were unable to solve the problems. / Graduation date: 1999

The aim of this study is to investigate the changes in problem-solving abilities and learning attitudes of two elementary second graders after integrating picture books into problem-posing instruction and administering tests on addition and subtraction word problems. The case study approach was adopted; where two second graders, having difficulty in comprehending addition and subtraction word problems, were selected from the researcher¡¦s class. Both students were given addition and subtraction word problems problem-solving pretests and were interviewed afterwards to further analyze their problem-solving abilities and attitudes so as to refer to remedial instruction. After instructional activities came to an end, addition and subtraction word problems problem-solving posttests were then given. Students were interviewed to explore the changes in problem-solving abilities and learning attitudes. Data were collected by observations, interviews and collections of related documents (including two cases¡¦ addition and subtraction word problems pretest and posttest, problem-solving worksheets, problem-posing worksheets, learning diaries, researcher¡¦s teaching introspection record table, audio-taping, video-taping, etc.). The changes in cases¡¦ problem-solving abilities and learning attitudes were analyzed and the findings indicated were four. First, picture books create problem-solving context that can raise cases¡¦ learning motives. Second, with problem-posing process of all types of addition and subtraction word problems and practice, problem-solving abilities of the cases were improved in four dimensions (Being able to locate unknown in problem targets and the known conditions from word problems; being able to select appropriate schematic drawing and to identify its relationship with the problem; being able to set up equations; and, being able to examine whether answers were reasonable.). Third, the remedial instructions designed were able to raise cases¡¦ level of confidence in problem-solving. Fourth, implementing remedial instruction by integrating picture books into problem-posing instruction enables not only transforming one case¡¦s passive learning attitudes to positive but also maintaining the other case¡¦s original positive attitudes. The above four results indicated that implementing addition and subtraction word problems remedial instruction to two second graders by integrating picture books into problem-posing instruction helped to improve children¡¦s problem-solving abilities and learning attitudes. Implications on research and practice were also given.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 88-93).

The 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. / text