Students' Algebraic Thinking in Using the Geogebra Application

. Algebra is knowledge in education. The ability to think should be known so that it can be maximized in the learning process, one of which is the ability to think in algebra. In the process of working on various algebra problems, students carry out generational activities, transformation activities, and global meta-level activities. Learning algebra will be easy if combined with technology. One of the technologies that can support algebra learning is Geogebra. The research aims to determine how students' algebraic thinking abilities use the Geogebra application. The method in this research is qualitative, with a case study type. The research subjects were students taking calculus courses in the Informatics Engineering study program at a private campus in Jakarta. The research results show that the algebraic thinking ability levels consist of high, medium, and low. High algebraic thinking abilities have high generational, transformational, and global meta-level abilities, while moderate algebraic abilities have moderate generational abilities; transformational abilities tend to be medium to high, and global meta-level abilities tend to be medium to low. Low levels of algebraic thinking ability tend to have moderate to low generational abilities, low transformational abilities, and low global meta-level abilities.

Algebraic thinking is also a human activity from which algebra emerged (Kaput, 2017).
The ability to think should be known so that it can be maximized in the learning process, encouraging algebra abilities to the maximum that students can do with their experience and abilities (Masnia et al., 2022).One is the ability to think algebraically (Kieran, 2004).In the process of working on algebra problems, students carry out generational activities, transformational activities, and global meta-level activities.In line with Wilkie (2016), algebraic thinking is an ability that consists of three primary skills, namely the ability to use algebraic symbols and relationships, use multiple representations (such as symbolic, graphical, and tabular), and formulate generalizations.As shown by research conducted by Jupri (2015) and Şengül & Erdoğan (2014), students do not understand basic algebra concepts such as variables and equations.Likewise, research by Farida & Hakim (2021) and Töman & Gökburun (2022) showed that students' algebraic thinking abilities are still low.
Learning algebra will be easy if combined with technology.Applications are more effective in learning mathematics (Masnia et al., 2020).Education and new technologies can make mathematics education easier (Weinhandl, 2020).
Applications are a technology that makes it easier for students to learn.One application that is often used for algebra is geometry."Geogebra" mathematics software combines interactive geometry, algebra, statistics, and calculus to create the most comprehensive application for generating and explaining mathematical ideas for elementary and university-level students (Dahal et al., 2019).
When technology is integrated into education, the focus should be on the learning process and students rather than technology.Research shows a difference in average learning outcomes between classes that use the Geogebra application and those that do not (Bedada, 2022).The results of learning using the Geogebra application have a good effect (Apriani & Hayati, 2022).
Based on background, this research focuses on how generational, transformational, and global meta-level abilities are based on medium and low-level algebraic thinking abilities.

Table 1. Algebraic Thinking Ability Groups
Based on the data in Table 1, data was then triangulated based on categories of algebraic thinking ability, and two students were selected from each category.
A. High Algebra Ability 1) Subject AT student AT subjects can determine equivalent algebraic forms in transformational activities, carry out algebraic operations, and solve equations.AT subjects are included in high transformational activities.AT subjects' Global meta-level activities can apply algebra in analyzing changes and relationships and predicting problems in mathematics; AT subjects are included in high global meta-levels.
The data triangulation process for AT subjects was carried out through interviews as follows: : What changes have occurred in the questions?AT : changes that occur when the problem is revealed can be solved Q : How did you solve the problem?AT : using the formulas given by the lecturer and looking at the internet as a reference for answers Based on the results of interviews, AT subjects understand the information in the questions given, the variables and their relationships with other variables, and the meaning of the answers given.AT subjects also understand algebraic forms, operate them, and can solve the equations given in the problem.Apart from being able to solve the problem as a whole, the AT subject can also understand the changes that occur in the problem.
The instruments given to AT subjects are in the form of interviews or assessments of students' understanding of algebraic concepts.Subjects called AT demonstrated high-level algebraic thinking abilities based on interview responses.
AT shows the meaning of the problem given, the definition of variables, the relationship between variables, and the algebraic form of the problem equation.
Apart from that, AT can operate and solve algebraic equations, understand changes that occur in the problem, and explain the steps taken to solve the problem.The interview results also showed that AT used formulas taught by teachers and internet references to solve problems.
The interview reflects AT's skills in understanding and applying algebraic concepts and the ability to solve problems using algebraic methods.His responses demonstrated a strong understanding of algebraic thinking and problem-solving skills.

2) GDS Student Subject
Based on Figure 2, GDS subjects answered the questions in order and correctly.The GDS subject is included in the category of high algebraic thinking ability.GDS subjects can engage in generational activities, namely understanding generalizations that arise, understanding variables, and presenting problems by connecting variables.DGS subjects are included in the high generational category.Based on the results of interviews, the GDS subject understands the questions, the variables and their relationships with other variables, and the meaning of the answers.GDS subjects also understand algebra, its operations, and solving equations in problems.Apart from that, GDS subjects can also solve the questions as a whole and understand the changes in the questions.
Based on interview data and tests of algebraic thinking abilities, it appears that GDS subjects demonstrate high-level algebraic thinking abilities.The interview responses showed that GDS understood the questions, the meaning of variables, the relationships between variables, and the algebraic form of the question equations.GDS can also operate and solve algebraic equations, understand changes in the problem, and explain the steps taken to solve the problem.The results of this search further support the GDS assessment of high-level algebraic thinking abilities because they discuss indicators of generational, transformational, and global algebraic thinking abilities in algebraic thinking.
Interviews and algebraic thinking ability test results show GDS's skills in understanding and applying algebraic concepts and the ability to solve problems using algebraic methods.Results demonstrate a strong understanding of algebraic thinking and algebraic problem-solving skills.The author considers that subject AF's answer is included in the moderate algebraic thinking ability category.AF subjects can engage in generational activities, namely understanding generalizations that arise, understanding variables, and presenting problems by making connections between variables, but not until they are finished with the fact that the question is not solved correctly.AF subjects fall into the medium generational category.Based on the interview results, AF subjects understood the questions given, the variables, and their relationships with other variables but did not understand the meaning of the answers.AF subjects also understand algebraic forms and their operations but are less able to solve equations in problems.Apart from that, AF subjects were also less able to solve the questions as a whole and less able to understand the changes in the questions.

B. Moderate algebraic ability 1) AF Student Subject
Based on interview data and the given algebraic thinking ability test results, subject AF shows a moderate algebraic thinking ability.The interview responses show that AF understands the problems, the meaning of variables, and the relationships between variables.However, AF's response lacked detail and did not fully answer the question.AF can determine the equivalent algebraic form of the problem, operate on the algebraic equation, and solve it.However, AF's Ability to analyze, relate, and predict problems using algebraic methods is limited.The results of this search further support AF's assessment of moderate-level algebraic thinking ability because it discusses generational, transformational, and global algebraic thinking ability indicators.
The results of interviews and algebraic thinking ability tests show AF's proficiency in understanding and applying algebraic concepts and the ability to solve problems using algebraic methods.However, AF's Ability to analyze, relate, and predict problems using algebraic methods is limited.
2) RMA Student Subject The process of data triangulation on RMA subjects was carried out through interviews as follows: The following is an excerpt from the RMA Subject's interview Based on the interview results, the RMA subjects showed a reasonably good understanding of the questions given, the variables, and the relationships between variables.RMA subjects can also explain the meaning of their answers and understand algebraic forms and their operations.However, RMA subjects are less able to solve equations in detail and understand the changes in the problem.It shows that the algebraic thinking abilities of RMA subjects tend to be in the medium category, especially in generational and transformational activities.However, RMA subjects still need to improve their abilities in global meta-level activities, especially in applying algebra and analyzing and predicting problems in mathematics.
RMA subjects apply algebraic thinking skills in solving problems, with the first step being deriving the function and determining the t value.RMA subjects understand the meaning of the variables in the problem, namely looking for conditions where the value increases and decreases and when the value reaches a maximum point.RMA subjects can also determine an algebraic form equivalent to the problem given and perform algebraic operations by deriving functions.Based on the interview results, MYH subjects did not understand the questions given, the variables and their relationships with other variables, or the meaning of the answers.MYH subjects also do not understand algebraic forms and their operations and cannot solve equations in problems.MYH subjects could also not solve the questions entirely and could not understand the changes in the questions.
Based on the analysis, the author concluded that the MYH subject's answers were included in the low algebraic thinking ability category.Subjects have low abilities in generational, transformational, and global meta-level activities.Subjects have difficulty understanding problems, variables, and relationships between variables.Subjects also have difficulty understanding algebraic forms operations, and solving equations.Apart from that, the subject cannot solve the problem as a whole and does not understand the changes in the problem.The interview results showed that the subject had difficulty understanding problems, variables, and relationships between variables.The subject also had difficulty understanding the meaning of the answer and its algebraic form.The subject cannot solve the problem and does not understand the changes in the problem.

Figure 1 .
Figure 1.AT Subject Answers

Figure 4 .
Figure 4. RMA Subject Answers The method is to use the derivative of each function in the problem The next activity is a global meta-level activity.In this activity, GDS subjects can apply algebra, analyze, connect, and predict problems in mathematics.GDS subjects are included in the high global meta-levelThe data triangulation process on GDS subjects was carried out through interviews as follows: