Developing Mathematics Written Communication through Case-Based Learning

ABSTRACT

when asked to articulate their concepts vocally. There are three distinct components to mathematical communication. Communication about mathematics, communication within mathematics, and communication with mathematics are some of these elements. In education, the usage of student-centered learning environments has grown (Baeten et al., 2016). Someone must communicate their thought process and problem-solving strategy while communicating about mathematics. The students need to externalize the process that might not happen when working alone in a traditional learning environment. As a result of dialogue in the classroom, the externalization process may support high-level reasoning. In mathematics, communication is defined as the use of language with mathematical symbols. How language is used when discussing mathematics is directly tied to the mathematical language style; communicating about mathematics is connected to using mathematics, which enables students to solve issues.
One of the learning models frequently used in classroom activities is the traditional one. This model starts with the instructor explaining an idea or topic. Before continuing with their practice, the teacher walks the students through the steps required to complete a task or problem. Teachers with extra concerns may further explain these steps (Chapko & Buchko, 2004). In this study, teachers actively participate in classroom activities, whereas passive pupils take the lectures (Aziz & Hossain, 2010). When the teacher merely acts as a conduit for knowledge, the learning activities are frequently referred to as one-way learning. Students' input and feedback are useless if a teacher is the only person driving the learning process. Sometimes the only resources provided are books and learning notes. Additionally, learning activities lack practical activities, teacher handwriting is not a reliable indicator of the clarity of the material because of its quality, there is insufficient student interaction in the classroom, existing theories are emphasized more than real-world situations and situations, learning is done by memorization rather than understanding, and learning is results-oriented (Damodharan & Rengarajan, 2007).
With traditional education, pupils become listeners rather than learners. Students must therefore learn to be more independent. Lessons are exclusively given to students by the teacher. Students cannot perform to the best of their abilities in class due to time constraints. Students, on the other hand, need to be able to control their learning. Learning quality and its potential improve when students learn to manage their time better. Independent learners are actively involved in optimizing their learning chances and capacities (Darr & Fisher, 2004). This makes sense, given that regulated learning involves students actively designing their learning objectives and then attempting to monitor, sustain, and monitor their awareness, motivation, and behavior that is guided and constrained by those objectives while highlighting the context in the environment (Pintrich, 2000). Students' quality cannot improve if traditional learning is always used to give material courses. Students will always be dependent on the teacher and require assistance in determining how to raise their level of performance.
Thus, the use of multimedia and many strategies by teachers is mandated by curriculum reform. Case-based learning is an alternative teaching method that may be employed. A teaching strategy known as "case-based learning" requires students to actively engage in realworld or hypothetical issue situations that reflect the experiences frequently encountered in the topic being studied (Ertmer & Russell, 1995). The Latin word cases, which means "occurrence" or "something that happens," is where the term "case" originates. A case's main objective is to force pupils to confront complex, unstructured situations and consider potential answers. Cases may be fiction or creative works that aim to describe actual circumstances accurately. In most situations, these components are combined in the design and narrative (Morrison, 2001). The following are the steps in case-based learning. The case is presented, the group examines it, brainstorms ideas, develops learning objectives, sorts the research, presents the findings, and students reflect (Williams in Stanley, 2021).
Dorit Alt (2020) stated that Case-based learning is a successful instructional strategy for enhancing students' capacity to apply the knowledge, concepts, and abilities they have acquired in the classroom to real-world situations. Case-based learning improves students' capacity for resolving ill-structured problems (Rong & Choi, 2019). For the transfer of learning in illstructured problem solving, case-based learning as a whole learning environment was beneficial (Choi & Lee, 2009). To assist educators in developing more productive case-based learning environments, suggestions for instructional design about the use of failure scenarios are presented based on discussions of the study's findings (Rong et al., 2020). Case-based learning differs from problem-based learning; problem-based learning sessions often need more guidance for case discussion. Students needed more time to prepare and frequently did their study as the case was presented; thus, learning happened as it happened. Problem-based learning the student needed more guidance during the case discussion and initial preparation. However, with case-based learning, practice is done in advance by both the instructor and the students, and there is a direction for the debate to ensure that crucial learning elements are covered (McLean, 2016).
A case is frequently presented as a narrative with a clear framework, a significant character, specimen, or element, where a problem needs to be solved. Cases generally resemble real-life events (Kulak, 2014). Using scenarios based on real-world educational problems, case studybased instruction helps instructors to engage students in the reality of teaching (Willems et al., 2021). Students can problem-solve varied outcomes and produce potential answers from various theoretical stances. Instances are conceptualized in ways beyond the conventional framework of cases as human experiences and contain phenomena crucial to comprehending complex ideas about perspective and space (Valentine & Kopcha, 2016). In the CBL group, students demonstrated high satisfaction and problem-solving skills (Bi et al., 2019). The problem in CBL is an ill-structured problem or open-ended problem, and Open-ended problems encourage more inventiveness and inspire a more extensive range of learners (Allchin, 2017). Baeten et al. (2013) stated that compared to students who solely engaged in case-based learning, students in a gradually implemented case-based setting worked more efficiently and with greater focus. Additionally, student participation in case-based activities scored much better on the more typical, algorithmic in-course exams (Fawcett, 2017). The majority of students felt that they learned positive attitudes throughout the course and had favorable opinions of CBL as a teaching strategy, according to the results (Watson et al., 2022). Çam and Geban (2011), in their research, stated that the findings revealed a substantial difference in views regarding school subjects between the experimental and control groups, favoring the group using a case-based learning approach. According to case-based reasoning, comprehension and interpretation of a case are incremental and dynamic; hence, the lessons learned from one case may alter throughout a case-based curriculum and in light of new experiences (Tawfik et al., 2019).
Since each student hopes to succeed in their academic endeavors, this research is crucial to finding solutions to issues. According to one study, students who were taught using case-based learning methodologies behaved significantly different than those who were not (Akanmu & Fajemidagba, 2012). There was much research that stressed teacher-student communication. However, more study was required to determine how case-based learning affected students' mathematical communication abilities, particularly in geometry.

B. METHODS
Quasi-experimental research methodology is employed. The primary distinction between this study and actual experimental research is the grouping of participants. To reduce bias in experimental investigations, participants were recruited at random. Quasi-experimental research is the best option if the individual selection is considered problematic or impossible. Because the quasi-experimental design does not offer total control, researchers must be mindful of variables that impact internal and external validity when interpreting their research findings (Suratno et al., 2018). The dependent variables in this study are mathematical communication abilities, while the independent factors are case-based learning. In this work, a post-test-only design with no equivalent groups was the basis for the quasi-experimental methodology. The experimental and control sample classes are separated by a dashed line, indicating that the experimental and control sample classes were not created by randomly assigning individuals or study participants to the sample classes. Forty-six pre-service mathematics teachers from two complete classes were the study's participants in the fifth semester. Casebased learning is used to teach students enrolled in the experimental class. The control class, in contrast, imparts traditional instruction to the students who served as the research subjects. With more outstanding direction, the instructor offers case-based learning services (Stanley, 2021). After the learning sessions, students in both sample classes took a test (O1 = O2) to assess their communication skills.

C. RESULT AND DISCUSSION
All grade levels indeed have varied mathematical communication skills. Students should be able to organize and consolidate their mathematical thinking skills through communication, communicate their mathematical thinking coherently and clearly to peers, teachers, and others, analyze and evaluate the mathematical thinking strategies of others, and use mathematical language to demonstrate mathematical ideas precisely in educational programs from kindergarten through Grade 12. It is essential to employ communication tools to improve pupils' communication abilities. Reading (numbers, graphs), writing (numbers), extracting information from media, translating information from media, interpreting information from media, and presenting information are some examples of communication abilities (tables, charts, graphs). Additionally, there are three different ways to communicate: orally, in writing, and physically (Morgan et al., 2004).
The communication abilities used to present data or mathematical issues in writing were tested in this study. The written language, symbols, diagrams used in mathematics textbooks, and verbal/spoken classroom engagement all contribute to the construction of particular beliefs about the nature of mathematics and expectations for student's participation in the mathematical activity (Alshwaikh & Morgan, 2018). The average and standard deviation can describe the students' mathematical communication abilities. The following is an overview of students' mathematical communication skills, as shown in Table 1. There were 46 students in case-based learning (CBL) and traditional classes. The standard deviation of the student's mathematical communication abilities in CBL class was 13,884; the average was 63,33. However, in a control classroom, the mean student's mathematical communication skill was 55,45, with a standard deviation of 8,579. The standard deviation for both groups was 12,194, and their average was 59,57. The range of student mathematical communication ability is 0 to 100, so both the CBL and conventional classes can be categorized as having moderate mathematical communication ability.
The normality test of the learning-based data revealed that the Kolmogorov-Smirnov test's p-value for both the CBL and traditional classes was more significant than (> 0.05). A p-value of < 0.05 was found for the CBL and Control classes in the test of homogeneity of variance. As a result, both test-based learning systems used data on students' mathematical communication skills drawn from a normally distributed sample. Data on students' mathematical communication, however, do not homogen. The statistical test utilized in this analysis is a nonparametric test based on the normality test and homogeneity of variance of student data on mathematical communication skills. The Mann-Whitney test is the nonparametric test that is employed. The independent two-sample t-test can be substituted with the Mann-Whitney test, as shown in Table 2.  Table 2 shows that the factor of the learning approach has a p-value < 0.05. It means that Although most students were still working on it, it needed to be finished. Some pupils drew a trapezoid that did not adhere to the guidelines, while others drew a triangle. Another trapezoidal has an inaccurate name, such trapezoid ABDC. Some pupils, however, are tackling this problem reasonably adeptly, as shown in Figure 2.