Learning signs of trigonometric function based on ASTC using body as Cartesian Coordinate system. PDF

Preview

Summary

A Research Paper
Presented to Mrs. Lovelyn Chen

MINDORO STATE UNIVERSITY, Calapan City Campus
Masipit, Calapan City, Oriental Mindoro

In Partial Fulfillment
Of the Requirements for the Subject
MATH 214-TRIGONOMETRY
BSED – Mathematics Major

Description

Learning signs of trigonometric function based on ASTC using body as Cartesian Coordinate system.

A Research Paper Presented to Mrs. Lovelyn Chen MINDORO STATE UNIVERSITY, Calapan City Campus Masipit, Calapan City, Oriental Mindoro

In Partial Fulfillment Of the Requirements for the Subject MATH 214-TRIGONOMETRY BSED – Mathematics Major

By: Boongaling, Roxann Mae M. Ceriales, Ariel C. De Guzman, Michelle Shane G. Evangelista, Pamela D. Villanueva, Jerico T.

March 2021

Chapter I THE PROBLEM AND ITS BACKGROUND Introduction Trigonometry is an area of mathematics that deals with the connections between sides and angles in triangles. It's being used to solve the issues in a variety of fields (Orhun, 2010). In mathematical explanations and demonstrations of new ideas and concepts, trigonometry is frequently employed. Although students on higher level has a clear picture of the subject, the difficulty of remembering simple concepts are present on them. For some instance, they prefer to preclude focus on basic trigonometry lessons where as it can help them to ease some view points on the subject. As part of trigonometry's lesson, signs of trigonometric function is considered as one of the basic fundamentals of trigonometry. For starters, trigonometric functions are likely students' first exposure with operations that cannot be evaluated algebraically, the types of processes that they struggle to reason about (Weber,2005). Students are frequently taught the mnemonic SOHCAHTOA to aid in the memorizing of these ratios, but this has the unintended consequence of causing them to stop attempting to make sense of the work because they now have a simple guideline to follow (Cavanagh, 2008). Students' knowledge of trigonometric functions as taking right triangles, not angle measurements, as their arguments improves when triangle trigonometry is taught before circle trigonometry (Thompson, 2008). In fact, it's possible that pupils will

never gain a consistent understanding of angle measurement. The same may be said of instructors to some extent (Thompson, Carlson, & Silverman, 2007). As an outcome, both teachers and students find it difficult to transition to circle trigonometry (Bressoud, 2010; Thompson, 2008), that also serves as the foundation for more advanced concepts in science and mathematics, as indicated by the fact that they must rely on yet another mnemonic, "All Students Take Calculus," to determine the signs of trigonometric functions in different quadrants (Brown, 2005). However, even with these lessons given to students with proper wordings and explanations it tends to be more confusing when being applied. On the other hand, based on a research submitted on IOP publishing, the use of visual aids helps students in order to improve their initial perception on Mathematics lessons. According to the results of the students' initial perception questionnaire, all pupils (100%) had a negative attitude toward mathematics study, particularly trigonometric topics. To put it another way, there are no pupils (0%) who are interested in learning trigonometry. However, after receiving trigonometric learning through visualization, 85 percent of students felt satisfied and found it simpler to grasp and get advantages, according to the results of the final student impression questionnaire. This demonstrates that students' reactions to better trigonometric learning using visualization are increasing. Visualization of the mathematical ideas supplied is included in the high effective category based on an increase in favorable responses from students. From this, we can assess that visualization is a better way for students to learn basic concepts like signs of trigonometric functions.

At some point, the resemblance of the body on a Cartesian plain is visible. As we move our arms sideward, we can easily visualization of each quadrant of the Cartesian coordinate system. The current invention is a three-dimensional Cartesian coordinate system with three perpendicular and intersecting planes for the human body. The current innovation is based on the widely recognized orientations of the three cardinal planes. Sagittal: mid sagittal plane, transverse: uppermost extension of the iliac crests, and coronal: anterior most aspect of the spinal canal are the cardinal planes according to the present invention. The intersection of these planes defines the 0,0,0 point in the human body. For such fact, the researchers aim to use human body as a basis of Cartesian coordinate system as visual aid for signs of trigonometric functions. The sole purpose of having this concept is for letting student imagine and visualize the lessons for them to easily apply it in class. This research will provide an evaluation on the effectiveness of using human body as Cartesian plane which the will be the basis for signs of trigonometric function.

Statement of the Problem The problem of this study is to determine if human body could be an essential instrument to visualize a Cartesian plane for ASTC concept on signs of trigonometric function and to analyze the following:

1. What is the level of understanding of students in terms of some basic concepts of trigonometry? 2.How do the students improve their skills in acquiring knowledge in Trigonometry subject? 3.Does visual aid help students in order for them to understand Trigonometry lessons? 4. Is there a significant relationship between the use of human body as Cartesian coordinate system and the students learning on ASTC concept for signs of trigonometric functions? 5. What improvement can the students get on using human body as basis for Cartesian plane on ASTC for signs of trigonometric function?

Statement of Hypothesis The following hypothesis was tested: There is no significant relationship between the use of human body as Cartesian coordinate system and the students learning on ASTC concept for signs of trigonometric functions. Significance of the Study Results of this study would be beneficial to the following:

Students. The students will benefit from this study because it will help them to develop their analytical skills and flexibility to embrace new strategy on how to learn concepts in Mathematics specially in Trigonometry. Teachers. The results of this study could beneficial for the teachers because it will provide data to determine the effectiveness of visual tools for student's learning. With this, it will serve as an eye opener for the teachers to develop new Visual Tools for new normal set-up of education. School Heads. The findings of the study will help them to assess if this kind of strategy will give a better engagement of students in their lessons specifically in Mathematics. Parents. Results of this study can provide them basis in understanding the needs of their children in terms of strategies on acquiring knowledge and learning mathematical concepts using Visual Tools. Future Researchers. The future researchers could use the findings of this study as reference in deepening the analysis and interpretation on the related variable and indicators they may desire to study in the future to develop new Visual Tools for Mathematical Concepts

Scope, Limitation and Delimitation of the Study This study focused in determining the evaluation on student respondents from Mindoro State University Calapan City Campus, second year level in

Bachelor of Secondary Education Major in Mathematics, of human body as Cartesian plane for ASTC Concept on Signs of Trigonometric Functions. The respondents will be 25 second year students Major in Mathematics from Mindoro State University, Calapan City Campus. However, the limitations of the study are only on the evaluation of Human Body Cartesian Representation for ASTC on Signs of Trigonometric Functions and the possible development of this visual tool to become a supplementary tool for teaching Mathematics concept for new normal. In addition, due to strict regulations because of the pandemic brought by COVID-19, the evaluations will be done through online platforms. Also, the evaluation will only be limited to the acquired knowledge of students in terms of basic trigonometric concept and some visual representation of this concepts. This study is a quantitative study.

Theoretical and Conceptual Framework This study was grounded in the most relevant theories in the combination of visual tools and learning basic concepts in terms of Mathematics specifically in trigonometry. According to a research by Chen(2004), for many years, a lack of understanding and disregard for notions that promote successful visual learning has stymied progress in the development of effective educational environments and resources. Since Arnheim published "Visual Thinking" in 1969, numerous

scholars have discussed the concepts of visual learning in education; however, a lack of academic research and training has resulted in a generation of educators who are unable to articulate and apply effective visual design principles in education. Recently, studies on visual processing explored basic concepts such as determining which part of the brain can process images most effectively have captured my attention. Based on the article of Matheson & Hunchinson (2014) it is tough to teach pupils how to make internal visual representations since they do not lend themselves well to explicit training. Despite this difficulty, teachers can help students acquire this talent by drawing diagrams of their mental images and thinking aloud while visualizing while solving problems. In mathematics, visual representations of information are frequently used to organize, expand, or replace traditional techniques of presentation. In mathematics, visual representation entails generating and forming models that depict mathematical data (van Garderen & Montague, 2003). Mnemonics and visual tools were also proven to provide a better understanding on concepts in mathematics. This is based on a research conducted by DeLashmutt (2007), were in the findings that many students benefit from mnemonics. This also help some of my students remember science and language arts subjects. "It's like adding a thread to a web when you learn something new." A mnemonic device becomes a tool for pupils with memory problems or processing disorders to establish threads from new to old knowledge" (American Institute for Research, 2004, p. 1).

This could be linked to the current study considering that ASTC is a concept on which visual tool is applicable. For such the human body as a Cartesian plane representation could provide a better visualization to better analyze and understand the signs of trigonometric function. This kind of visual ideas could certainly help students in order to think of ways on how they to memories or learn specific Mathematical concepts base on simple and easy to understand tricks. Visual tools also help 21st century learners improve the way of gaining information by means of visual interpretation of basic topics in Mathematics. The paradigm of the study is presented below:

Figure 1.1 The Figure 1.1 shows the connection with the evaluation that will be done during the research. The evaluation will be done by the researchers regarding the knowledge of the respondents on the basic concepts in trigonometry. It was followed by the evaluation of the respondents on the learning strategies being used in order to introduce new trigonometric concepts. After the evaluation, the researcher will analyze the significant of introducing the visual tool and the use of human body coordinate plane. The result of the analysis will be the basis for the application of Human Body as Coordinate plane on ASTC concept for signs of trigonometric functions.

Definition of Terms To further understand what this study is all about, the following terms were conceptually and operationally defined.

Visual tool. Materials for teaching. These are the objects or equipment that teachers utilize to make the lesson clearer to the students by providing auditory, visual, or both (Isola and Agina-obu, 2010). Textbooks, tasks, and additional resources are examples of instructional materials that organize and support instruction (adapted from Remillard & Heck, 2014). It refers to the human and nonhuman resources and facilities that can be used to make teaching and learning processes easier, more enjoyable, and more effective. This object was to be developed and evaluated in this study. Trigonometry. This is an area of mathematics that deals with the connections between sides and angles in triangles. It's being used to solve the issues in a variety of fields (Orhun, 2010). In mathematical explanations and demonstrations of new ideas and concepts, trigonometry is frequently employed. Cartesian Plane. It is a plane whose points are labeled with Cartesian coordinates. (Merriam Webster) The x and y axes of the Cartesian Coordinates System allow you to locate something. The plane's left-right direction is referred to as the x axis. The letter "x" is a cross, which can help you recall this. As a result, on the Cartesian plane, x moves "across." The up-down direction is represented by the y axis. Both the x and y axes are always present in a Cartesian plane.

Chapter II Review of Related Literature and Studies Trigonometry is an area of mathematics that deals with the connections between sides and angles in triangles. It’s being used to solve the issues in a variety of fields (Orhun, 2010). In mathematical explanations and demonstrations of new ideas and concepts, trigonometry is frequently employed. Furthermore, according to (Blackett & Tall, 2012)trigonometry is a crucial component of the high school curriculum. Understanding trigonometric functions is a prerequisite for comprehending trigonometric functions. Newtonian physics, architecture, surveying, and many other fields of science are among the topics covered engineering. In addition, trigonometry is one of the oldest branches of mathematics. It is a topic that connects algebraic, geometric, and graphical thinking and may be used as a foundation for comprehending pre-calculus and calculus. Unfortunately, learning about trigonometric functions might be tough in the beginning. Trigonometric functions are processes that cannot be described using algebraic equations or arithmetical techniques, and students have difficulty understanding about them and seeing them as functions (e.g., Breidenbach, Dubinsky, Hawk, & Nichols, 2014). Students must also link triangle diagrams to numerical relationships and manipulate the symbols involved in such interactions (Blackett & Tall, 2012), which many high school and college students are unfamiliar with.

Trigonometry is also very important in everyday life, and it has gotten a lot of attention from researchers because of its historical history and contemporary usefulness in mathematics education. Unfortunately, many high school pupils are unaware of its benefits, historical significance, or practical use (Tuna 2011). Students may regard trigonometry as a component of mathematics rather than a separate topic (Adamek et al. 2005; Dündar 2015), which is a more hopeful approach. Despite its relevance in high school and advanced mathematics and science, research shows that trigonometry is a tough subject for students and instructors alike. (Weber 2010; Brown 2011; Thompson et al. 2012). According to several studies, these issues explain why trigonometry is traditionally taught using two distinct and unconnected approaches: trigonometry of triangles and trigonometry of periodic functions (Orhun 2010; Brown 2012). According to the National Council of Teachers of Mathematics’ (NCTM N.D) “Standards and Principles for School Mathematics,” a new approach to teaching trigonometry – calibrated for the twenty-first century– is fundamental that emphasizes conceptual understanding, multiple representation and connections, mathematical modeling, and mathematical problem solving. A technologically rich environment that supports thinking, communication, problem-solving, and confidence development would make this feasible (Hohenwarter and Lavicza 2011; Güyer 2012). In trigonometry, an angle can be divided into six different functions. Sin (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosecant) are their acronyms and names (csc). The image depicts these six trigonometric functions in respect to a right triangle. The sine of A, or sin A, is the

ratio between the side opposite A and the side opposite the right angle (the hypotenuse) in a triangle, and the other trigonometric functions are defined in the same way. Before computers made trigonometry tables obsolete, these functions are properties of the angle A that are independent of the size of the triangle, and calculated values were listed for many angles. In geometric figures, trigonometric functions are used to calculate unknown angles and distances from known or measured angles. In professions like astronomy, mapmaking, surveying, and artillery range finding, trigonometry was born out of a necessity to calculate angles and distances. Plane trigonometry deals with problems involving angles and lengths in a single plane. In spherical trigonometry, applications to analogous issues in more than one plane of three-dimensional space are studied. Moreover, students are well-versed in the notion of trigonometry as a ratio of side right-angle triangles, according to studies. In comparison to the other concept, trigonometry as a function, this one has a small complication for both the teacher and the pupils (Byers, 2010; Cetin, 2015; Maknun, Rosjanuardi, & Ikhwanudin, 2018; Weber, 2005). Students do not gain a knowledge of trigonometric functions because the ratios approach in trigonometry focuses on procedural abilities and such expertise (Usman & Hussaini, 2017; Walsh, Fitzmaurice, & O Donoghue, 2017; Weber, 2005). It will take a long time for pupils to understand trigonometry as a function logically and methodically if they place too much emphasis on trigonometry as a ratio of right-angle triangle sides (Usman & Hussaini, 2017).

The efficiency of visualization is determined by the responses of students who have been taught trigonometry using visualization. According to the results of the students’ initial perception questionnaire, all pupils (100%) had a negative attitude toward mathematics study, particularly trigonometric topics. To put it another way, there are no pupils (0%) who are interested in learning trigonometry. However, after receiving trigonometric learning through visualization, 85 percent of students felt satisfied and found it simpler to grasp and get advantages, according to the results of the final student impression questionnaire. This demonstrates that students’ reactions to better trigonometric learning using visualization are increasing. Visualization of the mathematical ideas supplied is included in the high effective category based on an increase in favorable responses from students. Most children have vivid imaginations, and they have no difficulty visualizing make-believe scenes and characters. However, once they enter school, concrete learning methods often leave fantasy and self-generated visuals out of the learning equation. What’s more is that these little minds are overtaxed with the complicated tasks of basic reading, writing, and math, leaving little to no “cognitive space” for them to visualize content and ideas. The sad thing is that many teachers don’t realize that visualization can ignite the “fun factor.” In addition, it enhances learning and improves reading, writing, memory, emotional regulation, and more. The key, however, is for visualization to be trained to automaticity so that students can access mental imagery while focusing on learning basic academics.

Additionally, because traditional ways of teaching Mathematics have been discovered to be unproductive owing to a lack of resources, it is necessary to rethink your approach. According to Eng et al. (2010), in order to improve performance in particular areas of mathematics, an inventive adjustment must...