Effective Solutions in the Implementation of the K to12

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Effective Solutions in the Implementation of the K to12 Mathematics Curriculum Melanie T. Braza Sweden S. Supapo West Visayas State University College of Education La Paz, Iloilo City, Philippines [email protected] [email protected]

ABSTRACT This study was an attempt to find out the problems and solutions of one rural grade 7 teacher in a Philippine public high school in the implementation of K to 12 Mathematics curriculum. It is believed that knowledge is constructed when learners are able to draw ideas from their own experiences and connects them to new ideas while cooperative learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task. There were three main problem categories/themes including administrativerelated, teacher-related and student-related. The findings include: (a) lack of trainings, seminars, unclear standard operating procedures, (b) late arrival and lack of modules, (c) developing/weak teaching skills and strategies, (d) teacher’s difficulty in teaching the subjects or contents, (e)lack of time to tackle the content efficiently, (f) unavailability or lack of instructional materials, (g) non-mastery of the basic concepts and skills, (h) poor problem solving and critical thinking skills (i) indifferent student behaviour. The solutions are sharing of modules or guides, conducting cooperative learning class, giving extra time for research work, taking time in the preparation of the lesson, making use of the indigenous materials, reviewing basic concepts and giving examples, motivating and teaching students enthusiastically. Introduction Mathematics has always played a vital role in education. Mathematics teachers should therefore be adept at teaching the subject and must be equipped with the necessary skills or strategies needed. Moreover, it is crucial that their classroom goals be based on the current curriculum. Knowing its framework enables the teacher to develop and adapt lessons to suit the needs of the learners in this globally competitive world. Filipino graduates with previously 10 years of basic education, have been criticised in terms of their level of competency. Thus, Philippines has adopted the K to 12 curriculum to address the problem. The adoption of the new curriculum is said 12

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to enhance the quality of basic education in the country. Furthermore, it will help students to be prepared when facing the demands of the 21st century. This is in fact in line with Article XIV, Section 2(1) of the 1987 Philippine Constitution which states that “The State shall establish, maintain, and support a complete, adequate, and integrated system of education relevant to the needs of the people and society.” According to President Benigno S. Aquino III, “We need to add two years to our basic education. Those who can afford pay up to fourteen years of schooling before university. Thus, their children are getting into the best universities and the best jobs after graduation. I want at least 12 years for our public school children to give them an even chance at succeeding.” Cognizant of this urgent and critical concern and in line with the priorities of the Aquino Administration, the Department of Education is taking bold steps to enhance the basic education curriculum. Hand in hand with vigorous efforts to address the input shortages, DepEd intends to raise the quality of basic education through the enhancement of the curriculum and the expansion of the basic education cycle. (DepEd,2010). The Commission on Higher Education (CHED) believes that senior high will be college ready regardless of the track while the Technical Education and Skills Development Authority (TESDA) will provide Certificate of Completion (COC) or NC I after grade 10 and NC II after grade 12, which will improve employability in fields of agriculture, electronics and trade. The rural public high school is approximately 8 km away from the town proper of the local municipality or town in Iloilo City, Philippines. The school is the only community or local high school in the town. The school was established under the supervision of the Department of Education. It is accessible through jeepney transport, motor vehicles and other means of land transportation. The school is headed by principal 1 with 22 strong, young and committed teachers. There are 8 Math teachers, 4 Science teachers, 3 Language and 7 Makabayan teachers. It has 444 enrolled students coming from 18 nearby ‘barangays’ or villages. Students just walk going to school every day since their homes are far away and no other transportation could be used. The life of the people in this institution is very simple, yet the school has provided their stakeholders and its constituents the maximum learning experiences and teaches every learner with proper values and provides quality education to students. Despite the limited resources, funds, classrooms, and nonavailability of internet connections, the school strives a lot in order to produce competitive graduates to meet the demands of the community and the society as a whole. Hence, it is imperative that there is a need to conduct a study regarding the rural grade 7 teacher’s problems and solutions in the implementation of the new K to 12 Mathematics curriculum in the Philippines. Statement of the Problem The purpose of this study was to determine the different problems and immediate solutions of a grade 7 teacher in the implementation of K to12 Mathematics curriculum. 13

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Specifically, it aimed to answer the following questions: 1. What are the difficulties of a grade 7 teacher in the implementation of K to 12 Mathematics curriculum? 2. What are the immediate solutions to the difficulties of a grade 7 teacher in the implementation of K to 12 Mathematics curriculum? Significance of the Study The findings of this study would be beneficial to teachers most especially to Mathematics teachers, school administrators and principals and curriculum developers. Through this study, teachers will be more aware of the possible problems (or difficulties) they are most likely to face when an adoption of a new curriculum takes place, thus, making them more prepared. School administrators and .principals can gain insights as to what trainings and standard operating procedures should be given to teachers for the proper implementation of the new curriculum. Curriculum developers could also gain appreciation of the curriculums strengths’ and work on its weaknesses by making improvements. Definition of Terms For better understanding of the study conducted, the following terms are defined conceptually and operationally. Problem - In this study, it referred to a problem or any situation that caused the teacher some troubles or hindered him from giving an effective teaching of the lesson. Solution- In this study, it referred to the instant method made used by the teacher to solve the difficulty he encountered with regards to the problems met. Rural – In this study, it referred to a place located outside the town proper of the municipality/town of Iloilo City, Philippines. K to 12 Mathematics Curriculum – refers to curricular innovation in Mathematics Education in the Philippines that focused on critical thinking and problem solving. Review of elated Literature Conceptual Framework Learning is basic to human behavior. It may be defined as a relatively permanent change in behavior that occurs as a result of prior experience (Atkenson, 1975, cited by Devlin, 2000). 14

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The learning of mathematics is often viewed as an isolated, individualistic, or competitive matter – one sits alone and struggles to understand the material or solve the assigned problems. This study was based on the theory of constructivism which states that, ”Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to transfer mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into development steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept.” In the classroom, the constructivist view of learning can point towards a number of different teaching practices. In most general sense, it usually means encouraging students to use active techniques (experiments, real – world problem solving) to create more knowledge and then to reflect on and talk about what they are doing and how their understanding is changing. Constructivist teachers encourage students to constantly assess how the activity is helping them gain understanding. By questioning themselves and their strategies, students in the constructivist classroom ideally become “expert learners.” This gives them ever broadening tools to keep learning. With a well – planned classroom environment, the students learn HOW TO LEARN. This study also adopted the cooperative learning method in teaching mathematics. Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task. The mathematics curriculum allows for students to learn by asking relevant questions and discovering new ideas. Discovery and Inquiry-based learning (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships and concepts (Davidson, 1990). The behavior of the teacher varies from different phases of instruction, such as introducing new material, facilitating group activities, and summarizing. The teacher provides guidance and support during small group activities, observing the group interaction and their solutions on the board, and while visiting particular groups, checking their solutions, giving hints, clarifying notations, making corrections, and answering some questions. The teacher also performs social functions, such as providing encouragement, drawing members into the discussion, and helping the group function more cooperatively. According to reviews of research presented by Sharan, Slavin, and the Johnsons, research has shown positive effects of cooperative learning in academic achievement, self – esteem or self – confidence as a learner, intergroup relations including cross – face friendships, social acceptance of mainstreamed children, and ability to use social skills.

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Theoretical Framework “Life and death of an innovation are not simply a matter of providing appropriate supports for the innovation and making mutual adjustments as it is being installed. Rather, life and death of an innovation depend on the unique configuration of social, historical, political and ideological factors that make up the school and its social, community context.” K to 12 mathematics education is obviously a controversial area, so much so that, in countries like the US, the term Math Wars has been used for describing the kind of conflicts between communities that has been generated in recent years. We all regularly hear colleagues complaining that the students they receive have not been adequately trained and that, every year, the situation become worse, or that they are not pleased with the kind of mathematics education their children received. Today’s mathematics teachers are experiencing major changes not only in the mathematics content they teach, but also in the way they teach. Now teachers are called to teach new, more challenging mathematics to a very diverse audience using active learning approaches designed to develop understanding. Teachers engaged in current mathematics education reforms attempt to establish classrooms in which students engage actively and cooperatively in exploration and discussion to solve rich problems and reason mathematically (National Council of Teachers of Mathematics [NCTM], 1989, 2000). To support the conceptual framework of Mathematics Education, two goals of mathematics in the basic education was formulated in the implementation of the K to 12 Mathematics Curriculum. These two goals include critical thinking and problem solving. Critical thinking…the awakening of the intellect to the study of itself. Critical thinking is a rich concept that has been developing throughout the past 2500 years. The term "critical thinking" has its roots in the mid-late 20th century. We offer here overlapping definitions, together which form a substantive, transdisciplinary conception of critical thinking. Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. In its exemplary form, it is based on universal intellectual values that transcend subject matter divisions: clarity, accuracy, precision, consistency, relevance, sound evidence, good reasons, depth, breadth, and fairness (Scriven and Paul, 1987). Problem solving is the process of working through details of a problem to reach a solution. Problem solving may include mathematical or systematic operations and can be a gauge of an individual's critical thinking skills (Business Dictionary. Com).In the K to 12 Mathematics conceptual framework, problem solving is defined as finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown. 16

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The framework of the K to 12 Mathematics Curriculum is supported by the following underlying learning principles and theories: Experiential and situated learning, Reflective learning, Constructivism, Cooperative learning and Discovery, and Inquiry – based learning. As advocated David Kolb (1970), experiential learning islearning that occurs by making sense of direct everyday experiences. Experiential learning theory defines learning as “the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience” (Kolb, 1984). Reflective learning is a learning that is facilitated by reflective thinking. Experiential learning theory defines learning as "the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience"(Kolb 1984, p. 41). It is not enough that learners encounter real – life situations. Deeper learning occurs when learners are able to think about their experiences and process these allowing them the opportunity to make sense and meaning of their experiences. This study was also based on the theory of constructivism which states that, ”Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to transfer mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into development steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept.” In the classroom, the constructivist view of learning can point towards a number of different teaching practices. In most general sense, it usually means encouraging students to use active techniques (experiments, real – world problem solving) to create more knowledge and then to reflect on and talk about what they are doing and how their understanding is changing. Constructivist teachers encourage students to constantly assess how the activity is helping them gain understanding. By questioning themselves and their strategies, students in the constructivist classroom ideally become “expert learners.” This gives them ever broadening tools to keep learning. With a well – planned classroom environment, the students learn HOW TO LEARN. This study also adopted the cooperative learning method in teaching mathematics. Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task. The mathematics curriculum allows for students to learn by asking relevant questions and discovering new ideas. Discovery and Inquiry-based learning (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships and concepts (Davidson, 1990). The behavior of the teacher varies from different phases of instruction, such as introducing new material, facilitating group activities, and summarizing. 17

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The teacher provides guidance and support during small group activities, observing the group interaction and their solutions on the board, and while visiting particular groups, checking their solutions, giving hints, clarifying notations, making corrections, and answering some questions. The teacher also performs social functions, such as providing encouragement, drawing members into the discussion, and helping the group function more cooperatively. "Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common (Albert Einstein). Mathematics Teachers’Role Mathematics in the K to 12 Curriculum is a skill subject. By itself, it is all about quantities, shapes and figures, functions, logic and reasoning. Mathematics is also a tool of science and a language complete with its own notations and symbols and “grammar” rules, with which concepts and ideas are effectively expressed. Studies have shown that in mathematics instruction, especially at the high school level, remain overwhelming teacher – centered, with greater emphasis placed on lecturing than on helping students to think critically and apply their knowledge to real – world situations (Cobb, Wood, Yackel, and McNeal, 1992). According to Stodolsky and Grossman most high school mathematics teachers see mathematics as a rigid and fixed body of knowledge, and think that their responsibility is to transmit this knowledge to their students (1995, as cited in Staples, 2007, p. 165).Cuban (1984) delineated the features of such teacher – centered instructions as favoring teacher – talk over student – talk and include situations in which the teacher directs instruction to the whole class rather than working with small group of students or with individual students. In contrast to this approach, the National council of Teachers of Mathematics (NCTM) advocates for the development of an inquiry – based mathematics tradition. In an inquiry – based environment, learning is viewed as an active, constructive activity in which students are encouraged to explore, develop conjectures, and problem solving. Students are also encouraged to discuss and communicate their ideas and results, often within small, cooperative groups as well as with their teachers. Mathematics instruction should provide students opportunities to engage in mathematical inquiry and meaning making trough discourse, and teachers should encourage this process by remaining flexible and responsive to students’ response and feedback(NCTM, 2000). This study illustrates how a rural Grade 7 teacher orchestrated classroom conversation based on the current curriculum and promoted the development of mathematics language in order for students to better grasp the underlying mathematical concepts. The study also examines teacher’s problems in promoting the goal of mathematics in the basic education. 18

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The current shifts in curricular and instructional contexts place special emphasis on students’ active engagement, on solving non – routine problems, on applying mathematics to new situations and on communication regarding mathematical problems. Such changes in the curriculum, due to their novelty as well as their difficulty in implementation may cause more affective responses in students and teachers. Parents and educators agree that instructions and student learning in mathematics can and should improve even more. Numerous initiatives and projects are suggesting ideas that are likely to make mathematics teaching even more effective. Research Design This study was an attempt to find out the different problems and solutions of one rural grade 7 teacher in the implementation of the K to 12 Mathematics curriculum in the Philippines. It could describe the general experiences of the teacher as well. The participant of the study was purposively selected. This study was qualitative research since it produced information only on the particular case studied and focused on a single but focused sample. According to Holstein, J. A. and J. F. Gubrium (2012), the purpose of qualitative research is to gather an in-depth understanding of human behavior and the reasons that govern such behavior. The qualitative method investigates the why and how of decision making, not just what, where, when. The following hypotheses were tested: (1) there are problems encountered by a grade 7 teacher in the implementation of the K to 12 Mathematics curriculum, (2) there are immediate solutions to the problems of a rural grade 7 teacher in the implementation of the K to 12 Mathematics curriculum. Participant The participant of this study who was purposively selected to suit the need of the study was one rural grade 7 teacher of a public high school in the Philippines. The participant’s house is located 3 km away from the school. He is one of the hard working and ever dedicated teachers of the school. He started his first service last 2009 as a locally funded teacher sponsored by the local government unit of the town. He was nationalized last 2010 when the school was allocated with national teachers. He has been teaching the Grade 7 mathematics for almost 5 years and teaches the K to 12 Mathematics for 2 years. Sampling Design This study was an attempt to find out the different problems and solutions of a rural grade 7 teacher in the implementation of the K to 12 Mathematics curriculum in the Philippines. In general, this further found out the experiences of the teacher in the implementation of the K to 12 Mathematics curriculum in the Philippines. 19

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This study made use of purposive sampling design in the sense that the researchers only chose the participant to be a grade 7 Mathematics teacher to achieve the purpose. Data Collection This study started by asking permission from the principal and the grade 7 Mathematics teacher of a Philippine public high school. Interview questions were made and used as a guide during the interview. The data collected were taken from the observation of classes, reflection field notes, video-taped cooperativelearning class, various texts, pictures and other visual materials used by the teacher. The interview was done in Hiligaynon, a dialect in the Philippines. On the whole, this study ended by analyzing the data, summarizing it and giving conclusions and recommendations. Data Analysis Procedure In this study, the data was analyzed using thematic analysis. The teacher’s responses to questions and other data from observations, field notes and texts were categorised and interpreted. The interview was recorded, carefully transcribed and translated into English. Coding was done, themes emerged from the data set and the data extract was grouped depending on which theme they belonged to. Problems were identified as well as the solutions done by the rural grade 7 teacher. Multiple reviews of the data and themes were employed to secure the validity of the results. Results, Discussion and Recommendations This study sought some problems and solutions of one rural grade 7 teacher of a public high school in the Philippines. Based on the analysis, the following problem categories emerged: (1) Administrative-related problems, (2) Teacher-related problems and (3) Student-related problems. In the first category/theme, the findings include: (a) there was lack of trainings, seminars and unclear standard operating procedures since the teacher still found difficulty in handling classes or subject matters in relation to the implementation of the K to 12 Mathematics curriculum in the Philippines, (b) there was late arrival and lack of modules provided for the students. In the second category/theme, the findings are the following: (a) developing or weak teaching skills and strategies, (b) the teacher found difficulty in teaching hard subjects or contents and lack of time to tackle the content efficiently, (c) unavailability or lack of instructional materials. In the third category/theme, the problems include: (a) non-mastery of the basic concepts and skills, (b) poor problem solving and critical thinking skills and (c) indifferent student behavior. The solutions to the first problem include sharing of modules or guides and more research work for the teacher. 20

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The solutions to the second problem employed by the rural grade 7 Mathematics teacher stated above include: conducting cooperative learning class, giving extra time for research work, taking time in the preparation of the lesson, making use of the indigenous materials The following are the solutions to the third problem: reviewing basic concepts and giving examples, motivating and teaching students enthusiastically It is therefore concluded that there are indeed problems and immediate solutions encountered by a rural grade 7 teacher in the implementation of the K to 12 Mathematics curriculum in the Philippines.

Recommendation It is strongly recommended that there should be another study using a bigger sample or participant. Since this research made use of one participant only, it would not be valid to make a generalization of the entire population. There could be a specifically chosen rural public high school and a higher percentage of a sample can be drawn and employed. Furthermore, there could be longer time for more observations or the whole data collection process. There should be more interviews, much more careful analysis of the data and regular interval of observations of classes and interviews thereafter as well. REFERENCES Artigue,M.(2006). Controversial Issues in K – 12 Mathematical Education. Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006 European Mathematical Society. Panel A, pages 1645 – 1661 Bennie, K. and Newstead, K. (1999). Obstacles to implementing a new curriculum. In M.J. Smith and A.S. Jordaan(Eds.), Proceedings of the National Subject Didactics Symposium (pp. 150 – 157). Stellenbosch: University of Stellenbosch. Davidson, N. (1990). Small – Group Cooperative Learning in Mathematics.Teaching and Learning Mathematics in the 1990s, pages 52 – 61. Dickey, E. (1997). Challenges of mathematics teaching today: How can school leaders help?NASSP Bulletin (pp. 1 – 10) Graybeal, C. (2010). Teachers’ Obligation to Curricular Messages. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.plymouth.ac.uk/journal/graybeal.pdf Halagao, P. et. al.(2009). Critical Review of K-12 Filipina/o American Curriculum. AAPI Nexus. Vol. 7, No. 1, pp 1-16. 21

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Hew,K.F, et. al. (2007). Integrating technology into K-12 teaching and learning:current knowledge gaps and recommendations for future research. Education Tech Research Dev. DOI 10.2007/s/11423-006-9022-5. Huitt, W., & Hummel, J. (2003).Piaget's theory of cognitive development.Educational Psychology Interactive. Valdosta, GA: Valdosta State University. Retrieved [date] from http://www.edpsycinteractive.org/topics/cognition/piaget.html Isler, I. and Cakiruglo, E. (2009). Teachers’ Efficacy Beliefs and Perception Regarding the Implementation of New Primary Mathematics Curriculum. Proceedings of CERME 6, Middle East Technical University, Turkey. Pages 1704 – 1713 Kolb, D. A. et. al. (1999). Experiential Learning Theory: Previous Research and New Directions. Department of Organizational Behavior Weatherhead School of Management Case Westum Reserve University, 10900 Euclid Avenue, Cheveland, OH 44106. Kolb, D. A., Rubin, I. M.., and Mclyntyre, J. M. (1971). Organizational Psychology: A Book of Readings, 2nd Edition. Englewood Cliff, N. J.: Prentice – Hall. Longman Dictionary of Contemporary English, Updated Edition. The Living Language. Magno, C. (2010). Analysis of the basic education of the Philippines: K-12 Education Program. Retrieved from http://www.academia.edu/38814475/Analysis_of _the_ Basic_Education_of_the_Philippines. Mathematics Education at the Math Forum (2014).Constructivism in the Classroom. The Math Forum @ Drexel, Math Forum Internet Mathematics Library.2014 NCSM Annual Conference, New Orleans, Louisiana. Microsoft Student with Encarta Premium (2009). Philippine Basic Education (2012). DepEd K to 12: Teaching Math and Science. Philbasiceduaction.blogspot.com/2012/08/deped – k to 12 – teaching – math – and – science.html. Problem. [Def. 1] (n.d.) In Longman Dictionary English Online, Retrieved February 21, 2014, ldoceonline.com/dictionary/problem

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