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Browsing Faculty of Education by Subject "Research Subject Categories::MATHEMATICS::Algebra, geometry and mathematical analysis::Mathematical analysis"
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ItemStudents' Mathematics Problem Solving Difficulties and Coping and Strategies: A Model Building Study( 2019-08) Vidad, Dinah C.Problems, difficulties and pressures abound everywhere. In Mathematics, much has been said and heard of students struggling with problem solving. This study therefore primarily aimed to develop models that could address the problem solving difficulties of students through their coping strategies. Specifically, it aimed to determine the students’ strategies in coping with their difficulties along the four phases of problem solving namely: understanding the problem (UP), devising a plan (DP), carrying out the plan (CP) and looking back (LB) according to a) sex b) academic programs namely: The study employed a case-study-design approach. The respondents of the study involved thirteen classes with 425 college freshmen who were enrolled during the first semester of SY 2018-2019. Two hundred ninety-seven of them composed the model development group while 128 respondents composed the validation group. Results of the problem solving test revealed the following difficulties of the respondents: a) inability to distinguish the known from the unknown information and inability to identify the type of problem and recall basic concepts in the UP phase, b) inability to transform a problem into a mathematical equation and inability to draw tables/charts out of the information and organize information and connect to a concept in the DP phase, c) inability to completely perform the working procedure systematically and accurately and inability to start with the computational process in the CP phase, and d) inability to complete the checking procedure and inability to start the evaluation of the correctness of the obtained solution in the LB phase. Moreover, the study revealed that the looking back (LB) phase has the most encountered difficulty, followed by the carrying out the plan (CP) phase. There were more females who encountered the above mentioned difficulties in all phases of problem solving than males. The respondents were likewise grouped into two: STEM-related academic programs and the non-STEM-related academic programs. The study found out that the majority of the male respondents from the STEM-related academics programs encountered the observed difficulties in all phases of problem solving. The coping strategy questionnaire on the other hand elicited responses from the students on how they deal with their difficulties in each phase of problem solving. Forty-three strategies emerged and were grouped into two: 32 Problem-focused and 11 emotion-focused coping strategies. Association of the two variables let to the development of the two models: Coping strategies by sex by model and coping strategies by academic program by phase. Validation of the two models revealed that they can address the mathematics problem solving difficulties of the students through coping strategies. The study therefore recommends that teachers should focus on the phases where students find struggling during a problem solving scenario. They need to provide the students with activities and tasks that are real-life problems that require them to understand, compute and check their solutions so that they may be able to discover their own learning. It is also recommended that an assessment identifying the problem solving difficulties of students be administered at the beginning of the semester so that appropriate strategies will be implemented by the mathematics teachers. Lastly, another study underscoring an added variable like the track/strand which the student enrolled during his/her senior high school may be conducted.
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ItemThe Quality of the Student's Mathematical Proofs as a Function of Classroom Assessment A Qualitative-Quantitative Analysis( 2008) Callanta-Zamora, Lourdes A.In this quasi-experimental study mathematical proof writing is views as a problem-solving activity success at which requires adequate knowledge of relevant mathematical content and logical rules of inference, familiarity with heuristic proof-writing techniques, metacognitive skills, and positive effects towards self and mathematics. The extent to which two types of classroom assessment – traditional (TA) and learner-centered (LCA) – provided these cognitive and affective requisites is described on the basis of a quantitative and qualitative analysis of their effects on the quality of students’ mathematical proofs and selected affective variables such as attitudes towards mathematics, motivation, self-confidence, mathematics anxiety, and test anxiety. Two intact undergraduate classes of fifty-one (51) students in Linear Algebra at the University of the Philippines Visayas Main Campus in Miag-ao, Iloilo during the Second Semester, 2002-2003, constituted the sample for the study. The traditional and learner-centered classroom assessments were randomly assigned to the control and experimental groups, respectively. Each member of the experimental (LCA) and control (TA) groups wrote proofs for seven propositions which were scored blind by two raters using 4-point criteria (key mathematical understanding, logical validity, mathematical communication, and clarity and simplicity) specified in a researcher-constructed anaholistic proof-writing rubric. The proofs were also qualitatively assessed to determine the nature and extent of the subjects’ understanding of the key mathematical content and identify logical fallacies committed as well as instances of inappropriate use of language, mathematical terminology and notation. The long-term effects of classroom assessment on proof quality were determined through a comparison of the mean index values obtained by the two groups in all criteria indicators, including the frequencies of manifestations of validity, soundness, consistency, and fallacious reasoning in these profs. On the other hand, the differential effects of classroom assessment on the effect were analyzed based on the subjects’ pre-and post-test instruction responses in a 38-item Affective Inventory and clarified in greater detail by interview data on the perception and impressions of a sample of the subjects from the TA and LCA groups about their learning experiences in the course. Four categories of learning difficulties encountered by the TA and LCA groups in relation to proof-writing were identified and addressed: (a) difficulty with the form and substance of a proof, (b) difficulty in understanding a proof for a theorem and theoretical exercise, (c) difficulty in understanding the key content and their relationships in a proof, and (d) difficulty or confusion with associated mathematical terminology and notation. The findings of the study show no significant differences in the quality of TA and LCA proofs for Propositions 1-5. However, despite the greater difficulty of proving Propositions 6 and 7 as compared to Propositions 1-5, the LCA proofs for Propositions 6 and 7 obtained consistently higher ratings than those of the TA group. This difference was found to be significant in proofs for Proposition 7. This provides evidence of a consistent and significant improvement in the quality of LCA proofs during the last three weeks of the teaching experiment. The comparison of the mean index values obtained by both groups for the different criteria measures, as well as the frequencies of manifestations of validity, soundness, consistency, and fallacious reasoning in their proofs, reinforce the above findings. In all criteria measures, the cumulative change in LCA mean index values in Proofs 5-7 are greater than the TA groups. These indicate a greater cumulative improvement in the LCA group’s proof-writing skills over time as a result of classroom assessment. Moreover, as a result of their learning experiences in the course, the LCA subjects more significantly liked mathematics and regarded it as their most favorite subject in school and felt more challenged to solve difficult problems in mathematics. They too more strongly agreed on a teacher’s influence on their mathematics performance and felt less motivated to perform at their best in mathematics by material incentives like money. On the other hand, the TA subjects experience resulted in a significant reduction of their level of frustration with their previous learning of mathematics, a greater interest to know more about the subject and preference to discuss and learn mathematics with others, and a better understanding of geometry and trigonometry than algebra, along with increased levels of test anxiety and discomfort when dealing with numbers and mathematical symbols.