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Are math students supposed to be able to quickly and correctly apply algorithms to "evaluate" equations? Should they be able to pass tests? Should they be able to explain what they did to solve a problem and why they did it? Should they be able to use math to solve "word problems?" Should they be able to create their own mathematical solutions? Should they be able to solve problems even if we are not studying them?

Epistemology is deeply important to educators in the modern world, especially if they are going to be sufficiently flexible to evaluate recipes prompted by a range of folks, to adopt and adapt those that are useful, to discard them when they are no longer useful.

The reality for educators is that no recipe will work for all students in all areas (or even for the same students on different days).

"Knowledge is a set of facts that can be memorized and repeating those facts demonstrates knowledge of them." 🤦

As we becomes more sophisticated epistemologically, we recognize that knowledge changes and that much knowledge is not objective.

In general, educators are slow to adopt changes. In general, we believe that our existing instruction is excellent, and so we are hesitant to change.

Answers are generally uninteresting. Questions, on the other hand, are very interesting.

Human learning is complex and multifaceted, and different people experience the same events quite differently. Many educators seem oblivious to this fact.

Any school built following a “one-size-fits-all” solution is doomed to fail.

Adults are trying to improve schools by looking towards their past; “what worked for me will work for them,” is their misguided reasoning.

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