Continuity in teaching function-related concepts in general secondary schools and academic lyceums

Аннотация

Continuity in mathematics education is crucial for ensuring smooth cognitive development and conceptual understanding among students transitioning from general secondary schools to academic lyceums. COPYRIGHT © 2025 Original content from this work may be used under the terms One of the key areas requiring a structured approach is of the creative commons attributes 4.0 License. the teaching of function-related concepts. This paper examines the necessity of continuity in teaching functions, explores existing gaps in the curriculum transition, and proposes pedagogical strategies to reinforce students’ comprehension. By aligning methodologies and gradually increasing the complexity of function-related concepts, educators can facilitate deeper mathematical understanding, critical thinking, and problem-solving skills. The study highlights the importance of curriculum integration, differentiated instruction, and the use of technology to enhance continuity in teaching mathematical functions. Keywords: Continuity in mathematics education, teaching functions, curriculum alignment, mathematical reasoning, secondary school mathematics, academic lyceum, function concepts, digital learning tools, cognitive development, STEM education. Introduction: Mathematical functions play a central role in the study of algebra, calculus, and applied mathematics, forming the foundation for various disciplines such as engineering, economics, and physics. Ensuring continuity in teaching function-related concepts from general secondary schools to academic lyceums is essential for avoiding knowledge gaps and cognitive overload among students. In many education systems, a lack of structured transition leads to difficulties in understanding higher- level concepts introduced in academic lyceums. European International Journal of Pedagogics 68 https://eipublication.com/index.php/eijp European International Journal of Pedagogics Students often struggle with abstract mathematical concept definition affect students’ understanding of thinking, functional transformations, and real-world functions, advocating for early exposure to complex applications due to inadequate preparatory exposure function types. Hiebert and Lefevre (1986) differentiate in general secondary schools. This paper explores between conceptual and procedural knowledge, strategies for maintaining continuity in teaching recommending a balanced approach to teaching functions by bridging the curricular gap, incorporating functions. technology, and aligning teaching methodologies. Dubinsky and McDonald (2001) propose the APOS Mathematics education serves as a foundation for theory, which integrates action, process, object, and various scientific disciplines, and function-related schema to facilitate deeper understanding. Kilpatrick, concepts are among its core elements. In many Swafford, and Findell (2001) emphasize the need for educational systems, the transition from general structured instructional sequences that gradually secondary schools to academic lyceums poses introduce complex function concepts. These studies challenges in maintaining consistency in content collectively underscore the significance of continuity in delivery and student comprehension. Differences in teaching methodologies and curriculum design to pedagogical approaches, curriculum structure, and enhance mathematical competence. assessment methods often create gaps in knowledge METHODS retention. This study examines the factors influencing This study employed a mixed-method approach, the continuity of teaching function-related concepts incorporating both qualitative and quantitative and suggests improvements to bridge potential gaps. analyses. Data were collected from mathematics Literature Review Research in mathematics education curricula of general secondary schools and academic emphasizes the importance of continuity in conceptual lyceums to identify structural differences. Additionally, learning, particularly in function-related topics. Artigue a survey was conducted among mathematics teachers (2009) highlights the role of didactical design in and students to assess their perceptions of continuity in ensuring a seamless transition between educational function-related topics. Classroom observations and levels. Sfard (1991) explores the dual nature of interviews were also utilized to gain deeper insights into mathematical conceptions, emphasizing the need for teaching methodologies. process-oriented teaching approaches. Tall (2013)