A didactical transposition study on secondary students’ number sense of integers

Introduction This study examines junior secondary students' understanding of integers through the perspective of didactical transposition theory. It focuses on the development of students' number sense and investigates how teaching strategies transform mathematical concepts into classroom practices that influence student learning. Methods A qualitative descriptive approach was employed involving seventh-grade students in Indonesia. Data were collected through problem-solving tasks and semi-structured interviews. The analysis was based on five indicators of number sense: understanding of numerical concepts, use of multiple representations, comprehension of operations, development of equivalent expressions, and application of computational and estimation strategies. Results The findings reveal that students demonstrate varying levels of number sense competence. Two distinct patterns of understanding were identified. Some students exhibited strong conceptual understanding, such as recognizing that negative integers are unbounded and applying proportional reasoning in estimation. However, other students showed persistent misconceptions, including the belief that zero is the smallest number and reliance on procedural rules without conceptual understanding. Discussion The results highlight both the advantages and limitations of simplifying mathematical knowledge in instructional contexts. Effective teaching of integers requires balancing the simplification of content with the preservation of conceptual meaning. Instructional design and curriculum development should emphasize connections between formal mathematical concepts and students' intuitive reasoning to strengthen number sense and support deeper conceptual understanding of integers.