One of the expectations with the new common core math curriculum is that students will be able to critique each other's reasoning. This is not an easy thing to facilitate for many reasons and not just academic ones. First, the human ego runs away from criticism for fear of being hurt, human pride naturally takes a hit during criticism. Second, people do not know how to give criticism.

   But if we are going to teach kids to be receptive to criticism, I think that the best thing a teacher can do is to create a classroom environment where mistakes are seen as a good thing. Over the summer I took a course with Jo Boaler and she really does a great job of showing why mistakes are not just important but a necessary thing to learn Math. Now I have begun to realize also that creating a culture that is accepting of mistakes creates an environment where students feel motivated to experiment and as Ms. Frizzle would say "Get messy" and not just find right answers.

   So what does creating a culture welcoming of mistakes have to do with criticism? I believe that if your classroom environment is welcoming of mistakes then students would be more open to receiving criticism and giving it.

   Finally, I think that one of the best things a teacher can do to foster this environment is for the teacher himself/herself to be open to criticism. The teacher should not shy away from having students point out different ways of solving a problem or should not become defensive when a student tries to correct him/her (Even if the student is wrong), the teacher should always be open to being questioned and criticized. In conclusion, the best way to teach students to be receptive to criticism is to model it.

In my Advanced Algebra/ Trig class we’ve been doing a unit on statistics. Recently, we covered the topic of dispersion and looked at ways to measure it (Variance and Standard deviation). To make it interesting we looked at Tim Tebow’s rushing stats for that magical year (2011) in which he was the quarterback of the Denver Broncos.

One of the things we found was that there was a huge variance and standard deviation compared to other running backs.

This led to an interesting discussion on which sports exhibit low dispersions when it comes to final scores. The sports mentioned were, soccer and tennis because the scores usually stay consistent. One student had mentioned basketball because the scores are so high but then one student was quick to point out that high scores have nothing to do with dispersion, “It’s about data consistency” he remarked.

This again led to a discussion on Tebow, one student said “You know what’s consistent about him? His terrible passing stats, he consistently sucks at passing and his passing stats show it” One student remarked “Yeah. That would mean his passing stats should have low measures of dispersion. But not in a good way”

Then another student said, “But what about his game against the Steelers?” Someone then pointed out that would be an outlier, something that is considered out of the norm.

In retrospect this was great discussion, throughout the discussion students exhibited a strong grasp of what dispersion is and how data affects the measures of dispersion.