What’s taught vs. what’s learned

Posted on June 11, 2014

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A student is reviewing for our assessment test, and going over “simplifying expressions.” 

She is learning that u^2 + 1 + u – 1 is u^2 + u…

… she will probably understand which combinations of letters and powers can be added and which can’t. 

However, with the kind of examples and instruction in “test prep” mode  provided… it will be based on What The Symbols Look Like, not what they mean. There is no need to comprehend what raising something to the third power *means* to know that “if it’s a different power, they’re not like terms.”  

When I rule the world (or have my little team of instruction designers), conceptual reinforcement will be embedded in these “you already know what powers are so we won’t worry about that” parts of the curriculum.   

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