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Applying Occam's Razor to "(In)Equity in Mathematics Education"
|Posted By: Dick Schutz on March 12, 2010|
|Ellis gets several matters right. Contemporary standardized achievement tests are constructed and interpreted using statistical and psychological theory that created the eugenicist movement--with the same social and political consequences. But Ellis uses key terms, such as standard/standardized, norm,/normed/ normal, science/scientific, with mixed meaning to support a particular philosophy/ideology of math instruction.|
Application of Occam's razor appears in order.
A normal statistical distribution results when the determinants of a phenomenon are multiple and complex (such as flipping a coin). The causes of the phenomenon termed "intelligence" meet this statistical condition. The fact that the achievement test results also fit the condition tells us that instruction is far from a science. With effective instruction, whatever the aspiration, the results should pile up at the bottom of the curve at the beginning of instruction and pile up at the top of the curve at the end of instruction. The way standardized achievement tests are constructed does not permit that to happen.
Standardized achievement test results provide no information regarding the instruction that has been delivered. They provide no information regarding an individuals instruction status regarding the path or options for future instruction. Black boxes of instruction are bouncing around in a black hole of el-hi education.
El-hi schooling is a highly observable matter. Each year a new cohort of children enters Kindergarten. With few exceptions all children have the minimum pre-requisites for being taught how handle written language and the number system. You don't need standardized tests to confirm the delivery of instrurctional accomplishment. You do need transparency of what has been accomplished . This in turn requires advance attention to how anyone will know that a specified aspiration has been achieved.
With today's information and communication technology the means for implementing the perspective of the preceding paragraph are within the state of the art. But the political obstacles, within the el-hi endeavor and generally, are daunting.