Conference Agenda
Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
Please note that all times are shown in the time zone of the conference. The current conference time is: 19th Aug 2026, 20:19:00 EET
|
Daily Overview |
| Session | ||
24 SES 02 A: Mathematical Content Areas
Paper Session | ||
    | ||
24. Mathematics Education Research
Paper A Bibliometric Review of Studies on Algebra Education in the Past Three Decades 1: Eskisehir Osmangazi University, Turkey (Türkiye); 2: Bogazici University, Turkey (Türkiye) Presenting Author:Algebra is an essential area of mathematics and a content strand of mathematics education (NCTM, 2000). It is a fundamental area because "Algebra is a way of thinking and a set of concepts and skills that enable students to generalize, model, and analyze mathematical situations. Algebra provides a systematic way to investigate relationships; help to describe, organize, and understand the world" (NCTM, 2000, p. 1). Algebra education provides students with many skills, including generalization, representation, and problem-solving (Kaput, 1999).
Several concepts examined in the literature on algebra education, such as algebraic thinking (Kieran, 2004), algebraic reasoning (Kaput, 1999), functional thinking (Blanton et al., 2011), relational thinking (Jacobs et al., 2007), covarational reasoning (Confrey & Smith, 1995), and pattern recognition (Wang, 2008). Algebraic thinking is working on problems relationally by using various representations, modeling, working with numbers and letters, and understanding the meaning of equal signs (Kieran, 2004). Algebraic reasoning includes making generalizations about arithmetic relationships, generalizing patterns, using modeling, and representing various relationships (Kaput, 1999). Functional thinking, one of the main components of algebraic thinking, is associated with concepts such as covariance, correspondence, and change. It requires identifying patterns, describing relationships using variables and "understanding how quantities vary in relation to each other or covary" (Blanton et al., 2011, p. 52). Therefore, it is closely associated with covariational reasoning, which means understanding the variation between two quantities with respect to each other (Confrey & Smith, 1995). All of the mentioned concepts are related to relational thinking, which was defined as "looking at expressions and equations in their entirety, noticing the number relations among and within these expressions and equations." (Jacobs et al., 2007, p. 260) and also related to pattern recognition which can be defined as a higher cognitive process that helps to identify objects or the composition of various objects and denotes them (Wang, 2008). Algebra education is considered the "gateway to higher mathematics" (Stein et al., 2011, p. 454), and many studies have been conducted in this area, examining topics such as classroom practices in algebra and the impact of instructional methods (Hegedus & Kaput, 2003), teachers' perspectives (Glassmeyer & Edwards, 2016) and specific algebra content such as linear equations (Brizuela & Schliemann, 2004), the equal sign (Lee & Pang, 2021). Thus, over the past three decades, this field has grown significantly. On the other hand, there is a limited bibliometric review that allows for examining wide-range data on algebra education; there are, for example, a study on algebra education covering the last 20 years with the Scopus database (Veith et al., 2023) a study examining algebraic trends (Jamil et al., 2025); a study examining algebraic materials (Hayu & Angraini, 2024). To better understand the field, there is a need for more extensive bibliometric studies on algebra education. Therefore, this study aims to examine research on algebra education in the past three decades using bibliometric analysis. In light of this, the research questions of this study are:
Methodology, Methods, Research Instruments or Sources Used This study employs the bibliometric method, which enables the analysis of all aspects of documents. This type of analysis can extract information from large amounts of comprehensive data and provide objective metrics, such as the number of documents, citations, topics, keywords, and collaborations (Passas, 2024). This method reflects the current state of the topic and future trends. Therefore, it was expected to highlight the field of algebra education in a comprehensive and detailed way. The main steps of bibliometric analysis, as defined by Passas (2024), were followed: defining the research objective, collecting data, data cleaning and preprocessing, selecting bibliometric techniques, data analysis, visualization, interpretation, and reporting. Accordingly, the Web of Science (WoS) database was used to collect data because it includes qualified studies. Data were extracted on 23 May 2025. As mentioned in the literature, articles on algebra education include some concepts such as functional thinking, relational thinking, pattern recognition, covariational thinking, and covariational reasoning. Therefore, these terms were combined with terms about mathematics education with following search strings: TS= (((algebra* OR "functional thinking" OR "relational thinking" OR "pattern recognition" OR "covariational thinking" OR "covariational reasoning") AND (math* AND (edu* OR teach* OR learn* OR student* OR teacher OR curricul* OR classroom OR instruction))). Thus, the aim was to ensure that all relevant studies were captured. According to the inclusion criteria, studies published between January 1996 and May 2025, written in English, classified as articles, and indexed under the education/educational research category were included in the analysis. 1769 articles were obtained in total. These articles were exported in Plain Text File formats. Plain Text File formats were later imported to the VOSviewer program for analysis. During data cleaning and preprocessing, data were exported from VOSviewer to Excel, and repeated author names, incorrect country names, and keywords with the same meaning were corrected to ensure accurate results. In selecting bibliometric techniques, the data analysis techniques were determined to be citation analysis, co-occurrence analysis, and co-authorship. The minimum values requested when running the analysis, such as the minimum number of publications and citations, were set to best represent the data. Then, performance analysis was used to examine quantitative variables, such as the number of articles by year, and science mapping was used to identify the most dominant keywords and core topics in algebra education and to describe co-authorships among authors, countries, and institutions. Thus, visualization, interpretation, and reporting were conducted. Conclusions, Expected Outcomes or Findings Analysis showed that the number of articles has increased over the years. After 2005, there have been at least 25 articles each year. The number of articles is the highest in 2022 (7.6%), followed by 2024 (7.3%) and 2021 (7.0%), while 1996, 2001, and 2002 had the fewest articles (0.2%). The most used ten keywords are algebra, mathematics education, mathematics, problem-solving, linear algebra, early algebra, algebraic thinking, curriculum, computer algebra system, and function. The core topics are algebra, problem-solving, functions, and linear algebra. Curriculum, computer algebra systems, early algebra, and covariational reasoning are potential core topics. Moreover, the most productive author is Timothy Fukawa-Connelly, with 21 articles, followed by Eric J. Knuth and Ana Stephens, each with 14 articles. Besides, Eric J. Knuth and Ana Stephens are the most cited authors, with 754 and 648 citations, respectively, and are also the most collaborative, frequently working with each other and with other scholars on early algebra, equality, and algebraic and functional thinking. The most productive country is the USA, with 881 (50.1%) articles. Turkiye (6%) and England (4%) follow the USA in terms of productivity, with 122 and 76 articles, respectively. According to the links, the USA is the most collaborative country. It collaborates with many countries in both Europe and the East. The second-most collaborative country is England, followed by Spain. The USA has the strongest link with Turkiye, indicating the highest level of collaboration between the two countries. The People's Republic of China has the second-highest link strength with the USA. While most productive institutions are Temple University, followed by the University of Delaware and the University of Wisconsin, most collaborative ones are the University of Texas at Austin, followed by Temple University, the University of Delaware, and Arizona State University. References Blanton, M., Levi, L., Crites, T., Dougherty, B., & Zbiek, R. M. (2011). Developing essential understandings of algebraic thinking for teaching mathematics in grades 3–5 (Series in Essential Understandings). National Council of Teachers of Mathematics. Brizuela, B., & Schliemann, A. (2004). Ten-year-old students solving linear equations. For the Learning of Mathematics, 24(2), 33-40. Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for research in mathematics education, 26(1), 66-86. https://doi.org/10.5951/jresematheduc.26.1.0066 Glassmeyer, D., & Edwards, B. (2016). How middle grade teachers think about algebraic reasoning. Mathematics Teacher Education and Development, 18(2), 92-106. Hayu, S. R., & Angraini, L. M. (2024). Research trends of students’ mathematical ability on algebra materials based on gender: Bibliometric analysis. International Journal of Applied Learning and Research in Algebra, 1(2), 120-128. https://doi.org/10.56855/algebra.v1i2.1268 Hegedus, S. J., & Kaput, J. (2003). The effect of a simcalc connected classroom on students' algebraic thinking. International Group for the Psychology of Mathematics Education, 3, 47-54. Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., and Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. J. Res. Math. Educ. 38(3), 258–288. https://doi.org/10.2307/30034868 Jamil, N., Rosli, R., & Mahmud, M. S. (2025). Algebraic trends impact school mathematics education: A bibliometric review. Multidisciplinary Reviews, 8(9), 2025261. https://doi.org/10.31893/multirev.2025261 Kaput, J. J. (1999). Teaching and learning a new algebra. In Mathematics classrooms that promote understanding (pp. 133-155). Routledge. Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139-151. Lee, J., & Pang, J. (2021). Students’ opposing conceptions of equations with two equal signs. Mathematical Thinking and Learning, 23(3), 209-224. https://doi.org/10.1080/10986065.2020.1777364 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston. Passas, I. (2024). Bibliometric analysis: the main steps. Encyclopedia, 4(2). https://doi.org/10.3390/encyclopedia4020065 Stein, M. K., Kaufman, J. H., Sherman, M., & Hillen, A. F. (2011). Algebra: A challenge at the crossroads of policy and practice. Review of Educational Research, 81(4), 453-492. https://doi.org/10.3102/00346543114230 Veith, J. M., Beste, M. L., Kindervater, M., Krause, M., Straulino, M., Greinert, F., & Bitzenbauer, P. (2023). Mathematics education research on algebra over the last two decades: Quo vadis? Frontiers in Education, 8, https://doi.org/10.3389/feduc.2023.1211920 Wang, Y. (2008). On visual semantic algebra (VSA) and the cognitive process of pattern recognition. In Proceedings of the 7th IEEE International Conference on Cognitive Informatics (pp. 384–393). IEEE. 24. Mathematics Education Research
Paper Problem-Posing Skills of Gifted and Non-Identified Students on A Geometrical Task 1: İnönü University, Turkey (Türkiye); 2: Middle East Technical University Presenting Author:Problem-posing is considered as an important component of mathematics education and a powerful tool for fostering students’ mathematical thinking, creativity, and conceptual understanding. To show its importance in 1938, Einstein and Infeld wrote: “The formulation of a problem is often more essential than its solution, which maybe merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old questions from a new angle, requires creative imagination and marks real advance in science” (p. 92). Despite traditional evaluation tests and approaches, modern literature emphasizes that mathematical ability should be assessed not only in terms of results but also in terms of process (Sriraman, 2005). In this context, problem-posing comes to the forefront as a fundamental tool that makes students’ mental processes visible. In literature, different perspectives have been put forward in defining this concept. Silver (1994) defined mathematical problem-posing as both the generation of new problems and the re-formulation of given problems. Also, Stoyanova and Ellerton (1996) examined problem-posing under the light of instructional situations, and they defined problem-posing as “the process by which, on the basis of mathematical experience, students construct personal interpretations on concrete situations and formulate them as meaningful mathematical problems” (p. 518), and classified as free situation, semi structured situation and structured situations. When we look at the modern synthesis, research indicates that children lacking prior experience in problem posing can nonetheless formulate realistic, inventive, multi-step mathematical questions derived from diverse scenarios (Cai et al., 2015). This renders problem-posing an activity with a high-ceiling and low-floor affording all children the opportunity to make sense of mathematics (Cai & Hwang, 2021). In addition, English (1997) asserted that problem posing provides the opportunity for teachers to gain insight into students’ understanding of mathematical concepts and processes.
Geometry is a field of mathematics utilizing abstract and visual thinking. It holds particular importance in problem-posing exercises (Shriki & Lavy, 2012; Van Harpen & Sriraman, 2013). Research has shown that students often experience conceptual difficulties when posing problems in the context of geometry, but problem-posing activities improve students’ geometric reasoning, and with appropriate guidance, they can create meaningful and creative problems (Kontorovich & Koichu, 2013). In this respect, geometric problem-posing tasks are used as an effective tool distinguishing students’ level of mathematical thinking. Studies conducted with diverse student profiles, including gifted students, have examined how mathematical ability differs; some significant research has even directly compared gifted and non-gifted students. The literature indicates that gifted students, compared to non-gifted students, pose more original, complex, high-cognition problems that maintain logical consistency by making structural transformation rather than superficial changes in geometrical tasks, demonstrating greater success in transforming given situations and creating new mathematical structures (Aydoğdu İskenderoğlu & Yurtbakan, 2023; Espinoza et al., 2022). Compared to problem solving, problem posing represented a neglected area of research, but in recent years the mathematics education community has been increasingly focused on mathematical problem-posing for more than thirty years (Getzels, 1979; Kontorovich et al., 2012). Despite the increasing importance of problem-posing studies, there is a lack of studies in the field comparing gifted children with their peers who are non-identified as gifted, such as semi-structured problem-posing (Espinoza et al., 2022. This study attempts to close the gap by comparing gifted and non-identified students’ problem-posing process, which is under-studied relative to problem solving, using a geometric figure as the mathematical domain in order to contribute internationally. In this respect, the study has the following research question: How gifted students and their non-identified peers differ in the mathematical problem-posing based on given geometrical tasks? Methodology, Methods, Research Instruments or Sources Used This case study, as a qualitative approach, aims to investigate how gifted students and their non-identified peers differentiate in problem posing process based on the given geometrical task. In this regard, the participants consisted of four gifted students aged 14-15, two girls and two boys, two in the 8th grade and two in the 9th grade, and four non-identified students, three boys and one girl, in 9th grade studying in Türkiye. One of the gifted 9th-grade students stated that she has been diagnosed since the 3rd grade and love mathematics because of the problem-solving techniques she developed herself, while another stated that he has been diagnosed since the 2nd grade, enjoy listening to and learning mathematics in class, and do not accept anything without questioning it. Two other gifted students in 8th grade stated that they had been diagnosed since 2nd grade and had an interest in mathematics. Mathematics grades of non-identified students were served as a criterion, with two students achieving scores of 70 and two others attaining scores of 80 on their initial math examinations during the fall semester of 2025/2026, signifying moderate academic success, their general attitudes towards mathematics were determined as positive. In order to collect the data, an open-ended geometrical task (Xie & Masingila, 2017, p.116) was used with the item to reveal problem posing skills of the participants. As the students involved in the study were minors, parental consent forms were disseminated to their families prior to data collection, and these forms were subsequently retrieved with the requisite signatures of consent. On the same day, a 50-minute after-school session was used to implement the data collection task for gifted students. For non-identified students, the task was given over a 50-minute period in a classroom setting but outside of class time. The two participant group implementations are separated by one week. Data was analyzed based on “Scoring Rubric for Problem Pose Skills” (Cankoy & Özder, 2016) consisting of the following dimensions: 1) solvability; 2) reasonability; 3) mathematical structure (result-unknown vs start-unknown); 4) context (routine vs non-routine), and 5) language. Also, according to this rubric, the maximum score that can be obtained for each problem is 6. Throughout the data analysis process, both authors deliberated on their perspectives regarding the scoring system, and discussions persisted until they reached a consensus on the final scores and methodologies. Conclusions, Expected Outcomes or Findings Upon analyzing the problem-posing performance of gifted students, a 9th grade gifted student posed five problems and achieved a total score of 16 points, while another 9th grade student posed three problems and attained 10 points, with the maximum score for each problem being 6 according to the rubric. 8th grade gifted students posed four and five problems, achieving scores of 11 and 13 points, respectively. The findings suggest that the quantity and quality of problem-posing among gifted students do not consistently and concurrently advance. When analyzing the problem-posing performance of non-identified students, it was noted that although the quantity of problems they posed was largely comparable, there were marked discrepancies in their overall rubric scores. A non-identified student posed four problems and attained a total of 9 points, whereas the other students posed four problems and scored 6 and 5 points, respectively. Yet, another non-identified student, performed exceptionally well in the group and received a total of 20 points for posing five problems. These results show that among non-identified students, the number of problems posed is similar but the problems' quality can vary greatly. Besides, the problems posed by non-identified students contain misconceptions and inappropriate use of mathematical language (e.g. "round" instead of "circle" and "diameter of a square" instead of "side length of a square"). Gifted students perform more consistently in terms of quality during the problem-posing process. Moreover, none of the 8 students were able to pose a non-routine problem and to use start-unknown approach as a mathematical structure. This study's findings indicate that problem-posing performance cannot be evaluated solely by the quantity of problems generated, and that qualitative assessment using rubrics uncovers distinctions; thus, future research could investigate structured practices and methodologies to enhance the qualitative aspect of the problem-posing process of gifted and non-identified students. References Aydoğdu İskenderoğlu, T. & Yurtbakan, E. (2023). Comparison of problem-posing skills of gifted and non-gifted primary school students. International Journal of Contemporary Educational Research, 10(1), 120-130. https://doi.org/10.33200/ijcer.1185364 Cai, J., & Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: Conceptualization and initial findings of a problem-posing project. ZDM–Mathematics Education, 53(6), 1403–1416. https://doi.org/10.1007/s11858-021-01252-3 Cai, J., Hwang, S., Jiang, C.,& Silber, S. (2015). Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6258-3_1 Cankoy, O., & Özder, H. (2017). Generalizability theory research on developing a scoring rubric to assess primary school students' problem posing skills. Eurasia Journal of Mathematics, Science and Technology Education, 13(6), 2423-2439. https://doi.org/10.12973/eurasia.2017.01233a Einstein, A., & Infeld, L. (1938). The evolution of physics (p. 92). New York: Simon and Schuster. English, L.D., (1997). The development of fifth grade children’s problem posing abilities. Educational Studies in Mathematics, 34, 183–217. https://doi.org/10.1023/A:1002963618035 Espinoza, J., Lupiáñez, J. L., & Segovia, I. (2022). A study of the complexity of problems posed by talented students in mathematics. Mathematics, 10(11), 1841. https://doi.org/10.3390/math10111841 Getzels, J. W. (1979). Problem finding: A theoretical note. Cognitive Science, 3(2), 167–171. https://doi.org/10.1207/s15516709cog0302_4 Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the Billiard Task. Educational Studies in Mathematics, 83(1), 71-86. https://doi.org/10.1007/s10649-012-9431-9 Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149-161. https://doi.org/10.1016/j.jmathb.2011.11.002 Shriki, A., & Lavy, I. (2012). Problem posing in a dynamic geometry environment and the development of mathematical insights. The International Journal of Learning, 18(5), 61-70. Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? An analysis of constructs within the professional and school realms. The Journal of Secondary Gifted Education, 17(1), 20–36. https://doi.org/10.4219/jsge-2005-389 Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson(Ed.), Technology in mathematics education (pp. 518-525). Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96(1), 101-118. https://doi.org/10.1007/s10649-017-9760-9 24. Mathematics Education Research
Paper Key Concepts and Difficulties in Sketching Graphs of Polar Equations Hacettepe University, Turkey (Türkiye) Presenting Author:The development of polar coordinates dates back to the 17th century (Boyer & Merzbach, 2011; Eves, 1990). Polar coordinates are widely used in various disciplines such as mathematics, physics, engineering, and STEM (Borji & Voskoglou, 2016; Haro & Aguilar, 2025; Paoletti et al., 2013). At the collegiate level, the polar coordinate system is an essential concept for studying advanced mathematics and is involved across a variety of courses, including pre-calculus and multivariable calculus (Borji et al., 2020; Habre, 2017; Paoletti et al., 2013). In the context of calculus-related instruction, students are introduced to the relationship between polar and Cartesian coordinate systems, how to convert between them, and sketch polar curves (Borji et al., 2020). The polar coordinate system is defined as “a two-dimensional coordinate system where each point on the plane has two indicators: a distance from the pole, r, as the first coordinate and an angle from a reference direction, θ, as the second coordinate” (Borji et al., 2020, p.408). Unlike Cartesian coordinates, where each point has a unique representation, a point in polar coordinates can be represented in infinitely many ways (Borji & Voskoglou, 2016; Haro & Aguilar, 2025). This difference is considered one of the sources of students’ difficulties with polar coordinates (Haro & Aguilar, 2025). When engaging with polar coordinates, students often remain constrained by the habits and modes of thinking developed through their prior experiences with Cartesian coordinates (Moore et al., 2014). Even though it is critical for students’ mathematics learning, research on the polar coordinate system is notably limited (Moore et al., 2014). Moreover, the extant literature indicates that undergraduate students have difficulties with polar coordinates (Habre, 2017; Haro & Aguilar, 2025; Moore et al., 2014). More attention should be devoted to investigating how students construct their understanding of the polar coordinate system, and the challenges they encounter during this process (Montiel et al., 2008; Moore et al., 2014; Sayre & Wittman, 2007). In addition, although graphing has received considerable attention in mathematics education, comparatively little research has focused on graphing in polar coordinates (Habre, 2017). In this respect, this study aims to investigate the concepts that prospective mathematics teachers consider and the difficulties they encounter when sketching graphs of polar equations. Hence, this study aims to answer the following research questions: Which concepts do prospective mathematics teachers take into account when sketching graphs of polar equations? What difficulties do prospective mathematics teachers encounter when sketching graphs of polar equations? Methodology, Methods, Research Instruments or Sources Used This study was designed as a case study (Merriam, 2009) focusing on prospective mathematics teachers’ approaches and difficulties when sketching graphs of polar equations. Participants were second-year students enrolled in the Elementary Mathematics Education program at a state university. Within the scope of an undergraduate course, prospective mathematics teachers were instructed over a two-week period on fundamental concepts of polar coordinates. The instructional content included plotting points in polar coordinates, determining equivalent polar coordinates, converting between polar and Cartesian coordinate systems, transforming equations between polar and Cartesian forms, and sketching graphs of polar equations. Following the instruction period, Question 1 on sketching a polar graph was posed, and 70 prospective mathematics teachers responded. Question 2, which was similar in nature, was posed at the end of the semester and received 55 responses. Questions 1 and 2 are presented below. Question 1. Sketch the graph of the polar equation r=1+2sin3θ Question 2. Sketch the graph of the polar equation r=1+2cos2θ In the data analysis process, the six-step qualitative data analysis framework proposed by Creswell (2013) was employed to analyze both research questions. Initially, the data were organized and prepared through categorization. Next, the entire data set was examined to obtain a general sense of the responses. In the subsequent step, the data were coded by identifying meaningful units, and these codes were used to develop categories, descriptions, and themes. The results were then presented using tables. Finally, the findings were interpreted by relating them to the existing literature and drawing conclusions. Conclusions, Expected Outcomes or Findings According to the results, prospective mathematics teachers considered the following key concepts while sketching graphs of polar equations: examining possible symmetries of the graph with respect to the polar axis, the line θ=π/2, and the pole, considering the signs of r and θ values, determining the appropriate interval for θ to ensure the entire graph is captured, deciding how many points should be calculated to adequately represent the shape of the graph, identifying the points, and using them as references in the sketch. Regarding the second research question, it was found that some participants had limited content knowledge in particular concepts, such as trigonometry and functions. In addition, they had difficulties in plotting polar points with negative r and θ values. Some participants did not conceptualize polar graphs as curves, which may be attributed to their prior experience with Cartesian coordinates. Consistent findings were reported in the studies of Borji and Voskoglou (2016) and Haro and Aguilar (2025). Borji and Voskoglou (2016) stated that students’ difficulties in polar coordinate problems are related to limited prior knowledge of trigonometric angles and functions, limited understanding of Cartesian coordinates and polar coordinates and equations, and transitions between them. According to Haro and Aguilar (2025), learning obstacles in the polar coordinates can be grouped into two categories: epistemological and didactical. Epistemological obstacles included reliance on Cartesian knowledge and challenges with negative values, multiple representations of the pole, and intersections of polar graphs, while didactical obstacles involved graphing in polar coordinates, interpreting polar functions, and converting between Cartesian and polar forms. References Borji, V., Erfani, H., & Font, V. (2020). A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates. International Journal of Mathematical Education in Science and Technology, 51(3), 405-423. https://doi.org/10.1080/0020739X.2019.1578904 Borji, V., & Voskoglou, M. G. (2016). Applying the APOS theory to study the student understanding of the polar coordinates. American Journal of Educational Research, 4(16), 1149–1156. Boyer, C. B., & Merzbach, U. (2011). A history of mathematics (3rd ed.). John Wiley and Sons. Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE Publications. Eves, H. (1990). An introduction to the history of mathematics. Brooks/Cole- Thomson Learning. Habre, S. (2017). Students’ challenges with polar functions: covariational reasoning and plotting in the polar coordinate system. International Journal of Mathematical Education in Science and Technology, 48(1), 48–66. https://doi.org/10.1080/0020739X.2016.1220027 Haro, A., & Aguilar, M. S. (2025). Learning obstacles and teaching proposals associated with the polar coordinate system: A literature review. International Journal of Mathematical Education in Science and Technology, 56(5), 828–850. https://doi.org/10.1080/0020739X.2023.2295903 Merriam, S. B. (2009). Qualitative research: A guide to design and implementation (2nd ed.). John Wiley & Sons. Montiel, M., Vidakovic, D., & Kabael, T. (2008). Relationship between students’ understanding of functions in Cartesian and polar coordinate systems. Investigations in Mathematics Learning, 1(2), 52–70. https://doi.org/10.1080/24727466.2008.11790283 Moore, K. C., Paoletti, T., & Musgrave, S. (2014). Complexities in students’ construction of the polar coordinate system. The Journal of Mathematical Behavior, 36, 135–149. http://dx.doi.org/10.1016/j.jmathb.2014.10.001 Paoletti, T., Moore, K. C., Gammaro, J., & Musgrave, S. (2013). Students’ emerging understandings of the polar coordinate system. In (Eds.) S. Brown, G. Karakok, K. H. Roh, and M. Oehrtman, Proceedings of the Sixteenth Annual Conference on Research in Undergraduate Mathematics Education (pp. 366–380). University of Northern Colorado. Sayre, E., & Wittman, M. (2007). Intermediate mechanics students’ coordinate system choice. Electronic Proceedings for the Tenth Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education Conference on Research in Undergraduate Mathematics Education, San Diego. | ||