A Systematic Literature Review on Students Misconceptions in Mathematics

The misconception in mathematics education has been highlighted in various studies. However, there is still a limited literature review on students’ misconceptions in mathematics. The purpose of this study is to review and analyze articles on student misconceptions in mathematics published between 2014 and 2019. The literature search for this study was conducted using four online databases, namely ERIC, Scopus, ScienceDirect, and Google Scholar. To ease the process, the researcher has set several inclusion and exclusion criteria before conducting the review. This study found that there is a decline in the number of articles published between 2014 to 2019 and that most studies have focused on primary school students. The study found that most of the studies conducted were aimed at determining misconceptions rather than overcoming students’ misconceptions in mathematics education. Also, the instruments and methods for obtaining data that researchers often use are through tests and interviews. Some suggestions on overcoming misconceptions in mathematics are also highlighted for further study.


Introduction
Mathematics is a subject that is always given special attention in schools. This is because mathematics is related to many other fields and disciplines. However, many students find it difficult to learn mathematics in school, and it is often considered as a difficult subject to learn. Acharya (2017) states that difficulties in learning mathematics are largely due to the fact that teachers do not associate new mathematics concepts with previously learned mathematical concepts, anxiety towards learning mathematics, negative perceptions towards mathematics, economic factors, students educational background, school management systems as well as the lack of infrastructure in schools and the absence of a continuous assessment system. Therefore, it is not surprising that many students consider mathematics as a challenging subject, and as a result, students have little interest in learning mathematics (Rohani et al., 2014).
Like most other subjects, students also make misconceptions in mathematics. According to Mohyuddin and Khalil (2014), mistakes and misconceptions occur when students make inappropriate generalizations about an idea. Nurul et al. (2019) further explained that students' failure to master the basic concepts of mathematics would increase their probability of using the wrong strategies, which in turn, result in errors and misconceptions in solving mathematical problems (Nurul et al., 2019). Based on this statement, it is believed that students should possess a strong mathematical foundation to help them learn mathematics effectively.
Studies like Siyepu (2015) highlighted that misconceptions stem from the early phase of learning, either in the classroom or as they interact socially with the world outside. It was described that mathematical knowledge is cumulative and is based on prior mathematical knowledge and learning (Siyepu, 2015;Sawardi & Shahril, 2014). On the other hand, many students do realize the importance of prior information during the transition from school to higher learning. Such misconceptions can hinder the effectiveness of the teaching and learning process and affect students' mathematical achievement.
There are numerous studies on students' misconceptions in learning mathematics, which is focused on both local and international contexts. These studies include Sarwadi and Shahrill (2014), Yang and Lin (2015), Lin (2016), Trivena, Ningsih and Jupri (2017), Rakes andRonau (2018), andTabak (2019). Also, researchers have presented various definitions of misconceptions; Ojose (2015) defined misconceptions as misunderstandings that result from incorrect interpretations, while Korey and Bal (2002) pointed out that misconceptions constitute of wrong clarifications that most students accept as correct. Tippet (2010) further described that misconceptions are often used to illustrate beliefs that are incompatible with scientific explanations. Thus, misconceptions can be described as the differences of opinion between students and experts, where students' understanding produces systematic errors (Suprapto, 2013).
Although there are various definitions of misconceptions put forward by different researchers, many failed to distinguish between errors and misconceptions. Mistakes and misconceptions are related, but they are different as errors and students' negligence make mistakes. On the other hand, misconceptions are caused by students' misunderstandings, as they perceive they are right. This reflects the importance of distinguishing between errors and misconceptions in mathematical learning. Therefore, the most appropriate definitions of misconception and errors for this study are presented by Li, Julihi, and Eng (2017), who defined misconceptions as misunderstandings of ideas or concepts while errors reflect incorrect applications, concepts, theories, or formulas.
Studies by Eryilmaz (2002) mentioned that teachers need to identify and address common mathematical misconceptions among students to ensure the meaningfulness and effectiveness of mathematics lessons. Brodie (2014) argued that most misconceptions stem from incorrect previous knowledge. Ocal (2017) suggested that teachers should correct the misunderstandings of basic mathematical concepts before introducing a new concept. In this process, to avoid students from making the same mistakes, students need to be aware of the causes of the misconceptions and how to deal with them. In conclusion, determining misconceptions and identifying how to overcome misconceptions among students should be done continuously in making learning mathematics more meaningful.

Methodology
This study adopts the systematic literature review methodology, which involves reviewing previous studies on students' misconceptions in mathematics. This study follows the three phases proposed by Kithenham (2004). The phases involve: a) Phase 1: Planning the review, b) Phase 2: Conducting the review and c) Phase 3: Reporting the review Phase 1: Planning the review Preliminary searches started on September 17, 2019 using four databases, Google Scholar, Scopus, Education Resources Information Center (ERIC) and ScienceDirect. While the initial search found are many studies on the misconceptions in of mathematical concepts, there are limited number of studies that synthesized students' misconceptions in mathematics. Therefore, this study is important to fill this gap. As the purpose of this study is to conduct a retrospective review on studies synthesizing students' misconceptions in mathematics, the specific objectives of this study are as follow; 1. Who are the target group of the study? 2. What area of mathematics learning did the study focus on? 3. What is the main purpose for the study on misconception in mathematics? 4. What type of instruments or data source was used to determine misconceptions in mathematics? According to Wohlin et al. (2012), the methods used to conduct a systematic literature review should demonstrate the search strategy, including searching online databases to find relevant studies, as well as the inclusion and exclusion criteria. The studies reviewed here were derived from four databases, ERIC, Scorpus, ScienceDirect and Google Scholar. The researcher has also set several inclusion and exclusion criteria to evaluate the quality of the studies derived from the databases. The inclusion criteria for this study are (i) studies that used the qualitative, quantitative or mixed method (ii) available in full text (iii) peer-reviewed journals, (iv) written in English, (v) published between 2014 and 2019, (vi) focused on misconceptions in mathematics and (vii) involved elementary, middle, high school and higher leaning students.
The initial phase involved searching the databases for relevant articles using the keyword "misconceptions" and found numerous articles on misconception. To further filter the articles, additional keywords were added to the search, along, with additional restrictions that the "misconceptions" prefix should be featured in the articles' title, abstract, or keyword. The researcher also added other keywords into the article search, which are "misconceptions" AND "mathematics", "students' misconceptions" and "students' misconceptions in mathematics". Moreover, the researcher excluded dissertations, book chapters, action research, proceedings papers and survey studies in the search process, as well as articles involving teachers as study participants. The inclusion and exclusion criteria were set at the beginning of the study to ensure the study's focus is clear and directed.

Phase 2: Conducting the review
This study aims to find and review research articles focusing on misconceptions in mathematics. This study reviewed articles published on misconception in mathematics education, and articles indexed in the selected databases were analyzed to obtain data on misconceptions in mathematics. Systematic searches were conducted starting on September 20, 2019 to identify related articles in four online databases namely ERIC, Scopus, ScienceDirect and Google Scholar. This study only reviewed research articles written in English which were published between 2014 and 2019.
The first step involved finding relevant articles in the database, which highlighted the specified keywords in their title or abstract. An initial search found 453 articles. It was found while the initial search found many articles; many of them are not relevant to the main topic. 30 redundant articles were excluded and subsequently, the inclusion criteria were narrowed down to ensure only the appropriate articles were retrieved. Therefore, articles that do not have the word "misconceptions" in the keyword section and are not related to mathematic education were excluded. Thus, out of 453 articles found during the initial search, only 30 study articles published between 2014 and 2019 were retained for the review. The flow for the search process and the selection of articles for this review is illustrated in Figure 1.  Table 1 which details the name of the article's author (s), year of publishing, study area, study participant, study method, instrument or source, and whether the study was conducted to identify misconception or to overcome misconception.  Lesson plans which were prepared by pre service teachers Determining misconception

Results
The articles obtained during the analysis process were analyzed. Based on the findings, the results obtained are organized into five sections: a  In service student teachers 1 Total 30 Table 2 presents the target participants of the published research articles reviewed. It was found that the studies focused on students from various levels of education, including primary, secondary as well as higher learning students (university and college students, pre-service teachers, and in-service student teachers). Table 2 shows that the study's participants can be categorized into two types, which were students and higher learning students. School students include primary and secondary schools, while higher learning students include undergraduate (university and college) students, preservice teachers and in-service postgraduate students. The majority (20) of the studies involved school students, predominantly primary school students, and only 10 studies involved students in higher learning. This indicates that the research on misconceptions in mathematics education has primarily focused on students in the lower/elementary level, and less attention has been given to misconception among graduate students. This reflects the need to conduct studies on students from different educational levels to illustrate students' misconceptions in mathematics at various levels.
Some studies focused on in more than one area of mathematical learning, such as area and perimeters (Machaba, 2016), algebra, geometry, number and probability (Rakes & Ronau, 2018), as well as length, area and volume (Sisman & Aksu, 2016). However, most studies only focused on only one field.

Purpose of studies
In general, the primary purpose of these studies can be categorized into two, either to determine the type of mathematical misconception or to address and overcome mathematical misconceptions. Table 4 presents the main purpose of previous studies on student misconceptions in mathematics.

Instrument/sources used to Determine the Misconception in Mathematics
The studies reviewed have used various sources and instruments to determine students' conceptions in mathematics. It was found that 21 out of the 30 studies reviews used more than one source or instrument, while the remaining studies used only one source. Almost half of the studies used tests such as diagnostic tests, achievement tests and written tests and four studies used diagnostic tests. Two used two-stage diagnostic tests (Lin, 2016;Tabak, 2019) and one study used a four-level test (Yang & Lin, 2015). Another popular method for determining misconceptions in mathematics is through interviews. These interviews were usually conducted immediately after the test was performed. The interviews conducted, allowed the researcher to better understand the misconceptions demonstrated by the students based on the explanations given.

Discussion and Conclusion
This systematic literature review has focused on studies on students' misconceptions in mathematics education. This systematic literature review was carried out based on there is a lack of studies that synthesized students' misconceptions in mathematics. In all, 30 relevant articles were reviewed, and most have focused on determining misconceptions rather than overcoming misconceptions among students. These studies highlighted the challenges in resolving or overcoming misconceptions in mathematics (Uce & Ceyhan, 2019). This reflects there is a lack of studies that examined the effectiveness of mathematics learning and efforts done to overcome the mathematics misconceptions among students. Therefore, a better approach is to determine the common misconceptions and to identify the common mistakes made by the students.
The study also found that there is a decrease in the number of articles on misconceptions in mathematics published between 2014 and 2019. This finding contradicts a study conducted by Bulbul and Danisman (2015), who found that there is an increase in the number of mathematical misconceptions studies between 2008 and 2013. In terms of the target participants, most studies reviewed have focused on primary and secondary school students. In the same time, several studies focused on students in higher learning, including university and college students, pre-service teachers, and in-service student teachers. Lee and Ginsburg (2009) mentioned that most studies have focused on what children can do. From a young age, children try to understand their world using specific contexts and meanings. Still, many children would develop misunderstandings about the numerical concepts and operations that may hinder their learning of early mathematical skills. In this regard, in studying mathematics, the misconceptions that students developed during their early schooling will fossilize and create difficulties in learning mathematics at higher levels (Mohyuddin & Khalil, 2014). The findings of this study show that studies on students' misconceptions could help determine early conceptual misconceptions in mathematics to find possible reasons to better deal with misconceptions in mathematics.
It was also found that some of these articles have focused on similar areas, specifically numbers, fractions, algebra, geometry, and limits. The area of numbers has received the most attention as it is the most basic concept in mathematics education (Lin, 2016), and is extensively taught at the primary level. Furthermore, many students perform poorly in solving algebraic problems involving fractures (Booth, Newton & Twiss-Garrity, 2014). Therefore, it is not surprising that numbers and fractions are the most widely researched mathematical area.
The majority of the studies reviewed in this study used tests to obtain the data to determine the misconceptions among students. Also, some studies used interviews to determine misconceptions. According to Gurel, Eryılmaz, and McDermott (2015), interviews can help obtain complete and accurate data as it facilitates in-depth communication between the researcher and the study's participant. However, despite the numerous advantages of the interview method, it does take a lot of time to interview the study participants in large numbers. In this regard, it was observed that almost half of the reviewed articles were analyzed using the interview method without regard to time constraints. Therefore, it can be said that the data collected from this study provide significant data to future studies on a misconception.

Recommendation for Future Research
This study reviewed 30 articles published between 2014 and 2019, which focused on students' misconceptions in mathematics. The review found that most studies are aimed to determine misconceptions; however, the number of studies on how to overcome misconceptions is very limited. Therefore, further studies are proposed to extend the current studies on overcoming misconceptions in mathematics education. Furthermore, studies on misconceptions in mathematics education also need to be carried out at higher levels as most of the studies reviews involved primary and secondary students. Studies have also found teachers are the source of misconceptions among students (Zulnaidi & Oktavika, 2018). William and Ryan (2000) stated that this could happen when a teacher teaches the wrong concept but does not realize that the concept being taught is wrong. This reflects the need for studies to examine misconceptions among teachers. Also, the review found that studies have used various methods to obtain data and resources to determine misconceptions, but there is no indication of the best method for this process. However, almost half of the studies reviewed have combined different methods and resources to collect data. Therefore, further research could use a variety of methods and data sources to obtain more accurate findings.