Visual Representations In Primary Maths
2021年1月22日Download here: http://gg.gg/nyu9f
Developing the use of visual representations in the primary school 6 2. The research on visual representations (a) The importance of visual representations Research has highlighted the importance of visual representations both for teachers and pupils in their teaching and learning of mathematics. Students’ learning starts out with visual, tangible, and kinesthetic experiences to establish basic understanding, and then students are able to extend their knowledge through pictorial representations (drawings, diagrams, or sketches) and then finally are able to move to the abstract level of thinking, where students are exclusively using.Visual Representations In Primary Maths PastVisual Representations In Primary Maths WorksheetsVisual Representation Of WordsShe goes on to point out that often students use manipulatives to follow a rote learned procedure without a sense of the ways in which the apparatus reflects mathematical structures. Examining how the apparatus reflects and embodies mathematical structure is crucial to using it effectively and to the process of making the meaning of the manipulative transparent to the user. Once again wecome back to the notion of the learner as a sense maker in the classroom and the need to offer learners opportunities to make sense of both the manipulatives used and their relation to the mathematical ideas and problems which they are being used to solve.Moyer also draws attention to the need for familiarity of the learner with the resource that is being used as a tool so as to reduce the cognitive demand of its use. If a learner is very conscious of various attributes of the resource it is unlikely to facilitate its use as a representation of a specific mathematical structure. I have certainly been aware of this in my own teaching: it takes alot of play with Cuisenaire rods and familiarity with the proportional relationships between the rods of various colours, before learners can use them to aid the solution of complex calculations such as the addition of fractions. At a more elementary use, the desire to build walls with the little coloured sticks can get in the way of considering which pairs of rods are equivalent to one anotherfrom which the number bonds can be derived. In Hungarian classrooms, Kindergarten children are given many opportunities to play freely with the rods before their mathematical structure and relationships are drawn out when they enter formal schooling at the age of rising seven. One resource that I frequently use in work on geometry is loops of string and I find that unless I let learners of anyage have a chance to play freely with the string for a while before setting a mathematical task, they will be distracted by their desire to play and explore various properties of the loop of string – usually using it to play ‘Cat’s Cradle’!So once learners have access to a range of manipulatives with which they are familiar and which have intrinsic to them particular aspects of mathematical structure, how should we support them to use them? Moyer’s study is an important one focusing on actual observations of how teachers use manipulatives and asking them why they use them as they do. All the ten teachers involved were engaged in aprogramme of study that supplied them with a toolbox of mathematical manipulatives to use in their classrooms and offered them some professional support in doing so.The teachers involved gave various reasons for using manipulatives. One of these was that using them was more enjoyable than doing mathematics that was solely abstract and symbolic. This was substantiated by the researcher’s observations that students were active, engaged and interested in lessons when manipulatives were used. The enjoyment experienced by teachers and learners in usingmanipulatives meant that teachers tended to use them as a reward for good behaviour rather than solely when they would be a useful adjunct to learning. Some of the teachers used the manipulatives only at the end of the week, the end of the year or when they had time. They didn’t seem to view their use as intrinsic to the substance of the core of the curriculum but rather an addition that enhancedenjoyment.This contrasts dramatically with the use of manipulatives that I have observed in Hungary. There the use of manipulatives is perceived as being central to the early development of mathematical ideas especially for children under the age of eleven. One lesson that I observed was centred on introducing the number six to the children and in it the following manipulatives were used: dominoes,Cuisenaire rods, analogue clock faces, Hungarian number pictures and dominoes. Later in the week coins were used as well. In addition children counted sets of objects, sets of six actions and identified sets of six things from pictures. They showed the finger pattern for six, identified the Roman numerals for six andfinally the symbol 6 itself. This concentrated presentation of a variety of representations and manipulatives revealing ‘six’ enabled the children to generalise about the concept of six across all these different manifestations and, I would suggest, to abstract a deeper notion of the qualities of six. They made walls of Cuisenaire rods the same length as the six rod and collections of dominoeswith six spots on them and so gave themselves a concrete experience of the ways in which six can be partitioned in two sets.
Download here: http://gg.gg/nyu9f
https://diarynote-jp.indered.space
Developing the use of visual representations in the primary school 6 2. The research on visual representations (a) The importance of visual representations Research has highlighted the importance of visual representations both for teachers and pupils in their teaching and learning of mathematics. Students’ learning starts out with visual, tangible, and kinesthetic experiences to establish basic understanding, and then students are able to extend their knowledge through pictorial representations (drawings, diagrams, or sketches) and then finally are able to move to the abstract level of thinking, where students are exclusively using.Visual Representations In Primary Maths PastVisual Representations In Primary Maths WorksheetsVisual Representation Of WordsShe goes on to point out that often students use manipulatives to follow a rote learned procedure without a sense of the ways in which the apparatus reflects mathematical structures. Examining how the apparatus reflects and embodies mathematical structure is crucial to using it effectively and to the process of making the meaning of the manipulative transparent to the user. Once again wecome back to the notion of the learner as a sense maker in the classroom and the need to offer learners opportunities to make sense of both the manipulatives used and their relation to the mathematical ideas and problems which they are being used to solve.Moyer also draws attention to the need for familiarity of the learner with the resource that is being used as a tool so as to reduce the cognitive demand of its use. If a learner is very conscious of various attributes of the resource it is unlikely to facilitate its use as a representation of a specific mathematical structure. I have certainly been aware of this in my own teaching: it takes alot of play with Cuisenaire rods and familiarity with the proportional relationships between the rods of various colours, before learners can use them to aid the solution of complex calculations such as the addition of fractions. At a more elementary use, the desire to build walls with the little coloured sticks can get in the way of considering which pairs of rods are equivalent to one anotherfrom which the number bonds can be derived. In Hungarian classrooms, Kindergarten children are given many opportunities to play freely with the rods before their mathematical structure and relationships are drawn out when they enter formal schooling at the age of rising seven. One resource that I frequently use in work on geometry is loops of string and I find that unless I let learners of anyage have a chance to play freely with the string for a while before setting a mathematical task, they will be distracted by their desire to play and explore various properties of the loop of string – usually using it to play ‘Cat’s Cradle’!So once learners have access to a range of manipulatives with which they are familiar and which have intrinsic to them particular aspects of mathematical structure, how should we support them to use them? Moyer’s study is an important one focusing on actual observations of how teachers use manipulatives and asking them why they use them as they do. All the ten teachers involved were engaged in aprogramme of study that supplied them with a toolbox of mathematical manipulatives to use in their classrooms and offered them some professional support in doing so.The teachers involved gave various reasons for using manipulatives. One of these was that using them was more enjoyable than doing mathematics that was solely abstract and symbolic. This was substantiated by the researcher’s observations that students were active, engaged and interested in lessons when manipulatives were used. The enjoyment experienced by teachers and learners in usingmanipulatives meant that teachers tended to use them as a reward for good behaviour rather than solely when they would be a useful adjunct to learning. Some of the teachers used the manipulatives only at the end of the week, the end of the year or when they had time. They didn’t seem to view their use as intrinsic to the substance of the core of the curriculum but rather an addition that enhancedenjoyment.This contrasts dramatically with the use of manipulatives that I have observed in Hungary. There the use of manipulatives is perceived as being central to the early development of mathematical ideas especially for children under the age of eleven. One lesson that I observed was centred on introducing the number six to the children and in it the following manipulatives were used: dominoes,Cuisenaire rods, analogue clock faces, Hungarian number pictures and dominoes. Later in the week coins were used as well. In addition children counted sets of objects, sets of six actions and identified sets of six things from pictures. They showed the finger pattern for six, identified the Roman numerals for six andfinally the symbol 6 itself. This concentrated presentation of a variety of representations and manipulatives revealing ‘six’ enabled the children to generalise about the concept of six across all these different manifestations and, I would suggest, to abstract a deeper notion of the qualities of six. They made walls of Cuisenaire rods the same length as the six rod and collections of dominoeswith six spots on them and so gave themselves a concrete experience of the ways in which six can be partitioned in two sets.
Download here: http://gg.gg/nyu9f
https://diarynote-jp.indered.space
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