Importance of Prior Knowledge in Mathematics Education
There is an importance to understand children’s “prior” or “existing knowledge” along with several strategies employed by educators for revealing understanding of children of mathematical ideas. In educating the subject mathematics, early childhood teachers might focus on existing knowledge of children and observation of young children by means of play and discovery activities (Manuti et al.2015). The objective of this essay is to analyse the major ideas underpinning effective learning and teaching of mathematics. Moreover, the essay will focus on discussing the early childhood teaching specialization along with connecting to the ways in which individuals think, organise as well as use professional judgement on planning, implementation and evaluation regarding learning experiences.
The effective teaching and learning of mathematics are related with prior knowledge use in overall class teaching contexts of the mathematics subject. Early Childhood Australia (ECA) (2012) indicated the ways in which teachers conceptualise previous knowledge and examine whether the mathematics class teaching teachers are capable to ensure better connections. This is because the children are focussed on their previous and current learning experiences. Goos, Vale and Stillman (2017) stated that from the “socio-constructivist and cognitive psychologist” perspectives on learning there is an important part of prior knowledge. These researchers introduced “Schema Theory” which indicates previous knowledge as a major contributor of maintaining an innovative learning. Schemata serves to be a high-level complex structure employed for organizing along with interpreting experience. Hollis (2015) evidenced that this further facilitated in predicting, expecting along with understanding aspects relied on the existing schemata. These researchers also presented a viewpoint that prior knowledge acts as a better learning determinant as previous knowledge is stated within the “long-term memory” within “Schemata”. This might get retrieved within the short-term memory.
Macmillan (2009) revealed that the national mathematics curriculum can serve as the basis of panning, teaching along with evaluation of school mathematics. This can also serve to be useful for and usable by the experienced along with less experienced teachers of K-2 mathematics. These researchers also signified two vital recent reports related with educating and learning of mathematics such as “The Australian National Numeracy Review Report” and “National Mathematics Advisory Panel”. Relations (2010) indicated that critical importance of mathematics is deemed to be assumed by the mathematics curriculum and it also requires to be reflected in adequate time and emphasis focussed on mathematics learning within schools. Successful learning of mathematics offers workforce those are educated in mathematics to contribute productively in supporting an ever-changing international economy. Stacey (2008) added that such learning of mathematics considers both rapid revolutions within technology along with international and social challenges in learning.
National Mathematics Curriculum
From analysis of the previous literature on mathematics learning it has been gathered that the early years of any child develops foundation of learning mathematics. Children at this stage attain the opportunity to access effective mathematical ideas that are important for the current lives. Vartuli and Rohs (2008) stated that it is of great relevance to such learning that prepares them for attaining learning on mathematics which is important in the early years. In their early age children gain an opportunity to attain mathematical ideas through developing an understanding of numbers among them, sequence, order as well as pattern. Developing such understandings along with the experiences over the years offers a base of statistical, algebraic along with multiplicative judgment which will widen in the upcoming years. Vartuli and Rohs (2008) also revealed that developing certain understandings on mathematics along with experiences identify simple strategies for investigative solutions along with strengthening certain reasoning for solving personally meaningful solutions.
Children are observed to learn maths most of the times through a broad range of play experiences. Play serve as an efficient medium in fostering mathematical concepts along with developing positive attitude towards mathematics. The mathematic indicator program is focussed on carrying out tests that signifies level of achievements by young students. Early Childhood Australia (ECA) (2012) revealed that there are a range of practices that are associated with efficient delivery, planning, assessment and differentiation. There is an increased importance of recognising existing knowledge along with understanding diversity of student understanding. For assessment of effective student learning on mathematics collecting samples of their work can facilitate in attaining evidence of their achievement. Certain diversity is also observed to be present in teaching terms that can result in developing stronger and livelier curriculum. Interests of children’s mathematics are highly diverse and the mathematics early childhood curriculum connects and values practices of the children’s cultures and communities. This motivates them to attain learning achievement on mathematics.
Early Childhood Australia (ECA) (2012) stated that existing or prior knowledge and diversity of student’s understanding is deemed to be related as the existing skills and understandings can facilitate them in getting involved in learning programs that can demonstrate their competence. To enhance competence of children with deserve cultural background and interests effective planning and delivery of an integrated professional learning strategies for supporting implementation of mathematical learning programs is practiced. “Professional Learning Workshops” is delivered in offering mathematical learning programmes that is conducted by knowledgeable and experienced childhood educators.
Foundations of Learning Mathematics in Early Childhood
Stacey (2008) indicated the importance of attaining understanding on “Children’s prior” or “Existing knowledge” along with several strategies employed by educators in realising children’s understanding regarding mathematical ideas. These researchers validated that there is an exceptional role of prior knowledge in ensuring student’s academic success. Goos, Vale and Stillman (2017) identified that “red flag approaches” for teaching includes determining student learning and motivation. This encompasses connecting fresh study materials for student’s prior knowledge. It is clarified that in understanding mathematical ideas the students need two major classroom approaches for working with the prior knowledge. Goos, Vale and Stillman (2017) evidenced one among them is activating or tapping pre-existing knowledge and another one is developing a new background knowledge. These researchers confirmed that existing knowledge of children in math can be demonstrated though asking students certain relevant questions regarding key concepts. Moreover, clarifying their existing knowledge on the subject can increase sense of achievement among them.
Early Childhood Australia (ECA) (2012) explained that mathematics instruction provided to the students must be built on their existing knowledge and can be helpful in teaching them computational algorithms. This is for the reason that the students generally possess important information which can support them to master new content. It is also vital that the teachers teach and ask all the students to employ the mathematics language along with actual vocabulary experienced within the text and classroom. Early Childhood Australia (ECA) (2012) clarified that there are many alternatives for the direct instruction offered to the students for learning mathematics. These strategies encompass individual recording and reflection, interactive discussions, peer question along with answering sessions. This also facilitates the students in connecting concepts with their prior knowledge. Stacey (2008) stated that attaining prior knowledge encompasses writing, reading, discussing, thinking in details and organizing visual cues. Specific task, problem or activities can be practiced by the teachers through acting as a facilitator and bringing to children certain opportunities to discover more and attain deeper understanding of attaining further knowledge.
According to views presented by Hollis (2015) it is evidenced that children have different ideas regarding common shapes within mathematics. Moreover, young children are observed to learn in details regarding shapes because of which geometry construction must be initiated at an early stage. Focussing on the same, the teachers supplement curricula that are generally an aspect of a problem rather than solution. Hollis (2015) also added that drawing shapes with help of turtle geometry can support children in learning mathematical measurements and commands precisely. Moreover, employing a “right and tester” to recognise angles within classroom which is equal, larger or smaller than the right angle is necessary. Modern mathematical technologies must also be implemented by teachers that can support statistical, numerical, symbolic and graphical text functionalities those might be employed separately or in combination by the students. Stacey (2008) explained through help of this that students might get ideas of exploring several behavioural aspects related to a function or relation. This can be done trough graphically, numerically, algebraically and geometrically by employing technology in mathematics learning. This can also enhance teacher’s potential to make mathematics interesting to students through employing realistic data.
Conclusion
The objective of this essay was to analyse the major ideas underpinning effective learning and teaching of mathematics. It was gathered from completion of this essay that mathematics curriculum can serve as the basis of panning, teaching along with evaluation of school mathematics. This can also serve to be useful and usable by the experienced along with less experienced teachers of mathematics. Certain useful implications were also gathered from the essay that states specific task, problem or activities can be practiced by the teachers. This can be done through acting as a facilitator and bringing to children certain opportunities to discover deeper understanding of attaining further knowledge.
References
Early Childhood Australia (ECA)., 2012. Thinking about practice: working with the Early Years learning Framework.
Goos, M., Vale, C. and Stillman, G., 2017. Teaching secondary school mathematics: Research and practice for the 21st century. Allen &? Unwin.
Hollis, L.P., 2015. Implementation guidelines for indicators of preschool numeracy and literacy. Sage Open, 5(2), p.21.
Macmillan, A. 2009. Numeracy in Early Childhood Education: Shared contexts for teaching and learning. Ch: 11. Approaches to planning, pp. 184-203.
MacMillan, A. 2009. Shared contexts for teaching and learning numeracy. Chpt 4: The role of language in learning. South Melbourne, Victoria: Oxford University Press.
MacMillan, A. 2009. Numeracy in Early Childhood: Shared contexts for teaching and learning. Ch 2: Shared contexts for teaching and learning Numeracy. South Melbourne, Victoria: Oxford University Press., pp. 20-33.
Manuti, A., Pastore, S., Scardigno, A.F., Giancaspro, M.L. and Morciano, D., 2015. Department of Education, Employment and Workplace. International journal of training and development, 19(1), pp.1-17.
Relations, 2010. Educators: Belonging, Being & Becoming: The Early Years Learning Framework for Australia. Canberra: Department of Education, Employment and Workplace Relations, pp. 10-17.
Stacey, S. 2008. management Curriculum in early Childhood Education Settings. Ch 1: Emergent curriculum and your teaching journey, pp. 11-30.
Vartuli, S. and Rohs, J. 2008. Selecting content that stimulates thought. Early Childhood Education Journal v. 35, pp. 393-396.
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