Tangrams are a type of ancient Chinese geometric puzzle which contains seven pieces, made up of two large triangles, one medium triangle, two small triangles, one square and one rhomboid (or parallelogram) (Bohning & Althouse, 1997). These pieces can be assembled in different ways so as to make shapes such as...
A square...
A rectangle...
A triangle...
A trapezium...
A parallelogram...
And lots of other shapes e.g. birds, boats, etc.
What do you learn by working with tangrams?
According to Bohning and Althouse (1997), explorations with tangrams assist children’s skills development with “geometry vocabulary, shape identification, classification, discovering relationships between and among the pieces...recognising and appreciating geometry in their natural world.” (p.240).
In week 9’s workshop, through our explorations with tangrams I came to a deeper appreciation of how these skills may be developed. The use of geometry vocabulary was obvious as those of us present in our class tried desperately to assemble the shapes, in particular, the square shape. For example, in the spirit of collaboration, those of us who successfully assembled the square coached those of us who were less successful in our attempts, often by using location and direction terminology such as flip, slide and rotate. Furthermore, the names or the attributes of the shapes were also used to explain where they should go, for example, “Put the little two little triangles next to the square, but rotate the one on the right so that its longest side is on the edge”.
In terms discovering the relationships among the pieces, we discussed how each of the shapes was made up of certain numbers of the smaller triangle. For example, the square is made up of two of the smaller triangle, and the big triangle is made up of four smaller triangles. Therefore, in terms of area, the big triangle is actually equivalent to two squares. This discussion also led to the conclusion that using the tangram as a model can also be useful for discussing fractions, for example, if the total area of all of the shapes added together is understood to be the whole then the large triangle is one-quarter of the whole, which makes the medium triangle (which is one-half of the large triangle) one-eighth of the whole. This in turn makes the smaller triangle (which is one-half of the medium triangle) one-sixteenth of the whole, which also makes the square and the parallelogram (which both equal two small triangles) two-sixteenths or one-eighth of the whole.
Learning sequence of working with tangrams:
1. Placing shapes directly over the top of a diagram (of the same size) of the target shape with lines shown
2. Assembling the shapes by looking at a smaller-scaled example of the target shape with the lines drawn in
3. Assembling shapes by looking at an example of the target shape with some of the lines drawn in, e.g. Which shape can fit in here? How? Show me...
4. Assembling shapes without looking at an example at all (which effectively is the same as looking at an example without the lines drawn in) but with the correct-side-up identified
5. Assembling the shapes without looking at an example witht without the correct-side-up identified.
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