Chapter 1.docx

Chapter 1 INTRODUCTION Educational institutions, school administrators and teachers are looking for ways to improve the teaching paradigm by employing strategies which not limits the skill of the students to use formula, equation or with a known method in solving mathematical problems but also strategy that develops the skill of using it in real life situations. The ability to solve problem is important and integral reason for learning mathematics. Teaching students to use heuristic problem-solving reasoning and strategies can help them become expert problem-solvers and assist them in transferring and applying their contextual knowledge to novel problems and situations (Rudd, 2010). The PISA 2012 result revealed that 15-year old Malaysian students scored 421 in Mathematics and 422 in problem solving with the OECD average being 511 and 500 respectively. Rank wise Malaysia is placed at 52 out of 65 for mathematics and 39 out of 44 in problem solving. One of the causes for the unsatisfactory performance is that students’ ability to solve problems is not nurtured at the mainstream school (Khalid, 2015). Moreover, Farizan (2014) reported that Malaysian students are capable to

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solve problems involving one-step solution involving basic mathematical knowledge, and they can only solve simple problems. He suggested that Malaysian curriculum should emphasize on mastery of problem-solving skill and strategies. In the Philippines, the attention of the education system is dedicating to Mathematics; there are still various issues and difficulties arising in teaching and learning the subject. This is in agreement with the statement made by Alkan (2013) who pointed out that ever since the introduction of mathematics in the curriculum, mathematics has always been viewed as a problem area for pupils. In relation to that, it has been reported that during the 2003 Trends in International Mathematics and Science Study, the Philippines ranked near bottom: third from the bottom in the fourth grade and fifth from the bottom in the eighth grade (Culaste, 2011). Moreover, the country’s National Achievement test (NAT) result of Bukidnon National High School (BNHS) in Math for School Years 20122013, 2013-2014 and 2014-2015 are 52.17%, 63.17% and 44.47%, respectively (NETRC, 2015). For School Year 2014-2015, Mathematics NAT result in BNHS is the lowest of all the other fields. A low mean percentage score in NAT exam indicates that students have low performance and retention

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level in Mathematics. One factor that may affect the performance of the students is on how the teacher provides meaningful representations and situations to the students (Kang, 2012). Furthermore, in the Division of Davao del Norte, specifically in Asuncion National High School, statistics shows poor performance of Junior High School students in Mathematics. Grade 8 students have an average grade of 79% for the school year 2017-2018. Similar challenge is observed in the present school year 2018-2019. Grade 8 students scored an average grade of 78% in the first quarter. The result of the above mentioned grades only tell us that this problem still exist and will continue to exist if not avoided. There are several quantitative researches about strategy in problemsolving and its effects on academic performance of the students. However, I have seldom encountered qualitative studies that are made focusing on the application of Heuristic strategy. As a researcher, I believed there is a need to dig deeper to have an in-depth understanding about the application of Heuristic strategy to address the difficulties of the students in answering mathematical problems. Suchlike, as part of educational

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institution, this problem urge me to conduct this research to probe and disclose the application of heuristic strategy among Mathematics teacher. Purpose of the Study The purpose of this phenomenological study is to understand the experiences of Mathematics teachers in the application of Heuristic strategy in solving Mathematical problems. At this stage in the research, Heuristic strategy is a teaching approach employed by mathematics teachers where students are engaged in the principle of learning by doing and allowing them to employ practical strategy and method in solving mathematical problems. Research Questions This study sought answers to the following questions: 1. What are the lived experiences of the Mathematics teachers using heuristic strategy? 2. How do Mathematics teachers cope with the challenges encountered in the application of heuristic strategy? 3. What are the insights of Mathematics teachers about the application of heuristic strategy?

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Theoretical Lens This study is gleaned from the Heuristic reasoning and problemsolving theories of Polya (1945). Heuristic reasoning should not be regarded as final and strict, but should be considered provisional and plausible. The goal of heuristic reasoning is to create a set of practical reasoning rules derived from the 3 empirical, experimental methods that directs thinking along the paths most likely to lead to success. Heuristic strategies are devices which drastically limit the search for a solution in a large problem space. They provide a general suggestion or technique for solving different types of problems and can be used independently or in combination. The above mentioned theory is also supported by Schoenfeld (1985) who presented that understanding and teaching mathematics should be approached as a problem-solving domain. According to him, four categories of knowledge/skills are needed to be successful in mathematics: resources – proposition and procedural knowledge of mathematics, heuristics – strategies and techniques for problem solving such as working backwards, or drawing figures, control – decisions about when and what resources and strategies to use, and beliefs – a mathematical “world view” that determines how someone approaches a problem

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Gilfeather & Regato

(1999) supported that non-routine problem

solving stresses the use of heuristics and often requires little to no use of algorithms. Heuristics are procedures or strategies that do not promise a solution to a problem but provide a more highly probable method for discovering the solution to a problem. Building a model and drawing a picture of the problem are two basic problem-solving heuristics. Other problem-solving heuristics such as describing the problem situation, making the problem simpler, finding irrelevant information, working backwards, and classifying information are also emphasized. Scope and Limitations of the Study The scope of this study is delimited only to the following entities as basis in conducting the study. This study explored the experiences of teachers as they employ Heuristic Strategy in problem-solving. The participants were the 14 Mathematics teachers from the secondary schools of Asuncion. The data of this study was based on the responses of the participants following the interview guide as well as the lived experiences they shared during the conduct of the interview with the assumption that the participants were honest and precise when providing the data.

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Importance of the Study The product of this study would benefit the following entities: DepEd Officials. The results of this study would become a reliable source of information in the Application of Heuristic strategy Among Mathematics Teachers and how this strategy affected the learning outcomes. In addition, data could be basis in the selection of trainings and seminars that will be provided to the teachers to improve Mathematics performance of the students. Administrators. The teachers always seek support from their superiors. Hence, the result of this study will help the administrators to include various programs and activities that possibly implemented within the school to help teachers in teaching mathematics specifically problemsolving. This study would also serves as guide for the administrators to send the teachers in workshops and seminars that will help to improve their strategies in teaching mathematical problems. Teachers. Through this study, the Mathematics teachers can gain deeper understanding on the importance of the use of Heuristic strategy in teaching mathematical problems. Also, it will help and guide them to design learning instructions and activities that would cater the needs of the students in learning mathematics especially in problem-solving.

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Students. As the main client, the result of this study can be used as basis for altering the learning instruction and strategies in the classroom concentrating the need, abilities, and learning styles of the students. Other Researcher. This research study would uncover the important issues and help other researchers to have deeper understanding in the application of Heuristic strategy. Also, this will serve as guide to the other researchers to conduct study similar to this. Definition of Terms To give better understanding on the terms that used in this study, the following terms would define conceptually and operationally. Heuristic Strategy. In mathematics, heuristics is a general way or method of solving problems, and is particularly used to come to a solution that is hoped to be close to the best possible solution of a mathematical problem (Abonyi & Umeh, 2014). In this study, this refers to strategy in solving Math problems that employs different styles and methods which are preferred by the learners. Application of Heuristic Strategy. Heuristic methods of teaching are methods where students are engaged the principle of learning by doing. The method also placed the students in the ocean of discovery, as deep into the mode a discoverer opposed to the traditional mode of receiver of

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information or simply being told about things (Maheswari, 2016). In this study, this refers to the strategy employed by the teachers in teaching Math problems where students find the answers through their preferred style or method. Organization of the Study In this section, appropriate and comprehensive arrangements of the study are presented. Chapter 1 presented the purpose and significance of the study. The research questions are posed and the relevant terms used are operationally and practically defined. The limitations of this study are articulated in this part. Chapter 2 highlighted varied studies and readings on the application of heuristic strategy and the finding to other related studies. The content of this section contains the topics on the application of heuristic strategy. I obtained my related studies and reading from internet articles, book, and other publications. Chapter 3 described the design of the study, the role of the researcher, and the participants involved. Data collection and analysis is

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included. Trustworthiness and credibility of the study is illustrated together with its ethical consideration. Chapter 4 revealed the results of the study and contained analysis of data pertaining to the research questions. Results are come from the categorization of the responses of the participants about their lived experiences, coping mechanisms, and dreams about the application of heuristic strategy. Chapter 5 focused in the discussion and conclusion of the major themes which were drawn from the research questions. The recommended ideas and generalizations is also presented in this section.