Teaching Geometry Through Problem-Based Learning

CHAPTER 1 The Problem and Its Setting INTRODUCTION Rationale New mathematics are discovered and invented everyday and there is a great manifestation of growing recognition of the need among the mathematics educators to increase the emphasis placed on problem solving for all students. (Paja 2001). Mathematics evolved over the past few thousand years in many stages. In high school mathematics in Philippine settings involve elementary algebra, intermediate algebra, geometry and advanced algebra.

All of these were center in answering questions about real life. Ordinary people of all ages are endeavor of mathematics in which they constructs concepts, discover relationships, invent methods, execute algorithms, communicate and solve problems posed by their own real worlds. (Cangelosis, as quoted by Paja 2001). Often times, mathematics is a difficult subject for students who has difficulty in memorizing formulas and using logical thinking.

Students learn hardly anything of what they are taught but if they learn through hands on and minds on approach (Paja, 2001) and if it will incorporate into everyday activities and in subjects like languages arts, science, social studies, visual arts, music, physical education, life skills and performing arts. Posadas, as quoted by Paja 2001 said that they will learn more meaningfully and with longer retention. Students in today’s generation are practical work learners, investigational learners and sociable learner.

In relevant to that mathematics educators should explore another strategy of teaching that caters the needs of the students that we have today. According to Paja 2001 in his study on Practical Work Strategy in Teaching and Learning Plane Geometry: Its Effects on Students’ Achievement says that utilizing practical work strategy in teaching and learning plane geometry with the aid of manipulative materials has more reaching effect on students’ achievement in mathematical content and process skills than the traditional.

Problem – based learning is a student centered instructional strategy in which student collaboratively solves problems and reflects on their experiences. (http://en. wikipedia. org/wiki/Problem-based_learing). Dewey proposed that education should be built on the child’s interests and experiences (Ernest, 1991). Education becomes meaningful and real to students when it is connected to them personally, as opposed to using materials that may be abstract and unrelated to a child’s lived reality. (Douglas, 1994).

In today’s world of education, lots of researches that conducted promoting and encouraging active learning in mathematics. But still we are searching for other methods in teaching mathematics. In a particular University of Cebu – Main High School Department focuses merely on the tasks of improving students’ competence on conceptual knowledge. In teaching mathematics is usually it is a teacher – centered because less attempts for students to be involve in every class interaction, performing mathematical processes through investigation and discovery thus enhancing mathematics procedural skills.

This study aims to determine the effectiveness of problem – based learning on students’ attitude and performance in high school geometry in which we seek other strategy that caters the kind of learners that we have. It provide teachers with suggested teaching strategies that would greatly influence student’s motivation and enthusiasm as they develop deep understanding of the challenging topics in mathematics. This study also offers a strategy that designed for individual learning and it encouraged to take responsibility of their group and organize and direct learning process with support from an instructor.

Problem – based learning is used to enhance content knowledge and foster the development of communication, problem – solving and self direction learning skills. THEORETICAL BACKGROUND Problem – based learning (PBL) is an approach to structuring the curriculum which involves confronting students with problems from practice which provide a stimulus for learning. (Buod and Feletti, 1991). They used to enhance content knowledge and foster the development of communication, problem – solving and self directed learning skills.

In PBL classes, students also summarize and present their solutions in a culminating experience. The principle role of the teacher in PBL is that of a facilitator or educational coach guiding the learners in the PBL process. Educator is not the sole resource of information, but instead guides students as they search out appropriate resources. Problem – Based Learning (PBL) is a student – centered instructional strategy in which students collaboratively solve problems and reflect on their experiences, rather than learn primarily through lectures or textbooks.

Problem – based learning require the development of a number of component competences, such as the skills of communication, critical reasoning, logical and analytical approach to problems, reasoned decision making and self – evaluation. (Buod and Feletti, 1991). Engel sees problem – based learning as a means of developing learning for capability rather than learning for the sake of acquiring knowledge. The effectiveness of the PBL depends on the nature of student engagement and the culture of the classroom, as well as the appropriateness of the problem tasks assigned.

Proponents of PBL believe that when students develop their own problem – solving procedures, they are integrating their conceptual knowledge with their procedural skills. (Gilo, 2008). In 1960’s at McMaster Medical School, the PBL approach was started wherein the approach developed by the faculty out of the perceived need to produce graduates who were prepared to deal with the information explosion and who could think critically and solve complex problems. This institution developed its entire curriculum around PBL. (Buod and Feletti, 1991).

However medicine has also been among the pioneers in the application of problem based learning as a means towards rectifying the existing situation in undergraduate medical education (Spaulding as quoted by Buod and Feletti, 1991) and post graduate medical education (Jack and Engel as quoted by Buod and Feletti, 1991). Soon after medicine schools adopted PBL as their center of instruction not later other fields will be using problem – based learning in teaching. The movement has extended into the K-12 arena as well. Camp, 1996). Educators and administrators of the institution wanted students who could think critically, solve problems and work in teams. And many undergraduate institutions began to develop PBL programs and curricula. Aalaborg has one of the most comprehensive undergraduate PBL curriculum, and Maastricnt also has a develop PBL program of study. More recently, in the U. S. , the University of Delaware has turned attention toward Problem – based learning, as has Samford University in Birminghan, Alabama.

In addition to these more comprehensive efforts, individual faculty members at more than 300 institutions are using PBL at the undergraduate level (PBL insight, p. 7 as quoted by Gilo, 2008). Through the researches conducted in medical school, we can formulate expectations about the outcomes of problem – based learning. Medical researchers show that problem – based learning provides students with the opportunity to gain theory and content knowledge and comprehension.

According to Schmidt cognitive effects of problem – based learning are the following: (a) initial analysis of the problem and activation of prior knowledge through small-group discussion, (b) elaboration on prior knowledge and active processing of new information, (c) restructuring of knowledge, construction of a semantic network, (d) social knowledge construction, (e) learning in context, and (f) stimulation of curiosity related to presentation of a relevant problem. Constructivism and Problem – Based Learning

Constructivism is a philosophical view on how we come to understand or know. It is, in our mind, most closely attuned to the pragmatic philosophy of Richard Rorty (1991) as quoted Duffy and Savery, 2001. We will characterize the philosophical view in terms of three primary propositions by Rorty (1991) as well as vonGlaserfeld (1989). Firstly, understanding is in our interactions with the environment. This is the core concept of constructivism. We cannot talk about what is learned separately from how it is learned, as if a variety of experiences all lead to the same understanding.

Learning takes place only through self – activity. (Froebel 1976). Dewey proposed that education should built on the child’s interests and experiences. (Ernest as quoted by Douglas, 1994). Since understanding is an individual construction, we cannot share understandings but rather we can test the degree to which our individual understandings are compatible. An implication of this proposition is that cognition is not just within the individual but rather it is a part of the entire context. (Savery and Duffy, 2001).

Secondly, cognitive conflict or puzzlement is the stimulus for learning and determines the organization and nature of what is learned. When we are in a learning environment, there is some stimulus or goal for learning — the learner has a purpose for being there. That goal is not only the stimulus for learning, but it is a primary factor in determining what the learner attends to, what prior experience the learner brings to bear in constructing an understanding, and, basically, what understanding is eventually constructed.

In Dewey’s terms it is the “problematic” that leads to and is the organizer for learning (Dewey, 1938: Savery and Duffy,2001). For Piaget it is the need for accommodation when current experience cannot be assimilated in existing schema (Piaget, 1977; Savery and Duffy, 2001). Lastly, knowledge evolves through social negotiation and through the evaluation of the viability of individual understandings. The social environment is critical to the development of our individual understanding as well as to the development of the body of propositions we call knowledge.

At the individual level, other individuals are a primary mechanism for testing our understanding. Collaborative groups are important because we can test our own understanding and examine the understanding of others as a mechanism for enriching, interweaving, and expanding our understanding of particular issues or phenomena. As vonGlaserfeld (1989) has noted, other people are the greatest source of alternative views to challenge our current views and hence to serve as the source of puzzlement that stimulates new learning.

In PBL, students learn content, strategies and self – directed learning skills through collaboratively solving problems, reflecting on their experiences, and engaging in self – directed inquiry. It established principles of learning which have been explained through observation and research over the past century, principles such as motivation, relevance, practice, active learning and contextual learning operate significantly in a PBL environment, and to a much lesser extent in conventional curricula.

Figure 1: Schematic Diagram of the Theoretical – Conceptual Framework of the Study THE PROBLEM Statement of the Problem The main purpose of this study was to determine the effects of problem – based learning on students’ attitude and performance in high school geometry to the third year students of University of Cebu – Main, Cebu City of the school year 2010 – 2011. Specifically, the study sought to determine the following: 1. The profile of the students’ performance in the control group and the experimental group during the pre – test in terms of their high school geometry performance. . The profile of the students’ performance in the control group and the experimental group during the post – test in terms of their high school geometry performance. 3. The significant mean gain between the pre – test and post – test high school geometry performance profile of the students in the control group and the students in the experimental group. 4. The significant mean gain difference between the control and the experimental group’s performance in their high school geometry performance. . The significant change of the attitude towards mathematics before and after the exposure to the traditional teaching among the third year high school students of University of Cebu in the control group. 6. The significant change of the attitude towards mathematics before and after the exposure to the problem – based learning among the third year high school students of University of Cebu in the experimental group. Statement of Hypotheses

Ho1: There is no significant difference between the hypothetical mean and the actual mean of the control group and the experimental group during the pre – test in terms of their high school geometry performance. Ho2: There is no significant difference between the hypothetical mean and the actual mean of the control group and the experimental group during the post – test in terms of their high school geometry performance. Ho3: There is no significant mean gain between the pre – test and post – test high school geometry performance profile of the students in the control group and the students in the experimental group.

Ho4: There is no significant mean gain difference between the control and the experimental group’s performance in their high school geometry performance. Ho5: There is no significant change of the attitude towards mathematics before and after the exposure to the traditional teaching among the third year high school students of University of Cebu in the control group. Ho6: The significant change of the attitude towards mathematics before and after the exposure to the problem – based learning among the third year high school students of University of Cebu in the experimental group.

Significance of the Study The effects of problem – based learning on students’ attitude and performance in high school geometry to improve classroom instruction and the quality of education rendered to continuing growing population. This study will benefit the following individual in learning and teaching mathematics in different approach. Students. The students were the primary reason of this study. They would be directly affected with the benefits of the study since they were the focus of it.

Students would be relieved of the conventional classroom structure which they perceive as boring and unmotivating. They are given highly appropriate learning experiences to build positive attitude and productive individual. Teachers. The findings of this study would be of great help to the teachers not only in mathematics but also in some related areas of concern. Teachers at all levels would be able to select appropriate teaching techniques that complement problem – based learning. School Administrators.

School administrators would likewise be benefited by the outcomes of the study and would capture an insight and opportunity to include in the present scope of the mathematics program and help improve the curricular content to adopt students’ level of learning with the same weight, being in the position, they have the chance to persuade the teachers to adopt problem – based learning as part of students’ learning experiences. Curriculum Writers. The result of this study would also enable the curriculum writers to redesign or restructure curriculum materials which could better facilitate mathematics learning through problem – based earning. Scope and Delimitation Content Delimitation The area of the study was the level of performance in high school geometry and the attitudes towards problem – based learning of the third year high school students of University of Cebu High School Department – Main Campus in the school year 2010 – 2011. Place Delimitation This study was limited to University of Cebu High School Department – Main Campus located in corner Sanciangko and Juan Luna Streets, Cebu City. Time Delimitation The study conducted in the school year 2010 – 2011.

Subject and Area Delimitation The subjects of the study were the selected third year high students of University of Cebu High School Department – Main Campus in the school year 2010 – 2011. Chapter 2 Related Literature and Studies Observed that teachers are now being encouraged to move away from a tradition of teaching methods that are mechanistic in nature and inappropriate to the ways students learn into a constructivist approach where active learning is emphasized. (Alindada, 199 as quoted in Paja, 2001).

A teaching working from a multiculture, social – reconstructivist approach attempts to create a learning environment that is as democratic and open as the power asymmetries of the classroom allow, but with explicit recognition of this asymmetry. (Ernest 1991 as quoted by Douglas, 1994). Mathematics is our general education component that entails enriching a personal knowledge of the students that includes the opportunity to develop the power to explore, make conjecture and reason logically. This component helps students to become broadly educated, creative, cultured, morally pright and productive citizens. (Paja, 2001). Mathematics as an interdisciplinary language and tool. Mathematics can be used to help represent, communicate about, and solve problems in many different disciplines. Many jobs and other aspects of responsible adult life in our society require some mathematical knowledge and skills. Problem – Based Learning , which encourages students to work in groups to carry out research and think independently to solve problems, is growing into an international movement. Moncure, 2005). According to Stephien and Rosenthal (1992) that PBL instruction is designed to provide students with a guided experiences in solving an ill – structured problem. It orienting students toward meaning – making over fact – collecting. They learn via contextualized problem sets and situation. (Rhem, 1998). Ulmer says, this approach gives students immediate feedback. “It keeps a constant flow going between teacher and student, and you cant’t put a price tag on that. According to the study of Gilo (2008), that PBL can produce socially responsible citizens. This gives the youth a sense of awareness and participation in the community. They love the challenge being the problem solvers and it gives a sense of accomplishment for having been part of the society they belong. PBL is a motivating way to learn as learners are involved in active learning, working with real problems and what they have to learn in their study is seen as important and relevant to their own lives. (http://www. bli. org/pbl/pbl. htm). According to Spence that problem based learning gives you opportunities to examine and try out what you already know; discover what you need to learn; develop your people skills for achieving higher performance in teams; improve your writing and speaking abilities, to state and defend with sound arguments and evidence your own ideas; and to become more flexible in your approach to problems that surprise and dismay others. Despite the work and effort it requires, PBL is never dull and is often fun.

Problem – Based Learning proponents emphasize that it improves thinking and learning skills and cognitive abilities in students. It has been reported that PBL – trained students are more frequent users of libraries and other information resources, which support independent learning. They acquire life long study skills, especially in their early years of study, giving rise to sustained learning. PBL educated students have a more holistic approach to their subject, more readily integrate new information, adapt to change and work well as member of a team.

Generally PBL appears to increase students interest and enjoyment to the subject and enhance their professional development. (Gilo, 2008). Chapter 3 Research Methodology Methodology This study utilized the quasi – experimental method with a content group and an experimental group using the pre – post tests. The quasi – experimental method was used since the subjects in each group were matched in terms of some selected variables such as classroom setting, classroom environment, instruction and academic performance. The study conducted on the second quarter grade.

The two groups were given the pre – test on solid figures and its measurements to determine the mathematical achievement of each student. Intervention took place after conducting the pre – test which lasted for two weeks. The traditional way of teaching was given to the control group and the problem – based learning for the experimental group. After four weeks of experimentation a post – test was administered to determine the changes in their performance in high school geometry specifically in solid figures and its measurements.

Research Environment This research was conducted in University of Cebu – High School Department Main Campus is located at the corner of Sanciangko and Juan Luna Streets, Cebu City. It is private non – sectarian institution of higher learning. It provides the learners with the essential knowledge, skills and attitudes that allow them to improve their quality of life and increase their opportunities to participate in and benefit from social and economic development.

It aspires to provide the learners with academic, scientific, technical and vocational, knowledge, skills and attitudes essential in meeting the demands of time, enhance the individuals emotional, social – cultural and spiritual needs; deeper the learners’ awareness and willingness to be pro – active in community projects and activities including environment protection and preservation, produce graduates who are highly qualified for the world of work. And as testament of its desire to provide est education for the masses, it is now the fastest growing university, if not the most dynamic among all the universities in the city of Cebu in terms of the number of students coming from public and private schools in urban or rural areas. Research Respondents The subjects of the study were the 82 selected third year high school students of University of Cebu – Main who are enrolled in the school year 2010 – 2011. Table 1 The Population of the Study Year and Section |Total Population |Research Population | | | |Sample (n) |Percent (%) | |III – Sapphire |41 |41 |100 | |(Control Group) | | | | |III – Jade |41 |41 |100 | |(Experimental Group) | | | | As indicated in the Table 1, the sections of third year classes were the groups under treatment of the study. The III – Sapphire class with 41 students composed the control group while III – Jade class with 41 students constituted the experimental group.

Research Instruments The instruments in this study were the Mathematics Performance Test and an adopted Mathematics Attitude Scale. The achievement test was a teacher – made test about the high school geometry particularly solid figures and its measurement. To measure students’ attitude in mathematics, Mathematics Attitude Scale was used. This mathematics attitude scale was adopted from the study of Ruyca, 1994. It consisted of 20 positive and negative statements. This attitude questionnaire is a 5 – point Likert scale to which the subjects indicate SA for strongly agree, A for agree, U for undecided, D for disagree and SD for strongly disagree.

For reliability of the said test, split – half method was used. A coefficient of correlation of 0. 74 described that the test was highly reliable. Research Procedures The procedures of the study were done through data gathering and treatment of data. Data Gathering The researcher secured a written permit with the approval of the high school principal of University of Cebu –Main Campus. After the written permits signed and approved by the authorities, the researcher administered a 40 – item teacher – made test to the 40 third year high school students of University of Cebu – Main who are not respondents of the study to establish the validity of the test.

When the test was found to be reliable and valid, a pre – test was administered to the actual respondents, the third years Sapphire (control group and Jade (experimental group), a week before the experimentation started. The permit is found in appendix A. The III – Sapphire and III – Jade are the target subjects of the study. The III – Sapphire as the control group, which was exposed to traditional method; III – Jade served as the experimental group, which exposed to problem – based learning. In traditional way of teaching, lessons were presented by way of lecture, discussion and demonstration. Follow – up exercises were given in a form of seatwork and boardwork every after session. In this approach, teachers play an important role in learning process.

All the discussions and presentations were delivered by the teacher. The pacing of the lesson depended on the teacher’s evaluation of the students’ performance in their previous activity. Each lesson was taught for not more than two meetings. After a month of experimentation, a post – test was given to evaluate whether the students in the control group gained knowledge in solving the areas, surface area and volume of a plane and solid figures. On the other hand, the 41 III – Jade students were exposed to problem – based learning. In the PBL, the learner will be given a problem and they were attempting to answer it of the information of what they already know.

They will identify what they need to learn to better understand the problem an how to resolve it. Once they have worked with the problem and identified what they need to learn, the learners engage in self-directed study to research the information needed by finding and using a variety of information resources (books, journals, reports, online information, and a variety of people with appropriate areas of expertise). The learners then return to the problem and apply what they learned to their work with the problem in order to more fully understand and resolve the problem. After they have finished their problem work the learners assess themselves and each other to develop skills in self-assessment and the constructive assessment of peers.

Self-assessment is a skill essential to effective independent learning. The faculty in turn become resources, tutors, and evaluators, guiding the students in their problem solving efforts. To measure the attitude of each student towards mathematics who had some through problem – based learning and traditional method, a Mathematics Attitude Scale the level of interest, feeling, perception and trend of attitude of the student towards high school geometry in both control and experimental groups were gathered. Each student was expected to answer the questions for their Mathematical Attitude Scale. Treatment of Data The data that will be gathered will be treated quantitatively.

The following statistical treatments will be utilized for appropriate interpretation: 1. To determine the profile of the students’ performance in the control group and the experimental group during the pre – test and post – test in terms of their high school geometry performance, the z – test will be used with the formula: [pic] where: z = z – test value AM = actual mean HM = hypothetical mean SD = standard deviation N = number of cases/students 2. To determine significant mean gain between the pre – test and post – test high school geometry performance profile of the students in the control group and the students in the experimental group, the t – test will be used with the formula: [pic] here: t = t – test value [pic] = mean of the control group [pic] = mean of the experimental group SD1 = standard deviation of the control group SD2 = standard deviation of the experimental group N1 = number of cases of the control group N2 = number of cases of the experimental group 3. To determine the significant mean gain difference between the control and the experimental group’s performance in their high school geometry performance, the t – test will be used with the formula: [pic] where: t = t – test for the pre – post mean gain [pic] = mean of the difference SD = standard deviation of the difference N = number of cases 4.

To determine the significant change of the attitude towards mathematics before and after the exposure to the problem – based learning among the third year high school students of University of Cebu in the experimental group, the weighted mean will be used with the formula: [pic] where:[pic] = weighted mean f = frequency n = number of cases Level of Significance A 0. 05 level of significance with a two – tailed test of statiscal significance for rejecting or accepting the hypothesis was applied in this study. Definition of Terms This study contains terms and ideas which may vary from its definition. To facilitate a better understanding of the study, some terminologies will be defined based on how they are used operationally.

Mathematics Attitude refers to the significant contributors of detractors of effective performance. It is the behaviour shown by the students towards performing mathematics. Traditional Method refers to the ways of teaching mathematics used by teachers who depend on the teachers’ manual or textbook. It eliminates students’ experiences that are expected to motivate and sustain interest of the children. Plane Geometry refers to a branch of mathematics dealing with the properties and relations of lines, angles, surface and solids. Problem – Based Learning refers to a student instructional strategy in which students collaboratively solve problems and reflect on their experiences.

Student Performance refers to the academic achievement of the student specifically mathematics. Chapter 4 Presentation, Analysis and Interpretation The presentation, analysis and interpretation of data will be presented after the experimentation of the class will be done and if the data is being gathered. Chapter 5 Summary, Conclusion and Interpretation The summary, conclusion and recommendation of the study will be given after the data is being presented, analyzed and interpreted. Appendix A University of Cebu – Main High School Department Sanciangko Street, Cebu City June 15, 2010 DR. AGAPITO P. PINO JR. High School Principal University of Cebu – Main Sanciangko Street, Cebu City Sir: Greetings.

The undersigned has come up with a thesis concept entitled “PROBLEM – BASED LEARNING IN TEACHING AND LEARNING HIGH SCHOOL GEOMETRY: ITS EFFECTS ON STUDENTS’ ATTITUDE AND PERFORMANCE” In this connection, she would like to request permission to conduct an experimental study with the third year students (III – Sapphire, Control Group and III – Jade, Experimental Group), who are enrolled in school year 2010 – 2011. Your favourable consideration and approval will be highly appreciated. Very truly yours, (Sgd. ) Judy G. Gutang Recommending Approval MARCELO T. LOPEZ (Sgd. ) President, SUC III Cebu Normal University Appendix B Mathematics Attitude Scales (Adopted from Maxima Ruyca) Name: _______________________ Year: ____ Sex: ___ Age: ____ Date: _____

Directions: Each of the statement of this opinionnaire expresses a feeling, which a particular person has towards mathematics. Your answer is correct if it expresses your own opinion. This is not a test and you are not to be graded. Do not omit any item. You are to express, on a five – point scale, the extent agreement between the feeling in each statement and your own personal feeling. You are to check the better which indicators how closely you agree or disagree with the statement. The five – point scale are: SA – Strongly Agree; A – Agree; U – Undecided; D – Disagree; SD – Strongly Disagree. | |SA |A |U |D |SD | |1.

I am always under a terrible strain in Mathematics | | | | | | |class. | | | | | | |2. I do not like Mathematics and it scares me to have to | | | | | | |take it. | | | | | | |3. Mathematics is very interesting to me and I enjoy | | | | | | |Mathematics course. | | | | | | |4. Mathematics is fascinating and fun. | | | | | | |5.

Mathematics makes me feel scared and at same | | | | | | |time it is stimulating. | | | | | | |6. My mind goes blank and I am unable to think clearly | | | | | | |when working with Mathematics. | | | | | | |7. I feel a sense of insecurity when working with | | | | | | |Mathematics. | | | | | | |8. Mathematics makes me feel uncomfortable, restless, | | | | | | |irritable and impatient. | | | | | | | |A |U |D |SD | | | | | | | | | |SA | | | | | |9. The feeling that I have towards Mathematics is a | | | | | | |good feeling. | | | | | | |10. Mathematics makes me feel as if I am lost in a | | | | | | |jungle of numbers and I can’t find my way out. | | | | | |11. Mathematics is stimulating I enjoy a great deal. | | | | | | |12. When I hear the word Mathematics I have a feeling | | | | | | |of dislike. | | | | | | |13. I approach Mathematics with a feeling of hesitation, | | | | | | |resulting from a fear of not being able to do it. | | | | | | |14. I really like mathematics. | | | | | | |15.

Mathematics is a course in school, which I have | | | | | | |always enjoyed studying. | | | | | | |16. It makes me nervous to even think about having to | | | | | | |do Mathematics problem. | | | | | | |17. I have never liked Mathematics. | | | | | | |18. I am happier in a Mathematics classes than any | | | | | | |other class. | | | | | | |19.

I feel at ease in Mathematics and I like it very much. | | | | | | |20. I feel a definite positive reaction toward | | | | | | |Mathematics and it is enjoyed. | | | | | | UNIVERSITY OF CEBU HIGH SCHOOL DEPARTMENT TABLE OF SPECIFICATIONS Examination : Performance TestSubject / Year Level : Mathematics III Number of Items : 40Teacher : Miss Judy G. Gutang |SPECIFIC OBJECTIVES |CONTENTS |TIME FRAME |% ALLOCATION |NO.

OF ITEMS |LEARNING DOMAIN |ITEM PLACEMENT |TYPE OF TEST | | Apply formulas in solving problems | | | | |Applying |I. 1 – 10 |Multiple Choice | |involving areas |AREAS |4 hours |25% |11 |Solving | | | |Solve problems on surface areas of | | | | |Applying |I. 11 – 25 |Multiple Choice | |solid figures |SURFACE AREAS |6 hours |37. % |15 |Solving | |Problem Solving | |Solve problems on volumes of solid | | | | |Applying |I. 26 – 40 |Multiple Choice | |figures |VOLUMES |6 hours |37. 5% |14 |Solving | |Problem Solving | |TOTALS | |16 hours |100% |40 | | | |

University of Cebu High School Department PERFORMANCE TEST Name: __________________________ Year and Section: __________ Score: ____ I. MULTIPLE CHOICE. Read each item carefully. Encircle the letter of the correct answer. Use [pic]. 1. Find the area of a circular rug with 8. 5 cm radius. a. 182. 98 cm2b. 196. 68 cm2c. 226. 98 cm2 d. 53. 41 cm2 2. Find the area of a trapezoid whose altitude is 6 cm and whose bases are 4 cm and 2 cm, respectively. a. 18 cm2b. 12 cm2c. 10 cm2d. 8 cm2 3. A triangle has an area of 65 ft2 and a base of 6 ft. What height corresponds to this base? a. 12 2/3 ftb. 13 2/5 ftc. 18 1/3 ftd. 1 2/3 ft 4. Find the height of a parallelogram whose area is 74 mm2 and a base length of 27 mm. a. 2. 70 mmb. 2. 74 mmc. 2. 47 mmd. 2. 41 mm 5. What is the area of the base in the figure at the right? a. 12 cm2b. 14 cm2 c. 21 cm2 d. 84 cm2 6. A square garden has a perimeter of 43m. What is its area? a. 151. 53 m2b. 151. 56 m2c. 151. 26 m2d. 115. 56 m2 7. The area of the rectangle is 162 in2. How wide is the figure if its 9 in long? a. 12 in b. 16 in c. 18 in d. 20 in 8. What is the area of a 3. 2 ft square board? a. 10. 24 ft2b. 14. 20 ft2c. 41. 20 ft2d. 40. 21 ft2 9. Calculate the area of the shaded region in the figure. a. 8. 34 in2b. 9. 3 in2c. 10. 25 in2d. 11. 43 in2 10. A man is buying a lot for P5,000 per square meter. If the lot is 20 m long and 15 m wide, how much will he pay for it? a. P9. 2Mb. P8. 1Mc. P3. 5Md. P1. 5M 11. How many 4 – inch square tiles are needed to cover a floor whose length is 12 feet and whose width is 8 feet? a. 486 tilesb. 648 tilesc. 684 tilesd. 864 tiles 12. The lateral area of a pyramid is 228 ft2. Find the area of the base if it has a surface area of 372 ft2. a. 84 ft2b. 98 ft2c. 112 ft2d. 144 ft2 13. A volley ball has a diameter of 12 cm. What is its surface area? a. 425. 31 cm2b. 452. 34 cm2c. 452. 39 cm2d. 452. 49 cm2 14.

The side of a cube measures 6. 1 cm. How much foil is needed to completely cover its surface? a. 223. 36 cm2b. 226. 98 cm2c. 148. 84 cm2d. 37. 21 cm2 15. The sum of the areas of the bases of a cylinder is [pic] ft2. Find its radius. a. 6ftb. 8 ftc. 10 ftd. 12 ft 16. The side of a cube has length 9 cm. Find its surface area. a. 336 cm2b. 486 cm2c. 508 cm2d. 660 cm2 17. How much plastic is needed to manufacture five plastic balls of radius 2 cm? a. 521. 38 cm2b. 512. 33 cm2c. 215. 38 cm2d. 251. 33 cm2 18. Find the amount of cardboard needed to make a birthday hat with radius 4 in and a slant height of 10 in. a. 125. 7 in2b. 162. 7 in2c. 216. 5 in2d. 261. in2 19. A right cylinder has a lateral area of 2,480 cm2. The height is 16 cm. Find the radius of the cylinder. a. 7. 03 cmb. 8. 07 cmc. 9. 23 cmd. 10. 37 cm 20. The circumference of a basketball is 40. 8408 cm. What is its surface area? a. 453. 93 cm2b. 530. 93 cm2c. 533. 35 cm2d. 563. 53 cm2 21. How much paper is needed for the label of Youngstown sardines having a radius of 2 in and a height of 4. 2 in? a. 52. 78 in2 b. 95. 56 in2c. 99. 25 in2d. 112. 12 in2 22. Which of the statements is TRUE? a. No two spheres have the same volume and surface area. b. The lateral faces of a rectangular prism have two pairs of equal areas. c.

The surface area of a sphere is equal to the area of the Great Circle. d. The area of the base of a cone is lwh. 23. What is the radius of a cone whose area of its base is 22. 46 in2? a. 7. 62 inb. 6. 72 inc. 2. 67 ind. 1. 76 i 24. Two identical cubes, whose volume is 125 cm3, are placed side by side to forma rectangular prism. Find the surface area of the new solid. a. 150 cm2b. 250 cm2c. 350 cm2d. 450 cm2 25. The sum of the area of the bases of a rectangular prism is 120 ft2. How long is the solid if its width is 5 ft? a. 3 ftb. 4 ftc. 5 ft d. 6 ft 26. The surface area of a triangular pyramid, having four congruent faces, is [pic] mm2. How long is the base if its height is [pic]mm. a. ftb. 6 ftc. 8 ftd. 10 ft 27. Which of the following statements is FALSE? a. The ratio of volume of the cone to the volume of the cylinder is 3:1. b. The volume and surface area of a sphere can be equal. c. The volume of an irregular object can be determined by water displacement. d. No two cubes have equal volume. 28. How would the volume of the square pyramid be affected if the height is doubled? a. the sameb. doubledc. tripledd. quadrupled 29. Find the volume of a cube 3 meters high. a. 9m3b. 18 m3c. 27m3d. 54 m3 30. A spherical lollipop has a radius of 1. 5 cm. What is its volume? a. 14. 16 cm3b. 17. 07 cm3c. 28. 26 cm3d. 10. 60 cm3 31.

Find the amount of space contained in a book 12 in by 1. 5 in by 6. 1 in. a. 89. 01 in3b. 180. 9 in3c. 109. 80 in3d. 801. 9 in3 32. How much sand is contained in a can whose height is 5 inches and radius is 1. 5 in? a. 53. 32 in3b. 35. 34 in3c. 33. 53 in3d. 52. 33 in3 33. The volume of a pyramid is 20 m3. If its height is 12 cm, find the area of the base. a. 5 cm2b. 10 cm2c. 15 cm2d. 20 cm2 34. The height of a 7. 1 ft by 4. 2 ft waterbed mattress is 2. 5 ft. Find its volume. a. 79. 785 ft3b. 79. 857 ft3c. 79. 758 ft3d. 79. 875 ft3 35. The water content in an aquarium is[pic]. How high is it if it is 2 ft long and 1. 7 ft wide? a. 1. 8 ft b. 2. 4 ftc. 3. 1 ftd. 3. 3 ft 36.

A pipeline is 1200 ft long and has a diameter of 4 ft. How much cubic feet of gas can the pipe hold? a. 15,087. 68 ft3b. 17,950. 68 ft3c. 19,057. 86ft3d. 19,571. 68ft3 37. How much greater is the new volume than the original rectangular prism if its height is doubled and its height is halved? a. twiceb. the samec. thriced. can’t be determined 38. The radius and height of an empty Nido can are 4 in and 11. 8in, respectively. How much water it contains if it is one – half full? a. 296. 56 in3b. 296. 67 in3c. 296. 57 in3d. 296. 67 in3 39. A softdrink cup is cylindrical in shape. Its volume is 628 cm3 and the radius is 5cm. How deep is the cup? a. 6 cm b. 8 cmc. 9 cmd. 10 cm 40.

A stalactite in Bukilat Cave in Camotes, Cebu is shaped like a cone. It is 2. 5 ft and has a diameter at the roof of 1. 2 ft. Find the volume of the stalactite. a. 2. 83 ft3b. 3. 28 ft3c. 8. 23 ft3d. 8. 32 ft3 CURRICULUM VITAE JUDY G. GUTANG PERSONAL PROFILE Age:25 years old Birth date:March 26, 1985 Sex:Female Civil Status:Single Religion:Roman Catholic Citizenship:Filipino EDUCATIONAL BACKGROUND Cebu Normal University Master of Arts in Education major in Mathematics Units Earned: 27 units Cebu Normal University Bachelor of Secondary Education major in Mathematics Graduated 2006 Don Vicente Rama Memorial National High School (Basak National High School)

Graduated 2002 Don Vicente Rama Memorial Elementary School (Basak Elementary School) Graduated 1998 WORK EXPERIENCE University of Cebu – Main Campus High School Teacher (Math) 2007 – present Cebu Normal University Office Clerk – Accounting Department May 29, 2006 – January 1, 2007 Cebu Normal University Student Assistant – Accounting Department January 2003 – September 2005 EXAMINATIONS PASSED Licensure Examination for Teachers (LET) Secondary Level – August 2006 SEMINARS/WORKSHOPS ATTENDED Innovations in Classroom Teaching January 31, 2009 Computer Aided Instruction Seminar-Workshop November 29, 2008 Lecture – Forum on Numerical Analysis October 11, 2008

Seminar/Workshop on Strategies and Techniques in Teaching Mathematics for High School September 27, 2008 Good Citizenship Values Formation August 30, 2008 Book Launch and Seminar on Teaching Skills and Strategies December 1, 2007 Seminar on Empowering Teachers with Strategies Anchored on Learner- Centered Paradigm October 24, 2007 Lecture-Demonstration on Innovations in Teaching Mathematics August 13, 2007 Restructuring Learning Strategies and Experiences: Paradigm Reflective of the UC Secondary Education Vision-Mission-Goals (Year Three) May 16 – June 8, 2007 Wellness Seminar September 20, 2006 Living Values Education Program January 27 – 29, 2006 Basic Training Course for Unit Leaders

September 30 – October 2, 2005 ———————– CONSTRUCTIVISM THEORY |Post – test | |Achievement |Attitude | |Pre – test | |Achievement |Attitude | ? Understanding comes from our interaction with our environment. ? Cognitive conflict stimulates learning. ? Knowledge evolves through social negotiation and evaluation of the viability of individual understanding. Traditional Approach Control Group III – Sapphire Control Group III – Sapphire Problem – Based Learning Experimental Group III – Jade Experimental Group III – Jade Structured Plan in Mathematics (High School Geometry)