Earticle

The purpose of this study is to compare and analyze two papers on smart learning and digital learning activities based on cognitive paper and Sfard (2008)'s 'Thinking as communication: Human development, the growth of courses and mathematizing'. Through this, I would like to make a new operational definition of thinking, knowing, and understanding based on four papers. We compared and analyzed how mathematical discourse and meta-discourse are formed in papers related to smart learning and digital learning, how students' cognitive processes change, and what aspects of cognitivism were reflected in class composition. It also analyzes what thought, knowledge, and understanding are defined in each paper, and based on this, a new operational definition is made and concluded.

The purpose of the study was to examine the difference in modeling skills between students who solve modeling problems on their own and those who receive structured guidance from a teacher following the cycle of mathematical modeling. The study found that students who are new to mathematical modeling may struggle to solve problems on their own and may rely on non-mathematical approaches. The study suggests that a structured approach to teaching and learning mathematical modeling is necessary and that students require feedback to develop their knowledge and skills. The study also suggests that heuristic strategies are essential for supporting students' work, but their application in specific situations may be challenging. The role of the teacher is essential in supporting students' activities and helping them understand and apply the cycle and structure of mathematical modeling. The study proposes that providing students with motivated practice and a supportive learning structure is crucial for developing their modeling skills.

The purpose of the study was to analyze mathematical competencies in middle school third graders’ students. The research methodology involves a carefully designed case study of two average-ability students from a middle school in Seoul. Utilizing an IPAD, the students were tasked with solving a modeling problem termed 'Teacher's Diet,' conceptualized by the author. The entire process was meticulously recorded, with minimal teacher intervention, to preserve the authenticity of the students' problem-solving approach. The paper's theoretical contribution lies in its formalization of the evaluation process for mathematical modeling competencies. It delineates the sub-competencies required for each phase of modeling, encompassing Simplifying (translating real-world problems into mathematical representations), Mathematising (setting up mathematical models), Working Mathematically (deriving mathematical results), Interpreting (relating mathematical results to real-world contexts), and Validating (critically reflecting on the results and the model). The findings illuminate the potential efficacy of mathematical modeling as a pedagogical tool to navigate complex mathematical problems. They also accentuate the exigent need for a more robust integration of mathematical modeling in the Korean educational landscape. This paper's insights bear significant implications for curriculum development and pedagogical practices, contributing to the broader discourse on enhancing mathematical literacy and critical thinking skills in middle school education.

The purpose of this study is to investigate the effect of the teacher's questioning order on the expansion of students' mathematical thinking in mathematics class by analyzing the mathematical thinking process of students according to the order of the teacher's questioning. To analyze this, the EBS documentary "Best Mathematics Classroom" transcribed classroom situations and interviews for the first class of elementary school of Y teacher, and analyzed them by applying a grounded theory that generates a new theory based on this data. As a result, it shows that students' mathematical thinking expands according to the order of the teacher's questioning, and from this, the importance of the order of the teacher's questioning is recognized, and the development of a specific teaching method for the teacher's questioning accordingly is proposed.