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But you are aware that tests on math, particularly for school kids, generally do have a correct sequence of steps, right? The point isn't the answer, but rathe

But you are aware that tests on math, particularly for school kids, generally do have a correct sequence of steps, right? The point isn't the answer, but rather to demonstrate mastery of a particular technique. In this case, the test should present problems where one particular set of steps is arguably the best or most obvious one. If the student uses a different set of steps but gets the correct answer, then perhaps the question needs to be asked in a different way (e.g. "Use Euler's Method to determine...").

rbehrends 12y ago
Not really. Consider the following question, for example (taking from an actual eighth grade math test): "Combine the equation 8x+y/2 = 1/24 with a second equation so that the resulting system of linear equations has (a) exactly one (b) zero solutions. Justify your answer." That's leaving aside the fact that there are multiple ways to solve a system of linear equations with two variables to begin with (since you don't even need to solve such a system to answer the question).
- sp332 12y ago
  But if you're teaching a particular technique, then the test would not be whether you can answer the problem but whether you understand how to use the technique.
  - Retric 12y ago
    Take something real simple "Solve X + Y = 2; X + 2Y = 4 using substitution." At the basic level that has 4 choices, you can substitute X or Y in the top or bottom equation.
  - rbehrends 12y ago
    And that, in a nutshell, is what's wrong with American math education. Too much focus on rote learning rather than actual understanding. What you're describing is an accounting course, not mathematics. Mathematics is about problem solving, not plugging numbers into a black box and blindly following a prescribed sequence of algorithmic steps. You do not want to just test whether students can follow a procedure; you want to test whether they actually know what they're doing when they're using it (even if you specify the procedure, e.g. Gaussian elimination). This even applies to simple problems. See the comment by Aur Saraf responding to the original article: http://powersfulmath.wordpress.com/2014/04/30/who-or-what-broke-my-kids/comment-page-1/#comment-18 http://powersfulmath.wordpress.com/2014/04/30/who-or-what-br...
    - sp332 12y ago
      How is a student going to do any math if you never teach techniques? And how are you going to know if the student actually learned it if you don't test them? I never said they should be the focus, but you need to test them sometimes. Also, algorithmic thinking is one of the more powerful ideas we have right now. You can trust that a Turing machine has certain properties without being a genius yourself, for example.

rbehrends 12y ago

Not really. Consider the following question, for example (taking from an actual eighth grade math test): "Combine the equation 8x+y/2 = 1/24 with a second equation so that the resulting system of linear equations has (a) exactly one (b) zero solutions. Justify your answer." That's leaving aside the fact that there are multiple ways to solve a system of linear equations with two variables to begin with (since you don't even need to solve such a system to answer the question).

sp332 12y ago
But if you're teaching a particular technique, then the test would not be whether you can answer the problem but whether you understand how to use the technique.
- Retric 12y ago
  Take something real simple "Solve X + Y = 2; X + 2Y = 4 using substitution." At the basic level that has 4 choices, you can substitute X or Y in the top or bottom equation.
- rbehrends 12y ago
  And that, in a nutshell, is what's wrong with American math education. Too much focus on rote learning rather than actual understanding. What you're describing is an accounting course, not mathematics. Mathematics is about problem solving, not plugging numbers into a black box and blindly following a prescribed sequence of algorithmic steps. You do not want to just test whether students can follow a procedure; you want to test whether they actually know what they're doing when they're using it (even if you specify the procedure, e.g. Gaussian elimination). This even applies to simple problems. See the comment by Aur Saraf responding to the original article: http://powersfulmath.wordpress.com/2014/04/30/who-or-what-broke-my-kids/comment-page-1/#comment-18 http://powersfulmath.wordpress.com/2014/04/30/who-or-what-br...
  - sp332 12y ago
    How is a student going to do any math if you never teach techniques? And how are you going to know if the student actually learned it if you don't test them? I never said they should be the focus, but you need to test them sometimes. Also, algorithmic thinking is one of the more powerful ideas we have right now. You can trust that a Turing machine has certain properties without being a genius yourself, for example.