4 ms·

From what I've seen of the common core, 90% is fine and just plain old math stripped of any historical baggage. The 10% that is bad is the ideology that math i

From what I've seen of the common core, 90% is fine and just plain old math stripped of any historical baggage. The 10% that is bad is the ideology that math is more ambiguous or less certain than it has been portrayed in the past. This is partly based on politics, and partly on the misuse of mathematical philosophy. I remember being given problems that were plain wrong, e.g. Q: How many miles would a person walking 3miles/h walk in 2 hours? A: 6 miles. I always asserted that the answer is 6, not 6 miles, since the unit is given in the question. Small errors like this in teaching add up to math that looks like a collection of arbitrary commandments that must be memorized. It's understandable people want to move away from this. But this solution is to fix all aspects of teaching so that everything is completely correct, not to pretend that math allows multiple correct answers. We should be teaching that you can express a well formed question in words, to which there should be a unique correct answer. Word problems shouldn't be an added layer of obfuscation, but rather a map from the semantics of math to the semantics of the real world, to test that the student understands this mapping. It's a bit like talking to a backend programmer and saying "if a user did X, then they did Y, what would your function return, and is that correct"? It forces the programmer to consider not the internal logic of their own code, but how that ultimately maps to what the user sees.

lotharbot 11y ago
from what I understand of common core, the correct answer to your example would be "They would walk 6 miles total." There's an emphasis on clear communication and complete sentences. Many of the textbooks would even encourage the student to write out the sentence stem "They would walk _____ miles total" prior to performing any calculations, and then at the end of the problem to check that the number was actually measured in miles and that the sentence made sense and was a reasonable way to answer the initial question. This seems to be what you're encouraging in your final paragraph. This brings up the question: why is the common perception of common core so different from what common core is designed to do?
- nevdka 11y ago
  Common core is a specification that is implemented many, many times. It's not just each textbook or school system - each teacher will implement the spec in a unique way. With so many implementations, some of them are going to be terrible. But the common perception isn't built off an average or large-scale aggregate, it's built on what people see and hear. A single comically bad implementation can be seen by millions of people thanks to Reddit, Facebook, and the like. A single good implementation will be seen by the students, maybe their parents, and maybe a few more teachers. Most examples people see are comically bad, so the common perception is that common core is comically bad.
- jcranmer 11y ago
  The biggest problem with Common Core ends up being its implementation in testing. You end up with tests that ask students to describe how they solved the problem by working out the full mechanics... and woe be the student who learns a different but correct way to do multi-digit addition problems. Combine that with the pedagogy being different from how most parents learned it and you can easily end up with very frustrated parents.
- KMag 11y ago
  +1 for avoiding misuse of "begs the question".
- force_reboot 11y ago
  I don't think I've failed to understand common core, but you have misread my comment. How can you claim that I would support requiring a full sentence answer, when I already said "I always asserted that the answer is 6, not 6 miles, since the unit is given in the question."? I understand the common core requires full sentence answers (among other things) and I think this is wrong. I will repeat my reason. Math is not a different domain to ordinary reasoning, and word problems are not different to ordinary questions. So if "How many miles..." can be answered with "6" as a question in the English language (which it always can) then, "6" is a valid answer in the context of a math question. Requiring more, or accepting less (e.g. by accepting "6" as an answer to "How far..."), is obscuring the nature of math. Note this isn't an argument against showing work, but it is an argument that, in general, any valid reasoning should be accepted as showing work. The particular method should not be prescribed. But that is a less important point.

lotharbot 11y ago

from what I understand of common core, the correct answer to your example would be "They would walk 6 miles total." There's an emphasis on clear communication and complete sentences. Many of the textbooks would even encourage the student to write out the sentence stem "They would walk _____ miles total" prior to performing any calculations, and then at the end of the problem to check that the number was actually measured in miles and that the sentence made sense and was a reasonable way to answer the initial question. This seems to be what you're encouraging in your final paragraph. This brings up the question: why is the common perception of common core so different from what common core is designed to do?

nevdka 11y ago
Common core is a specification that is implemented many, many times. It's not just each textbook or school system - each teacher will implement the spec in a unique way. With so many implementations, some of them are going to be terrible. But the common perception isn't built off an average or large-scale aggregate, it's built on what people see and hear. A single comically bad implementation can be seen by millions of people thanks to Reddit, Facebook, and the like. A single good implementation will be seen by the students, maybe their parents, and maybe a few more teachers. Most examples people see are comically bad, so the common perception is that common core is comically bad.
jcranmer 11y ago
The biggest problem with Common Core ends up being its implementation in testing. You end up with tests that ask students to describe how they solved the problem by working out the full mechanics... and woe be the student who learns a different but correct way to do multi-digit addition problems. Combine that with the pedagogy being different from how most parents learned it and you can easily end up with very frustrated parents.
KMag 11y ago
+1 for avoiding misuse of "begs the question".
force_reboot 11y ago
I don't think I've failed to understand common core, but you have misread my comment. How can you claim that I would support requiring a full sentence answer, when I already said "I always asserted that the answer is 6, not 6 miles, since the unit is given in the question."? I understand the common core requires full sentence answers (among other things) and I think this is wrong. I will repeat my reason. Math is not a different domain to ordinary reasoning, and word problems are not different to ordinary questions. So if "How many miles..." can be answered with "6" as a question in the English language (which it always can) then, "6" is a valid answer in the context of a math question. Requiring more, or accepting less (e.g. by accepting "6" as an answer to "How far..."), is obscuring the nature of math. Note this isn't an argument against showing work, but it is an argument that, in general, any valid reasoning should be accepted as showing work. The particular method should not be prescribed. But that is a less important point.