MISCONCEPTIONS OF PROSPECTIVE MATHEMATICS TEACHER IN LINEAR EQUATIONS SYSTEM

Misconceptions are still a problem in learning mathematics. The causes are very diverse, ranging from the cognitive abilities of students who are not good at mathematics to the teacher who is the trigger for this misconception. The misconception diagnostic test provides benefits to readers as a reference and pressure point in conveying certain concepts that are prone to misconceptions. This study aims to diagnose the occurrence of misconceptions and to analyze the types of misconceptions that exist in 29 prospective mathematics teachers on the two-variable (SPLDV) and three-variable (SPLTV) linear purchasing system materials. A test to detect conceptual errors was given to these prospective teacher students to diagnose conceptual errors that occurred when they studied SPLDV in junior high school and SPLTV in high school before being given linear sales system material in Elementary Linear Algebra courses. The results show that there are still classificational, correlational and theoretical misconceptions. Theoretical misconceptions that occur in students are related to the definition of misconceptions and related to the definition and types of SPL solutions. Classificational misconceptions occur when students classify examples and non-examples of a given linear sales system. Correlational misconceptions occur in students, namely students cannot connect a statement related to SPLDV with its graphical representation of the statement given, also students are not precise in compiling mathematical models of everyday problems given so that the solutions obtained are not correct.


INTRODUCTION
Teacher candidate education is a level that must be taken to prepare someone to become a teacher. In this education, prospective teachers are given both educational material and material related to fields, such as branches of mathematics for prospective teachers of Prima: Jurnal Pendidikan Matematika ◼ 101

Misconceptions of Prospective Mathematics Teacher in Linear Equations System
Fardah, Palupi mathematics, branches of biology for prospective teachers of biology, and branches of economics for prospective teachers of economics. One of the compulsory courses given to prospective math teachers is Elementary Linear Algebra. This course is a basic Algebra course given in the first year. In the Mathematics Education Study Program, Surabaya State University (2021), this course is given with learning outcomes including students being able to explain and apply concepts and techniques for solving systems of linear equations (SPL) with Elementary Line Operations (OBE), matrices and their operations, space vectors and subspaces, bases and dimensions, row/column spaces, inner product spaces, linear transformations, eigenvalues, eigenvectors, and diagonalization as well as being able to solve problems related to these topics.
Algebra is nothing new for student teachers. Since taking elementary and secondary education, algebraic content has been given. At the elementary level, material related to algebra includes solving problems on numbers or geometry. At the junior high school level, material related to algebra includes linear equations, linear inequalities, straight line equations, SPLDV. At the senior high school level, material related to algebra includes SPLTV, inequalities, quadratic equations, polynomials and many others. In Elementary Linear Algebra courses in tertiary institutions, the initial material given is Systems of Linear Equations (SPL).
This material is the main material whose application appears from the beginning to the end of the lecture, so this material is very important to be given carefully. In order to be able to provide algebra material with the right concept to their students in the future, prospective teacher students must understand the concept so that later there will be no misconceptions occur.
During the COVID-19 pandemic, both students and teachers experienced various obstacles (Diana et al, 2021). The implementation of learning that was forced to change from offline to online made teachers less optimal in preparation, delivery of material, and evaluation. Less optimal implementation of learning, can lead to misconceptions. Wafiyah (2012) states that misconceptions are students' conceptions that do not match the conceptions of scientists, can only be accepted in certain cases and do not apply to other cases and cannot be generalized. In algebra, some of the most widely studied and misconceptions occur include those related to equality/inequality, negatives, variables, fractions, order of operations, and functions (Booth et al., 2017). SPL material is closely related to variables, so this material is prone to misunderstandings. This is reinforced by the opinion of AL-Rababaha et al. (2020) who classifies algebraic misconceptions into four main classifications, namely algebraic expressions, linear equations, polynomials, and exponential and radical expressions.
In fact, when studying at the previous level, students often only studied SPL completion procedures without understanding the concept properly. This triggers a misconception. The specific causes are very diverse. From the perspective of students, according to Kurniati (2007), there are several causes of misconceptions, namely: (1) lack of developing knowledge by doing exercises independently; (2) the lack of cognitive abilities possessed by students to learn and understand a concept; (3) students do not have good conceptual knowledge so they experience difficulties in completing the practice questions; (4) students' mistakes in understanding or interpreting a concept in practice questions and; (5) students have good concepts in solving practice questions but are not applied in completing practice questions.
Apart from the student's point of view, misconceptions are also very likely to occur because the delivery from the teacher triggers a wrong concept or because the approach used in learning is not suitable.

Misconceptions of Prospective Mathematics Teacher in Linear Equations System
Fardah, Palupi misconceptions that occur in school algebra, research by Booth et al. (2017) which focuses on algebra at the elementary level, and research conducted by Diana et al. (2021) which focuses on student errors in SPLDV materials. This research focuses on analyzing the misconceptions of prospective teacher students on Linear Systems material as a diagnostic step before students take Elementary Linear Algebra courses.

RESEARCH METHOD
This research is a descriptive research with a qualitative approach. As many as 29 students were given questions on understanding the concept of linear system material online using a Google form before they took Elementary Linear Algebra courses. The number of questions given is 7 questions with indicators of understanding the concept according to Heruman (2007) and corresponding question indicators as shown in Table 1. Evaluate the geometric representation of the SPLDV solution from the given statements "Jika terdapat tiga garis yang terletak pada bidang (koordinat cartesius) yang merupakan sisi-sisi dari sebuah segitiga, maka sistem persamaan yang tersusun dari persamaan-persamaan tersebut memiliki 3 solusi, masing-masing bersesuaian dengan tiap puncak." Benar atau salah pernyataan tersebut? Berikan penjelasan.

7.
Using and utilizing and selecting certain procedures or operations.
The seven questions are questions in the form of true-false statements that demand understanding of concepts from prospective mathematics teachers along with their arguments. The answers of prospective teacher students will be classified as understanding or not understanding the concept based on the definition described by Hasan et al. (1999) which can be seen in table 2.  Hasan et al (1999) developed a method that can be used to help identify misconceptions and distinguish between those who understand the concept and those who do not. This method is commonly called CRI (Certainty of Response Index). The CRI method is used as a method for measuring students' level of certainty when giving answers to each question, as an effort to differentiate students who have misconceptions or do not understand concepts (Tayubi, 2005). Tayubi then classified the four possibilities as shown in table 3 in order to identify students who understood, did not understand, or had misconceptions. Table 3. Criteria for students who understand, did not understand, and had misconception Answer's Criteria Low CRI (< . ) High CRI (≥ . )

Fardah, Palupi
Correct Answer The answer is correct but has a low CRI score means student understand the concept The answer is correct and has a high CRI score means student understand the concept well

Incorrect Answer
The answer is incorrect and has a low CRI score means student does not understand the concept the answer is incorrect but has a high CRI score means students has misconception From the students' answers which indicated misconceptions based on the guidelines in

RESULTS AND DISCUSSIONS
The results of this study are divided into two parts, namely 1) results of identification of misconceptions and their discussion and 2) results of classification of types of misconceptions and their discussion.

Results of identification of misconceptions and their discussion
The answers obtained from the diagnostic tests given to 29 prospective mathematics teacher students were analyzed based on whether the answers were correct and the level of confidence stated by the students as stated by Tayubi (2005). The percentage of misconceptions that occur in each item can be seen in table 4. The percentage is calculated based on the following formula: The percentage of misconceptions that occurred in question number 1 was 86.21% indicating that there were 25 out of 29 students who answered wrong question number 1 with a confidence level of ≥2.5 or specifically students chose a confidence level of 3, 4, or 5.
If seen from table 4, misconceptions the most was in question number 1, namely the concept of defining a system of linear equations, and the least misconceptions made by students were in question number 5, namely the concept of SPL solutions. This needs to be a teacher's concern because algebraic conceptual errors can be one of the main reasons for students' weaknesses in mathematics (Al-Rahababa et al., 2017). When giving definitions to students in algebraic expressions, for example in defining the general form of a linear equation for 1 variable, the teacher must also emphasize that the given expression has conditions. The teacher not only provides that the general form of a one-variable linear equation is + = 0, but also give the conditions that ≠ 0, , ∈ ℝ.

The results of the classification of misconceptions and their discussion
After obtaining the percentage of misconceptions as shown in table 4, then analyzed further for each of these items whether the misconceptions that occur are included in classificational, correlational, or theoretical misconceptions according to Moh's definition.
Amien (Salirawati, 2011). In question number 1, the misconception that occurs is a theoretical misconception, namely students do not understand that the SPLDV expression given in the problem requires conditions, namely the values a and b cannot be 0 together, as well as , ∈ ℝ. Twenty-five students stated that there was no problem with this definition and they answered with a CRI of 3, 4, or 5. This in line with the research result of Azis et.al (2020) which showed that student had misconception in definition that relate to algebra. Figure 1 shows an example of the answers and reasons given by students for question number 1.

Fardah, Palupi
In question number 2, the misconception that occurs is a classificational misconception.
Because   In question number 4, students experienced a misconception that SPLDV and SPLTV always have a solution. This may have the same cause as the misconception that occurred in question number 3, namely because at the previous level the examples were always like that, and they were never given an understanding at the beginning that there were 3 possible solutions for SPL. Figure 4 below presents an example of a theoretical misconception that appears in question number 4. In question number 5, the misconception that occurs is a theoretical misconception.
Students who experience this misconception in number 5 do not understand that the solution of an SPL must apply to every linear equation in the system. In the problem, two points are presented to be tested, one point is a solution and the other point only satisfies one of the equations in the given system. Figure 5 below shows the theoretical misconceptions that occur in question number 5. In question number 6, the misconception that occurs is a correlational misconception.
In solving this problem, students are required to be able to translate statements given in visual form, namely in two-dimensional forms. Students who have difficulty correlating statements that are presented verbally into their visual form, for example in Cartesian diagrams, have difficulty understanding this 6th statement. Concept errors made by students in question number 6 can be seen in Figure 6 below.

Misconceptions of Prospective Mathematics Teacher in Linear Equations System
Fardah, Palupi In question number 7, the misconception that occurs is a correlational misconception.
Students who experience misconceptions about number 7 are wrong in compiling a mathematical model of the problems related to the given SPLDV. Students cannot correlate the daily problems given in the form of mathematical models correctly in an effort to solve the problems given. At first, student model the word problem into mathematics model correctly. But, in the second step, students fail to translate the sentence of "half of the people who went by car with a capacity of 7 people failed to see the concert because the building was closed" in to mathematical model so that the last answer is incorrect. This result is in line with the research result of Egodawatte (2011) that showed The main difficulty in word problems was translating them from natural language to algebraic language. The concept error of number 7 can be seen in Figure 7 below. From the results above, it can be seen that the three types of misconceptions occur in students in SPL material before they take Elementary Linear Algebra courses. Analysis of misconceptions at the beginning before learning as in this study can provide a reference for teachers to pay more attention to concepts that are prone to these misconceptions. This is very important to do because student teacher candidates must have a mature understanding of concepts so that later they will not cause misconceptions in the students they teach. Booth (2016) suggests using the technique of explaining information to oneself while reading or studying (Self-explanation), replacing some (or even half) of the practice problems with worked-out solutions for students to study can increase learning of the procedures to solve problems (worked examples), presentation of errors for students to consider and study (cognitive dissonance) to strengthen understanding of concepts to prevent misconceptions.