HOW STUDENTS SOLVE PIZZA PROBLEMS: AN EXPLORATION OF STUDENTS' MATHEMATICAL LITERACY

The pizza problem was chosen because the question consistently appears in every activity conducted by the Program for International Student Assessment (PISA) to measure mathematical literacy. However, Indonesian students have not yet successfully solved the pizza problem correctly. The purpose of this study is to describe the mathematical literacy of students in solving pizza problems that have been adapted in the process component and differences. This study focuses on students' answers in solving pizza problems with different information in each question. Data collection was carried out using tests and interviews. The research method employed is qualitative with a descriptive approach. The research subjects were ninth-grade junior high school students. Data collection was carried out to identify students' mathematical literacy on pizza problems by analyzing the results of tests and interviews. The results showed that: 1. students had difficulty in solving pizza problems, formulating mathematical problems, performing calculations using the concept of specific formula rules


Kata kunci: Literasi matematis; masalah pizza; menyelesaikan; ruang dan bentuk
This is an open access article under the Creative Commons Attribution 4.0 International License

INTRODUCTION
Mathematical literacy is one of the essential abilities to respond to challenges in the continuously changing era of globalization (Kolar & Hodnik, 2021).

Someone
with great mathematical literacy can understand the role and use of mathematics in formulating the right decisions for mathematical problems in everyday life (Annisavitri et al., 2020;Botha et al., 2013;Genc & Erbas, 2019;Guler & Arslan, 2019;Mardiana et al., 2020).Mathematical literacy can be interpreted as the capacity of individuals to formulate, employ, and interpret mathematics in various contexts, including making accurate deductions and applying mathematical concepts, procedures, facts, and tools to describe and predict phenomena (OECD, 2015;She et al., 2018;Stacey & Turner, 2015) The Program for International Students Assessment (PISA) monitors results from student learning in each participating country.Essential aspects of mathematical literacy involve mathematics usage and mathematics processing in various situations (Gabriel et al., 2020;Holenstein et al., 2020;Ojose, 2011).PISA transforms the principles of mathematical literacy into three components, namely the content, process, and context components (Ahyan et al., 2014;OECD, 2021).
PISA results that measured the mathematical literacy skills of students aged 15 years in 2012 showed that Indonesia had a low ranking, 64 th rank out of 65 countries.Furthermore, in 2015 showed that Indonesia was ranked 63 out of 70 states, and in 2018 Indonesia was ranked 72 out of 78 countries (Schleicher, 2019;Utaminingsih et al., 2021) 2014) the quality of education in Indonesia, including mathematical literacy at the international level, tends to be below, even though they have been given questions adjusted to the Indonesian context (Mahdiansyah & Rahmawati, 2014).Most of the students answered the mathematics questions without explanation and the calculation steps.Additionally, several other previous studies also investigated students' low mathematical literacy (Julie et al., 2017;Larasati & Rianasari, 2017;Linuhung, 2014;Rachmaningtyas et al., 2022;Wijaya, 2016).In a preliminary study in Junior High School 1 of Banjar Baru, Lampung, we gave students mathematical literacy test questions on space and shape content about the pizza problem.The pizza problem was chosen because this question was found in every activity carried out by PISA to measure mathematical literacy.However, Indonesian students did not solve the pizza problem correctly.Several other studies carried out in Indonesia using the pizza questions also reported students' difficulty in solving the problems (Dewantara, 2019;Johar, 2012;Kurniati et al., 2016;Noviana & Murtiyasa, 2020).However, those studies have not investigated Indonesian students' difficulty solving the pizza questions comprehensively.
The questions given to students have been adapted into the Indonesian context (Rupiah and Indonesian language).An example of a question is "Kedai Lupizza serves pizza in two different sizes with the same thickness but different sizes.A small pizza (A) with a diameter of 40 cm is sold at Rp. 3576| 40,000.00.Large pizza (B) with a diameter of 50 cm is sold at Rp. 50,000.00.If you want to buy pizza, which size should you choose?" The problem was given to 10 students.The results suggested that all students answered that they should select a small pizza (A) because its price was lower without providing a reason and correct calculation.An example of students' answers is presented in Figure 1   Based on the student's answers in Figure 1, students can only answer that Pizza A is cheaper because the price is low to save more money.Then the students were interviewed to know the reason for their answers.Based on their answers, students have not carried out a systematic process of formulating and implementing procedures, as well as interpreting the problems.Students understand the use of the desired question, but they do not know what to do to solve problems.Additionally, there are indications that students made mistakes in interpreting the words of the questions asked.
Various studies have been conducted to improve students' mathematical literacy by applying learning models or methods (Atsnan et al., 2018;Babys, 2017;Rusli & Anas, 2017).Besides, Research analyzing students' mathematical literacy skills in solving PISA mathematics problems was carried out by (Lestari et al., 2021) This study explores how mathematical literacy in solving pizza problems is adapted to different explanatory sentences to determine the differences in the interpretation from the student's point of view.This study's importance lies in the attainment of information related to the reasons for students' difficulty in solving mathematical problems.Further, the information can be a reference in determining the right way to adapt mathematical literacy questions.Thus, this study aims to describe how is the mathematical literacy of students in solving pizza problems with different information in each question.

METHODS
In this study, the research method employed is qualitative with a descriptive approach.Descriptive analysis aims to portray a phenomenon, event, or situation that is currently occurring (Creswell, 2015).In this method, researchers strive to accurately This research involved 60 ninthgrade students from SMP Negeri 1 Banjar Baru.The students were then randomly divided into three groups of 20 students each, and each group was given the adapted pizza problem test.Subsequently, 3 students were selected from each group who solved the problem accurately, resulting in a total of 9 research subjects.
The pizza problem from PISA adopted in this study is presented in the following.
"A pizzeria serves two round pizzas of the same thickness in different sizes.The smaller one has a diameter of 30 cm and costs 30 zeds.The larger one has a diameter of 40 cm and costs 40 zeds.Which pizza is better value for money?Show your reasoning".
In this study, the first group of students was given that question with an adapted question, from "Which pizza is better value for money" to "Which size do you choose to save money?"In the second group of students, the question was defined as "If you want to buy that pizza and money is not a problem for you because you can afford any kind of pizza as long as the choice is more profitable, then which size would you choose?"This statement is intended to ensure that students are not affected by their allowance.In the third group of students, the question was altered to "Which pizza is more profitable in terms of the value for money?"These different explanatory sentences aim to explore whether different sentence interpretations may carry ambiguous meanings based on the student's point of view.The three questions that have been adapted are as follows: The instrument was validated by two expert validators in the fields of mathematics education and mathematics.Content validity was measured using a validation sheet to assess the appropriateness of the test instrument.Based on the validation results from both validators, the assessment concluded that the instrument is deemed appropriate and can be used to collect research data.
Furthermore, we used several techniques to assess the data validity.First, the extension of participation was completed by applying the involvement of researchers directly and for a long time.Second, data triangulation was carried out by utilizing something else outside of the data as a comparison of the data.Third, peer examination was carried out through discussion to compare and verify the truth and suitability of research data through analytic talks with colleagues and teachers in the mathematics field.
The data analysis conducted in this research involves three stages: data reduction, data presentation, and drawing conclusions (Miles et al., 2014).In the data reduction stage, preparation and organization of data involve collecting notes, students' answer documents, and selecting interview results.In the data presentation stage, a cohesive theme is presented, such as examining students' answers, research objectives, and mathematical literacy content.This should be included to describe the content in mathematical literacy data using mathematical literacy indicators.Finally, in the drawing conclusions stage, research results are summarized.

RESULT AND DISCUSSION
In the data collection process, we gave three test questions to sixty students, with twenty students for each question.After that, we selected 3 students who wrote complete answers from each group.The first group of students was assigned questions similar to the questions issued by PISA, with modifications to the questions, from "Which pizza is better value for money" to "ukuran mana yang kalian pilih, sehingga dapat menghemat uang?(which size of pizza do you choose to save money)."The recapitulation of student completion results is presented in Table 1.Answer: A small pizza (A) because: The small pizza costs Rp. 40,000.00measuring 40 cm A large pizza costs Rp. 50.000,00 measuring 50 cm I chose a small pizza to save my money because it saved money.Small pizzas and large pizzas differ only by 10 cm and differ in the price of Rp. 10,000.00.To save money, we better buy a small one because the thickness is the same and tastes the same.
Formulate Formulate the problem, but incomplete.

Employ
Not apply specific formulas or rules.

Interpret
The student interprets, but the answer is wrong.

Student 3
Answer: Pizza A, because Pizza A is smaller than Pizza B, so it saves more money and is cheap, so we can save.
Formulate Not formulate a problem.

Employ
Not applying specific formulas or rules.

Interpret
The student interprets, but the answer is wrong.
Based on the result of the interviews, it appears that the students may not fully understand that the issue at hand pertains to the width and thickness of the pizza, rather than just the price or the overall size of the pizza.Their responses suggest a lack of awareness or comprehension of the specific focus of the question or problem.
Student 1 chose pizza B based on its cost of only 10,000, without realizing that the actual issue is related to the width and thickness of the pizza.The response indicates that the student may have guessed the answers without a clear understanding; Student 2 selected pizza A because of the lower price of a small pizza, allowing them to save money with only a 10 cm difference.However, the student is unaware that the issue involves the width and thickness of the pizza, indicating a misunderstanding of the question; Student 3 explained their choice of pizza A by stating it is more affordable, to save money.Nevertheless, they do not realize that the actual issue concerns the width and thickness of the pizza.

3580|
their choices seem to be based on information that is not relevant to the actual aspect being tested.
Based on student answers in Table 1, and interview results to the type 1 problem, the students could not solve the given problem.Besides, one student systematically did problem-solving, but the answer was incorrect.The students perceive that money of Rp. 40,000 is less than Rp.50,000, so they buy a small-sized and cheaper pizza.This finding indicated students' minimum knowledge in solving the problem.Besides, one student answered correctly, but without an exact calculation process, so they just guessed.
Furthermore, the second group of students was given a problem with additional information to ensure that students do not get affected by their allowance.Consequently, the price is no longer a problem, and students only have to choose which pizza is more profitable.The question for these second group of students is "Jika Anda ingin membeli pizza tersebut, bagi Anda uang bukan masalah karena anda mampu untuk membeli pizza jenis manapun asalkan pilihan tersebut lebih menguntungkan, maka ukuran mana yang anda pilih?If you want to purchase the pizza without having money issues, which size of pizza will you choose?"The recapitulation of student results is presented in Table 2. Based on the interviews result, Student 4 stated that they chose pizza B because it was cheaper.They are aware that the issue involves the width and thickness of the pizza but are struggling with the calculations.This suggests that the student understands the nature of the problem but may lack the quantitative skills to perform the necessary calculations accurately; Student 5 mentioned choosing pizza A because of the lower price, without being aware that the issue involves the width and thickness of the pizza.This indicates a lack of comprehension regarding the specific focus of the question, as the student is emphasizing price rather than the dimensions of the pizza; Student 6 explained their choice of pizza A by stating that the sizes are different, and based on the circular shape, they counted pizza B as wider.However, the student did not consider dividing the pizza by the price.
Overall, the interview reveals variations in students' levels of understanding and approach to the problem.Some students are aware of the nature of the issue but struggle with calculations, while others may focus on irrelevant factors or overlook certain aspects of the problem.ISSN 2089-8703 (Print) Volume 12, No. 4, 2023, 3573-3588 ISSN 2442-5419 (Online) DOI: https://doi.org/10.24127/ajpm.v12i4.8997

3582|
Based on the results of the student's answers in Table 2, and interview, two students have not been able to solve the problem correctly.These two students presented the correct answer, but the calculation was still incorrect.Student 5 answered Pizza B, but the reason for choosing Pizza B was because by adding Rp. 10,000 rupiahs, the student can get an additional size 10 cm diameter Pizza.This student did not do the exact calculation, and the reason given did not represent a solution because the answer was incorrect.Additionally, student 6 only missed the calculation of the price for every cm 2 of the pizza by dividing prices by the area.Instead, student 6 answered with a suspicion that Pizza B is far greater than Pizza A with a different price of only Rp. 10,000.It turns out that the student's answer is correct.Although there is a possibility that the student's answer is wrong, at least this shows that students can formulate, employ, and interpret problem-solving.
Furthermore, the third group of students was given the same question from the source, "Which pizza is better value for money" which translated into "Pizza mana yang lebih menguntungkan dilihat dari nilai uangnya?"The recapitulation of student results is presented in Table 3.The size of a small Pizza = 3.14 x 40 = 125.6 with the price of Rp. 40,000.00so Rp.40,000, 00: 125.6 = 318.47,so the price is Rp.318.47 Size Pizza Big = 3.14 x 50 = 157 with Rp. 50,000.00,so Rp.50,000, 00: 157 = 318.47cm 2 , so the price is Rp.318.47 from the result that the price is the same the selection of Pizza A or Pizza B is equally profitable Formulate Formulate a problem Employ Apply certain formulas or rules

Interpret
Making interpreta tion and the answer correct Based on the result of the interviews, Student 7 chose pizza A because it is cheaper, but the student is not aware that the issue involves the width and thickness of the pizza.This suggests a lack of understanding regarding the specific focus of the question; Student 8 stated that they chose pizza A because its price is lower, without being aware that the issue involves the width and thickness of the pizza; Student 9 explained choosing pizza A after calculating the price and finding it to be the same.In summary, the common theme in these responses is a focus on the price of the pizzas, indicating a lack of awareness among the students that the issue being discussed pertains to the width and thickness of the pizza.

3584|
able to solve the given problem.However, one student can formulate and employ certain formulas.This student understood that this concept is a concept, but the student applied the formula around a circle to get the wrong conclusions.The results of the calculation were small pizza size = π × d = 3.14 × 40 = 125.6 cm 2 , so the price of Rp. 40,000.00:125.6 = Rp.318.47 every cm 2 .While the size of a large pizza = π × d = 3.14 × 50 = 157 cm 2 , the price of Rp. 50,000.00:157 = 318.47every cm 2 .From that calculation, the price is the same, so pizza A or pizza B is equally beneficial.There is a misconception here, and students are swapped between the formula of area and periphery of a circle.After the interview, the student forgot the formula of a circle area and used the formula for circle perimeter π × d instead.Student 7 chose Pizza A because Pizza A was smaller than Pizza B, so it was more profitable since it was cheaper than other types of pizza.Student 8 chose Pizza A because Pizza A is cheaper than Pizza B to save money.Then interviews were also conducted for students 7 and students 8.The interview results indicated that they already knew the purpose of the problem but did not know the procedures to solve the problem.
Based on the obtained research results, students still face several difficulties in solving pizza problems.Question type 1, the results suggested that students have not been able to solve the problems.For students, the money of Rp. 40,000 is less than Rp.50,000, so buying a small-sized and cheaper pizza A is the best choice for students since they do not know what to do to solve problems.For question type 2, two students have not been able to solve the problem correctly, and one student answered correctly.However, the reasons and calculations from this one student are still not right.Ideally, students must be able to identify the assumptions and arguments being used, assess the logic of the arguments on which they are based, identify other things that might be better, and make the right decisions.In question type 3, the results of students' answers indicate that students have not solved the given problem.However, one student can formulate and employ specific formulas, presenting an excellent understanding that this concept is a concept.However, the student applies the formula of a circle perimeter and gets the wrong conclusions.
The results show differences in students' responses to the three provided pizza problems.Students did not solve pizza problems correctly through accurate calculations and interpretations.However, on type 2 questions, a student performed better than the others.Our data suggest that students can understand questions more easily with more detailed explanations.Aligned with previous research conducted by Lestari et al. (2021), indicating that students have difficulty translating everyday situations into mathematical form, including concepts, and structures, making assumptions, and mathematical modeling.Therefore, the findings of this study provide further insight that these difficulties are attributed to the language used in adapting mathematical literacy problems from English to Indonesian, which lacks careful, thorough, and accurate translation.The strengths of this research indicate that the careful and precise adaptation of questions can aid students in better understanding mathematical problems.ISSN 2089-8703 (Print) Volume 12, No. 4, 2023, 3573-3588 ISSN 2442-5419 (Online) DOI: https://doi.org/10.24127/ajpm.v12i4.8997 | 3585 As revealed by Moschkovich & Zahner (2018), a guide to mathematical literacy can be used to design a mathematics learning experience in a multilingual classroom.In addition to using such guides for assignment design, the design of instructions that provide opportunities for the development of mathematical literacy should also consider the assignments.These two elements are inseparable in the class and affect the structure of activities for each assignment, texts, and contextual aspects for other relevant mathematical activities in each classroom setting.the context used in the classroom must be chosen to help students understand the meaning in real life (Bolstad, 2020;Geiger et al., 2015;Machaba, 2018;Pillai et al., 2017).In solving pizza problems, it is necessary to present to students the terms from the real world that must be interpreted because mathematics is a mathematically organized science with intercorrelated mathematical ideas (Altun & Bozkurt, 2017;Rawa et al., 2016).Therefore, in adopting a foreign language problem, the problem must be interpreted carefully, thoroughly, and carefully.

CONCLUSION AND SUGGESTION
The study found that students face difficulties in solving pizza problems, formulating mathematical problems, applying mathematical concepts, and interpreting mathematical processes correctly.The most challenging aspect for students was applying mathematical concepts to solve problems.The study in students' answers in solving three types of pizza problems.Students did not solve pizza problems correctly through the correct calculation and interpretation, but on type 2 questions, students performed better than the students working on the other two problems.
Students can easily understand the question with more detailed explanations.Therefore, in adapting a question from a foreign language, a careful, thorough, and accurate interpretation is required.
We suggest educators design questions that adapt foreign language questions into the mother tongue and interpret them thoroughly and carefully.Educators should also report the students' characteristics, the texts involved, and relevant contextual aspects.Furthermore, for future research stemming from this study, a broader investigation could be conducted, involving a more extensive pool of students from various educational levels and diverse backgrounds. below.

Figure
Figure 1.Student answers

Table 1 .
Students' answers to question 1 Answer: Pizza B, the reason I chose Pizza B is because by adding Rp. 10,000 rupiahs, I can get an additional size of a 10 cm diameter Pizza.DOI: https://doi.org/10.24127/ajpm.v12i4.8997| 3579

Table 3 .
Student answers to question 3Answer: small Pizza is Rp.40,000.00measuring diameter of 40 cm.big Pizza is Rp.50,000.00measuring diameter of 50 cm Answer: