In this case the more competent individual acted as a scaffold for the child. According to Vygotsky theory, scaffolding is the role of the more competent individual to provide support structures to enable progression to the next stage (Raymond, 2000, P.176). .
"The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics" According to the (Australian Curriculum, Assessment and Reporting Authority,n.d). This is encouraged within the Vygotsky's theory as he believed children learn through the interactions within their surroundings. For example teaching mathematics to children teachers would need to encourage children to share ideas, thereby not only do they learn maths, but also communication and team work. Using this Vygotsky's theory, communication is the base for learning. "The mathematics curriculum provides students with carefully paced, in-depth study of critical skills and concepts. It encourages teachers to help students become self-motivated, confident learners through inquiry and active participation in challenging and engaging experiences" (Australian Curriculum, Assessment and Reporting Authority,n.d).
Jean Piaget's theory of cognitive development explores how the children's thoughts and process change with development. Piaget looked at whether children viewed and made sense of the world in the same way as adults do According to (Smith, Cowie, Blades. 2003 P.32) Piaget's theory of cognitive development has four developmental stages which are sensori-motor stage, preoperational stage, concrete operations and formal operations (Ojose, 2008). Piaget believed that children thoughts and process develops as the progress through these developments and that each four stages have its own importance role.