Theories of Cognitive Development in Relation to Mathematical Knowledge

From birth, it is important for practitioners to support the early years’ mathematical development. Children learn emergent maths which is a “term used to describe children construct mathematics from birth” (Geist, 2010). The Early Years Statuary Frameworks (EYFS) (Department of Education) states that maths is one of the specific areas.

Jean Piaget is a key figure for development, focusing on cognitive constructivism – that being that we must learn from experience and development, building on knowledge that has already been developed. The strengths and weaknesses of Piaget 's cognitive development theory will be discussed.

Many child development centers, preschools, and school programs are passed on Jean Piaget’s cognitive development theory. When you combine the theory with teachers challenging a child’s ability without introducing concepts beyond their understand, hands on learning, field trips, art crafts, and games you have the perfect learning program for children.

Van de Walle, J, Karp, K. S. & Bay-Williams, J. M. (2015). Elementary and Middle School Mathematics Teaching Developmentally. (9th ed.). England: Pearson Education Limited.

Mathematical activities at Ysgol Dolafon are delivered in accordance with pupil’s individual needs and great deal of emphasis is given to continuity of learning. Ample opportunity is provided for pupils to discuss their understanding of concepts as they progress and teachers are aware of the importance of eliminating any gaps in the children’s mathematical knowledge. The Welsh Assembly Government guideline for Mathematical Development maintains that: ‘It is crucial that gaps in children’s mathematical learning are avoided, so that children do not miss out on essential elements in their understanding of mathematical concepts’ (WAG 2008) and Ysgol Dolafon fully agrees with that statement.

Every day, mathematics is used in our lives. From playing sports or games to cooking, these activities require the use of mathematical concepts. For young children, mathematical learning opportunities are all around them. Knaus (2013) states that ‘Young children are naturally curious and eager to learn about their surroundings and the world they live in’ (pg.1). Children, young and old, and even adults, learn when they explore, play and investigate. By being actively involved, engaging in activities that are rich, meaningful, self-directed and offer problem solving opportunities, children given the chance to make connections with their world experiences (Yelland, Butler & Diezmann, 1999). As an educator of young children,

Sarama, J., & Clements, D. H. (2006). Mathematics in kindergarten. (61 ed., Vol. 5, p. 38). YC Young Children. Retrieved from http://media.proquest.com.ezproxy.apollolibrary.com/media/pq/classic/doc/1129349361/fmt/pi/rep/NONE?hl=&cit:auth=Sarama, Julie;Clements, Douglas

The author explains how many students, especially those in the focused-upon second grade class, have difficulty explaining their “mathematical thinking process”. While they may provide correct answers using memorized calculations, they are unable to demonstrate their conceptual understandings or explain how they achieved the right results. As stated by the researcher, “it is important for students to be able to demonstrate their mathematical thinking as well as their method of solving a problem” (Kostos & Shin, 2010, p.223).

Piaget and Vygotsky both believed that young children actively learn from their hands-on, day-to-day experiences. Jean Piaget portrayed children as "little scientists" who go about actively constructing their understanding of the world. His theories hold the essence of developmentally appropriate curriculum since Piaget believed that children undergo cognitive development in a stage-based manner, such that a very young child would not think about things the same way that an adult might. He referred to the knowledge and the manner in which the knowledge is gained as a schema. In order to build on the cognitive stages that children experience, informal learning opportunities, formal instructional sessions, and the utilized curriculum must all dovetail with a child's current cognitive stage so that assimilation of the new knowledge may occur. Working with what the child knows and experiences, parents and teachers create bridges to the next cognitive stage that are characterized by the child's accommodation. Piaget argued that optimal learning took place in this manner and that adults should avoid thinking that they can accelerate a child's development through the age-based, maturity-referenced stages. This is because a child works toward establishing an equilibrium between the assimilation and application of new knowledge and changing their behavior to accommodate their newly adopted schemas.

Jean Piaget is best known for his theory that suggested children think differently than adults. His theory proposed that children’s cognitive development developed in

Piaget’s cognitive constructivism also has its place in the classroom. As discussed by Kamii & Lewis (1990), students doing maths problems learn better by constructing them internally, by ‘playing around’ with numbers, using games and real life situations to link the base knowledge they need to fulfil the learning outcome with concrete examples. Students can relate more to these

Cognitive developmental theory is founded on the idea that children gain knowledge by exploring and influencing the world that is all around them. According to Mossler (2014) “After many years of observing the mental limitations of children, including his own, Piaget came to the conclusion that children of

Jean Piaget is considered to be very influential in the field of developmental psychology. Piaget had many influences in his life which ultimately led him to create the Theory of Cognitive Development. His theory has multiple stages and components. The research done in the early 1900’s is still used today in many schools and homes. People from various cultures use his theory when it comes to child development. Although there are criticisms and alternatives to his theory, it is still largely used today around the world.

Several years ago, an insightful and profound man, Jean Piaget, established a theory of cognitive growth during childhood. This theory was viewed as a major model for understanding the intricate steps of mental development from the thinking to understanding for a child. This theory also gave rise to the mentality that cognitive processes during childhood are not minuscule versions of adults but rather an irrational yet unique process with its own rules. Even though Piaget’s theory seems quite reasonable and logical, under the light of recent speculation his theory has been widely challenged. However, Piaget’s theory holds great impact in today’s psychology.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).