Concrete Operation Schemas Relevant To Piaget's Theory

Students in a Year 4 class are completing numeracy group work via an online program. They are given the task of building a square based pyramid from a specific quantity of oranges and asked questions regarding the construction of the pyramid, the quantity of layers and the number of oranges in each layer. This case study will examine how the use of concrete materials assisted the students, the role of the teacher and the elements of Vygotsky and Piaget’s theories that can be identified in the children’s thinking.
The students are displaying a range of concrete operation schemas relevant to Piaget’s Theory. The concrete operation stage involves student’s thinking evolving to become dynamic, decentred and logical in operation. The students display

The teacher applies principles of Vygotsky’s Theory through scaffolding, instructional conversation and the PQS (Probe, Question, Scaffold) discourse model. The teacher introduced the topic and then indulged in two-way conversations with the use of probing – “How many oranges in the top layer of the pyramid?” and questioning – “Are the numbers starting to form patterns?” to allow the students to learn within the group context, or community of learners (Rogoff, Turkanis and Bartlett as cited in O’Donnell et al, 2012. p. 117). The teacher also used the principles of collaborative learning as each member of the group displayed differing levels of understanding and were able to collaborate to ensure they were working in each’s own Zone of Proximal Development (McLeod, 2015a). The teacher also demonstrated Piaget’s Theory that learning should be accomplish through active discovery (McLeod, 2015b). The teacher facilitated the learning rather than providing direct tuition and used evaluation techniques to decide on what was appropriate based on the children’s development – recognising that the numbers in the layers were square numbers but deciding to not introduce that concept at that

They display attributes of Piaget’s Concrete Operational stage. This can be witnessed through the development of mental operations with their use of manipulatives to solve the problem. The students demonstrate the emergence of conservation, through transitive inference – the size of each level of the pyramid is related to the others. They also display states of disequilibrium and equilibrium as they move through the process of solving the problem (Halpenny & Petterson, 2013; O’Donnell et al, 2012; Woolfolk & Margetts, 2015). Vygotsky’s theory is displayed through the student’s Zone of Proximal Development (ZPD) where the students were not able to solve the problem on their own, yet with support and guidance from the teacher and peers they were able to reach an agreed outcome (O’Donnell et al, 2012) along with scaffolding and collaborative learning by moving through the stages of solving the problem to reach an agreed outcome, building on the discoveries of peers to reach that