Appendix A
The history of Cuisenaire Rods
During a lifetime of teaching. Georges Cuisenaire’s inventive genius found many ways of helping his pupils with their studies. His writings on teaching Art, Geography, Biology and Music earned for him many years ago a place of respect among colleagues in his native Belgium. One of his inventions was a set of colored wooden rods and some similarly colored cardboard materials. He used these to teach arithmetic and found he achieved something rare with this subject. The standard of the results he obtained greatly improved and his pupils enjoyed and understood the work they did.
Nevertheless this invention remained almost unknown outside the village of Thuin for about 23 years until a providential meeting of this teacher with another resulted in the use of this invention spreading to classrooms throughout the world. And in the 13 years since that meeting the proven success of Cuisenaire’s rods has made his name a household word.
Dr. Caleb Gattegno met Cuisenaire during 1953 It seemed, he wrote some years later as if all his previous work as an educationalist had been in preparation for that moment. For many years he had been a leading figure in the movement to bring improvements to mathematics teaching at the primary and secondary school levels. His firm belief that special teaching techniques coupled with the development of a hitherto unexploited intellectual ability in young children could produce such improvements, had already been demonstrated with encouraging results where his influence had been felt, In Cuisenaire rods he saw what many had already seen but found at once what few had been sufficiently prepared to understand Physically the rods behaved in the way numbers behave, providing the learners with an algebraic model for the study of mathematics. But perhaps more important still, he realized that they provided teachers with a means for making the lesson a personal investigation of mathematics for every pupil.
Developing Mathematical Thinking
Cuisenaire rods are an attractive and versatile tool for developing mathematical thinking. in primary grades, rods are often used to develop the interpretation of addition as putting lengths together, leading eventually to understanding of the number line as a model for arithmetic. in upper grades, they are useful as a model for fractions. at all levels they are helpful in learning about metric units of length, area and volume, because the square base measures 1 cm on a side. finally, they invite play, which is likely to involve spatial concepts.
the lengths are color-coded, and students who will work extensively with rods should learn this code. note that the code corresponds to the first letter of most colors (white, red, light green, purple, yellow, dark green, orange), but for the 3 colors beginning with 'b', the last letters are used (brown, black, blue). a nice challenge might be to have students figure out why the code is formed in this way. some teachers have students memorize the number equivalents of the colors, however, others feel that this practice reduces the potential of the rods for later work with fractions and algebraic concepts.
The Advantages of using the new Teaching Methods
In the elementary school most of the teachers like to explain by giving chalk board demonstrations.
Also, the students will be called upon to respond to questions, then given the chance to try problems at their seats.
New teachers suggestions for helping and encouraging their students will be limited. Some approaches are inspired furthermore, no matter how careful teachers were in preparing lessons or how earnest they were in presenting them, to many students were unmotivated.
Many students will find math boring. neither they no their teachers experiencing success or satisfaction.
The idea of a new mathematic lessons approach is students to feel that learning mathematics was not only for those who are lucky enough to catch on quickly, but also for all children.
The learning procedure:
Mathematical learning has many aspects, in the past, children's school mathematics experience was often dedicated by the content of standardized tests, and was largely based on memory of computational skills, vocabulary, formulas, etc. however our modern world presents new challenges-complex problems requiring new and creative solutions, which have given rise to class for a broader view of the mathematics curriculum.
the role of manipulative materials:
one tool for exploring problems is manipulation of materials representing mathematical ideas.
Some advantages of this new approach:
children are naturally motivates especially if the materials are visually attractive and pleasant to handle.
secondly, manipulative can become a thinking tool, and embodiment of a child's reasoning. in fact, researchers indicated that the reasoning of many elementary school children, unlike that of adults, is tied to such physical embodiments.
third, moving materials around leaves no trace, as does a pencil, and thus is risk-free, allowing children to develop confidence in experimentation.
finally, certain manipulative have an inherent mathematical structure, and so provide a good context for posing challenges requiring the student to identify the mathematical characteristics of the material.
Previous Results from Using Cuisenaire Rods:
A review of research literature revealed that some researchers felt that the use of colored rods, such as the Cuisenaire materials, in teaching number work gave perceptual support to many relationships. Experiments conducted over 3 years attempted to test some of these relationships. During each year, experimental classes in grade one were receiving Cuisenaire instruction while control groups were not. Each ensuing year, classes in grade two and then grade three were included in the experiments. The results from standardized tests and teachers' questionnaires led to the following conclusions:
(1) children taught with Cuisenaire materials gained facility in manipulating whole numbers and fractions as shown on a Cuisenaire test; (2) Cuisenaire materials were more effective with bright children; (3) children who used Cuisenaire materials for 2 years scored higher than those using them for 1 year, and they in turn scored higher than the control groups; (4) first grade classes benefited more from the materials than second grade class; and (5) teachers and consultants were enthusiastic about the value of the materials