ANALYSIS OF MATHEMATICAL WRITING ERRORS RELATED TO THE ANGLE OF TRIGONOMETRY FUNCTIONS

Mathematical writ ing errors are often made by students, especially when writing mathematical expressions on the angle of trigonometric functions. One of the causes of this erro r is that students do not pay close attention to the difference between radians and degrees when writ ing questions or writing answers. These mathematical writing errors were made mainly by students who were oriented towards the resu lt of the answer to a question, without paying attention to good and correct writing rules. One form of writing errors in mathematical expressions of trigonometric functions is writing y = sin (x + 45), which is considered the same as writing y = sin (x + 45o). If they are asked to compare the graphical form of the function of the two mathematical expressions in the same image, the writ ing error will be recognized and seen. Counterexamples and technology in learning mathematics can help students understand and correct errors in writ ing mathematical expressions of trigonometric functions. ARTICLE INFORMATION


INTRODUCTION
Mathematics is formed from symbols that can be combined to make statements about the world around us (Brown, 2017). A combination of symbols that can assign numbers, constants, variables, mathematical operations, brackets, and other symbols is called a mathematical expression (Banfill, 2012). Writing mathematical expressions properly and correctly according to the rules is very important to not cause misunderstanding for those who read or learn the mathematical concepts that are being discussed.
Writing mathematical symbols that do not match the rules will cause errors in interpreting the mathematical sentences. One of the errors identified when solving a problem is in writing mathematical symbols (Irfan, 2017). This indicates that students should have the ability to understand and write mathematical symbols properly and correctly to solve problems because this ability will be related to mathematical modeling that is made as a solution to the problem-solving problem.
Errors in writing mathematical symbols in solving the problems given by students could be because students tend to be oriented towards the end result so that they only try to remember the complete procedure without understanding the mathematical concepts they have learned properly. Understanding a mathematical concept that is not comprehensive or only partial understanding will lead to misconceptions about the concept (Mulyono and Hapizah, 2017). According to Allen (2007), misconceptions must be deconstructed, and teachers must help students reconstruct the correct concepts. Counterexamples are very helpful in confronting students with their misconceptions (Allen, 2007).
One of the prerequisite materials for the differential calculus course is trigonometric functions. Mastering the prerequisite material is critical to understand new concepts that will be studied next.

METHOD
Identifying errors in writing mathematical expressions was done by observing student answers to problems about trigonometric functions. Students whose answers used as objects of observation were mathematics education students at a tertiary institution in South Sumatra.
The identification of errors, in this case, did not focus on how many students were making mistakes but rather to the presence or absence of errors made by students in writing mathematical expressions on trigonometric functions. Furthermore, the answers containing the errors in writing mathematical expressions of trigonometric functions were analyzed descriptively.
The identification results show that the writing of mathematical expressions that do not conform to the rules was sometimes done by students intentionally or unintentionally. This happened because when students wrote answers to these questions, they were only oriented towards the final result without paying attention to the rules of writing mathematical expressions properly. If this is done continuously, it might cause a misunderstanding of the mathematical concepts studied.
One of the most common errors in writing mathematical expressions is related to the form of angular units in trigonometric functions. This is because students consider writing degrees or not writing degrees, the final result remains the same. One example of misunderstanding that students experienced is that they assumed that 2 2 1 45 sin =  and 2 2 1 45 sin = .

RESULT AND DISCUSSION
Trigonometry recognizes two angular units used to determine the value of a trigonometric function: degrees and radians. It is known that radian.   Writing errors, such as 45 sin 4 sin =  X, were not realized by students since they did not see the difference in the final results they got. However, this will not happen if they were asked to graph the functions ) 4 sin( , and ) 45 sin( + = x y in the same image area. With the help of one of the dynamic geometry softwares, Geogebra, the three graphs of the trigonometric functions can be easily created, as shown in Figure 3. . Thus, students will realize that writing a mathematical expression of the angular magnitude of the trigonometric function must be correct If the errors in writing the mathematical expression of the trigonometric function are not corrected, and it is not considered an important problem, this will lead to a misunderstanding or misconception, that is, students will think that the writing of the degree magnitude symbol is not important. So when they get a question that asks the value of 60 cos , they will give an answer that the value of 2 1 60 cos = , because they assume that One way to correct a misunderstanding of a mathematical concept is by giving a question or counterexamples. According to Rollins (2020), counterexamples are very helpful because they allow one to easily and quickly show that an idea or thought is wrong. Giving assignments to describe graphs of the functions ) 4 sin( values, will provide a kind of trigger for students to think about the different results they will get, as shown in Figure 5. Teachers play a great role to correct and minimize students' errors in writing mathematical expressions. One of them is by designing questions or problems that train procedural skills in counting and make students think critically about the answers. The following sample problems can be used as a reference for designing other problems. Both examples of the questions have a question structure that aims to make students: 1. Able to perform procedures to calculate values and draw graphs of trigonometric functions using scientific calculators and the Geogebra application.
2. See the difference in the value of the function and the graph of the trigonometric function from the results they obtain.
3. See the similarity of function values and graph of trigonometric functions from the results they get.
4. Understand the value of trigonometric functions is influenced by the angle unit.
5. Understand that writing the angle unit of the trigonometric function properly and correctly is important.
The use of scientific calculators and the GeoGebra application is one of the uses of technology in learning mathematics. Many opinions support the need for innovative mathematics learning design aided by technology. According to Garner & Garner (2001), one of the main points of the calculus renewal movement is the use of technology (computers and calculators), and technology has an impact on learning mathematics for various reasons, mainly because the technological development is very fast. According to Liang (2016), using technology in the form of a graphing calculator supports an interactive, dynamic, and persuasive approach to teaching limits. According to Stols (2007), the latest technologies can help students visualize difficult-to-understand concepts and help to form an active problemsolving environment. According to Bhalla (2013), teachers who are equipped with computerassisted multimedia content to explain lesson topics teach better and make the teaching and learning process fun, interesting, and easy to understand. Thompson et al. (2013) stated that a radical reconstruction of calculus ideas is possible by using computational technology. The teacher is the key to the successful use of technology in the mathematics classroom but incorporating technology into teaching remains a challenge for many teachers (Drijvers et al., 2014).

CONCLUSION
This study concluded that writing errors as described above can cause a misunderstanding of the angular unit in trigonometric functions if not corrected as early as possible. Therefore, giving counterexamples will help correct and minimize errors in writing mathematical expressions of trigonometric functions and avoid misunderstandings of angular units in trigonometric functions. Besides, using scientific calculators to calculate the forms of mathematical expressions of trigonometric functions can help students understand the differences in the values of trigonometric functions that they initially consider the same. Also, the use of dynamic geometry software, in this case, GeoGebra, to graph the forms of mathematical expressions of trigonometric functions is another way to help students visually understand the differences in graphs of trigonometric functions which they initially consider to be the same. Thompson, et al. (2013). A Conceptual Approach to Calculus Made Possible by Technology.