The students’ strategic competence in solving mathematical literacy problems based on cognitive levels in islamic-based schools

DD Septiadi1,4,7 AC Lestari2,5,8 A Hariati3,6,9

1 IAIN Jember, Jl. Mataram No. 1 Jember, Indonesia
2 IAIN Jember, Jl. Mataram No. 1 Jember, Indonesia
3 IAIN Jember, Jl. Mataram No. 1 Jember, Indonesia
4 Jl. Citra Bougenville No 15 Waru Sidoarjo Jawa Timur
5 Jl. Arowana II Kebonagung Jember Jawa Timur  
6 Jl. Simpang III No 2 Oro-Oro-Ombo Pronojiwo Lumajang Jawa Timur
7 septiadi.dimasd@yahoo.com
8 ayuchinintya98@gmail.com
9 arikhariati01@gmail.com

Abstract. Strategic competence is one of the mathematical skills that need to be mastered by students in solving mathematical literacy problems. Therefore, this research aims to describe the process of students’ strategic competence in solving the problems of mathematical literacy based on cognitive levels . The method used in this research is descriptive with a qualitative approach. While the technique of determination the subjects, researchers used the technique purposive sampling by taking 3 subjects that are 15 years old and have high cognitive, moderate, and low in Islamic based school. Data collection technique are conducted with tests, interviews, and documentation. The result showed that students who have a high level of cognitive in solving mathematical literacy problems, namely by writing the known information on the questions, representing information obtained into a mathematical model, and has 3 strategies in interpreting to solved the problems mathematical literacy problems. Students who have moderate levels of intelligence tend not to write down known information, then use the chosen strategy to solve mathematical literacy problems using the PISA model. Meanwhile, students who have a low level of intelligence tend to be less able to understand the problems and difficulties in representing the information obtained.
Keywords: Strategic Competence, Mathematical Literacy Problems, Cognitive Level
1.	Introduction
Mathematicians believe that question can be a problem to be solved. However, not all question can be a problems (Hariati & Septiadi, 2019). Further, Goldstein (2011) define problem as situation cannot be predicted by students. There was a gap between the question and students' knowledge to solve. This condition ask students to use their own logical, analytical, critical thinking and a \ their all knowledge, by integrating it, to solve the problem. One serious condition nowdays is, students are faced a higher order problem, which force them to use such kind of higher order thinking skill. Agung & Schwartz (2007) emphasize nowdays, Indonesia face difficulties in solving word problems. Meanwhile, such kind of problem must be appeared in the Indonesian Curriculum (K13) at all levels of education. This is also supported (Auzar, 2017; Bernardo, 1999; Kristanti et al., 2018; Morin, Watson, Hester, & Raver, 2017) students experienced some difficulties on solving mathematics word problems because their ability to understand the meaning of the problem. Those happened because they are not familiar in solving real life problems, so there is a need for a mathematical approach in a contextual form.
	Mathematics in contextual form will be able to stimulate students' brains to discover and understand new things related to mathematics, because it is directly related to everyday life (Johnson, 2002). According to Crawford (2001), the stages of introducing mathematics in a contextual form consist of relating, experiening, applying, cooperating, and transferring which are abbreviated as REACT. In addition, according to De Corte (2003), mathematics in contextual form can allow students to develop more complex thinking patterns, because it involves formal and informal mathematical knowledge.
Septiadi (2014) states that problem solving can be using an unstructured strategy or structured strategy. In unstructured way, students are allowed to use their own strategy and it can be various from one to another. While, in a structure one, students can use a well-design strategy, it can appear in a specific and constant way. One of them is Polya's problem solving which includes understanding problems, planning strategies, executing strategies, and looking back. (Hayyulbathin, 2017). Consequently in solving problems, of course students need such kind of strategy which can be formed as strategic compentency.
According to Kilpatrick in (Firaisti 2013) mathematics can be mastered properly if students have 5 mathematical skills, namely productive attitudes (students' habits in seeing mathematics as something logical, useful and confident in their own success in mathematics), conceptual understanding (related student understanding mathematical operations, concepts, and relations in mathematics), procedural fluency (students' ability to use stages appropriately and efficiently), adaptive reasoning (students' logical thinking skills in reflecting on and estimating mathematical problems), and strategic competence (students' abilities) in formulating, presenting, and solving mathematical problems.  Therefore, strategic competence is the most important part in solving math problems. However, strategic competence is also influenced by the learning methods applied by the teacher and the level of intelligence and understanding of students. In that sense, students who have a high level of intelligence will be different from students who have a average or low level of intelligence in determining the right strategy in solving math problems, especially mathematics literacy problems in the PISA context which is closely related to the mathematical abilities of students (Sari, 2015).
	PISA or the International Student Assessment Program organized by the OECD (Organization for Economic Cooperation and Development) is a program that aims to assess the ability of 15 year olds in regular reading or reading literacy, mathematics or mathematical literacy, and science or scientific literacy (Edo et al., 2013). Based on the results of the OECD survey (in Lestari, 2020), Indonesia ranks 72 out of 79 participating countries with a score of 379, even though the average OECD member country for mathematics and science is 489. This is what shows that students 'mathematical literacy is still very low, in line with Septiadi's statement (2020) which states that students' ability to solve mathematical literacy problems in the PISA context is still very low. So that Indonesia is required to improve itself in improving students' mathematical abilities. Further, Septiadi at el (2020) explained that PISA-liked problem is a problem which develops outside real PISA-a problem which is developed by several experts outside the OECD . This problem also contains the domain of PISA problem provided by OECD.
	Based on the description above, the researcher feels it is important to analyze students' strategic competences in solving mathematical literacy problems in terms of the level of intelligence that students have. This research is expected to contribute in improving the mathematics achievement of Indonesian students in optimizing students' strategic competencies in solving mathematical literacy problems. Therefore the researcher took the title "Students' Mathematical Strategic Competencies in solving Mathematical Literacy Problems in terms of Cognitive Levels in Islamic-based Schools".

2. Methodology 
This research was conducted at three Islamic-based schools in Jember. It consist of 126 students both male and female. They come from various cognitive levels (low, moderate, high). The type of research used is qualitative with a descriptive approach. The instrument used was a test using mathematics literacy questions in the context of PISA, interviews, and documentation, namely student scores and teacher information through interviews. The data analysis technique used a modified Kilpatrick strategic competency indicator and used method and subject triangulation to test the validity of the data. While the subject determination technique used was purposive sampling technique, which selected several subjects based on the level of intelligence through student scores, with the following criteria:
Table 1. The categorization of the subject
Score	Category	
Score ≥ 80	High	
     Score <80	Average	
Score <70	Low	

Table 2. The modified Kilpatrict strategic competency indicators
Strategic Competence	Indikator	
Formulate	•	Students can understand the problem
•	Students can formulate known and unknown information from the questions
•	Students can select relevant information to the problem	
Represents	•	Students can choose a method as a solution
•	Students can present the problem in the form of a mathematical representation (for example)	
Complete	•	Students can choose strategies in solving problems 
•	Students can use or develop strategies in solving problems 
•	Students can interpret answers
•	Students can solve problems	

3. Result and discussion
The test instrument to gather the data consist of three numbers. Those questions have been already validated by some experts whom expert in designing PISA liked problems. The qustion can be seen at figure 1, figure 2 and figure 3 below. 

Figure 2. PISA liked problem number 2

Figure 1. PISA liked problem number 1

Figure 3. PISA liked problem number 3

To measure the strategic competence of students in solving literacy problems, a PISA model of mathematical literacy test is given which consists of 3 PISA-liked problem. After that, the data obtained from the results of the completion written by 3 subjects with high, moderate, and low intelligence levels and the results of the interviews used as a complement were processed and analyzed. After gathering the data, researchers clasified the result of the test based on the chategory of strategic competence could be reached by students. There were 126 students coming from high, moderate, and low cognitive level and each level consist of the same number of students. The result of 126 students can be seen at the tabel 3 below. 

Table 3. Students result in solving PISA-liked problem based on in strategic competence
Cognitive level	Percentage of students who passed each chategory of strategic competence (among 42 students each)	
	Formulate	Represent	Complete	
High	1.00	0.95	0.95	
Moderate	0.90	0.48	0.38	
Low	0.38	0.16	0.07	

It can be seen from tabel 3 that, the number of students who passed the test until the end getting lessen for every cognitive levels. At high cognitive levels, at the first time all students were able to understand the problem at the formulate stages. Further, it was getting lessen at 0.95 during 42 students could reach represent stage. At the at, this number remain stable. The lessen tendency also happened at moderate level. However, only 0.90 students passed the first stage, then jumped to 0.48 at the represent stage. In the end, only 0.38 who can pass the final solution. In the last level of cognitive level, only 0.38 students could understand the problem, which was at formulate stage. This number fell to 0.16 at the next stage, represent, and reached the lowest position at 0.07 who can find the correct solution. 
Based on the result, every cognitive level has their own strategic competence tendency while solving those problems. This section will describe how the strategic competences used by the subject to understand and formulate known and asked problems, how to represent a problem, and how to solve problem for each number. Students use certain strategies to understand problems so they can forma mental picture of the problem situation, then can represent the problem situation in another form (Kilpatrick, 2001). Using strategies in understanding, formulating, representing, and solving problems is greatly influenced bystudent learning experience.

3.1 High level students
High level students have their own pattern of strategic competence. It can be seen from the pattern in solving PISA-liked problem number 1, 2 and 3.Question 1, 2 and 3 were used to see the consistency of strategic competencies.

Question No. 1
Based on the results of problem solving in question number 1, S1 is able to understand the problem well. This can be shown from the following documentation of S1 work:

S1 wrote the information known from question and represented the information in the form of equation.

S1 found the strategy 1 by separating in Greenwich at 1 p.m.

 
Figure 4. Formulating and Representing

From the picture above, S1 has been able to meet the indicators of formulating and representing because it can find information and then write down what is known from questions such as Jakarta = 07.00 (morning), Ankara = 02.00 (morning), Greenwich = 23.00 (night), Sydney = 11.00 (noon) ), the duration is 1 hour, and can represent the information it gets in the form of an example as S1 wrote in the known section, namely Jakarta = 07.00, (morning), Ankara = 02.00 (morning), and so on, where the sign is equal to between the name of the city and the time is a form of example or representation of the information that S1 gets, besides that S1 can also mention what is asked in question number 1 during the interview. As stated by Gafur (in Surya, 2017) that students' initial abilities are the basis of student knowledge before solving math problems. S1 also fulfills the completing indicators because S1 can choose and use several strategies in solving question number 1 and S1 can interpret the answer.This is in accordance with Liang's (2010) research which states that after a mathematical strategy is formed, students can perform mathematical procedures to obtain a mathematical solution to the problem. S1 thinks strategy 1 failed because Sidney got the results at 12 in the evening after S1 took Greenwich at 1 in the afternoon. In strategy 2, S1 writes the results for the city of Greenwich at 2 in the morning after S1 for example in the city of Sidney at 1 in the afternoon and based on the interview, S1 says strategy 2 is wrong because the result for the city of Greenwich is 2 in the morning, while in strategy 3, S1 assumes that It is true by supposing the city of Ankara at 8 pm, resulting in the city of Jakarta at 3 pm, the city of Sydney at 7 pm, and in Greenwich at 5 pm. Of the 3 strategies used by S1, it can also be said that S1 has been able to solve the problem in question number 1 even though the concepts, strategies, and final results that S1 wrote are wrong. This is in accordance with Kurniawati's (2017) research that students tend to have weaknesses in relating information to concepts, representing problems, formulating hypotheses, developing strategies, and checking final results.

Question No. 2

S1 wrote the information known from question and represented the information in the form of equation.

S1 found the strategy using the  concept of difference

Figure 5. Formulating, Representing, and Completing
In the picture above, it can be seen that in question number 2, S1 has met the indicators of formulating as well as representing, because S1 can formulate the information needed or information known from the graph of question number 2 by writing the number of visitors who enter and the number of visitorswho leave in 08.00 to 13.00, and can present the information that is obtained in the form of an example like what S1 wrote in the known section, namely entering = 120, 84, 102. 97, 50,123 and so on. The equal sign of the representation is the form of the example written by S1. This is in accordance with Kilpatrick's (2001) description that students should only capture important parts of the questions and see the relationship.In addition, S1 also fulfills the completion indicator because it can choose and use strategies, as explained by S1 during the interview that the S1 strategy use in solving question number 2 is with the concept of the number of incoming visitors added up, and reducing the number of visitors who leave, namely , then and so on so that S1 can interpret the answer to question number 2 even though the final result written by S1 is wrong because there is an error in counting the end result.This is in accordance with the research of Sari, et al. (2016) which states that the problem in the PISA context that gets the most errors in encoding answers is the literacy context.

Question No. 3

S1 wrote the information known from question 

S1 found the strategy using the  concept of abroad

	
Figure 6. Formulating and completing
Whereas in question number 3, S1 has also been able to meet the indicators of formulating and representing information because through the interview S1 can mention information that is known from the questions as S1 wrote in the known section, namely the size of the land is 100 x 100 cm2and the distance between tobacco is equal to 60 cm, and 4 tobacco, requiring 260 x 260cm2of land. After that, based on the interview, S1 chose and used a strategy by dividing the land area by the area of ​​4 tobacco that was written down  and then 14.79 which was the result of the division multiplied by 4 tobacco and resulted in 59.16. Then S1 interprets the answer to question number 3 by rounding it down so that the final result is 59. 
From those three PISA-liked problems, it can be seen students’ strtegic competencies in solving the problems. Those strategic competency can be seen from figure 4 below.

Problem solved

Formulate

F3

F2

F1

Failed

Represent

MS

R2

R1

Failed

Complete

C1

FS

C2

Failed

Failed to solve

Figure 7. the flow of strategic competence in solving PISA-liked problem for high level students
	
Noted:
F1	State the given information	MS	Develop multiple strategies, more than one 	
F2 	Understand the problem	FS	Further strategy from beforehand strategy	
F3 	State the necesary information	C1	implement the strategy to solve the problem	
R1	Represent as another object/figure/picture	C2 	Write the conclussion	
R2	Reperesent by using students’ own sentences			

3.2 Moderate level student

Question No. 1
In question number 1, S2 which has a average level of intelligence fulfills the formulating indicators because it can mention the information contained in the questions, namely the land area of ​​100 x 100 cm2 and the distance between plants which is 60 cm. However, S2 could not understand the content of the questions, so S2 could not represent the information that S2 found and could not find a strategy that should be used in solving problem number 1. Likewise, according to Wijaya (2016), it turns out that Indonesian students in solving PISA problems have difficulty understanding problems, solving context-based problems, and turning them into math problems. Therefore S2 did not do problem number 1. Students 'problem solving difficulties do not always stem from a lack of mathematical knowledge, but rather from students' ineffective knowledge, because they lack the metacognitive skills needed to control, monitor, and reflect on the process of finding solutions (Schoenfeld, 1992).
In question number 2, S2 is able to understand the problem in question well. This can be shown from the documentation of the following S2 work:

Question No. 2

S2  represented the information in the form of equation and found strategy using the concept of difference

Figure 6. Representing and Completing
In the picture above, S2 does not write down the information that he finds, but S2 can mention the information contained in the question, namely the number of incoming and outgoing visitors at different times and can explain the information needed to solve question 2, namely the number of visitors entering and left 08.00 to 13.00 because the number of visitors was expected at 13.00, at the time of the interview. In representing the information on the graph presented in the questions, S2 writes the number of visitors entering until 13.00 = 120 + 84 + 97+ ... and so on where the equal sign is the form of the example representation that S2 uses. While solving problem number 2 , S2 chooses and uses a strategy by adding up all incoming visitors from 08.00 to 13.00, totaling all visitors leaving from 08.00 to 13.00 as well. This includes the development of a strategy, because first adding incoming and outgoing visitors will be more efficient and faster when looking for the number of visitors at 1:00 p.m., namely by reducing the number of incoming visitors with the number of visitors leaving until 13:00 so that S2 can immediately interpret the answer to question number  2 namely 576 - 530 and the final result was 46 visitors.

Question No. 3
In question number 3, S2 is also able to understand the problem well. This can be shown from the documentation of the following S2 work:

S2  found strategy using a broad concept

S2  represented the information into the iamge form

Figure 7. Representing and Completing
From the picture above, it can be seen that S2 fulfills the formulating indicators by writing and mentioning the information in question number 3. In representing information, S2 illustrates what he understands from the problem. Then S2 solves problem number 3 by using the strategy of dividing the land area, which is 10000 m2 with the distance between plants, which is 3.6 m2 and based on interviews to facilitate calculations (without commas) S2 multiplies both numbers by the number 10 so that it becomes 100000 divided by 36 and the result is 2777.77, then S2 rounds up to become 2777.78 which is the final result of the answer to question number 3.This is in accordance with Lutfianto's (2013) research that when students do not pay attention to what is being asked in the questions, of course the answers written by students are not complete.
From those three PISA-liked problems, it can be seen students’ strtegic competencies in solving the problems. Those strategic competency can be seen from figure 5 below.

Problem solved

Failed to solve

Formulate

F2

F1

Failed

Represent

SS

R2

R1

Failed

Complete

C1

C2

Failed

Figure 5. the flow of strategic competence in solving PISA-liked problem for moderate level students

           Noted:
F1	State the given information	SS	Develop single strategy, more than one 	
F2 	Understand the problem	C1	implement the strategy to solve the problem	
R1	Represent as another object/figure/picture	C2 	Write the conclussion	
R2	Reperesent by using students’ own sentences			

It can be seen from those figure that in this level was bit different with the high level. There were several parts did not exist in this level. 

3.3 Low level student

Question No. 1
In question number 1, S3 which has a low level of intelligence fulfills the formulating indicator, because S3 can briefly mention the information known in question number 1, namely the difference in hours in several cities. However, S3 could not understand the contents of the questions well. This is in line with the research of Ismail et al. (2018), which revealed that students' abilities were still very low in understanding the information provided in the questions. As a result S3 could not represent the information he had found and could not solve question number 1, because based on the interview S3 did not understand, was confused, and had difficulty finding the right strategy to solve the questions on number 1 so that S3 does not do question number 1. This is in accordance with what Kurniati (2017) states that students can find information on questions correctly, but cannot represent data in a mathematical model.
In question number 2, S3 is able to understand the problem in detail. This can be shown from the documentation of the following S3 work:
Question No. 2

S3  represented the information into the form of symbol and found strategy using the concept of difference

       Figure 8. Representing and Completing
From the picture above, it can be seen that S3 fulfills the formulating indicators because it can mention and write down the information contained in the questions in detail, namely writing down the number of visitors who enter and the number of visitors who leave based on the time from 08.00 to 16.00. This is in accordance with Durant's (2020) research which states that students 'mathematical competence describes students' ability to identify questions, variables, relationships, or assumptions that are relevant in everyday life. From what is written, it is also a form of representation, for example, the symbol M which means the number of incoming visitors, the symbol K which means the number of visitors leaving, and the equal sign between the time, symbol, and number of visitors. Meanwhile, in solving question number 2, based on the S3 interview, a strategy was used by adding incoming visitors and reducing the number of visitors leaving until 16.00. S3 immediately adds visitors who enter from 08.00 with visitors who enter at 09.00 because at 08.00 there are no visitors leaving, after that S3 reduces the results with visitors who leave at 09.00, and so on until 16.00 the number of visitors is 0. From the process, S3 can interpret the answer to question 3 (number of visitors at 1:00 p.m.), which is 46, so that S3 writes a conclusion on the answer to question number 3, namely at 1:00 p.m. there are 46 people (number of visitors). As stated by Turner (2010) that solving mathematical problems involves a collection of critical control processes that direct individuals to recognize, formulate and solve problems effectively.

Question No. 3	
Whereas in question number 3, S3 was not able to understand the problem in the question. This can be shown from the documentation of the following S3 work:

S3  represented the information into the form of symbol and found strategy using abroad concept

Figure 9. Representing and Completing
In the picture above, it can be seen that in question number 3, S3 is also a formulating indicator because it can mention and write down information on the questions, namely the land area of ​​100 x 100 m2 and the distance between plants is 60 cm, even though S3 is actually still confused. From the information obtained, S3 represents it in the form of the symbol L which means the area of ​​land and converts units of m2 to cm2. This is in line with Sari's (2017) research, which states that most students are less able to interpret the data provided in PISA questions and find it difficult to use mathematical concepts and procedures to solve problems. Meanwhile, in solving question number 3, based on the S3 interview, he felt confused about choosing the right solution strategy, he had to use the circumference concept or the broad concept, but according to S3 the broad concept was more appropriate to solve the problem in question number 3. And in the process of solving math problems, students must be able to translate mathematical reasoning or solutions into the context of the problem and determine whether the results make sense or not (Ambarita, 2018). After multiplying the land area and the result is 100000000 cm2, S3 reduces it by 10000 which is the edge distance on the land. After that, S3 divides the results of the measurement by the distance between plants, namely 60 cm and the final result is 1666660 seeds.
From those three PISA-liked problems, it can be seen students’ strtegic competencies in solving the problems. Those strategic competency can be seen from figure 6 below.

Complete

Represent

Formulate

Problem solved

C1

R1

R2

F1

F2

C2

SS

Failed to solve

Failed

Failed

Failed

Figure 10. the flow of strategic competence in solving PISA-liked problem for moderate level students

Noted:
F1	State the given information (unlclear)	SS	Develop single strategy, more than one (unclear)	
F2 	Understand the problem(unlclear)	C1	implement the strategy to solve the problem	
R1	Represent as another object/figure/picture/symbols	C2 	Write the conclussion	
R2	Reperesent by using students’ own sentences (unclear)			
It can be seen from those figure that in this level was totally different with the high and moderate level. There were several parts did not exist in this level and unclear things in the path.

4. Conclusion
Based on the description of the results of the discussion above, it can be concluded that in Islamic-based schools, students who have a high level of cognitive in the formulate indicator he writes the information on the question. On the represents indicator he found 1-3 strategies to solve the problem. As for the complete indicator, he developed the strategy, resolved the problem and wrote down the conclusion that was the solution to the problem. In students who have moderate cognitive levels, can mention the known though not written so as to include the formulate indicator. In the Represente indicator, he presented the information to the form of sentences and images, and found only 1 startegi. As for the complete indicator, he can solve the problem and write down the conclusion.
Meanwhile, in students with low cognitive levels, they can write down the known questions at a glance which include the formulate indicator. In the Represente indicator, he presented the information to the form of symbol. As for the complete indicator, he solves the problem according to his abilities and knowledge.

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