The use of local material's contexts in the introduction is a platform to ensure the learning transfer of everyday mathematics to abstract mathematics Boaler, From real objects, the students learned the abstract concepts of the circle, then eventually apply back to situational problems.
Since it is locally made in Sorsogon, students easily recognized it and grasp the context of the circle based on the given scenario. Contextualization is also integrated into assessments, like the circles on the ceiling of Sts.
Contextualization is an avenue for students to appreciate, and an authentic transfer of mathematics concepts. Figure 2. Parabola concepts are also applied to other different situational problems such as radio signal satellite dish, the cable of suspension bridges, sound reflector, bridge arch, and television dish antenna. Pili see Figure 3 uses its trace to introduce the concept of the ellipse, and its determined parts are used further in abstraction.
Furthermore, the concept of an ellipse is also applied to pili sculpture at Sorsogon City Boulevard and its platform, situational planet's orbit, semi-elliptical dome and tunnel, Colosseum at Rome, and Sputnik I's artificial satellite orbit. Different sceneries such as an image in the middle of Bulusan Lake at the foot of Mt. Bulusan, Bulusan, Sorsogon, the mountains around the lake, and its reflection to the water traces the image of the hyperbola and the hyperbola image at the ceiling of Sts.
Peter and Paul Cathedral were used as a platform for the abstraction of the hyperbola concept and used also in scenarios for real-world application of the concept. Added to these scenarios are a hyperbolic mirror for panoramic photography, explosion scenario, hyperbolic shaped pillar, long-range navigation LORAN , and the aerial view of crossroads at Sorsogon City see Figure 4. The contextualization feature relates to the environment in the transfer of mathematics ideas conic section to students.
Realistic mathematics' principle is the transition from informal knowledge to formal knowledge through contextual problems Yilmaz, Here, learners have ownership and control of their learning Livingston, Using the modules, students independently learn the lessons.
The modules use precise and simple language Jamison, , concrete illustrations, the relation of each mathematics concepts to explain the context of conic sections. The relatedness of information gives users a general outlook on how to execute the step by step solutions. Solutions of examples are readily prepared with complete and comprehensive explanations to guide the readers.
It also determines the value of worthiness, appropriateness, goodness, validity, and legality of modules Kizlik, All learning modules accumulated passing points from each criterion. The scope, range, and depth of content and topics are appropriate to their learning needs.
The level of difficulty of modules is appropriate for their age and stage of learning, and the level of detail is appropriate for the achievement of the specified learning outcomes. The result tells that the learning modules contributed and supported the achievement of the specific objectives Rosita, Presentations are engaging, interesting, and understandable. The flow of ideas is logical, smooth, clear, and evident. Vocabulary level is appropriate to the experiences and understanding of the students.
The sentence length used was suitable for the target Jamison, All of these factors help the students in meaning-making DepEd, Most of the jurors identified very minor errors such as conceptual, factual, grammatical, and computational, use of obsolete information, and other errors i. There is no conceptual error that may lead to the development of misconceptions or misunderstanding of the content nor factual errors which means that the content was accurate and up-to-date, and without outdated information.
Metcalfe emphasizes that committing minor errors should not be exaggerated, rather it should be handled sensitively, and teachers and learners should be open to mistakes, and actively use them in becoming prepared for the test that counts.
The identified minor errors can still be used as a way to facilitate new learning, to enhance memory for the generation of correct responses, to facilitate active learning, and to direct the attention of the learner while letting the teacher be aware of the focus of discussion. Table 2 presents the summary of the jurors' evaluation along with the presence of the features — contextualization and independent learning. It is depicted that the jurors are satisfied that contextualization and independent learning features are present in the learning modules.
Table 2. Table 3 presents the evaluation of the students along with the acceptability of the developed contextualized learning modules in conic sections. Table 3. This implies that the language and information used in the modules are presented in such a manner that it can deliver the concept of the conic section logically and independently.
Activities cater to unique differences, attitudes, and capabilities, with suitable prescribed topics that are relevant, interesting, and self-motivating Singh, Sufficient and salient information is provided in the delivery of the concept. Adequate activities provided enhance their knowledge, critical thinking, skills, and attitudes.
Situational problems motivate them and provide a mechanism to organize ideas. The modules and their features are appropriate to be used as an urgent, tactical, transformative solution to the 21st-century educational challenges and issues NEDA, Another student also stresses, well-prepared module, and for this, it can help the student to understand the topic easily. This comment concluded that the developed contextualized learning modules help them bridge the learning to the subject Calculus with Analytic Geometry.
These learning modules serve as supplementary materials to learn the concept independently and excite them to learn. The learning modules were positively evaluated and validated by jurors' experts' — who are Mathematics Professors. Consequently, for further development of quality supplementary materials that promote independent learning and holistic development of critical thinking, it is highly recommended to contextualize or even localize the concepts.
Contextualized learning modules can be used in the conduct of different academic remediation such as bridging courses, remote learning in times of unwanted circumstances such as pandemic e. COVID , and among others. It is also highly recommended to test the effectiveness of the use of contextualized learning modules to the student learning outcomes. Ethnomathematics and culturally relevant mathematics education in the Philippines Chapter 8. Alrajeh, T. Student Engagement and Math Teachers Support.
Journal on Mathematics Education, 11 2 , Amerian, M. Scaffolding in sociocultural theory: Definition, steps, features, conditions, tools, and effective considerations.
Scientific Journal of Review, 3 7 , Ampa, A. The development of contextual learning materials for English-speaking skills. International Journal of Education and Research, 1 9 , Andrews, P. A new look at secondary teachers' conceptions of mathematics and its teaching. If you have been searching for a site where you can download advanced, intermediate and introduction to calculus pdf free download books online for free, here is a bit of information that can help you download popular calculus pdf books on fundamental, advanced and specialized calculus books that will equip you with the right knowledge to help you coast through college.
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Stay tuned to the Testbook App or visit the testbook website for more updates on such similar topics from mathematics, science, and numerous such subjects, and can even check the test series available to test your knowledge regarding various exams. Chapter 1 - complete PDF - 2. Chapter 2 - complete PDF - 3. Chapter 3 - complete PDF - 3. Chapter 4 - complete PDF - 1.
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