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It's so unmathematical to use the equal sign there... and of course there are plenty of people who live their entire lives without any of those three things. M

by j2kun 14y ago

It's so unmathematical to use the equal sign there... and of course there are plenty of people who live their entire lives without any of those three things. Math is also about finding structure and patterns that don't arise in any of those three contexts. It's about learning how to generalize and specify. It can be about isolating the relevant parts of a real-world problem so you can solve it in a way that matters. None of those skills involve or benefit from memorization, but they're damn well more important than memorizing a multiplication table or knowing facts about convex polygons.

001sky 14y ago
There is a lot of value in this comment. For example, the notion of abstraction as seperate from logic. Isolation and prioritization. etc. The importance of basic structures. But: I'd be carful with language. Example (1) None of those skills involve or benefit from memorization But consider <Memory> management is important from the perspective of <cognitive science>. Memorization helps you process and prioritize. Consider the notion of abstracting structure from data, using pattern matching. How does one get better at this? (1) you have empirical data; or (2) you process it efficiently. Memorization facilitates data processing. It also provides for important empirical data-sets and a means of prioritization both of which are crucial for heuristic reasoning. Not to mention formal modes of analysis. Example (2) Math is also about finding structure and patterns that don't arise in any of those three contexts. Where do you think the "pattern" in pattern matching comes from (if not Geometry)? It's the basic things that are most often overlooked. Consider the most elementary use of applied statistics: Linear regression. The abstraction Y=mX+B? That has nothing to do with geometry, rigt? The point is that these most basic things are <critical> to more advanced concepts. Things you seem to take for granted, but are things of great value to the novice and advanced practitioner alike. And if they are not learned (so they can be "forgotten" in memory) they are <impediments> to progress for many students.

by j2kun 14y ago

001sky 14y ago

There is a lot of value in this comment. For example, the notion of abstraction as seperate from logic. Isolation and prioritization. etc. The importance of basic structures. But: I'd be carful with language. Example (1) None of those skills involve or benefit from memorization But consider <Memory> management is important from the perspective of <cognitive science>. Memorization helps you process and prioritize. Consider the notion of abstracting structure from data, using pattern matching. How does one get better at this? (1) you have empirical data; or (2) you process it efficiently. Memorization facilitates data processing. It also provides for important empirical data-sets and a means of prioritization both of which are crucial for heuristic reasoning. Not to mention formal modes of analysis. Example (2) Math is also about finding structure and patterns that don't arise in any of those three contexts. Where do you think the "pattern" in pattern matching comes from (if not Geometry)? It's the basic things that are most often overlooked. Consider the most elementary use of applied statistics: Linear regression. The abstraction Y=mX+B? That has nothing to do with geometry, rigt? The point is that these most basic things are <critical> to more advanced concepts. Things you seem to take for granted, but are things of great value to the novice and advanced practitioner alike. And if they are not learned (so they can be "forgotten" in memory) they are <impediments> to progress for many students.