Mathematics is one of the subjects that plays an important role in the field of education. Mathematics is a basic science that needs to be taught to students from the early stages of formal education. Mathematics is a science that can be applied to all aspects of everyday life. ((Djamilah et al., 2023); (Nurmeidina et al., 2022); (Lestari et al., 2021)). Moreover, mathematics itself is also a subject that has a significant role in improving students' abilities and human civilization. (Zaqiyah & Djamilah, 2021). According to value of mathematics, the idea behind mathematics education is to foster higher-order thinking skills, such as mathematical creativity through problem-solving (Baiduri et al., 2022).

According to the National Council of Teachers of Mathematics NCTM (Suci Rahmawati et al., 2019), There are five competencies in learning, namely: mathematical problem solving, mathematical communication, mathematical reasoning, mathematical connections, and mathematical representation (Ulfah, 2022).

Problem solving skill is needed by students to develop their mathematical skills, as expressed by (Husna et al., 2013), Problem solving ability is referred to mathematical power or mathematical skills (doing maths). So mathematics can be categorised into lowlevel thinking and high-level thinking. Polya in (Hendriana & Sumarmo, 2017) stated that problem solving is an effort to find a way out of a goal that is not easy to achieve immediately. Based on the description above, it can be concluded that problem solving is a process of overcoming the difficulties faced by using the knowledge possessed to achieve the goal. This research will use Polya's problem solving. The indicators of Polya's problem solving stages are as follows: Understanding the problem, Developing the plan, Implementing the plan, and Looking back (Hanifah, 2021)(Simarmata & Hijriani, 2020).

The mastery of problem solving does not only improve students' understanding of mathematical concepts, but also equips them with logical and systematic thinking skills that are useful in various aspects of life (Nurmeidina et al., 2021). However, the observations during online PPL at MA Muhammadiyah 2 Al-Furqan showed that there were still many students in class X IPA who experienced difficulties, especially in SPLTV material.

The majority of them had problems in determining the right strategy to solve the problems that was presented by educators, so it had result in unsatisfactory learning outcomes (Wijaya et al., 2019). One of the factors is the lack of students' attention to the material that was presented and the lack of active involvement in the learning process. Even when there was an opportunity to ask to educators about the clarity of the material, students' responses tended to be silent. After being interviewed, students admitted that they felt embarrassed to ask questions. They were more willing to give opinions after being appointed directly by the educator, even without understanding the material presented fully. Therefore, it is important for students to be able to determine the right strategy in solving problems as an indicator of successful problem solving (Sa'adilla et al., 2020) Measuring students' problem-solving skills can be done by solving problems which relates to the System of Linear Equations of Three Variables (SPLTV) material. (Afriansyah et al., 2023). SPLTV was chosen for the research because this material always be met by students in school mathematics problems.

Measuring students' problem-solving skills can be done by solving problems which relates to the System of Linear Equations of Three Variables (SPLTV) material. (Afriansyah et al., 2023). SPLTV was chosen for the research because this material always be met by students in school mathematics problems.

SPLTV involves various types of problems, both in pure mathematics format and in the context of life stories. (Asok & Hashanah, 2021;(Rani & Maarif, 2021)).

In solving the problem context, students are expected to be able to construct a mathematical model of the story problem, make a plan, and fulfil the indicators of problem solving ability. If students are able to fulfil these indicators, it can be assumed that they have good problem solving skills so that it will make it easier for them to deal with problems that arise in SPLTV material.

Beside paying attention to problem solving ability as students' cognitive aspect, it must also pay attention to affective aspects in the learning process. One of these affective attitudes is the habit of mind. Based on (Syukria et al., 2013) in learning, students must have attitudes and behaviours that are conducive in learning and utilising thinking skills, namely students must connect new knowledge and skills with what they have already knew.

It can help students broaden their horizons so that the important goal of learning is to be able to use their knowledge meaningfully. In general, all mathematics materials require problem-solving skills ((Faiziyah et al., 2024);(Wahyudi et al., 2020)). Three-variable linear equation is a subject that requires problem-solving skills to learn. Based on (Akbar et al., 2017), in learning process, habits of mind can be observed in the classroom, such as enthusiasm in responding to questions from educators, students' desire to develop problem-solving strategies, and how willing students are to explain the solutions they get.

Habits of mind are the tendency of students' intelligent behaviour in problems solving that are not immediately known. Habits of mind consists of two words, namely "habits" and "mind". In this study, habit of mind is defined as 'habit of thinking'. Habits of mind are defined by Costa dan Kallick in (Dwirahayu et al., 2018) as a characteristic of intelligent people when faced with problems that do not easily know the solution. Based on (Marita, 2014), habits of mind are a group of skills, attitudes, and values that enable a person to develop performance or behavioural intelligence based on the stimulus provided to guide students in facing or solving existing problems. Based on the understanding above, habit of mind is the tendency of students' intelligent behaviour in problems solving that have no known the solution immediately.

(Costa & Kallick, 2015) identified 16 habits of mind when individual address problems in a cerebral manner, which are as follows:

a. Endure or never give up.

b. Regulate conscience.

c. Listening to other people's opinions with empathy.

d. Think flexibly.

e. Metacognitive thinking.

f. Seeking to work thoroughly and precisely.

g. Asking questions and raising issues effectively.

h. Utilising old experiences to form new knowledge.

i. Thinking and communicating clearly and precisely.

j. Utilise the senses in collecting and processing data.

k. Inventing, imagining and innovating.

l. Enthusiastic in responding.

m. Dare to take responsibility and face risks.

n. Funny.

o. Interdependent thinking.

p. Continuous learning.

From 16 characteristics in this research, only 9 habits of mind will be used in this research, namely: (1) persevere or never give up, (2) regulate conscience, (3) think metacognitively, (4) be thorough and precise, (5) ask questions and raise problems, (6) utilise old experiences to form new knowledge, (7) be enthusiastic in responding, (8) dare to take responsibility and face risks, and ( 9) learn continuously.

Based on Masnis' research result (2017), it explained that the relationship between the ability in mathematics problem solving and mathematics habits of mind. The difference between this research and the previous research is that this research will describe the problem solving ability and habits of mind habits of students and the questions that will be used to test the problem solving ability are contextual questions. ((Kamaruddin et al., 2020);Noviantari, 2018). (Nurmeidina et al., 2022) stated that the ability to think creatively is closely related to the habits of mind of high school students. In this case, the indicators of creative thinking are also in line with problem solving ability. Therefore, it is needed the research that can find out students' problemsolving skills, including the mistakes they often make and their relationship with habits of ts. The results of this analysis can be used to evaluate learning methods and motivate students in solving mathematics problems.

Polia in (Hendriana & Sumarmo, 2017), states that problem solving is an effort to find a way out of a goal that is not easy to achieve immediately.

According to Krulik dan Rudnik (Hendriana & Sumarmo, 2017), Problem solving is a process in which individual uses the knowledge, skills, and understanding that they have acquired to solve problems in unusual situations. Based on the `description above, it can be concluded that problem solving is a process of overcoming the difficulties faced by using the knowledge possessed to achieve goals (Saifulloh et al., 2024).

There are four stages of problem solving ((Madya et al., 2023);(Basadur et al., 2014);(Cahyani & Setyawati, 2017);(Savic, 2016)) namely understanding the problem, planning to solve the problem, planning the problem, and reviewing the results obtained. Polya's four stages are as follows:

The first stage in problem solving is understanding the problem. Students need to identify what is known, what information is present, the relationships and values involved, and what they are looking for (Widodo & Turmudi, 2017). There are some suggestions that can help students to understand complex problems, namely: asking questions about what is known and what is sought, explaining the problem in their own words, explaining the problems with their own words, relating it to other similar problems, drawing attention to important parts of the problem, developing models, and drawing diagrams.

Students need to identify the operations involved as well as the strategies required to solve the given problem. (Montague et al., 2000). Students can do this by: guessing, developing models, sketching diagrams, simplifying problems, identifying patterns, creating tables, experiments and simulations, and sorting data/information.

What is implemented depends on what has been planned before and also includes the following: interpreting the given information into mathematical form and applying strategies during the on going process and calculations. In general, at this stage students need to defend the plan they have chosen. If the plan can not be implemented, then the student can choose another method or plan.

The following aspects need to be paid attention when reviewing the steps previously involved in problem solving, namely: re-examining all the important information that has been identified, re-examining all the calculations that have been made, considering whether the solution is correct or logical, looking at other alternative solutions and re-reading the question and asking yourself whether the question has been answered.

Meanwhile, according to Gagne (Budiarti & Mahendra, 2020)(Shishigu et al., 2018)(Wagner et al., 2014), there are five steps that must be taken to overcome this problem, namely:

a. Present the problem in a clearer form,

b. Stating the problem in an operational (solvable) form,

c. Develop alternative hypotheses and working procedures that are considered good for use in problem solving.

d. Test the hypothesis and make efforts to obtain results (data collection, data processing, etc.), the results may be more than one.

e. Re-examine whether the results obtained are correct, or perhaps choose the best alternative solution.

Based on the stages of problem solving previously described, it is concluded that this research will use Polya's problem solving. The indicators of Polya's problem solving stages are as follows:

a. Understanding problem indicators include: determining what is known and asked about the problem and explaining the problem in your own words.

b. Indicators of plan making include: using all available information to solve the problem and make a plan for the solution steps.

c. Indicators of plan implementation include: using the solution steps correctly, applying strategies during the process and calculations.

d. Indicators of Looking back include: writing conclusions on answers.

Linear equations with three variables are considered as challenging material for students. ((Imaroh & Ulumul Umah, 2021); (Hariati & Septiadi, 2019); (Laksana & Fiangga, 2022); (Sasmita & Qohar, 2021)). Problem-solving skills are required to solve contextualised problems in this subject (Ahdhianto et al., 2020). In addition to problem-solving skills, habits of mind are also needed so that students can correctly interpret the meaning of contextual problems. ((Wardani et al., 2022); (Yandari et al., 2019)).

In this class, the learning of linear equations of three variables is carried out using blended learning method that combines face-to-face and online learning methods ((Helsa et al., 2021); (Minarti & Hakim, 2022)). Blended learning alternates between these two approaches each week. ((Kurnia et al., 2022); (Setiyani, 2019)). This method allows students to get benefit from the advantages of offline and online teaching, create a dynamic and interactive learning environment that enhances their understanding of the subject matter. Based on this explanation, it is important to examine the analysis of students' problem solving ability in solving contextual problems of linear equations of three variables in terms of habits of mind ((Hamzah et al., 2022); (Purnomo & Suparman, 2020)).

This research will discuss in depth the importance of problem solving skills in learning mathematics, especially on the subject of System of Linear Equations of Three Variables (SPLTV). The researchers will elaborate Polya's problem solving stages and how these stages can be applied in the context of SPLTV learning. In addition, this study also will explore the relationship between students' habits of mind and their ability to solve mathematical problems. Observation data from class X IPA at MA Muhammadiyah 2 Al-Furqan will be analysed to provide insights into the students’ challenge to face and the strategies that can be implemented to improve their problem-solving skills. Readers will get better understanding of effective learning methods, as well as how habits of mind can contribute to students' academic success in mathematics,

This type of research is qualitative research with descriptive method. This research uses a qualitative research design by giving a problem-solving ability test and a habit of mind questionnaire as well as indepth interviews to the research participants. Qualitative research uses various scientific techniques to obtain an in-depth understanding of the events experienced by research participants, as well as providing oral and written explanations in a unique natural environment. The analysis of problem solving ability based on habits of mind in the context of this study aims to provide an explanation that the use of a qualitative approach is to explore the relationship between problem solving ability and habits of mind which are believed to be interrelated. The results of the reseach are expected to provide a deeper understanding on how students' problem-solving skills and habits of mind affect their ability to solve contextual problems after participating in online learning about the system of linear equations of three variables (SPLTV).

This research aims to confirm or refute the alleged relationship between problem solving ability and students' habits of mind in the previous research. The results of this research are expected to provide a clear description of students' problem-solving skills and habits of mind. Students who have high-level thinking skills are also expected to have high problem-solving skills, and vice versa. To collect data, this research used several methods, including the use of questionnaires about thinking habits, problem solving ability tests, and in-depth interviews.

The respondents of this research were st udents of class X IPA MA Muhammadiyah 2 Al-Furqan. These students took part in learni ng mathematics using blended learning. The learning was done in two ways, namely offli ne in class and online using Zoom. The selec tion of the respondents in this study used pur posive sampling technique, namely sample s election with certain considerations. The resp ondents of this study were students who carr ied out online learning on SPLTV material. They were given tests to measure problem so lving skills and habits of mind. The selection of respondents were based on the results of t he answers to the problem solving questions and the habit of mind questionnaire that had previously been given to groups of students i n the high, medium, and low classifications. The research location was MA Muham-madi yah 2 Al-Furqan, class X IPA, even semester of the 2020/2021 academic year.

The problem-solving ability assessment score is adapted from (Akbar et al., 2017), where the assessment sheet refers to the four stages of problem solving. The assessment sheet can be seen in the following table:

In this research, the questionnaire instru ment was used to measure students' habits of mind. The assessment of students' habits of mind uses a Likert scale.

The data collection technique was adap ted from (Wijayanto et al., 2018) using the highest score 10.

The steps in determining the category of habit of mind was taken from (Arikunto, 2013). The data analysis techniques which was used : (1) data reduction, (2) data presentation, and (3) conclusion drawing and verification (Baring & Berame, 2022).

The data in this study were obtained through three methods, namely written tests, questionnaires, and interviews. The written test instrument given to the participants of research contained each of the measuring instruments for the ability to construct mathematical proof. ((Herdiansyah et al., 2024); (Lazwardi et al., 2022).). The results of this research will describe the results obtained during the research. The 6 participants who took the SPLTV question and the habit of mind questionnaire can be seen in Table 6.

Based on Table 6, it is known that students have high problem solving skills, and their mathematical thinking habits are also high. Students who have moderate problem solving ability so they have moderate mathematical thinking habits. Students who have low problem solving ability, then their mathematical thinking habits are also low. The interview results show that there were three participants who don’t be able to understand all of the information in the question. They are not familiar with the problems that was presented in the form of a story. In (Fuady et al., 2021) research stated that students felt that they didn’t understand well about the material that was explained by the teacher in online class. In line with the research above,(Djamilah & Lazwardi, 2020) stated that regarding students' difficulties in associating many concepts with the problems so the students had difficulty in determining the steps that must be taken in proof, and difficulty imagining the general properties of an object or number due to different experiences.

Based on the results of the research and the discussion, several main findings can be concluded. Firstly, students' problem-solving ability is closely related to their habits of mind. The students who have high problem-solving ability tend to have high thinking habits as well, and vice versa. Second, students' problem-solving ability in solving contextual problems in blended learning on SPLTV material is high in the indicator of understanding the problem. Third, students' problem-solving skills are medium on the backward-looking indicator, and relatively low on the indicators of making plans and implementing plans. In addition, students' habits of mind is vary from moderate to high on the indicator of perseverance or never giving up, and from moderate to low on the indicator of enthusiasm in addressing and taking responsibility and facing risks.

These findings answered the research questions by showing the relationship between problem-solving skills and students' habits of mind, as well as providing a detailed picture of students' level of ability in specific aspects of problem-solving in SPLTV material in blended learning. These condition contribute to a broader understanding of how habits of mind can influence students' problem-solving skills in an online learning context. This conclusion also directly relates to the research objectives outlined in the introduction, namely to identify the relationship between thinking habits and students' problem-solving skills, and to evaluate students' problem-solving skills on SPLTV in the context of online learning.

For future research, it is recommended to further explore teaching strategies that can improve students' critical and analytical habits of mind, as well as to investigate other factors that may affect students' problem solving ability in the context of blended learning. In addition, further research can be conducted to overcome the limitations faced in this study, such as a larger sample and a variety of different learning methods.