Mathematics Learning with Concrete Manipulatives among Second-Grade Students at SDN Tridadi: A Perspective on the Concrete Operational Stage

Abstract

Mathematics learning in elementary schools needs to consider students’ cognitive development, particularly among second-grade students who are beginning to develop logical thinking while still relying on concrete experiences. Although Jean Piaget’s theory of cognitive development has been widely discussed in relation to elementary mathematics education, empirical evidence of how characteristics of the concrete operational stage are manifested in actual classroom learning remains limited. This study aims to examine the characteristics of the concrete operational stage in mathematics learning among second-grade students and to explore the role of concrete manipulatives in supporting their understanding of mathematical concepts. A descriptive qualitative approach was employed involving 15 second-grade students at SDN Tridadi selected through purposive sampling. Data were collected through structured classroom observations and clinical interviews, while source and method triangulation were used to strengthen the credibility of the findings. The data were analyzed using an interactive qualitative analysis model consisting of data reduction, descriptive data presentation, and conclusion drawing. The findings indicate that the students demonstrated characteristics of the early concrete operational stage. Classification and number conservation were observed during mathematics learning, while reversibility was still developing and required support through concrete objects. The use of concrete manipulatives provided opportunities for students to directly manipulate, compare, and represent mathematical quantities when solving addition and subtraction problems. Clinical interviews further showed that students’ reasoning was closely related to their ability to visualize and manipulate concrete quantities. The study concludes that empirical observation of second-grade students provides important insight into the manifestation of the concrete operational stage in actual mathematics learning. Mathematics instruction that considers students’ cognitive developmental characteristics and incorporates concrete manipulatives can provide learning experiences that connect mathematical concepts with concrete and observable experiences.