This thesis studies to automatically solve Arabic Math Word Problems (MWPs) by deep learning models. MWP is a text description of a mathematical problem, which should be solved by deriving a math equation and reach the answer. Due to their strong learning capacity, deep learning based models can learn from the given problem description and generate the correct math equation for solving the problem. Effective models have been developed for solving MWPs in English and Chinese. However, Arabic MWPs are rarely studied. To initiate the study in Arabic MWPs, this thesis contributes the first large-scale dataset for Arabic MWPs, which contain 6,000 samples. Each sample is composed of an Arabic MWP description and the corresponding equation to solve this MWP. Arabic MWP solvers are then built with deep learning models, and verified on this dataset for their effectiveness. In addition, a transfer learning model is built to let the high-resource Chinese MWP solver to promote the performance of the low-resource Arabic MWP solver. This work is the first to use deep learning methods to solve Arabic MWP and the first to use transfer learning to solve MWP across different languages. The solver enhanced by transfer learning has accuracy 74.15%, which is 3% higher than the baseline that does not use transfer learning. In addition, the accuracy is more than 7% higher than the baseline for templates with few samples representing them. Furthermore, The model can generate new sequences that were not seen before during the training with an accuracy of 27% (11% higher than the baseline).

In educational research, the cognitive activity of problem posing is recognized as an important component of mathematics teaching and learning. Compared to the prevailing educational paradigm of problem solving, problem posing features less commonly in classroom instruction. During the past 20 years, numerous studies examining the use of problem posing in school mathematics instruction have documented positive outcomes in terms of students’ knowledge, problem-solving abilities, creativity, and attitudes and beliefs regarding the study of mathematics. However, despite these promising results, problem posing in mathematics instruction has rarely been studied in the population of students with learning disabilities (LDs). This study describes a problem-posing intervention that draws on existing Conceptual Model-based Problem Solving program (COMPS, Xin, 2012) and conceptual research into the problem posing task. The COMPS-based problem posing intervention is designed to teach word problem posing skills to students with LDs under structured problem posing situations. The study applies a single-subject multiple-baseline design across three participants to investigate the effects on participants’ word problem solving and problem posing skills. The results showed that all three students demonstrated increased math performance on both problem solving and problem posing tests when the COMPS-based Problem Posing intervention was used. In addition, both immediate and maintenance effects on student learning were noted.

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.

Algebra I encompasses several topics that serve as a basis for students’ subsequent mathematics courses as they progress in school. Some of the key topics that students struggle with is solving linear equations and algebraic word problems. There are several factors that may contribute to this ongoing struggle for students such as the structure of the textbooks, the teacher instruction and misconceptions of components of algebraic equations. A promising solution to the potential contributing factors is concrete fading. In this study, concreteness fading refers to an instructional technique that represents topics in a particular sequence from a concrete, real-world representation to a semi-concrete diagram (e.g., tape diagram) to an abstract representation (e.g., algebraic equations). The current study aims to investigate the influence concrete fading has on student learning while studying concrete fading in two ninth grade Algebra I general education classes at an urban high school. In particular, the study aims to answer the following: 1) What are some ways that students who received concrete fading think differently than the control group? 2) How do these differences seem to be related to the intervention? Both classes were taught by the same teacher. One class was assigned to the treatment group that received the concrete fading lessons and the other class was assigned to the control group that was taught as business as usual by the teacher. The study was intended to be quasi-experimental study, but due to challenges, it was primarily qualitative in nature focusing on eight students where the analysis included analyzing student work and student interviews responses along with quantitative analysis of the pre and two post-tests. Results revealed that the treatment group does think differently than the control group based on student work and the interview responses. / Math & Science Education

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

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24929号 / 情博第840号 / 新制||情||140(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)特定教授 黒橋 禎夫, 教授 河原 達也, 教授 西野 恒 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

College Algebra is a gatekeeper course that serves as an obstacle for many students pursuing STEM careers. Lack of success in this course could be a key reason why the United States lags behind other industrialized countries in the number of students graduating with STEM majors and joining the STEM workforce. Of the many topics presented in College Algebra that pose problems, students often have particular difficulty with the application of systems of equations in the form of word problems. The present study aims to identify the factors associated with success and failure on systems of equations word problems. The goal was to identify the factors that remained significant predictors of success in order to build a theory to explain why some students are successful and other have difficulty. Using the Opportunity-Propensity Model of Byrnes and colleagues as the theoretical guide (e.g., Byrnes & Miller-Cotto, 2016), the following questions set the groundwork for the current study: (1) To what extent do antecedent (gender, race/ethnicity, socioeconomic status, and university) and propensity factors (mathematical calculation ability, mathematics anxiety, self-regulation, motivation, and ESL) individually and collectively predict success with systems of equations word problems in College Algebra students, and (2) How do these factors relate to each other? Bivariate correlations and hierarchical multiple regression were used to examine the relationships between the factors and word problem set-up as well as correct completion of the word problems presented. Results indicated after all variables were entered, calculation ability, self-regulation as determined by homework score, and anxiety were the only factors to remain significant predictors of student performance on both levels. All other factors either failed to enter as significant predictors or dropped out when the complete set had been entered. Reasons for this pattern of results are discussed, as are suggestions for future research to confirm and extend these findings. / Math & Science Education

Blockmodellen är en visuell metod som används inom matematik vid arbete med problemlösning och textuppgifter. Metoden utvecklades i Singapore på 1980-talet och har sedan dess visats vara framgångsrik inom matematik. Dess framgång har gjort att den spridits internationellt och även används i svenska skolor. Syftet med studien är att bidra med kunskap om hur elever i årskurs 2 som är bekanta med Blockmodellen väljer att lösa textuppgifter. Syftet uppfylls genom två frågeställningar som berör vilken metod eleverna använder, samt vad som påverkar deras val av metod. Studien genomfördes i två olika klasser med totalt 36 elever. Samtliga elever fick ett antal textuppgifter att lösa och utifrån elevlösningarna valdes tio elever ut för individuella intervjuer. Materialet analyserades utifrån tematisk analys. Studien visar att elever väljer att använda olika metoder för att lösa textuppgifter trots att de är bekanta med Blockmodellen. Vid de individuella intervjuerna framkom det att eleverna valde, enligt dem, den effektivaste metoden för att lösa uppgiften. Eleverna beskrev Blockmodellen som tidskrävande men samtidigt hjälpsam. Genom att använda blocken får de syn på vad som finns, vad som saknas och vad som söks i uppgiften. En slutsats är att elevernas val av metod varierar vilket tyder på att eleverna har olika preferenser när det gäller vilken metod de väljer att använda vid arbete med textuppgifter. / The Bar Model is a visual method used in mathematics when working with problem- solving and word problems. The method was developed in Singapore in the 1980s and has since been shown to be successful in mathematics. Its success has led to its international spread and is now used in Swedish schools as well. The aim of the study is to contribute knowledge about how students in second grade who are familiar with the Bar Model choose to solve word problems. The aim is answered through two questions that concern which method the students use and what influences their choice of method. The study was conducted in two different classes with a total of 36 students. All students were given several word problems to solve and based on the student solutions, ten of the students were selected for individual interviews. Thematic analysis was used to analyze the material. The study show that students choose to use different methods to solve word problems despite being familiar with the Bar Model. During the individual interviews, it emerged that the students chose what they considered to be the most effective method for problem solving. The student describer the Bar Model Bar Model as time-consuming but also helpful. By using the bars, they could see what is present, what is missing and what is being sought. One conclusion is that students' choice of method varies, indicating that they have different preferences regarding which method to use for solving word problems.

1 Solving strategies of word problems depending on the context topicality ABSTRACT The thesis deals with word problems solvable by linear equations. The aim of the work is to show if the context, on which the word problem depends, influences how pupils participating in the research solve it and verify if word problem phrasing and modern language usage help pupils solve the word problem. It is accomplished by assigning pupils a set of varied word problems and assessing their solutions. More results were gained by assessing questionnaires related to the context of the word problems being calculated. The second aim of the thesis is to explain various definitions of word problems, putting the term into the context of school mathematics and a brief summary of the historical development of mathematics focusing on word problems. The work consists of three parts. In the first part, problems and word problems are defined and it is shown how word problems are included in the Framework educational programme. Word problems are put into historical context. The second part shows the conception of motion word problems, word problems on joint work and word problems on dividing a whole into parts in the present-day mathematical textbooks in the second stage of elementary schools and in the lower classes of secondary grammar...

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