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Problem solving is one of the central activities performed by computer scientists as well as by computer science learners. Whereas the teaching of algorithms and programming languages is usually well structured within a curriculum, the development of learners’ problem-solving skills is largely implicit and less structured. Students at all levels often face difficulties in problem analysis and solution construction. The basic assumption of the workshop is that without some formal instruction on effective strategies, even the most inventive learner may resort to unproductive trial-and-error problemsolving processes. Hence, it is important to teach problem-solving strategies and to guide teachers on how to teach their pupils this cognitive tool. Computer science educators should be aware of the difficulties and acquire appropriate pedagogical tools to help their learners gain and experience problem-solving skills.

Many students who are proficient with basic math facts struggle for understanding when it comes to word problems. Teachers time and time again teach and re-teach problem solving strategies in hope that their students will one day acquire all the skills necessary to become proficient in this area. Unfortunately understanding problem solving skills is not the only answer to solving word problems. There has been a significant amount of evidence linking reading comprehension to mathematical reasoning. The development of a website to assist teachers and students who are having difficulties with mathematical word problems is extremely beneficial. The website is designed with links, power points, and examples that enhance reading comprehension within mathematical word problems. Through this project, it has been determined that students who are exposed to an additional mathematical program related to breaking apart word problems show evidence of a greater understanding and mastery of solving mathematical word problems.

In this thesis we study four groups of students in grade 8, 9 and 10 when they try to solve a classical mathematical problem: Which rectangle with given circumference has the largest area? The aim of the study was too see how the students did to solve a mathematichal problem? The survey shows that students have rather poor strategies to solve mathematical problems. The most common mistake is that students don’t put much energy to understand the problem before trying to solve it. They have no strategies. This was clearly obvious when you look at Balacheff’s theory in an article from 1988. His first, and lowest, level is called naive empiricism. Typical for that level was that the student’s efforts to solve the problem just consisted of social interaction without any direction and structure. One reason can be that the students don’t recognize mathematical laws and general concepts well enough. Another problem is that they don’t check their results. Why they don’t do this is hard to say. Earlier results indicating that one reason can be that the students don’t take tasks in school as an intellectual challenge. The just consider it like something the must do.

The purpose of the study is to investigate the problem-solving strategies of children in fourth-grade, fifth-grade and sixth-grade. The investigators tried to guide children through a variety of problem-solving strategies that were in written, figural, or symbolic forms. Then the investigators examined the variation of children¡¦s spatial concepts by analyzing the problem-solving strategies used in calculating the volumes of various solids. In order to improve the teaching materials, the investigator identified the performance of spatial concepts by referring to QCAI (QUASAR Cognitive Assessment Instrument). For the purpose of designing future lessons, the investigator examined the relationship between children¡¦s problem-solving strategies level and the performance in the seven content areas in the curriculum. There are two results of this study: The first result is on the problem-solving strategies found within the same grade (4th; 5th; and 6th) and there are 3 findings. First, strategies of fourth-graders are focused on low-levels and middle-levels; strategies of fifth-graders focused on middle-level geometric space concept, and finally, strategies of sixth-grades students focused on middle-levels and high-levels. Second, there are no significant differences relating to gender. Third, the higher the grade of children is the higher the levels of their spatial concepts. In addition, the second result is the relationship between strategy levels and performance in seven content areas: revealing position corrections, and having mathematics as the most significant, and the rest in order: social studies, language arts, science and technology, arts and humanities, integrative activities, health and physical education.

This research referred to Basic Competency Test from 2001 to 2006 to construct test and analyzed 207 ninth-graders¡¦ problem-solving strategies as well as errors in solving linear equations with two unknowns. Furthermore, the investigator referred to the contents of interview, to investigate the factors that cause students¡¦ mistakes. Results shows that the main strategy for solving equations is 'to add and subtract the elimination approach', while for solving application problems is 'organizing side by side'. The errors for solving equations are mistaking concepts including Equality Axiom, etc. The errors for solving application problems are mostly concerned about the translation and holistic mistake. Through analyzing data from interviews, the reasons for mistakes in solving equations are: mutual interference of experience; mixed up different operation rules; or, solving a problem with the wrong concept built by themselves. The reasons for mistakes in solving application problems are: insufficient language ability; the lack of the self-monitoring; and limitation in strategies for solving problems. Finally, based on the results of this research, the researcher gave suggestions in three aspects. Hopefully, this research can assist teachers to have more variety in teaching methods heading towards an aim to benefit in students¡¦ learning.

<p>In this thesis we study four groups of students in grade 8, 9 and 10 when they try to solve a classical mathematical problem: Which rectangle with given circumference has the largest area? The aim of the study was too see how the students did to solve a mathematichal problem?</p><p>The survey shows that students have rather poor strategies to solve mathematical problems. The most common mistake is that students don’t put much energy to understand the problem before trying to solve it. They have no strategies. This was clearly obvious when you look at Balacheff’s theory in an article from 1988. His first, and lowest, level is called naive empiricism. Typical for that level was that the student’s efforts to solve the problem just consisted of social interaction without any direction and structure. One reason can be that the students don’t recognize mathematical laws and general concepts well enough. Another problem is that they don’t check their results. Why they don’t do this is hard to say. Earlier results indicating that one reason can be that the students don’t take tasks in school as an intellectual challenge. The just consider it like something the must do.</p>

With increasing opportunities to study abroad, learning to read in a foreign language has become increasingly important for countless second language learners. International students in pursuit of higher education degrees are required and expected to read in the target language at the same level of fluency and comprehension as their native-speaking counterparts. The number of international students studying in Arabic higher education institutions has followed the general ascending trend. For these second language speakers of Arabic, good reading skills in Arabic are essential for their academic success. Since the use of reading strategies is an important component of first and second language reading, this study aimed to investigate the use of reading strategies by native and non-native speakers of Arabic when reading academic materials in Arabic. In addition, it aimed to explore possible differences in the use of reading strategies between these two groups. For this purpose, a total of 305 students participated in the study. A survey composed of 30 items was administered to 222 non-native speakers of Arabic, and the same survey with 28 items was administered to 83 native speakers of Arabic. The survey included demographic questions adapted from Mokhtari and Sheorey (2008) and employed the questionnaire SORS used by Mokhtari and Sheorey (2002). These 30 items belonged to three strategy subscales: Global, Problem-solving, and Support strategies. To analyze the collected data, descriptive statistics and multiple independent t-tests were performed. In addition, an analysis was performed to find the most and least used reading strategies by both groups as well as possible differences between them in terms of reading strategy use. Problem-solving strategies were the most frequently used by both groups with a slightly higher use by the non-native speakers. Regarding the other two types, the native and non-native speakers showed different preferences. Specifically, Support strategies were the second most favored type among the non-native speakers, whereas for the native speakers, the second most frequently used type were Global strategies. However, even though Global strategies were the least used among non-native speakers, the non-native speakers' mean score on Global strategies use was higher than the native speaker score of use. Overall, the similarities and differences in the use of reading strategies by native and non-native speakers of Arabic deserve attention because they carry implications for both reading research and pedagogy. These empirical findings can be used by Education policy makers to create training courses and workshops that will help students improve their reading skills in general and reading strategies in particular. This study also suggests that there is a need for further research that will examine how the use of reading strategies is related to the academic performance of native and non-native speakers.

The purpose of this study is to investigate students¡¦ understanding of the equal sign, problem-solving strategies of equations with one unknown, and the strategies of solving equations with one unknown under different understanding types of the equal sign. To achieve this purpose, the investigator did a survey and development instruments. The participants were 203 seventh-grade students in a convenient sample. Descriptive statistics were used to analyze data in frequency and percentages. The main results was that participants with a relational definition of the equal sign were the most (close to 50%), and an operational definition of the equal sign was approximately 1/4. There was a higher successful performance associated with a relational definition than an operational definition. The primary strategy of operations on the left-hand side of equal sign is the mathematical operations; the main strategy of an unknown quantity on the right-hand side of the equal sign was by going to the parenthesis-reverse and bringing different denominators into a common denominator; the principal strategies of one number on the right-hand side of the equal sign, equations with operations on the right side of the equal sign and equations with operations on both sides of the equal sign are cover-up and transposing. To use the strategies of trial and error substitution and undoing is minority in a linear equation with one unknown. The strategy of an operational definition participant in five equal sign topics is similar to the strategy of one with a relational definition. However, those with a relational definition apply multiple strategies and exhibited varying particular and algebraic property. On the other hand, participants with an operational definition used arithmetic strategies more frequently than participants with a relational definition. From the above results, the researcher suggested instruction to include strategies with algebraic property to help learners to develop stable understanding of the equal sign in Algebra. In addition, the recommendation is to have teachers to encourage students to apply multi-dimensional thinking and different strategies in algebraic problem-solving.