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3.1 ConceptsConcrete models can help students represent numbers and develop number sense, . . . , but using materials, especially in a rote manner, does not ensure understanding. NCTM Standards 2000, page 80Describe two different concrete models for representing numbers and developing number sense. Explain how these models can be used effectively. Give an example for each model of how they might be used ineffectively for learning in a rote manner. 3.1 Concepts It is customary for people in some countries to count to five by using the right index finger to point to the fingers on the left hand, as opposed to using the left index finger to point to the fingers on the right hand. This counting by fives resulted in the early development of base five numeration systems. Describe a numeration system that might have developed if we had three fingers on one hand and four fingers on the other. 3.1 Teaching One mathematics educator expressed the opinion that we should not teach about ancient numeration systems, that is "leave ancient numeration systems to the ancients." Make a case for or against teaching ancient numeration systems in schools. |