Strategic Competence of Pre-Service Mathematics Teachers in Solving Environment and Culture-Based Combinatorial Problems

. Strategy is a very important part in solving mathematical problems. Pre-service mathematics teachers must master a variety of problem solving strategies. The aim of this study is to describe the strategy of the pre-service mathematics teachers in combinatorial problem solving. The instrument used is combinatorial problem-solving with maritime cultural nuances. The results of this study show that the strategies of pre-service mathematics teachers are diverse which are categorized into strategic cognitive, strategic processes, and strategic solutions. In addition, the strategic competence of pre-service mathematics teachers in solving combinatorial problems is categorized into very low strategy, low strategy, medium strategy, high strategy and un-strategy.


Introduction
Mathematical skills are needed by students to solve everyday problems.The National Research Council (NRC) defines mathematical proficiency as an aspect that summarizes what students must master in order to be successful in mathematics.According to Kilpatrick et al., [1] there are five components of mathematical skills in solving problems, namely 1) conceptual understanding, 2) procedural fluency, 3) strategic competence, 4) adaptive reasoning, 5) productive disposition (productive disposition).It can be said that mathematical proficiency is a unity that must be possessed in order to solve mathematical problems properly.
Strategic competence is one of the important components in mathematics skills.Suh [2] said "Strategic competence is one of the strands of mathematical proficiency".Kilpatrick et al., [1] said that "Strategic competence refers to the ability to formulate mathematical problems, represent them, and solve them".Özdemir & Pape [3] said that strategic competence includes knowing, and using strategies to analyze and complete tasks and activities or solve problems in mathematics learning materials.In line with that, Syukriani et al., [4] said that strategic competence is a mental activity in using strategies to formulate, represent and solve problem situations.Ostler [5] states that strategic competence is the ability to form a suitable mathematical model and determine the correct strategy to solve a problem.Egodawatte & Stoilescu [6] said "Strategic competence is necessary to determine the direction of problem solving and to understand which stages to follow through in order to reach a solution".So it can be concluded that strategic competence is a person's ability to formulate and model problems correctly so as to get the right solution.
Mathematical problems can be solved if someone has a strategy to solve them.A strategy is defined as a logical series of actions, such as analyzing information, constructing a problem representation, selecting tools for the solution, and planning the various steps to be carried out to reach the solution [7].So strategy is a logical action in each stage starting from planning, implementation and evaluation.Every student has a different strategy of dealing with problems.
Clements et al., [8] groups three types of strategies in problem solving, namely strategy cognitive, strategy processes, and strategy solutions.Strategy cognitive is a goal-directed and effort-directed procedure that students use to help solve problems.Strategy processes are a form of procedural knowledge where a child knows how to do something so as to improve their ability to solve problems, and strategy solutions are the final form of problem solving.
Combinatorial material is very important material to be taught to students, because it is closely related to everyday life.So that combinatorial material is included in the high school mathematics curriculum.Therefore, educators must be able to teach well to students.The results of the study said that combinatorial material is one of the materials that is difficult for students to teach and understand [9].Combinatorial problems are often used to introduce looping relationships.Most problems do not have a method for solving them, and it creates a lot of uncertainty about how to approach them, making combinatorial a difficult subject to teach and learn.Difficulties in solving combinatorial problems can be overcome by the way educators convey concepts to their students.Therefore, the teacher's strategic competence needs to be improved so that students also have good strategies in solving problems.
So, the aim in this study to describe the strategies used by pre-service mathematics teachers in solving combinatorial problems based on three types of strategies, namely strategy cognitive, strategy processes, and strategy solutions.The problem formulation of this research is how is the strategic competence of pre-service mathematics teachers in solving combinatorial problems?

Participants
This research involved 17 pre-service mathematics teachers who had studied combinatorial material.They come from various areas in the Riau Islands and have seen the Jong Boat (Perahu Jong) Festival in their respective areas.

Procedure
This study begins with giving combinatorial problems (Figure 1) to 17 mathematics pre-service teachers.Furthermore, the answers to the problems were analyzed according to the following strategic competency indicators.

Aspect Indicator strategy cognitive
The subject is able to explain the information and the meaning of the problem Subjects are able to categorize problems into concepts strategy processes The subject is able to describe the problem in mathematical form (symbols, algebra, pictures, etc.) strategy solutions The subject solves the problem so that it gets the correct solution Then the results of the analysis of answers from 17 pre-service teachers were categorized and presented according to the criteria of strategy: a. High strategy, if the correct strategy cognitive, strategy processes and strategy solutions b.Medium strategy, if the correct strategy cognitive and strategy processes, but the wrong strategy solutions c.Low strategy, if the wrong strategy cognitive, strategy process exists but is wrong and the wrong strategy solutions d.Very low strategy, if the wrong strategy cognitive, there is no strategy process and the wrong strategy solutions.
After categorizing pre-service teachers into these levels, one of the pre-service teachers representing each level is chosen to be interviewed further to see the validity of the answers made.They are P1, P2, P3, P4 and P5.

Instrument
The task given to participants was a combinatorial problem related to the culture of the people in the Riau Islands area (Figure 1).Before this task was given to the participants, it was first validated by two experts in the field.After that, the task was tested on one person to see its readability, which aims to determine whether the designed task can be understood.

Results
Based on the combinatorial problems that have been given to 17 mathematics pre-service teachers, the teacher can be grouped into four levels, as shown in Table 2.

Table 2. Strategic Competency Levels of Pre-service Teachers
No Strategic Competency Level Amount (%) From Table 2 it can be seen that only 0.18% of pre-service teacher are included in Level High strategy.This means that only 3 out of 17 pre-service mathematics teachers have the correct strategy until the final answer to the given problem is also correct.And there is 1 teacher candidate who has the right strategy but the final answer to the problem is wrong.While there are still 2 prospective mathematics teachers who enter the level Very low strategy.The unique thing that was found was that 1 pre-service mathematics teacher could not be categorized into that level, so further interviews were conducted.
(Source.edisiana.com)"Perahu Jong" or Jong Boat is a typical Malay folk game that is legendary in the Riau Islands.These Jong Boats rely on strong wind, the festival participants will place their Jong Boats so that they are carried by the wind out to sea in a row.If there are 3 participants from Bintan, 4 participants from Tangjungpinang, 3 participants from Lingga, 3 participants from Karimun, and 4 participants from Batam who will take part in the "Perahu Jong" festival, then determine the number of different arrangements of jong boat if each participant those from the same area must be side by side verbally P3 describes the concept as a process to get a solution.This means that the strategy processes of P3 exist and are correct.When determining the final solution, P3 made a mistake, so an interview was conducted.The researcher asked P3 about the answers that were crossed out.It turned out that the participant hesitated to get the final result whether to use multiplication or addition.Previously the P3 used the multiplication operation, but because the result is large, the subject feels unsure and finally he decides to use the addition operation.This means that P3's strategy solution is wrong, so that P3's strategic competence is categorized into Medium strategy level.

Fig.4.
P3's answer d.High strategy Participant 4's (P4) strategic competence is categorized into high strategy level.This can be seen from the results of interviews and problem solving that have been made by P4 (Figure 5).P4's strategy cognitive is correct, where the subject rewrites important information from the problem posed, and writes down the intent of the problem.After the P4 knows the problem is included in combinatorial material, then the P4 describes the problem into a "model" and is accompanied by words.This means that P4 has carried out the strategy processes correctly.The final solution obtained is also correct, because the subject performs multiplication operations to get as many possible arrangements.This means that the P4's strategy solution is correct.In addition, the researcher also conducted interviews and asked other strategies they could think of to solve the problem besides using models and words as they had been made.It turns out that the P4 has no other strategy to solve it.P5's answer From Figure 6 it can be seen that the P5 directly answered the problems given.Researchers conducted interviews with P5, related to the answers given.The researcher asked where the answer came from and asked the P5 to explain it, it turned out that the subject was able to explain the reason why the answer was like that.Based on the results of the interview, the author concludes that the strategic competence of P5 belongs to Un-strategy.

Discussion and Conclusion
The strategic competence of pre-service mathematics teachers in solving combinatorial problems can be seen from three aspects, namely strategy cognitive, strategy processes, and strategy solutions.In strategy cognitive, most participants at each level rewrite important information, write the intent of the problem.Participants with medium and high levels were able to decide on the concept that should be used to solve the problem.While participants with very low strategy and low strategy levels still made mistakes in formulating concepts.
In strategy processes, participants represent concepts by listing possible arrangements, verbally, making models and algebraic representations.In strategy solutions, can be seen from checking the answers that have been obtained by looking back at the results of previous work.No other strategy is used to see the correctness of the solution obtained.This is in accordance with the research results Keleş & Yazgan [10], Keleş & Yazgan [11] despite the thoughtprovoking questions, most students who correctly answered the problem did not approach the problem from a different perspective.
The strategic competence of mathematics pre-service teachers in solving combinatorial problems is categorized into very low strategy, low strategy, medium strategy, high strategy.Because P5 does not formulate problems and does not create strategies, a category of strategic competency level for pre-service mathematics teachers can be added, namely Un-Strategy, where the description of the level is that there is no strategic cognitive, no strategic processes, and the strategic solution is wrong or right.
This research was conducted online and with limited time, so external factors cannot be controlled.Further research should be conducted face-to-face or offline.Even though there are limitations, it is hoped that the results of this research can be useful for looking at the strategies used in solving mathematical problems related to environment and culture.For example, determining how much waste is produced after a Jong Boat festival is held.