DIFFICULTIES ENCOUNTERED IN MATHEMATICAL SOLVING PROBLEMS AMONG GRADE 11 SENIOR HIGH SCHOOL STUDENTS A Qualitative Research Presented to the Faculty of Senior High School Sacred Heart College Lucena City In Partial Fulfillment of the Requirements for the Subject Practical Research 1 Agravante, Ayesa O. Borromeo, Wave A. David, Jearard P. Ileto, Lei D. Libao, Ashley C. Maza, Vanessa C. Palero, Kenji Yulde, Kurt G 11-STEM -9 April 2020 ii ACKNOWLEDGEMENT The study entitled “Difficulties Encountered In Mathematical Solving Problems Among Grade 11 Senior High School Students” turns into a reality with the thoughtful help and support of many individuals. The researchers would like to extend their profound appreciation to every one of them. To the parents of the researchers who assisted and encouraged them throughout the whole research process by making them feel at ease with their moral support. A deep sense of acknowledgement and appreciation to Mr. Michael E. Regalario, the research teacher who helped the researchers walk into the right path by guiding them with supervision open-handedly throughout the study. The researchers also recognized all the valuable comments and suggestions he offered to make the study more perfect from the start to the completion of the study. The researchers would also like to acknowledge some students from grade 11 who became the participants of the study by openly sharing their thoughts about the difficulties that students encounter when answering mathematical problems. Without them this study would not be finish within time and come up to its conclusion. To the friends who supported the researchers and stayed with them during the making of the study and comforted them when in trouble. The researchers truly appreciate their efforts. Finally. the researchers give their highest appreciation to God, for His guidance and motivation to finish the study and for boosting their knowledge and patience. The researchers, iii DEDICATION The researchers would like to dedicate this study to the following people who showed their continuous support, and care and contributed to make this study possible To the researchers’ family for their unconditional love and support To the researchers’ friends and classmates for enlightening the researchers’ concerns, and for being a source of motivation To the researchers’ teacher Mr. Michael E. Regalario for being a good mentor and the researchers’ source of knowledge, and skills To the future proponents, may the study be a good contribute and help to your study And lastly, to God, who guides the researchers in their everyday lives, and for always making things possible The researchers, A.K.O.A W.A.B J.P.D L.O.D.I A.A.G.C.L V.R.C.M K.D.G.Y iv TABLE OF CONTENTS Title Page TITLE PAGE ................................................................................................................... i ACKNOWLEDGMENT ................................................................................................ ii DEDICATION................................................................................................................ iii TABLE OF CONTENTS ............................................................................................... iv LIST OF FIGURES ....................................................................................................... vi CHAPTER I THE PROBLEM Introduction… ........................................................................................... 1 Statement of the Problem… ...................................................................... 2 Assumptions….......................................................................................... 2 Theoretical Framework ............................................................................. 2 Conceptual Framework ............................................................................. 3 Scope and Limitations................................................................................4 Significance of the Study ......................................................................... .4 Definition of Terms… ................................................................................5 II REVIEW OF RELATED LITERATURE AND STUDIES Related Literature......................................................................................6 Related Studies..........................................................................................7 III RESEARCH METHODOLOGY Research Design.........................................................................................9 Research Locale ........................................................................................ .9 Population and Samples ............................................................................ 10 Research Instrument.................................................................................. 10 Data Gathering Procedures ....................................................................... 11 Data Analysis ............................................................................................ 11 Ethical Considerations .............................................................................. 12 REFERENCES................................................................................................................ 13 v LIST OF FIGURES Figure Number 1 Title Page Input-Process-Output showing the process in showing the plan to discover the reason for mathematical struggle. 3 Input Process Output What is the demographic profile of the participants in terms of the following: 1.1. age 1.2. gender 1.3. strand What are the struggles of the selected students on mathematical with preference to: 2.1. analysis 2.2. reasoning; and 2.3 communication Analysis and Interpretation on the Student's Struggle with Mathematical Equation Solving and Lived Experiences of Figuring with Mathematical Problems through the instrument of one on one interview. Informative motivational and math-related content posts that aim to ease the attitude and mind of students, who are having difficulties in Mathematics. 1 CHAPTER 1 THE PROBLEM Introduction It has been observed when it comes to education there are a lot of things to consider especially knowing some subjects that are hard to comprehend. It’s not only in today’s generation, but also from the past. Many students have trouble with understanding mathematics and its key concepts, but most of them find mathematics more difficult than others. This poor understanding of mathematics is called ‘Math Disability’ and it greatly affects the performance, reasoning, and sense of logic of a student. Repeated underperformance in math affects the eagerness of the student to learn. The teacher is the core when it comes to understanding the key points of a lesson, but most of the students find mathematics boring. Math disabilities can arise at any age and it seems evident that students do experience not only differing intensities of math dilemmas, but also different types of diverse classroom emphases, adaptations and divergent methods. (K Garnett, 1998) Sacred Heart College, one of the most known catholic schools in Lucena City has a lot of students who are evident in failing to pass math. Almost the majority of the students in Sacred Heart College are struggling with dealing and understanding math, resulting in the school to have a record of poor accumulated grades in mathematics. Based on the recent international assessment for mathematics and science of the K-12 program of the Department of Education (DepEd), Philippines has the lowest scores among participants from 58 countries in the Trends in International Mathematics and Science Study. (Philippine Daily Inquirer, 2020) This research is mainly for the purpose of knowing the cause of the student’s bad performance in terms of dealing with math and improving the student’s skills in answering difficult mathematical questions by enabling them to perform better. Statement of the Problem The present study will aim to discover the struggles experienced by selected senior high school students in mathematical problems. Specifically, it will seek to answer the following questions: 1. 2 What is the demographic profile of the participants in terms of the following: 1.1. age; 1.2. gender; and 1.3. strand? 2. What are the struggles of the selected students on mathematical problems with preference to: 2.1. analysis; 2.2. reasoning; and 2.3. communication? 3. How did they cope with their struggles in understanding mathematical problems? Assumption The following assumptions are made by the researchers regarding this study: 1. The students under the STEM strand find mathematics more difficult to understand than the others. 2. The students who fail to understand mathematics face anxiety. 3. Boys find math more difficult. Theoretical Framework In this theoretical framework, it presents the theory which explains why Difficulties Encountered in Mathematical Solving Problems Among Senior Highschool Students exists. It contains the collection of defined concepts and constructs with propositions stating how they are related. The theory serves as a basis for conducting the research. Constructivist Theory of Learning by John Dewey (1933) states that learners construct knowledge rather than taking the information into their brain. The construction and representation of information is based on the learner’s experiences. The learners will incorporate their new learned information into a pre-existing knowledge. The constructivist approach is based on the idea that knowledge can never be transferred from one person to another. Thus, the only way to learn is to be able to create or construct them. 3 The relevance of Constructivism theory is using it as a strategy to improve the learning process of a student. The teacher will serve as the core in the learning process and responsible for creating a flexible learning method and communication to meet the student’s needs. According to (Anna Vintere, 2018), it is believed that the constructivist approach radically changes the process of teaching and learning mathematics, connecting it with daily life, rather than teaching only abstract formulas and using a creative approach to mathematical tasks solving. This study also shows that using a constructivist approach to teaching mathematics is needed for sustainable development to be boosted. Conceptual Framework Input Process Output What is the demographic profile of the participants in terms of the following: 1.1. age 1.2. gender 1.3. strand What are the struggles of the selected students on mathematical with preference to: 2.1. analysis 2.2. reasoning; and 2.3 communication Analysis and Interpretation on the Student's Struggle with Mathematical Equation Solving and Lived Experiences of Figuring with Mathematical Problems through the instrument of one on one interview. Informative motivational and math-related content posts that aim to ease the attitude and mind of students, who are having difficulties in Mathematics. Figure 1. Conceptual Paradigm showing the Difficulties Encountered in Mathematical Solving Problems Among Grade 11 Senior High School Students. To create a clear view of the study regarding the difficulties encountered of students figuring with mathematical problems, the researchers employed the Input-Process-Output approach as its conceptual paradigm.. The input frame states different concerns regarding the study. It consists of the demographic profile and struggles of the selected students on mathematical problems with preference to analysis, reasoning, and communication. The effects of selected students’ experiences on mathematical problems in their academic performance. 4 The second frame is the process which states the process the data will undergo to come up with a result. The gathered data are from the provided interview. The output discusses the result and recommendations derived from the gathered information and data. The researchers aim to create a solution to help students who are struggling in Mathematics through the use of modern technology. Scarpello (2007) evaluated that seventy-five percent of people, in America alone, stop the studying of Mathematics and stay away from the jobs that were related to it. Scarpella also claimed that those people have anxiety in Mathematics. According to Novriani and Surya (2017), students with weak skills in Math find the subject scary, boring, and less desirable. Mathematics has been stereotyped to be the most difficult subject in school which is why most students find the subject intimidating. Significance of the Study This study entitled “Difficulties Encountered in Mathematical Solving Problems Among Grade 11 Senior High School Students” is being created to benefit the following: To the teachers, this is for the purpose of having knowledge of the struggles of the students about dealing with mathematical problems. Since they are exposed to students every day, they can understand once after the results are concluded. To the current proponents, this study will benefit the students because they are the subject in this research and their opinions will be known to the teachers and the others responsible for them if there is any negative implication. To the future proponents, this will serve as a guide or factor to have references as related studies or literature to their future studies. Scope and Limitation This study focuses on the experience of senior high students of Sacred Heart College who are struggling with figuring out mathematical problems. The study considers the student’s personal information such as gender, age, and strand. 5 The researchers limited the study to 15 to 20 of selected senior high students of Sacred Heart College who will represent to be participants. This study will not cover other problems that are not included as one of the participants. The researchers will utilize an online interview in gathering data, each of the participants is given the same questions to answer. The outcomes of this study will only refer to the participants of this study and will not be used by any students outside of this research Definition of Terms The terms that will be used in this research are operationally defined: Analysis. A detailed examination of anything complex in order to understand its nature or to determine its essential features. Constructivism. Is a theory in education that recognizes the learners' understanding and knowledge based on their own experiences prior to entering school. Infographics. A visual image such as a chart or diagram used to represent information or data. Logic. The science that investigates the principles governing correct or reliable inference. Mathematics. The science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. Math disability. A disability in having difficulties of learning mathematics. Mathematical Problems. A problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics Reasoning. The action of thinking about something in a logical, sensible way. Skills. The ability to use one's knowledge effectively and readily in execution or performance. Underperformance. To perform less well than (another of its kind, a general average, etc.) or less well than expected. 6 CHAPTER II REVIEW OF RELATED LITERATURE AND STUDIES In order to clearly illustrate the nature of the problem, the researchers have reviewed references that are relevant to the study. This chapter contains the summaries of related literatures by foreign authors, as well as unpublished studies that have contributed important ideas to this research problem. Related Literature Mathematics Anxiety is a negative emotional reaction to mathematics that can be debilitating. It has been defined as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in … ordinary life and academic situations. The severity of Mathematics Anxiety can range from a feeling of mild tension all the way to experiencing a strong fear of math. (Brooks, 2020) The negative relationship between the math anxiety and math performance is an international issue. The PISA (Program for International Student Assessment) statistics measuring a wide variety of countries and cultures depict that the high level of negative correlation between math anxiety and mathematical performance is remarkable (Foley et al., 2017). Although it is not clear to what extent the math anxiety affects the mathematical difficulties and how much of the experience of mathematical difficulties cause mathematical anxiety, there is considerable evidence that math anxiety affects the mathematical performance that requires working memory (Dowker et al., 2016). The math anxiety is associated with the cognitive information processing resources during arithmetic task performance in a developing brain (Young, Wu & Menon, 2012). The above-mentioned literature is all about the Math anxiety affects the student’s Mathematical Solving Problem Performance negatively. 7 There is evidence that secondary students with math learning disabilities score significantly below grade level in mathematics and that their growth rate in mathematics slows considerably in secondary schools (Cortiella, 2011; Wei, Lenz, & Blackorby, 2013). The mathematics underachievement of these students as they enter middle and high school grades maybe due to several reasons, such as increasingly difficult mathematics content as the mathematical ideas become more abstract (Witzel, 2016) The above-mentioned literature is about the students who have math learning disability, will remain if there is no action taken. Related Studies From the study entitled “The Lived Experiences of the Low Performing Students of Bachelor of Industrial Technology of Samar State University in Making Portfolio in Mathematics” (Araza, 2017), Mathematics is a necessity for people of all ages to be successful in life. The school subject can be found in a lot of fields such as; economics, science, sports, etc. This study is relevant to the present study as it supports that numerous factors affect students' ability to understand and apply mathematics and its concepts, despite its efficacy in life. Mathematics is almost involved in other school subjects. Students tend to lose interest in the class and their overall participation and performance. As stated in “Bringing Math to Life: Provide Students Opportunities to Connect their Lives to Math” (Benson-O’ Connor, Carr, and McDaniel, 2019), it has been observed that students, who hate and are afraid of mathematics, immediately panics and signs of stress can be seen in their body when the mere mention of mathematics and its application is being brought up. This study supports the current study as it provided information that student who grew up in a nature where the subject Mathematics is being hated on develops a fear in mathematics or also known as Math anxiety. Since Mathematics is has been stereotyped as a subject only “gifted” students can comprehend, regular students are often found intimidated by the school subject. The findings on the study “Students Difficulty in Solving Mathematical Problems” by Siniguian, suggest a focus that trying new and different problem solving strategies on teaching mathematical concepts and formulas to students that requires them to think analytically will also help in getting the students exposed to variety of mathematical problems. 8 The relevance of the study above mentioned supports the current study’s plan to use a new way and strategy in helping students to learn math. 9 CHAPTER III METHODOLOGY This chapter will include the research design used by the researchers, the research locale where the researchers will conduct the study, the research population and sample, the research instrument going to the used, the data gathering procedures, and ethical considerations. Research Design The present study deals with a non-statistical method that provides understanding of reasons and opinions. This qualitative research approach focuses more on interpreting and understanding research questions as a humanistic approach. By the supporting assertion of (Bhandari, 2020), cited that qualitative is used to understand how people experience the world and qualitative research tend to be more flexible and focuses on retaining rich meaning when interpreting data. Phenomenological approach will be utilized as a strategy in data collection since it focuses on the lived experiences of the participants and showcases how an individual experience a phenomenon. For (Lester, 1883), the purpose of a phenomenological study is to illuminate the specific, to identify phenomena through how they are perceived by the actors in a situation. The researchers will conduct a semi-structured interview with their selected participants that will be used for basic data collection. The researchers used this design for the study because they are aiming to examine the personal lived experiences of mathematical struggle to students. Research Locale The research study is to be conducted at Sacred Heart College, Lucena City, Quezon. The researchers decided to carry out the study on the place they have an easy access with. Sacred Heart College is one of the oldest educational institution in Quezon Province mainly located 1 Merchant St. Lucena City. It was the first catholic learning school founded in 1884 by Hermana Fausta Labrador and is still the oldest catholic school in Lucena City, Quezon managed by the Daughters of Charity. 10 With an upgraded quality education that molds students into virtuous individuals, Sacred Heart College is accredited by Philippine Accrediting Association of Schools, Colleges and Universities (PAASCU) to cater excellent academic programs to equip young people with knowledge and morality. Population and Sampling The researchers selected teenagers as their participants in this study who are struggling with coping and handling mathematical problems than other students. The target population of the study are all teenagers, however, the researchers have a lot more access to the students of Sacred Heart College which is the reason why the participants will only be selected there. The researchers applied the convenience sampling because of their convenient accessibility and proximity to the researchers. Research Instrument The researchers will use the survey method as the main instrument in gathering the data available for the research. The survey will help the researchers to get the data of grade 11 students from Sacred Heart College about their struggles in dealing with mathematical equations. The researchers will use the recognition type questionnaire so if the respondent might add their alternative, the option is already provided. The study covered 14 participants in Grade 11 Senior High School: 5 students from STEM (Science, Technology, Engineering and Mathematics), 5 students from HUMSS (Humanities and Social Science), and 4 students from ABM (Accountancy, Business and Management) will be chosen from the Grade 11 populace. Semi-structured interview with open-ended questionnaire will be the instrument use to collect the data from the participants’ phenomenological experience and point of view in broadening the result of the study. The researchers used this method because it is the most appropriate and convenient for this qualitative research and to get the information and opinions of the students. This type of open-ended questionnaire is divided into three parts: Part 1. The participant’s demographic profile which include their age, gender and strand. Part 2. The struggles of the selected participants they are experiencing on answering mathematical problems with preference to analysis, communication and reasoning. Part 3. The solution or way on how the selected participants cope up with their struggles in understanding mathematical problems. Data Gathering Procedures 11 The researcher will adhere to all established protocols in conducting a study. In accomplishing this study, the following procedures will be considered and followed: A letter to the Senior High School principal and the research teacher will be sent asking the permission of the study. After securing permission, consent from each participant will be obtained discussing the nature and purpose of the study, then they will be informed regarding the recording of the interview. The researchers will also coordinate and seek for an assistance with the class advisers of the chosen respondents and as well as the faculty members in the conduction of the study. A small sample of 14 participants among senior high school students will be chosen for the focus group discussion. Interview questions will be open-ended in order to allow the participants to fully describe the experience from their own view point and to seek understanding on how the participants experience their difficulties in solving mathematical problems The researchers will personally conduct the Focus Group Discussion (FDG) in determining their experiences in mathematical problems. The activity will be explained in details and audio recording will be facilitated for data storing. More importantly, the participants will be asked for voluntary consent about the recording. Data to be collected is qualitative and analysis will include an attempt to identify the difficulties in solving mathematical problems that is actually perceived or experienced. Two weeks will be allotted for the facilitation of data gathering. The data gathered from the participants of the study will be collated. Afterwards, it will be analyzed, interpreted, and presented in figures and tables to facilitate better understanding Data Analysis 12 After gathering the collected data from the participants, the researchers will now interpret the data into text, interpret the meaning and analyze themes from the data collected from the participants. For the analyzation and interpretation of the data, the researchers used and utilized thematic analysis to facilitate the analysis and interpretation of the data. The researchers used thematic analysis because it was the appropriate method to conduct in this qualitative research thus providing the researchers an in depth interpretation of the data and information. After the researchers gathered the collected data, they will transcribe it into text and will look through it to fully overview the data and to easily analyze the participant’s responses. The researchers will organize the data by codes. The researchers will use axial coding since it connects the main and sub-categories together which influences the phenomena that is being studied. After identifying and generating the themes and patterns, the researchers will now check the validity of the data by reviewing through the transcript and check the reliability of the data. The researchers can now present the data as a whole. According to (Nowell, 2017), Thematic analysis is a qualitative method that can be used when working in research teams and analyzing large qualitative data sets it also shows that thematic analysis conducts framework to a positively contributes to qualitative research as a method. Ethnical Consideration The researchers bear in mind the following ethical guidelines throughout the process and completion of their study. Honesty, the researchers make sure that the transcribed collected data from interview schedules are not falsified and fabricated. As the researchers and the study are aimed to be a trusted study that can help spread solution to the issue. Objectivity, the researchers make sure that biases towards the presented data are going to be avoided. It is important for the researchers to come up with a solution that will not cause harm effects on both parties. Carefulness, the researchers make sure that errors and negligence will be avoided. The gathered data and findings should be protected properly to maintain a good condition. Respect for Intellectual Property, the researchers makes sure that proper citation, references, and sources are recognized. This is to ensure that encountering legal problems will be avoided upon the completion of the study 13 REFERENCES Anna Vintere (2018) Constructivist Approach to the Teaching of Mathematics to Boost Competences Needed for Sustainable Development https://content.sciendo.com/view/journals/plua/39/334/article-p1.xml?language=en Araza, J. (2017) The Lived Experiences of the Low Performing Students of Bachelor of Industrial Technology of Samar State University in Making Portfolio in Mathematics. http://uruae.org/siteadmin/upload/UH0117832.pdf Benson O., Carol M., Carr, J. (2019) "Bringing Math to Life: Provide Students Opportunities to Connect their Lives to Math," Networks: An Online Journal for Teacher Research: Vol. 21: Iss. 2. https://doi.org/10.4148/2470-6353.1299 Lorelli N. (2017) Thematic Analysis: Striving to Meet the Trustworthiness Criteria https://journals.sagepub.com/doi/full/10.1177/1609406917733847 Singuian (n.d.) Students' Difficulty in Solving Mathematical www.academia.edu/Students_Difficulty_in_Solving_Mathematical_Problems Stan L. (1883) An introduction to phenomenological research https://www.rgs.org/CMSPages/GetFile.aspx?nodeguid=7ad9b8d4-6a93-4269-94d2585983364b51&lang=en-GB Pritha B. (2020) An introduction to qualitative research https://www.scribbr.com/methodology/qualitative-research/ Problems 14 Vanessa Rose C. Maza Alpsville 3 Lucena City kimreneqt@gmail.com 09397632588 PERSONAL INFORMATION Date of Birth : March 24, 2004 Place of Birth : Lucena City Age : 16 Civil Status : Single Sex : Female Religion : Roman Catholic Height : 5’7 ft. Parents : Randolph Gymson V. Maza : Armela Consesa C. Maza EDUCATION Secondary : Senior High School Sacred Heart College 2020-20201 Junior High School Sacred Heart College 2016-2020 Elementary : Sacred Heart College 20 – 2016 ASSOCIATIONS Luisas Club 2016 – 2020 Teatro 2016 – 2020 Science Club 2016 – 2020 15 KURT DARRYL G. YULDE Purok Santolan Lucena City yulde.kdg@shc.edu.ph 09000000000 PERSONAL INFORMATION Date of Birth : May 2, 2004 Place of Birth : Lucena City Age : 16 Civil Status : Single Sex : Male Religion : Roman Catholic Height : 5’6 ft Parents : Jocelyn Yulde : Kurt Glenn Yulde EDUCATION Elementary : Sacred Heart College 2010 - 2016 Secondary : Sacred Heart College Junior High School 2016 – 2020 Senior High School 2020 - present ASSOCIATIONS 16 WAVE A. BORROMEO Sitio Pag-asa, Barangay Bukal, Pagbilao, Quezon waveborromeo@gmail.com 095116447666 PERSONAL INFORMATION Date of Birth : May 23, 2003 Place of Birth : Lucena city Age : 17 Civil Status : Single Sex : Female Religion : Roman Catholic Height : 5’4 ft. Parents : Welihado U. Borromeo Jr. : Ma. Roanne A. Borromeo EDUCATION Secondary : Senior High School Sacred Heart College 2020-2021 Junior High School : International School for Better Beginnings 2017-2020 Elementary : International School for Better Beginnings 2010-2016 ASSOCIATIONS 17 Jearard P. David Southville Subd. Brgy Lusacan, Tiaong, Quezon davidiyad6@gmail.com PERSONAL INFORMATION Date of Birth : February 13, 2004 Place of Birth : Tayabas City Age : 16 Civil Status : Single Sex : Male Religion : Roman Catholic Height : 181 cm Parents : Jeanilyn P. David : Gerardo C. David EDUCATION Secondary : Senior High School Sacred Heart College 2020-Present Junior High School Saint John Parochial School 20162020 Elementary : Southside Integrated School 2010 – 2016 ASSOCIATIONS 18 ASHLEY AYEN GHAIL C. LIBAO Nabatasan St. Brgy.08 Poblacion Catanauan, Quezon libao.aagc@shc.edu.ph 09284392080 PERSONAL INFORMATION Date of Birth : August 30, 2004 Place of Birth : Lucena MMG General Hospital Lucena City, Quezon Age : 16 Civil Status : Single Sex : Female Religion : Roman Catholic Height : 5’2 ft. Parents : Emilie C. Libao : Alexzander N. Libao EDUCATION Secondary : Senior High School Sacred Heart College 2020-2021 Junior High School Parochial School of Catanauan 2016-2020 Elementary : Parochial School of Catanauan 2008 – 2016 ASSOCIATIONS 19 Lei Oliver D Ileto Wesmar st. Marville subd. Lucena Leiileto981@gmail.com 09100508824 PERSONAL INFORMATION Date of Birth : 1/23/04 Place of Birth : Lucena City Age : 17 Civil Status : Single Sex : Male Religion : Roman Catholic Height : 5'8 Parents : Nerissa D Ileto : Ronnel D Ileto EDUCATION Secondary : Senior High School Sacred Heart College 2020-2021 Junior High School Parochial School of Catanauan 2016-2020 Elementary : Kanlurang Mayao Elementary School 2008 – 2016 ASSOCIATIONS