The World of Maths

It is crucial to develop in children the ability to tackle problems with initiative and confidence…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, 2006, p.2).

Mathematical understanding influences all areas of life from social to private and civil. Therefore maths education is widely believed to be the single most important aspect to establishing opportunities for young people; unfortunately, many struggle with mathematics and become indifferent as they continue to encounter obstacles with regard to engagement (Anthony & Walshaw, 2009). Knowing a person’s ability to learn is greatly impacted by teaching beliefs and practices, it is imperative that educators are able to develop and deliver information in an inclusive and cohesive learning environment. Reviewing and developing improved pedagogy to reflect these changes in understanding learning and teaching beliefs in response to the changing needs of society. This essay will explore past teaching practices, the recent findings regarding maths learning development and pedagogy, comparison of learning theory, and the way ahead for improvements to mathematic pedagogy utilising constructivist learning theory within maths-learning environment.

History indicates children were previously thought of to be receptacles for information to be placed or transmitted – this form of learning was known as ‘behaviourist learning’. Simply put, behaviourist learning is based on drill and practice, with reinforcement by reward for desirable behaviour in the form of correct answers and punishment or lack of reward for undesired behaviour. Although effective to explain the learning of animals, years of study and research has now proven, children respond better to learning when given the opportunity to engage and make connections in the knowledge they are acquiring (Anghileri, 2006). This view is shared by many including Abrams and Lockard (2004) who state, “The core of behaviourism – reinforcement – does not adequately explain the complexity of thinking, memory, problem solving, and decision making” (pp.6) because the role of a student, from a behaviourist view, entails students working independently and quietly taking notes at a desk. A student is best described as an accumulator of details and materials, memorizing facts, formulae and procedures. This learning system is flawed when a child is unable to memorise, think for itself, problem solve or justify their findings to others.

The cognitive revolution replaced behaviourism in the1960’s. Cognitive learning theory focuses on inner mental activities. It is suggested that a child’s mind is a ‘black-box’ (Learning Theories and Models Summaries (in Plain English), 2015) that should be opened and understood. This particular learning theory implies a child is similar to a computer, where information enters, is processed and leads to an outcome. This theory of learning relies heavily on the assumption of past learning and experience, it is the providing information rather then the enabling of a child with the skills required to source and assess information and problem solve to achieve the correct outcomes.

The findings of recent studies regarding children’s learning are best related to Constructivist Learning Theory; suggesting children are best able to develop their own understanding and further enhance their knowledge through experiencing a variety of things and reflecting on those experiences (Wadsworth & Wadsworth, 1984). It is clear that when a child becomes actively involved in their learning they are able to develop skills required to gather and construct their knowledge and understanding. Through this involvement a student will learn how to obtain, manipulate and assess the variety of information that is available to them from a range of sources. As a result of these skills a student will be able to tackle problems with initiative and confidence as identified by Anghileri (2006).

According to Anthony & Walshaw, (2009) within a constructivist view, it is a teacher’s role to facilitate the learning of a child by providing a resource rich environment from which they guide a students learning. A student within a constructivist-learning environment must become engaged in the learning process by becoming a researcher, identifying a problem, collecting and analysing data and formulating a conclusion. This process of engagement provides a student with endless opportunity to develop his or her own understanding and knowledge. An educators ability to understand this learning theory as a process of construction and development provides a conceptual framework from which to build a teaching practice.

In comparison, the behaviourist theory assumes a learner is a ‘clean slate’, essentially a passive learner responding to external stimuli. This assumption is flawed in the sense that a child is not simply a ‘clean slate’. In fact, a child is introduced to, and engages in mathematical thinking at a very early age. In recent years, the field of early childhood education and care has embraced sociocultural theory (Australian Government Department of Education, Employment and Workplace Relations, 2007), providing children with opportunities through play and day to day activities, to begin their interactions with maths concepts, for example, a child begins learning about concepts such as recognising and creating shapes, spatial awareness, grouping, measurements, and developing patterns, this can be achieved by simply taking turns with others whilst participating in group activities or engaging in playful activities utilising common items such as building blocks. It is imperative that an education professional is able to recognise these learning opportunities and knows how to connect with build upon these everyday practices and concepts to develop a strong and lasting relationship with learning.

A further consideration to learning is the Humanism Learning theory; it is based on the child’s desire to learn. Humanism focuses on human freedom, dignity and individual potential. Humanism is in direct contrast to behaviourism as it argues that people act with intention and values rather than response to reward. Humanism proposes all humans have a hierarchy of needs, thoughts and actions are influenced by these psychological and intellectual needs being meet (Ingleby, 2013) Within a learning environment Humanism can be less effective as it is student centered, meaning it relies solely on learner initiation, motivation and goal setting. It is important to note that a child may disengage with learning and social activities at any time as a result of either internal or external influence; this disengagement will impact the development and learning process of the child. Although not readily applied as a dominant learning practice within education environments, Humanism is considered to be influential in effective early years practices (Ingleby, 2013).

Learning from past experiences and developments leads to the maths practices and teaching beliefs of today to consider the effects of playfulness and inclusivity within the education environment. It has been shown to be an extremely important and a useful aspect of childhood learning. Studies and research conducted by Parten (1932) have indicated there are specific types of play conducted by children, Unoccupied play, Onlooker behaviour, Solitary play, Independent play, Parallel play, Associate play and Cooperative play. Parten found that as children grow and develop they are exposed to more opportunities for interaction, and those who learned to share, take turns, work and play with others through social types of play such as associative and cooperative, had a greatly likelihood of achieving and experiencing a degree of success later in life. (Parten, 1932) Furthermore, Bergen’s (2001) studies suggest play is beneficial in many areas of childhood development, including language, social, physical and thinking skills. It is suggested that improvement and development of these skills can have a dramatic effect on a child’s self-esteem and relationship with self and others.

The sole aim of an educator is to best serve the needs and requirements of a learning child in today’s society. It is imperative that educators and governing bodies produce pedagogy and curriculum that is based not on what has worked in the past, but what has been learnt from the past, and what is relevant to the schooling experience of today. Educators must understand the theories and contemporary perspectives and support the development of mathematical thinking; this knowledge leads to the conclusion that, as Anghileri (2006) states children’s development of mathematical thinking has not changed, but the understanding of how children engage and disengage with learning has. It is apparent, through decades of studies and research, the inclusion of play-based, fun, creative and social activities are imperative to the crucial development of a child’s ability to approach, tackle and problem solve with confidence and initiative that is so important in today’s society and the future successes of todays children. Mathematical pedagogy must prepare children for the world of tomorrow and the challenges they may face.

References

Anghileri, J. (2006). Children’s mathematical thinking in the primary years perspectives on children’s learning (Repr. 2006. ed.). London: Continuum. Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics. Brussels: International Academy of Education. Australian Government Department of Education, Employment and Workplace Relations, (2007). Early Childhood Literacy and Numeracy: Building Good Practice. Commonwealth of Australia. Bergen, D. (2001). Pretend play and young children’s development. Champaign, IL: ERIC Clearinghouse on Elementary and Early Childhood Education. Learning Theories and Models Summaries (in Plain English). (2015). Cognitivism | Learning Theories. Accessed January 2015, from http://www.learning-theories.com/cognitivism.html Lockard, J., & Abrams, P. (2004). Computers for twenty-first century educators. Boston: Pearson/Allyn and Bacon. Ingleby, E. (2013). Early childhood studies. New York: Blossumbury Publishing Plc. Parten, M. (1932). Social participation among pre-school children. The Journal Of Abnormal And Social Psychology, 27(3), 243-269. doi:10.1037/h0074524 Wadsworth, B., & Wadsworth, B. (1984). Piaget’s theory of cognitive and affective development. New York: Longman.