Comments on: What “critical thinking” might mean in math http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/ education | teaching | math | technology Fri, 20 Nov 2009 23:57:58 +0000 http://wordpress.com/ hourly 1 By: Casting Out Nines»Blog Archive » Critical thinking, visualization, and physical intuition http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4051 Casting Out Nines»Blog Archive » Critical thinking, visualization, and physical intuition Wed, 11 Oct 2006 20:24:26 +0000 http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4051 [...] Robert: I coined the phrase "intellectual courage" at the end of the post to describe what JimMC... [...] [...] Robert: I coined the phrase “intellectual courage” at the end of the post to describe what JimMC… [...]

]]> By: Robert http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4049 Robert Wed, 11 Oct 2006 17:07:44 +0000 http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4049 I coined the phrase "intellectual courage" at the end of the post to describe what JimMC and Jami are saying. It's the quality that makes a person take action on something intellectual or academic they did which they know isn't right, getting help when it's obviously needed despite one's level of shyness or scaredness or whathaveyou -- and if not actually *caring* about the work being done, at least realizing that getting the work done right is more important than one's feelings about it. I coined the phrase “intellectual courage” at the end of the post to describe what JimMC and Jami are saying. It’s the quality that makes a person take action on something intellectual or academic they did which they know isn’t right, getting help when it’s obviously needed despite one’s level of shyness or scaredness or whathaveyou — and if not actually *caring* about the work being done, at least realizing that getting the work done right is more important than one’s feelings about it.

]]> By: Jami http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4047 Jami Wed, 11 Oct 2006 16:48:48 +0000 http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4047 I have to agree with JimMc. It probably isnt the critical thinking that most students are missing. I can remember countless times where I came up with an answer that I knew didnt make any sense, but I gave up because I couldnt figure out how to fix it. Now in response to that I know that you'll say this was a homework set so the students had plenty of time and resources to fix this issue. But I think that might be more of the problem than the critical thinking issue. My guess is 1/2 of them just dont really care, or they are too shy (or whatever quality it is) to get help. I have to agree with JimMc. It probably isnt the critical thinking that most students are missing. I can remember countless times where I came up with an answer that I knew didnt make any sense, but I gave up because I couldnt figure out how to fix it.
Now in response to that I know that you’ll say this was a homework set so the students had plenty of time and resources to fix this issue. But I think that might be more of the problem than the critical thinking issue. My guess is 1/2 of them just dont really care, or they are too shy (or whatever quality it is) to get help.

]]> By: JimMc http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4046 JimMc Wed, 11 Oct 2006 14:28:24 +0000 http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4046 In addition to critical thinking, which you're absolutely right about, some minimum amount of caring or interest on the student's part might be missing too. You can be a critical thinker but rarely apply it to things you don't care about (I'm plenty guilty of that). If a student just doesn't give a hoot about math, then they're just sunk. In addition to critical thinking, which you’re absolutely right about, some minimum amount of caring or interest on the student’s part might be missing too. You can be a critical thinker but rarely apply it to things you don’t care about (I’m plenty guilty of that). If a student just doesn’t give a hoot about math, then they’re just sunk.

]]> By: Eric http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4045 Eric Tue, 10 Oct 2006 21:42:37 +0000 http://castingoutnines.wordpress.com/2006/10/10/what-critical-thinking-might-mean-in-math/#comment-4045 I think that your definition of "critical thinking" is pretty accurate. The trick is how to teach students to have good intuitions, because many of them have a whole mess of bad ones. Oh, and by the way, 10 years later and I still remember enough calculus to apply L'Hospital's rule. I must have been awake that morning. :) I think that your definition of “critical thinking” is pretty accurate. The trick is how to teach students to have good intuitions, because many of them have a whole mess of bad ones.

Oh, and by the way, 10 years later and I still remember enough calculus to apply L’Hospital’s rule. I must have been awake that morning. :)

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