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Assessing Dyscalculic Tendencies Among Children Through a Mobile Application Screening Tool

( 2022-01) Santos, Arman DC.

This study aimed to develop and validate the psychometric properties of the first Philippine mobile application screening tool for dyscalculic tendencies and establish norms and cut-off scores for Grade 3 pupils. Additionally, it investigated the weaknesses of at-risk pupils and compared them to the different core deficit hypotheses of dyscalculia. Also, the study assessed the experience of children in using the mobile application. The screening tool consisted of 11 tasks divided into arithmetic calculation, basic number skills, and other cognitive tasks. The norming group is comprised of 248 Grade 3 pupils. The findings revealed that the screening tool has an excellent level of face and content validity and an acceptable to excellent level of internal consistency and test-retest reliability. This suggests that the screening tool is a valid and reliable instrument to identify children with dyscalculic tendencies. The study provided stanine norms and cut-off scores that can be easily utilized by teachers, parents, and other researchers. In terms of the analysis of weaknesses, children with dyscalculic tendencies obtained relatively lower scores in arithmetic calculation, number line estimation, and verbal Arabic matching tasks. These weaknesses favored the approximate number system (ANS) deficit and access deficit hypotheses of dyscalculia which supported the assumption of multiple deficit hypothesis. To add support, using the K-means clustering approach, five distinct profile clusters of children with dyscalculic tendencies were identified. Finally, in terms of children's experience in the use of the mobile application, the children had high level of engagement and overall satisfaction as indicated by their enjoyment and interest in completing all the tasks. Likewise, the app quality in terms of functionality and aesthetics were evaluated to be very good. Hence, resulting in an overall positive experience. The use of the mobile application screening tool is highly recommended to mathematics teachers and parents for the initial identification of dyscalculic tendencies among children. To strengthen the psychometric properties and the quality of the instrument, measures of concurrent and predictive validity, sensitivity, specificity, and continuous norming and testing in a larger population could be explored.
Conceptual and Procedural Knowledge in Proportional Reasoning of Undergraduate Students

( 2013) Noche, Joel Reyes

This study investigated the causal relationships between conceptual and procedural knowledge in mathematics using an East Asian perspective. In particular, it studied if supplemental self-paced instruction that focuses on the mastery of either concepts or procedures through repetition with variation helps young adults improve their performance in tasks designed to assess their proportional reasoning understanding and skills. It also studied if a task’s type of physical principle of type of mathematical principle influences the effects of a type of instruction. This experimental research used a pretest-posttest control group design with participants randomly assigned to three groups (conceptual, procedural, and control). The participants were 46 undergraduates (mostly freshman) from three sections of a college algebra course in a private, Catholic, coeducational university in the Bicol Region. The pretest/posttest consisted of 69 multiple-choice questions that varied in physical and mathematical principles. Each participant in the two treatment groups was to answer one worksheet per day for eleven consecutive days. The worksheets for the conceptual group involved non-numeric tasks and those for the procedural group involved numeric tasks. Because of the small sample size, a non-parametric two-tailed test of hypothesis (Kruskal-Wallis one-way analyses of variance by ranks) was used. There was evidence that supplemental procedural instruction significantly differed from supplemental conceptual instruction and from the absence of supplemental instruction in affecting the degree of procedural knowledge. There was no evidence that the type of supplemental instruction affected the degree of conceptual knowledge, or that the type of physical principle or the type of mathematical principle affected how a type of supplemental instruction affected the degree of conceptual knowledge. Future studies using larger sample size and a longer treatment period could provide additional evidence for this study’s findings.
Design Research Approach in Developing Technology-mediated Learning Modules in Practical Mathematics for Technical Vocational Education

( 2020-07-24) Aves, Benedicto Norberto V.

This study aimed to develop technology-mediated learning modules in practical mathematics for the technical vocational track of the K to 12 curriculum using the design research model of Mckenney and Reeves (2003). It also sought to: a) characterize the these learning modules in terms of the selected design principles; b) determine their effectiveness; c) determine how beneficial the design research approach is in developing these modules compared to a traditional curriculum development approach; d) compare the practical mathematics test scores of the design research group and comparison group; and e) make improvements on the learning modules. The theoretical and practical outputs of the study are of significant use to curriculum developers, mathematics teachers, technical vocational schools, and practitioners of design research. Two iterations were done in developing the modules, where data were gathered from randomly selected samples form a private sectarian college using researcher-made instruments. Test results indicated a non-significant difference in the gain scores of the design research group and the comparison group. However, research participants’ assessment of the modules show that the modules developed using the design research were effective in learning practical mathematics concepts. The focus group discussion with research participants and the review of the subject expert both show preference in the modules developed using design research. The study thus recommends the use of design research in developing technology-mediated learning modules in mathematics for the technical vocational track of the K to 12 curriculum, and the use of its practical output in the online learning and teaching of practical mathematics concepts.
Enhanced-Group Moore Method: Effects on Van Hiele Levels of Geometric Understanding, Proof-Construction Performance and Beliefs

( 2007) Salazar, Douglas A.

This study aimed to improve the van Hiele levels of geometric understanding, enhance proof-construction performance and determines the beliefs about proofs of the prospective mathematics teachers using the Traditional Method (Instructor Based) and the Enhanced-Group Moore Method. The impact of the two teaching methods was analyzed to find out which would yield better results in terms of raising van Hiele levels and enhancing beliefs about proofs and proof-construction performance. The study used the quasi-experimental method of research and employed qualitative and quantitative analysis. The Bachelor of Secondary Education (BSEd) major in Mathematics students (20) officially enrolled in Math 233 (Plane and Solid Geometry) at a State University in the Eastern Visayas were the subject of this study. These future teachers were alternately distributed into two groups (control and experimental) based on their ranked mean grade on their prerequisite subjects (Basic Mathematics and College Algebra). The two groups were comparable in terms of their mathematical ability. The study used three instruments, the van Hiel Geometry Test, the Proof-Construction Test and the Proof Beliefs Questionnaire. Given some limitations of the study, the Enhanced-Group Moore Method raised a higher van Hiele level (from level 1 to 3) of the future teachers compared to the Traditional Method (from level 1 to 2). The proof-construction performance of the prospective mathematics teachers was improved from clueless to intermediate which was better compared to that of the control group (from clueless to novice). In regard to the future teachers’ beliefs about proofs, they believed that a theorem has no exception, the dual role of proof is to convince and to explain and the validity of proof depends on its internal logic. Quantitative results revealed that there was a significant difference in the van Hiele levels and proof-construction performance of the future mathematics teachers before and after the study. The future teachers exposed to the Enhanced-Group Moore Method yielded better results in terms of van Hiele levels and proof-construction performance compared to those exposed to the Traditional Method (Instructor Based). In addition, there was a significant relationship between the proof-construction performance and van Hiele levels of the future teaches in the experimental group. However, no noteworthy changes occurred in the future teachers’ beliefs about proofs. Qualitative assessments showed that the Enhanced-Group Moore Method created the “damay effect”, helped develop self-confidence, effective communication, and exchange of idea among future mathematics teachers. It also developed the values of sharing and helping others and both groups expressed their difficulties in proving theorems attributed to poor prerequisite skills. They prefer the two-column form of proof associated to direct proof compared to the paragraph form which they associate to proof by contradiction. The future teachers from both groups were in favor of the sequence of the presentation of the lesson and were agreeable to the incentives given.
Institutional Characteristics, Mathematics Teacher Educator Qualities and Extent of Curriculum Adaptation

( 2016-05) Tamoria, Ferdinand V.

The study aimed to explore institutional characteristics, qualities of mathematics teacher educators (MTEs), and extent of curriculum adaptation by an institution and by MTEs as to adaptation time, compliance level, and degree of innovation in adapting the revises Bachelor of Secondary Education-Mathematics (BSEd-Math) curriculum, as well as the effects of institutional characteristics and MTE qualities on the extent of curriculum adaptation at the institutional and classroom levels. At the classroom level, curriculum adaptation by the MTEs focused on the use of inquiry mathematics teaching and technology integration in their BSEd-Math classes. Combining qualitative and quantitative approaches, the mixed-methods research was conducted in 10 state teacher education institutions (TEIs) in Central Luzon offering the BSED-Math curriculum. Initially, survey data were collected from 10 administrators and 37 MTEs from the 10 states’ TEIs. For the follow-up inquiry, one low-performing, one middle-performing, and two high-performing institutions were selected based on the numbers of their BSED-Math graduates and percentages of passers in the Licensure Examination for Teachers in the last five years prior to the survey. Data were gathered through interviews with MTEs and BSED-Math students, classroom observation, and related documents. The content-validated survey instruments were tried out in two satellite campuses of a state university in the Region, yielding acceptable Cronbach alpha coefficients (0.77 to 0.85). Triangulation was used to establish the credibility and authenticity of the information. Qualitative data were content analyzed and coded using appropriate rubrics for quantitative treatment. Quantitative data were analyzed using descriptive statistics, linear regression, and correlation. Critical comparative analysis was also used to explores the underlying factors of curriculum adaptation at the institutional and classroom levels. Typically, the Level III accredited multi-campus state TEIs with corresponding budget allocations from the national government showed prompt adoption, high compliance, and moderate innovation in their adapted BSED-Math curricula. The MTEs generally indicated eclectic views and practices that emphasized both traditional and inquiry teaching, as well as high levels of self-efficacy and technological pedagogical content knowledge (TPCK). Likewise, they typically indicated early adoption, moderate compliance, and high innovation in inquiry teaching; but late adoption, low compliance, and moderate innovation in technology integration. Teachers, students and administrators shared categorically similar perceptions about the MTEs’ high innovation in inquiry-based activities but low to moderate use of technology integration. In general, data from the respondents and related documents provided support of the extent of curriculum adaptation by the TEIs and MTEs. From the combined analysis of quantitative-qualitative data, institutional factors of curriculum adaptation include accreditation, structural setup, budget and resources, as well as leadership of administrators, number of qualified faculty, stakeholder participation, and external linkages. However, only the number of accredited programs had a significant effect on compliance level. Meanwhile, significant factors affecting teacher adaptation are self-efficacy and TPCK, as well as attendance in and conduct of seminars and training. Additional factors of classroom adaptation drawn from the qualitative data include teaching philosophy, readiness for innovation, and creativity, as well as recurrent themes like professional development, administrative support, availability of resources, and cognitive demand of subjects. Suggestions for improving policy and practice were recommended for the TEIs to intensify accreditation and upgrading of facilities with the active participation of stakeholders, for the MTEs to continuously improve their qualities like self-efficacy and TPCK for effective curriculum implementation in their classes, and for the national agencies and recognized centers to continue assisting the TEIs through faculty development and curriculum revision in view of the ASEAN integration. Recommendations for further research include the conduct of studies with similar or modified research designs, selection of larger sample sizes with random sampling, use of more objective measures, and inclusion of other variables associated with curriculum adaptation to address reliability, credibility, validity, and generalizability of results.
Mathematics Pedagogical Content Knowledge of Pre-Service Teachers and Didactics in Mathematics Course Prototype

( 2014) Conde, Rosie L.

The Philippines’ future elementary and secondary teachers ranked among the bottom compared to other countries around the world in the three areas of Mathematics: Algebra, Geometry, and Number according to the Teacher Education Development Study in Mathematics (TEDS-M) of 2008. In particular, our country ranked 8th or 9th out of 10 in terms of Mathematics Content Knowledge (MCK) and Mathematics Pedagogical Content Knowledge (MPCK). These findings of TEDS-M manifest the low levels of understanding of Filipino future teachers in the basic content and content pedagogic skills in Mathematics. This study aimed to provide an intervention to the teacher education programs in response to the dismal results in TEDS-M 2008. The intervention is called the Didactics of Mathematics Course (DMC). The study developed a DMC prototype which may be replicated to help improve the Mathematics Pedagogical Content which may be replicated to help improve the Mathematics Pedagogical Content Knowledge (MPCK) of pre-service teachers to develop MPCK. Courses in MPCK are part of pre-service teacher education programs in most countries around the world. MPCK courses such as Didactics of Mathematics, History of Mathematics, Problem Solving, Teaching Algebra, and Teaching Geometry are staples in some countries (e.g., Korea, Germany, France, Denmark, and Spain). These courses are timely for future mathematics teachers in the Philippines as the country begins implementing the new K to 12 Basic Education Curriculum. Moreover, the DMC created for this study focused on teaching Instrumentation in Mathematics within the notions of the Anthropological Theory of Didactic (ATD) as Didactics of Mathematics Course using Research and Study Course (RSC) approach and praxeologies. The participants of the study were the 28 pre-service teachers with 75% female and 25% male in a state university in Butuan City enrolled in the Second Semester of SY 2012-2013 and in the First Semester of SY 2013-2014. This study utilized the design study approach in developing DMC Prototype which is composed of three phases namely: 1) needs and content analysis: preliminary research; 2) prototyping phase: iterative cycles of design and formative evaluations; and 3) assessment phase: semi-summative evaluation. Thus, DMC is a product of cyclic process. It is a course that could be taken by future teachers in their preparatory programs. Moreover, using quasi-experimental methods, the study also probed the effects of DMC on pre-service teachers’ MPCK. The study adopted the pre-test-post-test group design and the data was analyzed using Wilcoxon Signed Rank Test. It also used qualitative and quantitative research methods. It was concluded that the DMC Prototype is valid, practical, implementable, and effective. Results showed that DMC enhanced the pre-service teachers’ MPCK (z = -2.96, p = .003). Integrating the Didactics of Mathematics Course (DMC) in the pre-service teacher education not only enhances their MPCK but it also provides pre-service teachers with substantial professional opportunities and thus upgrades their skills in teaching mathematics inside the classroom.
Nontraditional Problem Solving for Developing and Assessing Critical Thinking, Affective and other Cognitive Skills of Students

( 2004) Raffinan, Corazon C.

This study compared the effects of the nontraditional problem solving or problem-based approach and the traditional or algorithmic approach on students’ critical thinking skills, conceptual knowledge in mathematics, competence in problem-solving, attitude and confidence towards mathematics and problem solving, and their learning patterns and behavior. Both approaches included the use of non-routine mathematic problems, small-group discussions, journal writing, and a free choice of appropriate problem-solving techniques in solving given problems. While the nontraditional problem-solving approach introduced concepts by using problem situations, the traditional approach introduced concepts by using problem situations, the traditional approach introduced the same concepts mainly through lecture discussions. Research-designed lessons were used to implement and assess the treatments involved. The study used the quasi-experimental method of research and employed both qualitative and quantitative analyses. Two intact classes consisting of a total of 100 students enrolled in College Algebra I during the second semester of AY 2001-2002 in the University of San Carlos, Cebu City, were the subjects of the study. These students were classified as high ability and low ability on the basis of their IQ scores. The students in both the experimental and control classes showed initial comparability on all the factors being compared. The performance scores improve after the students were exposed to their respective treatments. Based on the pretest-to-posttest measures, which contained more algorithmic items, the difference in gains between the two classes was significant in favor of the control class with respect to conceptual knowledge. In terms of problem-solving abilities, the results were significant at p =.10 in favor of the experimental class. Although the results did not differentiate significantly in the critical thinking skills and the confidence and attitude towards mathematics and mathematics problem solving between the experimental and control groups, the qualitative results showed that the trend was still in favor of the experimental class. The qualitative assessment done on the performance of each member of representative students of the respective classes indicated that the experimental group generally outperformed the control group. This was indicated by the former group’s numerically higher scores and better-quality solutions and responses which manifested their critical thinking skills, conceptual knowledge, and problem-solving abilities. Journal entries, interview protocols, and observation notes also indicated that there was a raised level of motivation and enthusiasm in solving mathematics problems among the students of the experimental class as compared to the control class in spite of the former group’s disadvantage with respect to the class schedule. The overall assessment of the data showed these benefits obtained by the students exposes to the treatment: an indicated increase in the frequency of critical thinking skills indicators in their overall performance; a better understanding and retention of the concepts covered in the course; improved problem-solving abilities and better quality of problem-solving solutions presented; a more positive attitude and confidence towards mathematics and mathematics problem solving; and positive changes in the learning patterns and behavior of the students. The results also show that with respect to problem-solving abilities between different ability levels and different gender types across treatments, the difference between the mean scores obtained by the male student groups of the two classes was significant at p =.10 in favor of the males from the experimental class; between the high ability groups of the two classes, the difference is very significant in favor of the experimental group. No significant difference was found between the low ability groups from the two classes: neither from the female groups of the two classes. The nontraditional problem-solving approach in the classroom increased the students’ confidence in their ability to solve problems, which in turn improved their overall performance in the course. The teacher became aware that students can show and improve their capabilities in problem-solving if allowed to solve these using their own chosen technique with the help of peers. The teacher also became more aware of the thinking process of the students, which allowed her to make connections at improving understanding of concepts using the students’ point of view as jump-off point.
Realistic Mathematics Approach, Mathematical Communication and Problem-Solving Skills of High-Functioning Autistic Children: A Case Study

( 2012) Kalaw, Maria Theresa

This study involved an investigation of the effectiveness of the Realistic Mathematics Education (RME) approach in developing mathematical communication and problem-solving skills of six children diagnosed with autism but classified as high functioning. The RME approach, a research-based instructional pedagogy based upon real-life experiences was implemented over the course of two months. The A-B-A Single-Subject research design was employed using the principles of discrete trial training to mark the students’ progress. The researcher recorded the level of assistance needed to accomplish given tasks in the areas of mathematical communication and problem-solving. Two sets of data were analyzed to determine the effectiveness of the independent variable (intervention lessons). The first data consisted of pre and post-test performance of the students evaluated using a rubric created by the researcher. The second data consisted of baseline, intervention and post-intervention performance of the students collected through recorded video clips and classroom observation forms filled up by the researcher. A total of six students (five males and one female) with high functioning autism (HFA) whose ages ranged from 8 years and 0 months to 10 years and 0 months participated in this study. The six subjects were observed under the baseline condition until the dependent variable stabilized. Then the experimental treatment, three lessons using a realistic mathematics approach, were introduced by the teacher participants and the subjects were again observed to determine whether a change occurred in the mathematics communication skills and the problem-solving skills of the children after the implementation of the RME approach. The study showed that the training of teachers and the exposure of the students to the RME approach led to an improvement of the students’ ability to communicate mathematically and solve problems meaningfully.
Situated-Cognition Model in Teaching Mathematical Problem Solving Skills and Their Transfer to Other Domains

( 2008) Costillas, Juanita M.

This study primarily aimed to determine the effects of the situated-cognition teaching model on the mathematical problem-solving skills of the students and their extent of transfer of these skills to other domains, namely Analytic Geometry, Solid Mensuration and General Chemistry. This study specifically compared the mathematical problem-solving skills and the extent of transfer of these skills to other domains of the students exposed and not exposed to be situated-cognition teaching model. Moreover, the study also investigated if English proficiency moderated the problem-solving skills and extent of transfer of the skills to other domains. The study used the Non-Equivalent Control Group Design with two intact classes of first-year engineering students enrolled at SLSU in the first and second semesters of the academic year 2007-2008 as the research subjects. A total of 42 hours of instruction called Enrichment Math for each of the two groups, (the experimental-BSME and BSEE and the control-BSCE), was conducted in a regular schedule of the same time slot and room and taught by the researcher herself. The contents considered were problem in Arithmetic, Advanced Algebra and Trigonometry. The instruments used include a Semantic Differential Scale for Content Validation of the pretest/posttest, then the Formative Tests, and interview schedule, 28 situated teaching plans for the experimental group, journals and the problem-solving tests in the other domains. Within the framework and delimitations of the study, the situated-cognition teaching model posted significantly better mathematical problem-solving skills (p-value=0.023) than the conventional teaching model. The situated-cognition model affected significantly better extent of transfer of the problem-solving skills to General Chemistry (p-value=0.000) with 58% of the students in the experimental group who were able to solve until the fourth phase of step of Polya’s framework (“Looking Back”) against only 23% from the control group. The conventional teaching model showed a significantly better extent of transfer of problem-solving skills to Solid Mensuration (p-value=0.033). No significant difference was found on the extent of transfer of problem-solving skills in Analytic Geometry. Moreover, English proficiency moderated the mathematical problem-solving skills of the students; those with higher English proficiency tended to have better problem-solving skills. English proficiency significantly moderated the extent of transfer of these skills to other domains, in Solid Mensuration (p<-0.05) and in General Chemistry (p<0.01). No interaction effect was found between English proficiency and the teaching model used.
Students' 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.
Teacher Mathematical Pedagogical Content Knowledge, Student Learning Style, Instructional Plan, and Classroom Interactions in Mathematics: A Multi Case Study

( 2021-08) Orteza, Flordelina Jr. C.

This multiple case study examined the interaction patterns in selected Grade 8 mathematics classrooms in a science high school through a systematic observation approach of the most prevalent classroom interactions of the students and teachers. It also determined how these interactions differed by student learning style and by teacher mathematical pedagogical content knowledge (MPCK). Three Grade 8 classes and their teachers participated in the study. Data were collected using the interaction patterns instrument, classroom observation snapshot, questionnaires, interview guides, tests, and the instructional plan rubric. Content analysis was performed on classroom interaction patterns, classroom observation snapshots, instructional plans, and interview transcripts. A thematic analysis was also performed to examine interaction patterns. Resuits show that the most prevalent classroom interactions were scaffolding student learning (teacher-initiated) and initiating unnecessary remarks/behaviors (student-initiated). It was also observed that mathematics classes were still teachercentered and students were predominantly auditory and kinesthetic. Furthermore, the three teachers had almost the same level of MPCK and the same most prevalent classroom interaction pattern-scaffolding student learning. Teacher MPCK also influenced instructional planning of teachers. The study further found that experienced teachers considered the student learning style in instructional planning and novice one considered it even while in the process of implementing the instructional plan.
The 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.

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