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 another from 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 any age 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 a programme 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 using manipulatives 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 enhanced enjoyment. 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 and finally 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 dominoes with six spots on them and so gave themselves a concrete experience of the ways in which six can be partitioned in two sets.
Linked activities focusing on multiple representations can be found here: Matching Numbers and Matching Fractions. My sense from any observations is that Hungarian teachers offer young children this wide range of experiences of specific mathematical concepts in the hope that they will generalise from them and abstract the central mathematical point that is being made.
One of the pieces of research that resonated most strongly with me was reported on by Lio Moscardini in which he analyses the use of apparatus in teaching subtraction to children with moderate learning difficulties. Although children with special needs are his focus, his analysis and findings are no less relevant to all learners.
He makes a valuable distinction between using manipulatives as tools and as crutches. In the same way, manipulative materials serve as concrete models for students to use to solve problems.
Math Manipulatives make learning math interesting and enjoyable. Give students the choice of working on a page of problems or solving a problem with colorful and interestingly shaped blocks, and there's no contest.
Manipulatives intrigue and motivate while helping students learn. Parents Store Cart. School Success. The Scholastic Store. Key understandings in mathematics learning: Summary papers. Nuffield Foundation.
Student Performance in Mathematics, Reading and Science. Thomson, S. Volume I Student Performance. Have you considered the rationale behind the use of manipulatives to support students' exploration and understanding of mathematical concepts?
Think about your own classroom practice. Are you under-using, or over-using, manipulatives to support learning? Apple Podcasts. RSS feed. Keyword s. Teaching resources: Using manipulatives in mathematics learning. Short articles Mar 16, 0. At home, a pegboard or cork board with a uniformly spaced grid will do. Parents can supply pegs or thumbtacks and rubber bands or string. This is just a start; other teachers and parents will have additional ideas.
Keep in mind that virtual models of these manipulatives are available online and offer another mode for students using the same approach. The answer is easy: household items found in pantries, toy boxes, sewing kits, and junk drawers. Math Manipulatives From Household Items Here are additional ways you can offer parents support as they search for manipulatives that can be found or created in the home: 10 frames: First explain what a 10 frame is a 2x5 rectangular frame of squares and how they support instruction they give students visual benchmarks to help see how numbers fit together and develop number sense; teachers often have magnetic versions.
For either version, advise parents to find small objects that fit in the spaces to count.
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