Welcome to Jit's Blog

This website brings together my journey as a mathematics educator and researcher. Here, I share my research work, classroom reflections, and resources like worksheets and videos to support meaningful learning in mathematics.

Understanding Learning through Piaget and Bruner

Cognitive Theory and Major Contributors 

        When I look at this representation, I see how strongly it aligns with my understanding of learning as a gradual, constructive process rather than as something transmitted directly from teacher to student. Drawing on Piaget, I interpret learning as deeply connected to the child's developmental stages. For instance, in the sensorimotor stage (0–2 years), children engage with the world through their senses and actions. As they move into the preoperational stage (2–7 years), I notice how their thinking becomes more symbolic, though still intuitive and not yet logical. By the time they reach the concrete operational stage (7–11 years), which is where most of my students fall, they begin to think logically, but only when concepts are tied to concrete experiences. Finally, in the formal operational stage (11+ years), abstract reasoning starts to emerge.

            This progression reminds me that my teaching must be developmentally appropriate. I cannot expect abstract reasoning from students who are still grounded in concrete thinking. That is where Bruner’s ideas complement Piaget in a very practical way. Bruner’s three modes of representation, enactive, iconic, and symbolic, resonate closely with what I try to implement in my mathematics classroom.

            I often begin with enactive learning, where students physically engage with manipulatives. For me, this is not just an activity but a necessary foundation. When students touch, move, and construct, they are not memorizing; they are experiencing mathematics. Then, I gradually shift to the iconic stage, where they interpret images, diagrams, or visual models. I see this as a bridge between doing and thinking. Finally, I guide them toward the symbolic stage, where they can use numbers, formulas, and abstract representations with understanding.

            What stands out to me is that both Piaget and Bruner emphasize that learning is active. Students are not passive receivers; they are constructors of knowledge. This directly connects with my research interest in manipulatives for active engagement and conceptual understanding. I see manipulatives not as supplementary tools, but as essential in helping students move from enactive to symbolic understanding. In my practice, this framework pushes me to reflect: Am I allowing students to experience concepts before abstracting them? Am I respecting their cognitive stage? And most importantly, am I creating opportunities for them to actively construct meaning rather than simply follow procedures?