how do you apply the 6 stages of dienes theory to a mathematics counting game for grade r learner's
Answers
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Stage 5.
It will now be possible to study the representation or “map” and glean some properties that all the games naturally must have. For example it could be checked whether a certain series of operations yields the same result as another series of operations. Such a “discovery” could then be checked by playing it out in one or more of the games whose representation yielded the “discovery”. An elementary language can then be developed to described such properties of the map. Such a language can approximate to the conventional symbolic language conventionally used by mathematicians or freedom can be exercised in inventing quite new and different symbol systems. Be it one way or another, a symbol system can now be developed which can be used to describe the properties of the system being learned, as the information is gathered by studying the map. This stage can be called the symbolization stage.
Stage 6.
The descriptions of the symbolization stage can get very lengthy and often quite redundant. There comes a time when it becomes desirable to establish some order in the maze of descriptions. This is the time to suggest that possibly just a few initial descriptions would suffice, as long as we appended ways of deducing other properties of the map, determining certain definite rules that would be allowed to be used in such “deductions”. In such a case we are making the first steps towards realizing that the first few descriptions can be our AXIOMS, and the other properties that we have deduced can be our THEOREMS, the ways of getting from the initial axioms to the theorems being the PROOFS. This stage could be called the formalization stage.