Cognitive System of Students in Solving Proportion Problems

: Cognition and learning mathematics is two things that aren’t could separated. Cognitive is related to “thought” domains with how a student obtain process and use knowledge. Cognitive systems are implemented from the domain of memory, manipulate knowledge and use that knowledge. Besides this, system is tasked with processing information or knowledge effectively in completing tasks. This research purpose is to describe students’ cognitive system in solving proportion problem based on Marzano's taxonomy. This research is descriptive qualitative research using test about proportion and an interview guide to collect data. subject in this reseach are 2 students at SMPN 3 Sumenep. The results showed that the subject has do system cognitive that is retrieving knowledge, comprehending knowledge, analyzing knowledge, and using Knowledge even if one subject not yet perfect


INTRODUCTION
Cognition and learning mathematics is two things that aren't could separated. This is because somebody could said study if cognitive processes occur in himself, included in the study math (Burner in Sutaro , 2017). Piaget argued that cognitive development has a very important role in the learning process ( Sutarto, 2017). Cognitive is an important aspect in child development related to learning or thinking skills (Andarwulan, et al , 2021). Besides that realm Cognitive is also one aspect in achievements learning (Permendikbud , 2013). Because that very urgent for educators for understanding the cognitive processes participants he taught.
Cognitive is related "thought" domains with how a student obtain process and use knowledge and domain is also familiar for educator ( Kasiligam, 2014 ). Cognitive is a thought process to relate, judge, and consider occurrence (Susanto, 2011). Cognitive is also interpreted as a mental activity related to perception, thought, memory, and information processing that allows a person to gain knowledge, solve problems, and plan for the future (Daryanto, 2010 ). Cognitive systems are implemented from the domain in memory, manipulate knowledge and use that knowledge besides this system is tasked with processing information or knowledge effectively in completing tasks (Marzano & Kendall, 2007). Marzano and Kendall (2007) split the system cognitive into four components namely retrieving knowledge, comprehending knowledge, knowledge analysis analyzing knowledge, and using Knowledge. Following this position system cognitive in completion task on Marzano 's taxonomy model.
As in the knowledge component of Bloom's taxonomy, retrieving knowledge involves recalling information from memory. At a higher level, comprehending knowledge requires identifying what is important to remember and assigning information to appropriate categories. analyzing knowledge is more complex than simple understanding, the cognitive processes in knowledge analysis are adjustment, classification, error analysis, and specification. The last process is the using knowledge is the process of using the knowledge they have acquired. The following is Marzano's taxonomic knowledge processing (Marzano & Kendall, 2007).
The following tables show the categories of reasoning processes and terms (expressions) used to indicate these reasoning processes in Marzano's taxonomic cognitive system (Marzano & Kendall, 2007).

Reasoning Process
Information Recalling Reproducing the required information Recognizing Carefully identify the statement to which it relates Executing Performing a mental process or physical procedure.   Proportion is one subject in mathematics taught in grade 7 (seven). According to mathematic dictionary, proportional can be interpreted Describes the relationship between 2 quantities are such that they both change by the same factor. Proportion is something method assessment or investigation with stage compare two or more object study for add and deepen knowledge about object studied (Basah, 1994: 7). Example proportion problem in life daily that is compare speed a student paddle bicycle going to school based on distance and time traveled to school. Another example is compare many workers needed for complete job certain with difference specified time.
Although impressed simple, however fact many students who are still difficulty complete related with proportion problems. Based on results interview with a teacher at SMPN 3 Sumenep who said that still many students who obtain score under 75 on a test on the material proportion. Most student still confused if do different matter from about exercises that have been discussed. However there are also students who have capable apply draft proportion in complete problem. it showed with student answer about the exam with right.
Based on the description above, in research this will study about system cognitive students in solving proportion problems.

METHOD
The data obtained in this study are verbal data, therefore this research includes descriptive qualitative research (Arikunto, 2010: 21). The main instrument in this research is the researcher himself, while the supporting instrument is the test and interview guide . cognitive system of subject described based on completion written from about story Theory that comparison given as well as results interview with subject related the resolution .
Subject 1 (S1) and Subject 2 (S2) in study this are 2 students SMP Negeri 3 Sumenep. The subject chosen based on completion results proportion problems and considerations of mathematics teachers about the flexibility of students in communicating and expressing their ideas in finishing about. proportion problems. Following this is proportion problems given to Subject. -The process of thinking and how the thinking process of students in solving material story problems comparison in terms of Marzano's taxonomy Level 1 ( retrieving knowledge ) : Recognizing and Executing , namely recognizing difference unit time and make it to in unit same time. Level 2 ( comprehending knowledge ) : Symboling , namely making lots of comparisons machine capped bottles in 2 minutes by symbolizing as a certain variable. Level 3 ( analyzing knowledge ) : Comparison, namely compares linkages many bottle that can closed and time machine that has is known for know method complete question. Specifying, namely predict what will appen to total bottle that can closed if machine work with a different time.
Generalizing, namely making a mathematical model in direct proportion. Level 4 ( Using Knowledge ) : Problem solving, namely completing the direct proportion that has been made to in a mathematical model. Decision making , namely drawing conclusions from what is being asked. Problem 2 The ratio of money savings Ayu , Bianca and Caca are 8:7:3. Difference in money savings Ayu and Caca are IDR 2,000,000.00. how much total money savings all three? Purpose Through this question will be studied: -The process of thinking and how the thinking process of students in solving material story problems comparison in terms of Marzano's taxonomy Level 1: Recalling and Executing, namely registering and creating ratio total money Ayu , Bianca and Caca as well other known information on the question. Level 2: Symboling, namely making an example of a amount money Ayu , Bianca and Caca by symbolizing as a certain variable.
Integrating is making connections between variables, known information and comparative concepts. Level 3 : Comparing that is compare linkages total money Ayu , Bianca and Caca as well as difference total money savings Ayu and Caca for know method complete question . Generalizing, namely making a mathematical model in direct proportion .
Level 4: Problem solving, that is completing direct proportion that already made .
Decision making, namely drawing conclusions from what is being asked.
In research also conducted check data validity, this is done in order to obtain valid findings. Checking technique the validity of the data used in research this is data triangulation. Triangulation is a data validity checking technique that utilizes something from outside the data for checking purposes or as a comparison to that data (Moleong , 2010 ). This research use triangulation source made to compare results completion proportion problem , interview with subject, and discussion with a mathematics teacher at SMP Negeri 3 Sumenep .

RESULT AND DISCUSSION
Based on Marzano's taxonomy that has put forward first, cognitive system own four component that is retrieving knowledge, comprehending knowledge, analyzing knowledge, and using knowledge. The following will be described system cognitive S1 and S2 in solving proportion Problem base on Marzano's taxonomy.

Nita Fatma (Cognitive System of Students in Solving Proportion Problems)
Journal of Education and Learning Mathematics Research | Volume 4, Number 1, 2023 90 S1 cognitive system, namely processing knowledge in solving problems in the first problem. At level 1, namely retrieving knowledge , S1 did "recognizing and executing" , namely S1 recognizes unit different times on the problem and then make it to in same unit with change 2 minutes to 120 seconds.
At level 2, namely comprehending knowledge, S1 did "symboling". S1 did "symboling" which is marked with S1 makes an example by symbolizing with the variable x to exemplify the number of bottles that can be closed by machine in time 120 seconds. This is known based on the completion sheet S1 and the results of interviews with S1.
At level 3, namely analyzing knowledge, S1 did "comparison" that is compare linkages many bottle that can be closed and the time that machine need. it seen from table that has made by S1. Based on results S1 interview also conducted "specifying" ie predict what will happen to total bottle that can be closed if machine work with different time. S1 said if machine work longer so bottles that can be closed are also more many. Based on Thing the S1 can conclude that about could done with use direct proportion. With thus S1 did "generalizing", namely making a mathematical model in direct proportion with write 14 = 84 120 .
At level 4, using knowledge, S1 did "problem solving and decision making". S1 did "problem solving", namely completing the mathematical model that has been made. S1 made direct proportion mathematical models. S1 did trick multiplication cross for know score of variables , ie = 14•120 84 = 20. S1 also did "decision making" at level 4, this is shown from S1 drawing conclusions from what was asked in the problem. This is shown by S1 writing "so, the number bottle that can closed by machine is 20 bottles " on the completion sheet. The above is as shown in the following image S1 thinking in completing about proportion, the researcher interviewed S1 as follows. Q : "Please explain the completion you wrote down to solve this problem!" S1 : " In the matter it says if something the factory is able to install bottle caps for 14 bottles in 84 seconds. then asked a lot of bottle caps that can be closed within 2 minutes. Means we can use a direct proportion method." Q : "Where are you know if that direct proportion?" S1 : "From what is known in the Problem Ma'am." Q : "What does it mean from the known?"

Nita Fatma (Cognitive System of Students in Solving Proportion Problems)
Journal of Education and Learning Mathematics Research | Volume 4, Number 1, 2023 91 S1 : " So if the machine closes the bottle, the longer the time he works with means the more the bottle is too closed." Q : " Ooo so it is. Continue to try the next explanation just now about the method of solving it." S1 : " Here first I convert 2 minutes To seconds , 2 minutes is equal to 2 times 60 seconds, so we have 120 seconds . after the same unit of time, I solved it by way of a comparison of worth. Q : "So what does this mean?" (pointing to the word "botol (buah) dan waktu (detik)" on the completion sheet ). S1 : " "I made the data first ma'am, like a table to avoid placing the wrong value in the proportion." Q : "So this means a kind of table huh?" S1 : "Yes ma'am." Q : "Yes next?" S1 : "Then I finished the proportion, and the result is 20. So the number of bottles that the machine can close in 2 minutes is 20 bottles.
S2 cognitive system in solving the first problem S2 cognitive system, namely processing knowledge in solving problems in the first problem. At level 1, namely retrieving knowledge, S2 did "recognizing" but didn't "executing", that is S2 recognize unit at different times on the problem this thing seen from the chart that S2 wrote on the completion sheet, but the S2 doesn't change it to in-unit same time. Based on the results of the interview, S2 admitted that he did not know if the time units had to be equated At level 2, namely comprehending knowledge , S2 did "symboling" which is marked with S2 makes an example by symbolizing with variable a for example many bottles that can be closed by machine in 2 minutes time. This is known based on the completion sheet S2 and the results of interviews with S2 .
At level 3, namely analyzing knowledge , S2 did "comparason" that is compare linkages many bottle that can closed and time that machine need. it seen from visualization that has made by S2 with sign arrow . S2 also "generalizing", namely making a mathematical model in direct proportion. Based on results of interview, S2 didn't "specifying" ie predict what will happen to total bottle that can closed if machine work with different t e that is if machine work longer so bottles that can be closed are also more many. S2 only focuses on the numbers written down and immediately finish it for find solution .
At level 4, using knowledge , S2 did "problem solving" and didn't "decision making". S2 did "problem solving", namely completing the mathematical model that has been made. The mathematical model in question is direct proportion . The S2 didn't " decision making" at level 4, this is shown from S2 didn't made conclusions from what is asked in the problem. The above is as shown in the following image . , then what is asked how many bottle that can closed in time 2 minutes, because we don't know how many bottles are installed within two minutes I wrote down with dots. So these points are what we're looking for. We work on it by making equations" Q : "This means how come you can find equations like this using what model/concept?" S2 : " This use proportion ma'am." Q : "What proportion?" S2 : " Eeeee proportion" Q : " Direct proportion or inverse Proportion?" S2 : " Direct proportion Ma'am" Q : "Yes , try next the explanation!" S2 : "The equation is 14 per 84 equals per 2." Q : " a here as what?" S2 : " a is a lot of bottles that we want to look for Ma'am, those dots." Q : "Many bottles how?" S2 : "Many bottles are machine-sealed within 2 minutes Ma'am" Q : "Okay." S2 : "Then cross-multiplied, it is found that the value of is 28 per 24." Q : "Are you sure the answer is 28 per 24?" S2 : " Actually, no Ma'am because I found a fractions, it seems impossible." Q : " you know where it is not very thorough?" S2 : " Where's Mom?" Q : "This is a different unit of time, it should be equated first into all minutes or seconds." S2 : "Oo so it should be equalized first, ma'am.." Q : "Yes." S1 cognitive system in solving the second problem S1 cognitive system, namely processing knowledge in solving problems in the second problem . At level 1, namely retrieving knowledge , S1 did "recalling and executing", namely S1 register and create ratio amount of Ayu, Bianca and Caca's money, the difference between Ayu and Caca's money into a table form as it is on the completion sheet.
At level 2, namely comprehending knowledge , S1 did "symboling and integrating". S1 did "symboling" which is indicated by S1 making an analogy by symbolizing with variables A, B, C and x to exemplify for the amount of Ayu's money, Bianca's amount of money, Caca's amount of money and the amount of money of the three. S1 is also "integrating", namely making connections between variables, with subtract ratio of amount of Ayu's money and the amount of Caca's money that is − = 8 − 3 = 5 as a ratio for difference money both of them that is IDR 2,000,000.00. Besides it, s1 also adds ratio of total money all three that is + + = 8 + 7 + 3 = 18 which will then be used to determine the amount of money for the three. This is known based on the completion sheet S1 and the results of interviews with S1.
At level 3, namely analyzing knowledge, S1did"comparison" that is compare linkages between amount of money Ayu, Bianca and Caca as well as difference in amount of money Ayu and Caca. it seen from table that has made by S1. S1 also did "generalizing", namely making a mathematical model in direct proportion, ie At level 4, using knowledge, S1 "problem solving and decision making". S1 did "problem solving", namely completing the mathematical model that has been made that is direct proportion. S1 complete the proportion that have been she made for find ie = 18•2000000 5 so found is 7,200,000. S1 also did "decision making" at level 4, this is shown from S1 made conclusions from what was asked in the problem. This is shown by S1 writing "jadi jumlah tabungan ketiganya adalah Rp 7.200.000 " on the completion sheet. The above is as shown in the following image . S1 thinking in completing about proportion, the researcher interviewed S1 as follows. Q : " Try to explain the solution that you wrote to solve this problem!" S1 : " So from the problem We know ratio money savings Ayu , Bianca and Caca are 8:7:3, here I write down as table, this is ma'am ( pointing completion sheet ). This is also A-C difference ratio money savings Ayu and Bianca are the same with 5 and A+B+C is total ratio money savings Ayu, Bianca and Caca" Q : " This is what the words "comparison of many candies"?" S1 : "Oh this is i mean savings not candy Ma'am, when i write, i don't focus on Mom maybe". Q : "So this is just a miswriting, huh?" S1 : " Yes ma'am." Q : " Try next explanation in the completion?" S1 : " Then I write direct proportion, because that is known is difference money savings Ayu and Caca, that is of 2,000,000 then what I am comparing is that difference ratio money savings Ayu and Bianca are the same with 5 compared difference money Figure 4. S2 Completion Sheet in solving the second problem. Q : " Try to explain the solution tha you wrote to solve this problem!" S2 : " ( reading First I wrote down the ratio money savings Ayu to Bianca to Caca with 8:7:3. After that, i write down difference money Ayu , Bianca and Caca 2,000,000. After that, i write down what is asked total money all three , because We still don't know, so i write down + + = ⋯ Ma'am. " P : " Means A means is money savings Ayu , B is money Bianca and C is savings money Caca? S2 : " Yes ma'am." Q : " Okay, try to continue the explanation on the completion sheet!" S2 : " Yes ma'am. Then I write it down − = 2.000.000 because it is known that the difference between Ayu and Caca's savings is two million rupiah. Then I substitute value − with 8 − 3 because ratio saving mone Ayu is 8 and Caca is 3. Finally got equality 5 = 2.000.000. so if we have the 5 equal 2,000,000 then 1 it is same with 400,000 ma'am." Q : " What do you think writing equation 5= 2,000,000 is? Is it true that 5 can be assumed with 2,000,000?" S2 : " No ma'am, there I mean comparable not the same." Q : " Yes , if comparable, writing it should not be the same as, what value will be compared, write the comparison." S2 : " Yes ma'am, I am confused how to wrote it, what should be compared". . Then substitute A-C with 2,000,000, that is 2.000.000 . From this equation you will find Ayu's savings. For money Bianca and Caca's savings get use the same way." S2 : " Yes ma'am." Q : " Yes, no problem, next time you can repaired if find similar problem. Now try explained next completion." S2 : " Next I looking for money each from Ayu , Bianca and Caca. Because of me just now assume the ratio 1 it is same with 400,000 so for looking for money each I multiply 400,000 by the score ratio each . So that found results for money Ayu is 3,200.00 rupiah, Bianca 's money is 2,800,000 rupiah, and Caca 's money is 1,200,000 rupiah. Then I add up and we could total money all three ." Q : " Yes , thank you for the explanation ."

Nita Fatma (Cognitive System of Students in Solving Proportion Problems)
Journal of Education and Learning Mathematics Research | Volume 4, Number 1, 2023 96

CONCLUSION
S1Cognitive system in complete first problem, at level 1, namely retrieving knowledge , S1 did recognizing and executing. At level 2, namely comprehending knowledge, S1 did symboling. At level 3, namely analyzing knowledge, S1 did comparing, specifying and generalizing. At level 4, using knowledge, S1 did problem solving and decision making .
S2 cognitive system in complete first problem, at level 1, namely retrieving knowledge, S2 did recognizing but didn't executing. At level 2, namely comprehending knowledge , S2 did symboling. At level 3, namely analyzing knowledge , S2 did comparison and generalizing but didn't specifying. At level 4, using knowledge , S2 did problem solving and didn't decision making . S1 cognitive system in complete second problem. At level 1, namely retrieving knowledge, S1did recalling and executing. At level 2, namely comprehending knowledge, S1 did symboling and integrating. At level 3, namely analyzing knowledge, S1 did comparison and generalizing. At level 4, using knowledge, S1 did problem solving and decision making.
S2 cognitive system in complete second ratio, at level 1, namely retrieving knowledge, S2 did recalling and executing. At level 2, namely comprehending knowledge, S2 did symbolizing and integrating. At level 3, namely analyzing knowledge, S2 did comparison but the S2 didn't Generalizing. At level 4, using knowledge, S2 did problem solving, but didn't decision making.

ACKNOWLEDGMENTS
Study This provides an overview to researchers , prospective teachers and teachers about system cognitive student in complete about comparison . There is some interesting on the results cognitive system research in research this . If usually We used to only could say completion students correct or completion students wrong, on research this We could look more in what to think student when do questions and explanations they about method do about proportion. By knowing system cognitive students, expected researchers, prospective teachers and teachers can study system cognitive student more in more on other material and can design more learning innovative .
This research provides researchers, prospective teachers and teachers with an overview of students' cognitive systems in solving proportion problems. There are some interesting things in the results of cognitive system research in this reseach. If we are usually used to only being able to say a student's solution is right or wrong, in this study we can take a deeper look at what students think when solving problems and their explanations of how to solve proportion problems. By knowing the cognitive system of students, it is hoped that researchers, prospective teachers and teachers can examine students' cognitive systems more deeply on other materials and can design more innovative learning.