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Item Reading comprehension and ability in solving word problems in basic mathematics(2011-02) Calub, Reynaldo CerezoOne of the topics taught in mathematics is solving word problems. Since the medium of instruction in mathematics is English then the students ability in solving word problems may be related to their knowledge of the English language particularly their level of reading comprehension as solution of word problems require their translation into the right mathematical phrases or equations. The main purpose of the study was to determine if there is a significant relationship between reading comprehension and word problem solving in basic mathematics. It also sought to find out the ability of the respondents in reading comprehension and word problem solving. The respondents of the study were 142 HRM/HRS freshmen students of the Urdaneta City University in the first semester of 2010-2011. Separate multiple choice type tests in reading comprehension and word problem solving in basic mathematics were administered to the respondents. The arithmetic means of the respondents' scores in the tests were used to determine their competencies in the said areas based on the rating scale presented under data gathering procedure. 1. The respondents have poor reading comprehension and they lack English communication skills which in turn indicates that they have poor foundation and knowledge of the English language. 2. The respondents as a whole have difficulties in solving word problems in basic mathematics. 3. There is a significant correlation between the reading comprehension and word problem solving in basic mathematics of the respondents. In light of the findings of the study, the following are the conclusions: 1. Majority of the respondents have a poor level of reading comprehension. 2. Majority of the respondents have a poor level of word problem solving ability in basic mathematics. 3. There exists a significant relationship between reading comprehension and word problem solving ability in basic mathematics. In relation with the findings and conclusions of this research, the following are recommended: 1. To enhance the students' reading comprehension skills, they must be taught how to decipher word meanings through the use of context clues, word relationship, and part of speech. They must be taught how to establish meaning of text content through the use of various techniques such as visualizing and summarizing. Students must be encouraged to develop good reading habits and consult the dictionary for unfamiliar words encountered to enrich their vocabulary knowledge. Emphasis must be given to the importance of meaningful reading in acquiring knowledge from books and other reading materials. 2. To improve the students' word problem solving ability in basic mathematics, teachers must provide students enough classroom activities such as practice exercises/drills on mathematical operations of fractions, ratio and proportion, and percent. It is important that they have adequate numerical competence prior to the introduction of word problems. 3. The teacher must familiarize students with the key words associated with addition, subtraction, multiplication, and division to facilitate translation of word problems into the required mathematical phrases or equations. 4. The teacher must present a variety of heuristics; heuristics are methods or strategies that increase probability of solving a problem. An example of which is teaching the students a systematic, step-by-step approach in solving word problems. 5. To familiarize the students with the different strategies in solving word problems, the teacher must present similar types of problems with similar solving strategies at a time. Students should be divided into groups in solving word problems since group efforts can be less threatening to students than working individually. 7. Teacher must start with simple problems that can easily be solved by the students. This builds the confidence of students when they experience success in solving word problems quickly. 8. Teachers must be aware of the advancements and developments in the teaching of mathematics by attending lectures and seminar-workshops in the improvement of the quality of Mathematics Education. 9. The action plan focusing on the following must also be considered: a. Administration of reading comprehension test at the beginning of the semester to gauge the students reading comprehension ability. b. Workshop on Reading Techniques using Context Clues, word relationships and parts of Speech. c. Seminar/Workshop on the teaching methods in mathematics.Item Mathematical procedure and field readiness of PMA cadets(2017-12) Carual, Norman Avila.Once cadets graduate from the Philippine Military Academy (PMA), they will be deployed to the different field units of the Armed Forces of the Philippines (AFP) to defend the country. PMA graduates are expected to be highly competent in military skills and ready to lead soldiers in combat and their successful career depends upon their ability to assimilate knowledge from many fields and to apply it to a wide variety of social and technical problems. As military leaders, they are mandated to think critically and evaluate the c-uality of their decisions with the current challenges the country is facing. It has been settled that mathematics and the ability to use it are particularly important to military officers, who are leading soldiers in a complex and dynamic world. Mathematics course success has a significant relationship between students' critical thinking and problem solving skills and this could be equated to their readiness on This study aimed to take the relationship between mathematical performance and field duty readiness of PMA cadets. Specifically, this sought answers to the following: 1. What is the level of mathematical performance of PMA cadets along the areas of: a. College Algebra b. Plane Trigonometry c. Analytic Geometry d. Elementary Analysis? 2. What is the level of field duty readiness of PMA cadets along the areas of: a. Military Leadership b. Military Science? 3. What is the relationship between the levels of mathematical performance and field duty readiness of PMA cadets? Hypothesis: There is a relationship between the levels of mathematical performance and field duty readiness of PMA cadets. This study used the descriptive-correlational type of research to determine and correlate the level of mathematical performance of cadets based on their grades as obtained from the Office of the Registrar, and their field duty readiness based on their grades in military courses and through a survey questionnaire. The gathered data were statistically treated using mean, weighted mean, Pearson-Product Moment Correlation Coefficient, and Coefficient of Determination. The respondents of this study were the 238 first class or graduating cadets from the original class strength of the Philippine Military Academy Class of 2018. The following are the major findings of the study: 1. The overall level of mathematical performance of PMA Class 2018 cadets is satisfactory. They obtained an above average level of mathematical performance in Analytic Geometry while satisfactory level of mathematical performance in College Algebra, Plane Trigonometry, and Elementary Analysis. 2. The level of field duty readiness of PMA Class 2018 cadets is very good. They obtained an excellent level of field duty readiness in the area of military science while very good level of field duty readiness in the area of military leadership. 3. The level of mathematical performance of PMA Class 2018 cadets has a significant relationship with their field duty readiness. In light of the findings of the study, the following are the conclusions: 1. The PMA Class of 2018 cadets has a fair mathematical performance in general. Though they have a very good understanding of Analytic Geometry, the cadets were challenged in College Algebra, Plane Trigonometry, and Elementary Analysis. 2. The PMA Class of 2018 cadets is highly ready to lead soldiers in the field and they are well-equipped for their future role as military officers. 3. The level of mathematical performance of PMA Class of 2018 cadets significantly influences their field duty readiness. In relation with the findings and conclusions of this research, the following are recommended: 1. A connection between instructors and cadets has to be created in order to produce a lively discussion and interaction inside the classrooms to improve the mathematical performance of the cadets. 2. Sustainment of the different aspects of the military training for the cadets to maintain desirable field duty readiness. 3. Since mathematical performance is an indicator for field duty readiness, cadets need to give importance on their mathematical performance.Item Learning psychology and learning performance of students in college Algebra(2015-05) Benis, Vanessa Ganipis.Mathematics education is one of the most challenging fields in terms of students' ability to perform and retain substantial knowledge and skills that would aid them in real life situations. Hence, improving mathematical performance for all students is an important policy issue and educational concern (Gales & Yan, 2001). As claimed by Soon, Lioe and McInnes (2001): Students have problems seeing the connection between real life contexts and mathematical representations. The learning of students is affected by what is emphasized in mathematics classrooms. Either a teacher focuses on developing a conceptual knowledge or a procedural skill. On the other hand, a person's learning psychology determines his/her beliefs and practices. Since learners have varied backgrounds and upbringings, it is expected that they have diverging learning psychologies. The ways they perceive mathematics education vary in a sense that they have different emphasis on how to acquire learning. As supported by the claims of Anderson, Reder and Simon (1999) on their study of Applications and Misapplications of Cognitive Psychology to Mathematics Education: Behavioural psychology has given way to cognitive psychology (based on models for making sense of real-life experiences), and technology-based tools have radically expanded the kinds of situations in which mathematics is useful. The study focused on comparing the differences of the learning performances of learners in terms of conceptual knowledge and procedural skills in college algebra based on their learning psychology. The main aim of this study was to determine the differences in the learning performance of freshman Accountancy students based on their learning psychology in college algebra. Specifically, the study answered the following: 1. What are the learning psychologies of the students? 2. What is the level of learning performances of students in college algebra in terms of conceptual knowledge, procedural skills and overall learning? 3. What is the difference in the level of learning performance of student in terms of conceptual knowledge and procedural skills? 4. What is the difference in the levels of learning performance of the students based on their learning psychology according to conceptual knowledge, procedural skills, and overall learning performance? 5. What teaching and learning guides would be proposed to enhance the level of learning performances of students in both conceptual and procedural skills in college algebra? The major findings of the study are the following: 1. There are more freshman Accountancy students who are behaviorist learners as compared to the number of constructivist learners. 2. Freshman Accountancy students performed on a high level in terms of procedural knowledge but at a low level in terms of conceptual knowledge in college algebra. 3. There is a significant difference in the procedural skill and conceptual knowledge of students in college algebra. 4. No statistical differences were found in the learning performances of students based on their learning psychologies. Based on the findings of the study, the following are therefore concluded: 1. Most freshman Accountancy students focus their learning by changing and conforming their behaviours and responses towards stimuli and reinforcements presented and expected by teachers, classmates, and learning environments in college algebra. 2. Freshman Accountancy student are able to perform well in terms of executing procedures and algorithms to solve mathematical problems but are not well-versed in applying or relating conceptual understanding and developing connections and networks of concepts in college algebra. 3. The procedural performance of freshman Accountancy students is higher than their conceptual performance in college algebra. 4. The learning performances of constructivist learners and behaviourist learners are at similar levels in terms of procedural skills and conceptual knowledge in college algebra. After a careful review of the findings and analysis of data, the following recommendations are forwarded: 1. Factors affecting the development of a learner's psychology in college algebra have to be identified and analyzed by determining their effects to a learner's learning psychology. Teachers have to be aware as well of the learning psychology of his/her students in order to be able to conduct necessary approach for both learning psychologies. 2. The levels of learning performances of students in terms of procedural and conceptual knowledge have to be gathered by teachers as a basis for knowing the strengths and weaknesses of learners and for guidance in determining the focus, the instruction, and the assessment to be used and to locate where to continue development. 3. Procedural instruction has to be supplemented by conceptual instruction in order to enhance the balance between procedural and conceptual performance in college algebra. Curriculum developers and teachers have to gain knowledge and skills on how to incorporate conceptual instruction and assessment in their algebra classes. 4. Although there are no significant differences in the learning performances of learners in terms of conceptual knowledge, procedural skills, and overall performance based on their learning psychology, beneficial practices and beliefs of each learning psychology have to be pursued by teachers and researchers to improve both conceptual knowledge and procedural skills in college algebra. Math teachers and curriculum developers have to further understand and analyze the relationship between procedural skills and conceptual knowledge in college algebra for them to be able to implement improved and effective plans. 5. Other recommendations: a. The correlation of a learner's learning psychology to his/her learning performances in terms of conceptual knowledge and procedural skills in college algebra is recommended. b. Another study to pursue is an experimental study in determining the effectiveness of conceptual approach in teaching as compared to procedural approach in college algebra. c. A study on the existing perceptions and biases of students regarding the value and usefulness of conceptual knowledge versus procedural knowledge in college algebra is highly advocated for a study. d. The study could be replicated in other fields of mathematics and other subject areas. e. The adoption of the teaching and learning guide for propounding balance between conceptual knowledge and procedural skills in college algebra for both teachers and learners is recommended.Item Factor correlates of mathematics achievement of the Philippine Science High School (PSHS) freshman students(2013-05) Bastian, Maria Cecilia Colar.Mathematics education is to a nation what protein is to a young organism. As protein is needed for physical growth, mathematics education contributes greatly to nation building. This is because education essentially defines the quality of human capital on which depend the wise use of the natural resources and monetary capital of a nation. If the quality aspects of education is continually ignored, then the important role of education cited above is completely ignored. For students to be computationally fluent to carry out mathematical procedures flexibly, accurately, efficiently and appropriately, an effective mathematics program is a dire need. A program that allow students to learn to reason and communicate mathematically, value mathematics, and become confident in their own mathematical abilities to solve problems helps in the growth of a nation. Aside from developing an effective mathematics program, it is also important to assess an existing mathematics teaching-learning situation by determining the mathematics achievement of the students and investigating factors that are influential to such achievement. Results of such assessment and investigation will give administrators a concrete basis for important decisions in the selection of scholars and in enhancing the existing curriculum. Likewise, based on the gathered information, teachers will be able to better apply approaches, methods, strategies and activities that will bring out the best in every student thereby improving the student's level of mathematics achievement. The generated result may also lead parents to be better involved in the mathematics education of their children thus building a better support system for their children. Lastly, this study is geared to provide the students essential information that will challenge and inspire them to maximize the learning opportunities offered in their respective mathematics classes from the proposed Mathematics Achievement Enhancement Plan (MAEP). Studying the factor correlates of the mathematics achievement of the respondents in this study is but a step towards mathematics achievement and in the years to come, nation building. The study dealt with the assessment of the level of mathematics achievement of the PSHS Freshman Students in Elementary Algebra. Specifically, the study sought to answer the following questions: 1. What is the level of mathematics achievement of the PSHS freshman students in Elementary Algebra? 2. What is the degree of relationship between the level of mathematics achievement of PSHS freshman students and the following factors: a) sex; b) type of elementary school graduated from; c) mathematics 6 achievement; and d) National Competitive Examination (NCE) achievement in mathematics? Hypothesis: There is a significant correlation between the level of mathematics achievement and the following factors: a) sex; b) type of elementary school attended; c) mathematics 6 achievement; and d) National Competitive Examination (NCE) achievement in mathematics. 3. What action plan can be formulated to improve the mathematics achievement of the students? The researcher made use of descriptive-correlational method. Participants in this study were the 80 freshman students of the Philippine Science High School CAR Campus. The level of mathematics achievement in elementary algebra was determined using a teacher made-test guided by a table of specification found in Appendix D. The information about the student's sex, type of elementary school graduated from and mathematics 6 achievement were derived from the students answer sheet during the administration of the teacher-made test. The student's National Competitive Examination (NCE) achievement in mathematics was retrieved from the PSHS-CAR Campus Registrar's office. The weighted mean was used to determine the level of mathematics achievement of the respondents. The Point-Biserial Correlation and the Pearson Product-Moment Correlation were used to determine the degree of relationship between the level of mathematics achievement and the specified variables. Microsoft Excel was utilized in all computations. Findings in the study concerning the PSHS freshman students reveal the following: 1. The PSHS-CAR freshman students manifested a good level of mathematics achievement in Elementary Algebra. 2a Sex had a slightly high correlation with the level of mathematics achievement. 2b The type of elementary school graduated from had a slight correlation with the level of mathematics achievement. 2c Mathematics 6 achievement had a positive slightly high correlation with the level of mathematics achievement. 2d The National Competitive Examination (NCE) achievement in mathematics had a positive moderate correlation with the level of mathematics achievement. From the foregoing findings and results of this study, the following conclusions are drawn: 1. The PSHS-CAR students have an average performance in Elementary Algebra indicating that they have a good grasp and understanding of the essential mathematical concepts of the said subject. 2. The degree of relationships between the level of mathematics achievement and the specified factors is varied. The National Competitive Examination (NCE) achievement in mathematics had a substantial relationship; sex and mathematics 6 achievement presents a small but definite relationship; and the type of elementary school graduated from do not have a significant relationship with the level of mathematics achievement in Elementary Algebra. Based on the findings and conclusions, the researcher posits the following recommendations: 1. To acquire better levels of mathematics achievement in elementary algebra, students should consider all content learning areas equally important by giving each the appropriate time needed. This will likewise help students become more confident, competent, engaged and persistent problem solvers. The result of the teacher-made test may also serve as a credible basis regarding what the teacher should do in terms of methodologies, strategies and emphasis. Teachers may refer to appendix H which contains the level of mathematics achievement along the content areas of Elementary Algebra. This will help them in allocating the necessary time and resources and the degree of emphasis needed for each content area. Emphasizing the vital role of effort and determination hand-in-hand with innate ability in mathematics achievement to the students may also be of greatly help. Also, it is important to conduct faculty enhancement training for mathematics teachers on the necessary strategies and approaches aligned with the K-12 curriculum and teaching context as well as giving due consideration to the type of students they cater to. 2a Teachers and the guidance machinery in the school should encourage more female participation in effective mathematics learning and in mathematics competitions whether within or outside-campus representations. Specifically, it is necessary for mathematics teachers to provide opportunities for male and female students to compete collaborate and learn from one another in Mathematics teaching and learning. In this way, males and females will see each other as equals capable of competing and collaborating in classroom activities. 2b There is a need to review the system used in distributing students to their respective sections. Students who come from either public or private elementary schools should be evenly distributed to the three sections. In this way, they can be given the opportunity to learn together and collaborate with each other thereby making each mathematics class more relevant and meaningful. 2c Aside from looking into their mathematics 6 achievement as basis for early intervention, mathematics teachers should also conduct a diagnostic test as early as the start of each school year. Looking into the students mathematics 6 achievements, validated by the diagnostic of test will help the teacher identify the student's areas o strength and weaknesses. Thus, the teacher can quickly plan courses of action that will help improve future mathematics teaching-learning experiences in the classroom. 2d Having identified National Competitive Examination (NCE) achievement in mathematics as a predictor of mathematics achievement in elementary algebra, the educational leaders should look deeply into the existing system of selecting scholars and thus make amendments/modifications as needed in the selection process. Meanwhile, teachers should go over the student's NCE achievement in mathematics as early as the first week of June in order to identify those students at risk for potential mathematics difficulties. After such move is completed, the teacher then provides the necessary and immediate interventions to students identified as at risk either on a daily or tri-weekly basis. 3. The proposed Mathematics Achievement Enhancement Plan (MAEP) found in Appendix A be considered by the Philippine Science High School (PSHS-CAR) for adoption to help improve the mathematics achievement of the students. 4. Conduct further study to determine the degree of relationship between the level of mathematics achievement and individual factors that can be influential to student achievement such as self-directed learning, self-efficacy and motivation.Item Mathematical proficiency in geometry of high school students(2013-09) Barbado, Silvin A.Geometry is a vital part of mathematics and mathematics is a vital part of one's life. Changes in society and in the use of technology require that one has a strong background in mathematics. The emphasis of which not only on Geometry skills, but on developing one's mathematical power. Mathematical power develops the knowledge and understanding of mathematical ideas, concepts and procedures. It emphasizes the ability to use mathematical tools and techniques in reasoning and thinking critically. It likewise develops the ability to communicate using mathematics in the world beyond the classroom. Education makes people easy to lead, easy to govern. This means development of the Filipino youth so that one can participate and live successfully in a highly competitive and technological world which defines the undertakings of the nation to attain its vision to nurture the educational growth of the Filipino children for better productivity. In a book by the National Research Council (NRC) called Adding It up: Helping Children Learn Mathematics explores how students in grades pre-K-8 learn mathematics. The editors discuss how teaching, curricula, and teacher education should be changed to improve mathematics learning. It also illustrates the five interdependent components of mathematical intertwined strands - conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition - were the critical strands for developing mathematically proficient students. The NRC's five strands of mathematical proficiency are; Conceptual understanding; a student's grasp of fundamental mathematical ideas. Procedural fluency (computing): skill in carrying out mathematical procedures flexibly, accurately, efficiently, and appropriately. Strategic competence (applying): ability to formulate, represent, and solve mathematical problems. Adaptive reasoning (reasoning): capacity for logical thought, reflection, explanation, and justification. Productive disposition (engaging): habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy The study is all about the Mathematical proficiency of Third year students of Irisan National School, school year 2012-2013. The researcher wondered why students' mathematical proficiency is deteriorating, so the researcher would like to investigate on this area of the mathematical proficiency of student with regards to its five strands, sex and the quarterly scores of the students. As the objective of the researcher is to know the mathematical proficiency of students regarding to the five strands, sex and the quarterly examination score. The main aim of the study was to determine the level of mathematical proficiency in Geometry of the third year students. Specifically, it sought to answer the following problem: 1. What is the level of mathematical proficiency of the third year students in Geometry along the five strands: 1.1.Conceptual understanding, 1.2. Procedural fluency (computing, 1.3. Strategic competence (applying), 1.4. Adaptive reasoning, 1.5. Productive disposition (engaging)? 2.What is the difference on the level of mathematical proficiency of the third year students in Geometry when compared according: 2.1 sex; and 2.1. grades in quarterly examination? Hypothesis: There is significant difference on the level of mathematical proficiency of the students in Geometry when compared according to sex and grades in quarterly examination. The researcher used the descriptive-survey research design. It sought to find the mathematical proficiency of the respondents through the analyses of variable-relationships (sex and quarterly grades). Further, the record of their grades in Geometry for the academic year were used. The mean was computed to determine the level of mathematical proficiency in Geometry along the five strands of mathematical proficiency. The t-test was used to determine the mathematical proficiency level when compared according to sex while Analysis of Variance (ANNOVA) was used to determine the differences in the level of mathematical proficiency according to the quarterly grades. The following are the major findings of the study: 1.The students' level of proficiency in Geometry along the five strands is below average 2.The level of mathematical proficiency of the male and female students is both below average. 3.The mathematical proficiency of the students when classified according to their quarterly grades shows that in the first and second grading period is average while in the third and fourth grading is below average. When classified according to their final grade their mathematical proficiency is average. In light of the findings derived from this study, the following conclusions were deduced: 1.The mathematical proficiency of the students along the different strands of mathematics was predominantly below average. Students at this level can employ basic algorithms, formulae, procedures, or conventions. They are capable of direct reasoning and of making literal interpretations of the results. 2.Sex and quarterly grades of the students has no difference in the mathematical proficiency of the students along the different strands of mathematics. After a careful review of the findings and analysis of data, these recommendations are presented: 1. The students' mathematical proficiency along the different strands of mathematics has to be analyzed to determine the strengths and weaknesses as basis for planning a program of mastery learning along the areas covered. 2. There is a need to improve the mathematical proficiency of the students from below average to above average or higher. This may be done through improved instruction. 3. other Recommendations 3.1 Teachers' professional development has to be high quality, sustained, and systematically designed and deployed to help all students to develop mathematical proficiency. Schools should support, as a central part of teachers' work, engagement in sustained efforts to improve mathematical instruction. This support requires the provision of time and resources. 3.2 The coordination of the curriculum, instructional materials, assessment, instruction, professional development, and school organization around the development of mathematical proficiency should imply school improvement efforts. 3.3 Efforts to improve students' mathematical learning have to be scientifically evidenced, and their effectiveness has to be evaluated systematically and periodically. Such efforts should be coordinated, continual and cumulative. 3.4 Additional researches have to be undertaken on the nature, development, and assessment of mathematical proficiency. 3.5 An action plan is made to further enhance student's mathematical proficiency.Item Analysis on students' common algebraic errors(2019-07) Bantasan, Merino Albano.Algebra has a wide range of applications that open doors to countless opportunities especially for students who are pursuing Science, Technology, Engineering and Mathematics (STEM) Program. This program in the K 12 Curriculum that was implemented in the Philippines in 2013 aims to produce graduates of secondary level who will take science, research, mathematics and engineering - related courses in tertiary level and thereby add to the scientific and scholarly workforce of the country. The introduction of STEM in the Basic Education paved to the way of putting great effort in enhancing students' performance in mathematics particularly in algebra that is considered as a gateway to higher level STEM - related careers (Adelman, 2006 as cited by Booth, Barbieri, Eyer Biagoev, 2014). These careers include Aircraft Operations Aviation, Aeronautical Engineering, Commerce, Civil Engineering, Actuarial Science, Computer Programming, Computer Science, Computer engineering, Accountancy, Industrial Engineering and Data Analysis and Statistics which are the highest paying jobs in the Philippines based on the 2016 Occupational Wages Survey released by the Department of Labor and Employment (Nucum, 2018). However, despite the efforts exerted to improve learning in algebra, researchers have still observed that this is the most difficult for students to grasp because of its underpinning complexities. Researchers like Rushton (2014), Owusu (2015), Shahrill and Matzin (2015) revealed that this difficulty experienced by the students is greatly influenced by different errors they commit when dealing with algebraic problems. Thus, this study highlights on classifying and analyzing algebraic errors of STEM students which will serve as baseline data to design appropriate intervention plan that aims to enhance mathematics learning and pedagogy. This study generally aimed to classify common algebraic errors committed by students currently enrolled in the Third Trimester of the Academic Year 2018 - 2019 in the University of the Cordilleras - Senior High School under the Science, Technology, Engineering and Mathematics (STEM) Program. Specifically, it sought to answer the following questions: 1. What algebraic errors are committed by students along learning contents on a. Exponent; b. Radical; c. Polynomial; d. Linear Equation; and e. Linear Inequality? 2. What is the difference on the frequency of errors committed by the students along a. Exponent; b. Radical; c. Polynomial; d. Linear Equation; and e. Linear Inequality? Hypothesis: There is a significant difference on the frequency of errors committed by students along learning contents on a. Exponent; b. Radical; c. Polynomial; d. Linear Equation; and e. Linear Inequality. Descriptive survey was employed in this study to classify and describe the algebraic errors committed by the students along learning contents on exponent, radical, polynomial, linear equation and linear inequality. The respondents were purposively selected based on their academic performance in their calculus courses which is fairly satisfactory. Data were gathered through a self-made competency test validated by experts in the field of mathematics. The collected data were then subjected for treatment using frequency count that will determine the number of errors committed per learning area and chi-square goodness-of-fit test at 0.05 level of significance that will measure the difference on the frequency of errors committed by the students. The process of triangulation was also utilized to further analyze and verify the findings of the study. The researcher organized a focus group discussion with the students and calculus teachers of the institution. The salient findings of the study include the following: 1. The students who are specifically taking STEM Strand committed different errors in each learning content which were classified into Conceptual Error, Computational Error and Careless Error. 2. There was a significant difference on the frequency of errors committed by the students along learning contents on exponent, radical, polynomial, linear equation and linear inequality. Based on the aforementioned findings, the researcher framed the following conclusions: 1. Science, Technology, Engineering and Mathematics students are not still prepared to succeed higher mathematics courses necessary in their field. 2. Conceptual error is the most prominent type of error committed by the students followed by computational error and careless error, respectively. In view of the findings and conclusions, the following recommendations are hereby posited: 1. There is a need for a diagnostic assessment to entering grade 11 students so that intervention scheme like learning module can be implemented to alleviate algebraic errors. 2. A training on pedagogical strategies and techniques that can refine and enhance student's conceptual understanding may be provided for teachers. 3. A different sample may be considered specifically in other strands or grade level. 4. Further study may explore the sources of these algebraic errors through a qualitative approach so that a profound analysis will be provided. 5. The proposed module may be evaluated for utilization to lessen students' errors when dealing with algebraic problems.Item Cooperative learning in college algebra : a team-achievement-challenge (TAG) model(2011-05) Bulaon, Michael Anthony M.College Algebra is one of the most difficult and feared subjects not only in high school but in college as well. The difficulty lies from the fact that Algebra is an abstract subject where symbols are used to represent unknown numbers. In Arithmetic where everything is concrete, all operations involve numbers without any need for interpretation. In contrast, Algebra involves symbols that need interpretations, concepts, rules and mechanics that should be followed in harmony in order to perform the required tasks correctly. One can imagine a child being taught with concrete things and then suddenly is taught something that is abstract. It is like asking someone to appreciate a painting of a portrait and then asking him to appreciate an abstract painting when he has no idea as to what it represents. This paradigm shift from the concrete to the abstract has confused and frustrated many students of Algebra including UC freshman students. The learning of Algebra requires so much interpretation of these symbols and ideas, understanding of many different concepts, following numerous rules, and knowing the mechanics in applying these concepts and rules. The lecture method can provide much of these tasks though it becomes quite incomplete when all of these tasks are not experienced first hand by the learners. Leherer (2008) cites Dewey, a pragmatist, as having said that the basic fact in learning is that the brain learns by doing. Constructivists believe that children learn when their beliefs or presumptions are challenged by new ideas or knowledge foreign to them. They also believe that children learn by experiencing new things. Cooperative learning, more specifically the TAC model, offers to provide all of these. For one, it is preceded by a lecture to provide the concepts, rules and mechanics. Next, it gives the students the opportunity to make their own examples based on what they have learned; then these are disputed by the other teams in the team challenge. The students are motivated by the team challenges and the rewards, and their individual assessments are measured by the teacher challenge. This study aimed to determine the effect of cooperative learning, more particularly the Team-Achievement-Challenge, in the performance of UC freshman students taking up College Algebra. More specifically, this study wanted to resolve the following questions: 1. What is the performance of UC students in factoring polynomials and simplifying rational and radical expressions before and after the treatment? Hypothesis: The performance of UC students in factoring polynomials, simplifying rational and radical expressions before and after the treatment is average. 2. What is the difference in the performance of UC students before and after the treatment? Hypothesis: The difference in the performance ,of UC students before and after the treatment is significant. 3. What is the difference in the performance of UC students in the TAC model and in the Traditional Method of teaching? Hypothesis: The difference in the performance of UC students in the TAC model and in the Traditional Method is significant. 4. What instructional material can be developed using the Team-Achievement-Challenge (TAC) model to enhance the teaching of College Algebra in UC? The researcher used the quasi-experimental design to compare the effects of the TAC model and traditional method of teaching. More particularly, a matching only pre-test-post-test control group design was used to eliminate as many intervening variables as possible. The subjects of the experiment were from the four Algebra classes of the researcher during the lit Trimester of the school year 2010-2011. There were 49 students each from the two criminology classes, 38 from a business administration class, and 32 from another business administration class combined with criminology students. The researcher managed to match 27 pairs from the two criminology classes and 21 pairs from the two business administration classes, or a total of 48 pairs. The data gathered were statistically treated using frequency distribution, mean, weighted mean, Pearson product moment correlation coefficient, Spearman-Brown whole test reliability, Cronbach alpha, and the t-Test for paired sample mean. The following summarized the findings of this experiment: 1. The performance of UC students in factoring polynomials, simplifying rational and radical expressions was low failing. 2. There was a significant difference in the performance of UC students before and after the TAC model was applied. 3. There was significant difference in the performance of UC students in the TAC model and in the traditional method of teaching as applied to factoring polynomials and simplifying rational expressions. For simplifying radical expressions, the difference in their performance was not significant. Based on the findings, the following conclusions are drawn: 1. The over-all performance of UC students in factoring polynomials, simplifying rational and radical expressions was low failing. For each of the three topics, their performances in factoring polynomials and simplifying radical expressions were both low failing, while for simplifying rational expressions, it was fair. 2. The difference in the performance of UC students before and after the treatment was found to be very significant over-all and for each of the individual topics. 3. The difference in the performances of UC students in the TAC model and in the traditional method as applied to factoring polynomials and simplifying rational expressions were both significant. In simplifying radical expressions, their performance was not significantly different from each other. The TAC model and the traditional method were equally effective when applied to simplifying radical expressions. Therefore, the TAC model was prove to be more effective than the traditional method in increasing the performance of students in two out of the three topics included in the experiment. In response to the conclusions arrived at in the study, the researcher recommends the following actions: 1. Adopt the TAC model and the TAC manual as an additional teaching method and learning tool in teaching College Algebra. 2. Conduct further studies as to the reasons for the minimal advancement in performance of UC students in College Algebra. 3. Conduct further studies on different cooperative learning models in order to determine which model is the most effective in improving the performance of UC students in College Algebra. The researcher also recommends the following to increase students' performances in College Algebra: a. Increase the awareness of students on the importance and application of Algebra in their chosen careers to reduce surface learning by the students. b. Familiarize math teachers with the TAC model in order for them to learn how to use it effectively and appropriately, and become aware of its limitations. c. Students must take advantage and make the most of the TAC model to improve not only their intellectual but their social skills as well.Item Factors influencing the difficulties encountered by freshman high school students in Mathematics(2014-05) Buance, Rufo F.In this new era, the influence of Mathematics can be clearly seen in the life of man even more. The starting point of the development and progress of the other branches of science is the development of Mathematics. Indeed, Mathematics is a response to the changing societal conditions. However, there are many students who cannot comprehend and analyze word problems in Mathematics. Mathematics is generally perceived as a difficult subject. In fact, Mathematics is one of the common subjects having the most number of failing students. Improving the educational system for students with mathematical learning difficulties has been one of the key foci of educational reforms. This led the researcher to focus his study on the factors influencing the difficulty of students in Mathematics. This study determined the factors influencing the difficulties encountered by freshman high school students at San Jose High School for the school year 2010-2011. Specifically, it sought answers to the following questions: 1. What is the level of difficulty of the freshman students in Mathematics along: a. Real Number System; b. Measurement; c. Scientific Notation; d. Algebraic Expressions; and e. First Degree Equations and Inequalities in One Variable? 2. How do the levels of difficulty of the students differ when compared according to gender? Hypothesis: There is a significant difference on the level of difficulty of the students when compared according to sex. 3. What is the extent of influence of the following factors in the difficulties of the students? a. Learner-related factors b. Teacher-related factors c. Learning-environment-related factors 4. What action plan can be developed to minimize student difficulties in mathematics? The descriptive survey method of investigation was used in this study on freshman high school students in Mathematics at San Jose School of La Trinidad-High School Department for the School Year 2010-2011. There were 196 student-respondents chosen through random sampling by lottery with replacement. The survey questions focused on the factors that influence the difficulties of the freshman high school students in Mathematics such as learner-related factors, teacher-related factors, and learning environment-related factors. The data collected were tabulated, computed, analyzed, and interpreted using the appropriate statistical tools. The following were the major findings of the study: 1. As perceived by the respondents, they encountered moderate difficulty in scientific notation, first degree equations and inequalities, and algebraic expression. 2. The male and the female first year high school students do not differ significantly in terms of level of difficulty encountered in Mathematics. 3. The learner-related factors, teacher-related factors, and learning-environment-related factors had little influence on the difficulty of the students in Mathematics. Based on the salient findings, the following conclusions were drawn: 1. Most freshman high school students encounter moderate difficulties in Algebra Mathematics like scientific notation, first degree equations and inequalities in one variable, and algebraic expressions. 2. Sex is not a factor that influences the level of difficulty of students in Mathematics. 3. Learner-related factors, teacher-related factors, and learning-environment-related factors still influence the difficulties of students in Mathematics. In relation with the findings and conclusions of the study, the following were recommended: 1. The freshman students have to enhance their Mathematics skills by improving their reading comprehension and mathematical skills such as manipulating mathematical knowledge and concepts. 2. The male and the female students have to be given the same treatment in dealing with simple and complex mathematical problems. 3.a. The freshman students have to help themselves to overcome their difficulties in learning mathematical concepts in order for them to perform well in the subject. 3.b The freshman Mathematics teachers have to equip themselves not only knowledge of a particular subject matter but also pedagogical knowledge and knowledge of their students. They have to enhance their teaching strategies and develop different kinds of instructional Activities that promote student achievement. 3.c The school environment has to be kept from any disturbance from learning. It has to be a place where the teaching-learning process takes place effectively and smoothly. 4. Other Recommendations: a. The school administration may help teachers enhance their skills by providing avenues for training and seminars in Mathematics teaching. b. Researchers in the future may study on other variables and find out some other factors that affect the difficulty of students in Mathematics.Item Mother tongue-based instruction and academic achievement in some selected topics in grade 1 mathematics(2016-10) Allaga, Ivy Belingon.The perceived problem of low mathematics achievement is an alarming situation for educators. Education requires a flexible teaching approach that responds to the social and cultural contexts that influence the learners' learning experiences, behavior and attitudes. To cope with the varied needs of today's learners, educators are trying to do some paradigm shift in terms of teaching approach. As a result of the rapid changes happening around us, the use of mother tongue as a medium of instruction has become inevitable. For schools to be part of the educational paradigm shift, mother tongue-based education is now being employed in the teaching-learning process. In Nagacadan and Julongan Kiangan Ifugao, where the majority of learners are 'Tuwalis' (Ifugao tribe that speaks tuwali), this calls for a teaching approach that promotes the use of mother tongue education in the foundation phase. This study emphasizes mother tongue as the language of learning and teaching in the foundation phase on the account of promoting communication, cultural identity, mental or cognitive growth and the benefit of bilingualism or multilingualism. This study is entitled, "Mother Tongue-based Instruction and Academic Achievement in some Selected Topics in Grade 1 Mathematics." Its main aim was to determine the effect of mother tongue-based instruction in the academic achievement in mathematics of Grade 1 learners of Nagacadan Elementary School and Julongan Elementary School. Specifically, it sought to answer the following questions: 1. What is the learners' level of academic achievement in some selected topics in Grade 1 mathematics with the use of: a. Tuwali, and b. English as a medium of instruction? 2. Is there a significant difference in the learners' academic achievement in some selected topics in Grade 1 Mathematics? 3. Is there an effect of mother tongue-based instruction on the level of academic achievement in some selected topics in Grade 1 mathematics? 4. What action plan can be proposed in relation to the use of mother tongue as a medium of instruction? The following are the major findings of the study: 1. The learners' level of academic achievement in either of the two medium of instruction is outstanding. 2. Generally, there is a significant difference in the learners' academic achievement in simple word problems and fraction under the two medium of instructions. 3. There is an effect of mother tongue-based instruction on the level of academic achievement in word problems and fraction. In connection with the findings of the study, the Following are the conclusions: 1. The learners have the essential knowledge, understanding and skills and are able to perform related tasks under simple word problems and fraction. 2. Mother tongue-based Instruction helps improve the academic achievement of the learners. 3. Mother tongue-based instruction has a positive effect in the academic achievement of the learners. In relation with the findings and conclusions of this study, the following are recommended: 1. To help the learners gain more knowledge, skills and understanding and perform related tasks, teachers have to present the lesson in mathematics through real life situations or interactive activities using the Tuwali as a medium of instruction. 2. To improve the learners' academic achievement in the foundation phase, maximize the use of mother tongue as a medium of instruction in the teaching and learning process by providing more supplemental lessons and enhancement activities that the learners can work on in school or even at home. Such lessons should be challenging and engaging. 3. Use mother tongue-based instruction more frequently in order to encourage and motivate the learners to participate during discussions and activities. 4. The proposed action plan may be considered for more effective implementation of MTB instruction.Item Computer assisted instruction on the performance of selected CITCS students in problem solving(2017-05) Aquisio, Charlie Menzi.The problem solving in mathematics is a multi-tasked activity that requires competencies in different cognitive domain. Thus, every mathematical instruction should optimize the opportunity for the students to grasp the necessary concepts for them to be prepared for problem solving. Researchers have shown that Computer Assisted Instruction (CAI) supports both audio and visual learning which can be interactive and self-paced at the same time. In such view, CAI can be a viable teaching support for teachers to promote students' learning performance along problem solving. This study seeks to determine the effect of CAI on the performance of selected students in problem solving through the consideration of the generalized rudimentary problem- solving categories which are: comprehension of the given sentence problem, translation of the worded problem to mathematical sentences, and numerical analysis which involves both computational skills and abstract thinking. By giving light to any further advantages and disadvantages of CAI along problem solving, the study hopes to further contribute towards the better understanding on teaching problem solving. The study sought to define a more comprehensive difference between the CAI method and the lecture method. It intended to answer the following queries: 1. What is difference on the performances of the lecture method group and the CAI group in the pretest and posttest? Hypothesis: There is a significant difference on the performances of the lecture method group and the CAI group in the pretest and posttest. 2. What is the difference on the pretest of CAI and the lecture method group in algebra considering the following performance foci in problem solving: a) Comprehension Skills on Problem Solving? b) Semantic Structure of Worded Problems? c) Numerical Analysis of Worded Problems? Hypothesis: There is a significant difference on the pretest of CAI and the lecture method group in algebra considering the following performance foci in problem solving: a) Comprehension Skills on Problem Solving; b) Semantic Structure of Worded Problems; and c) Numerical Analysis of Worded Problems. 3. What is the difference on the posttest of CAI and the lecture method group in algebra considering the following performance foci in problem solving: a) Comprehension Skills on Problem Solving? b) Semantic Structure of Worded Problems? c) Numerical Analysis of Worded Problems? Hypothesis: There is a significant difference on the posttest of CAI and the lecture method group in algebra considering the following performance foci in problem solving: a) Comprehension Skills on Problem Solving; b) Semantic Structure of Worded Problems; and c) Numerical Analysis of Worded Problems. The researcher made use of the experimental method of research with a quantitative type of approach. Pretest-posttest design was utilized as the type of experimental design. The samples for the study are Information Technology students who enrolled in two Algebra classes for the school year 2006-2007, 2nd Trimester. One of the classes was identified for the control group (Lecture Method Group) and the other as the experimental group (CAI Method Group). The same teacher facilitated both classes and both were of morning schedule in order to minimize, if not negate, any effects of teacher and time factors. The scope of the study along problem solving was delimited to the applications of linear equations with one unknown. Both groups underwent the pretest prior to the conducting the problem-solving lesson. The respective teaching methods were conducted to the two groups after the pretest and the posttest was taken thereafter. The number of students who represented each group on the pretest and the posttest were gathered considering the balance of the mean IQ scores and pretest scores for both groups. The following statistical tools were utilized in order to meet the objectives of the study: The mean, as validated by the within-range computation of the standard kurtosis and standard skewness, was used in order to determine the performance interpretation of the lecture method group and CAI through the Descriptive Equivalent Rating Scale. The t-test for uncorrelated data was used in order to test the hypotheses which state that there is no significant difference on the pretest performance of the lecture method group and CAI group; there is a presence of significant difference between the said groups along the posttest, and that there is a significant difference between the groups per performance foci on both pretest and posttest. The t-test for correlated data was used in order to test the hypothesis that the posttest scores of both the lecture method group and CAI are higher than their respective pretest scores. The comparison also included any significant differences under comprehension, semantic structure and numerical analysis categories per teaching method along pretest and posttest. Lastly, the single factor - Analysis of Variance was used as a supplementary formula for testing the hypothesis that there is a significant difference between the groups per performance foci on both pretest and posttest. The identified formula was used for the comparison between different performance foci under a teaching method. The following were the major findings of the study: 1. The pretest performance of the lecture method group CAI are poor (mean= 8.778) and fair (mean= 14.458), respectively. The t-test results showed that the computed t- value is equivalent to 3.732 which larger than the tabular value of t (2.021) under the significance level 0.05 thus there is a significant difference between the CAI and the lecture method group at 0.05 level of significance in their pretest scores. 2. The posttest performance of the lecture method group and CAI group are poor (mean= 10.611) and good (mean= 19.833, respectively. The t-test results showed that the computed t-value (5.647) is larger than the tabular value of t (2.021) at 0.05 significance level. Thus, there is a significant difference between the CAI and the lecture method group. 3. In the lecture method group, there was a significant difference between the pretest and posttest comparison along semantic structure while results along the CAI group revealed that there was a significant difference between the pretest and posttest for all the three performance foci. 4. The t-test and ANOVA results of the pretest determined that the CAI group performed better than the lecture method group at 0.05 level of significance. 5. The t-test and ANOVA posttest results revealed that the CAI group performed better than the lecture method group at 0.05 level of significance. In addition, the CAI group displayed a more profound performance on all the three foci as compared to the lecture method group. In light of the findings of the study, the following are the conclusions: 1. The performances of the lecture method group and the CAI group differ in both the pretest and posttest. 2. The performances on the pretest of the lecture method group differ along semantic structure while the performances on the pretest of the CAI group differ for all the three performance foci. 3. The performances on the posttest of the lecture method group differ along semantic structure while the performances on the posttest of the CAI group differ for all the three performance foci. In relation with the findings and conclusions of this research study, the following are recommended: 1. The homogeneity of the pretest results of both the control group and experimental group have to be prioritized in order to establish the idea that the respective groups used in the study started at the same footing. 2. A wider scope of the study regarding the effect of Computer Aided Instruction along the cognitive domain has to be given emphasis. 3. Universities have to observe the integration of CAI within the classroom due to the observed positive academic improvement among students. In addition, further focus has to be emphasized on how to translate any given math information into mathematical sentences and then how should it be translated in linear equations. 4. Computer Aided Instruction has to be a suitable tool to develop the cognitive abilities of the students whether on the lower order skills (comprehension) and the higher order skills (application, analysis, etc.).