Tuesday, September 21, 2010

Giant Geoboards

We made these giant geo boards for family math time fun. Wink. Just putting the thing together was educational. The boys eyes were glued to the Home Hardware guy as he cut the peg board into squares for us. Then we found the bolts to put through the holes and the kids put did that part themselves and twisted on all the nuts too. Then the rubber band design action began. 

So far we've worked on learning all the shapes- cool ones like trapezoids, rhombus, parallelograms...
Then we did patterns, symmetry, and perimeter so far. The geoboard possibilities are endless though let me tell you. Next on the agenda is coordinates- possibly some geoboard battleship. The coolest thing, is that we have been working on this Asian party thing (more on that later) and Origami has been happening daily and I have become quite enchanted with it. It makes me feel powerful to make crazy objects out of paper :0) Jane has been into it too, but Charlie only is only half way interested since some of the paper folding moves are pretty tricky like for example the reverse fold is too hard for him so that limits his Origami possibilities. Anyways, where in the world am I going with this nerdy post? Right, back to geoboards, well, I found out that the geoboard was designed as a manipulative tool for teaching primary geometry in schools and guess what else is a manipulative tool??!! ORIGAMI. Apparently I have a seamlessly connected curriculum happening here all at once and it totally happened by accident. Sweet.

Here is some info on Geoboards that I found:

Invented by English mathematician and pedagogist, Caleb Gattegno (1911-1988). Traditionally made out of plywood and nails, geoboards today are usually made out of plastic and come in a variety of different sizes and colours. Rubber bands are placed around the nails or pegs to form different shapes. As a learning tool, it provides a means to act upon the world and can be used as a cognitive scaffold that facilitates the extension of knowledge.

How can geoboards be used in teaching? Here is way more info than anyone will care to read:

The geoboard is versatile and can be used at all levels for teaching and learning about different areas of mathematics. It has been found to be a particularly useful aid for investigational and problem solving approaches (Carroll, 1992). There is no set sequence to use with geoboards when using them to teach a mathematical concept and so, is an easy tool to incorporate into mathematic units and learning sequences. Like every tool, however, time needs to be allowed for free play, so that students have the opportunity to explore and experiment with new equipment. Another advantage of the geoboard is its design, as it allows for even young children, and those who may experience difficulty in drawing shapes, to construct and investigate the properties of plane shapes (Carroll, 1992). 

Carroll (1992) suggests that geoboards can be used in different areas of mathematics. It is suggested that geoboards be used in conjunction with isometric dot paper, so that exploration can be furthered and work can be recorded easily. The areas of mathematics in which geoboards can be used in include:

* plane shapes
* translation
* rotation
* reflection
* similarity
* co-ordination
* counting
* right angles
* pattern
* classification
* scaling
* position
* congruence
* area
* perimeter.

From this it can be seen that geoboards, can particularly support learning in the measurement, space and geometry strands of the primary mathematics curriculum. The following example illustrates the versatility of geoboards and how they can be used to develop students' understanding in the strands of space and geometry. 

The K-6 mathematics syllabus document (Board of Studies New South Wales, 2002) classifies space and geometry as the study of spatial forms and is organised into three substrands: three-dimensional space, two-dimensional space and position. It considers recognising, visualising and drawing shapes, and describing the features and properties of three and two-dimensional objects, as important and critical skills for students to acquire. The development of geometric understanding as set out by the syllabus document, incorporates the first three levels of van Hiele's theory (Clements & Battista, 1992). Table 1 describes these three levels and provides examples of activities which can be used to assist students' progress through the levels. 

From Table 1, it can be seen that geoboards can be used to support all three levels of geometric thought and of course there are many other activities that could be done. Furthermore, through using geoboards, students can not only work towards space and geometry outcomes, but also be engaged in working mathematically (Board of Studies New South Wales, 2002). 

Overall geoboards have the potential to develop students' understandings in the mathematical strands of measurement, space and geometry. This learning can be further enhanced when students, under the guidance of their teacher, have the opportunity to engage in the hands-on experience of using geoboards, followed up by the more abstract experiences accessible through technology. Geoboards should not be forgotten in the mathematics classroom, but like other tools, should be used to engage students and facilitate their learning. 

Examples of manipulatives:
i) paper folding, ii) geoboards, iii) straightedge and compass, iv) computers, and
v) mira or reflecta and tracing paper. 

By providing a meaningful representation for most geometry ideas, this emphasis helps keep our focus on grounding all ideas in concrete examples. These models provide motivating examples that are used to “develop” basic geometric relationships in a believable way. Models can also stimulate conjecturing as well as provide a means for checking tentative ideas — higher order thinking skills basic to learning geometry. The instructor, however, plays a critical role as a mediator between the physical models and the underlying geometric ideas.

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