Statistically speaking, 90% of the time someone says "statistically speaking" what they're saying is made up

Wow! What a crazy week.  At one point or another I've covered every aspect of probability at some point in K-12, but I've never done them all at once in one week.  This week I was introduced to a few concepts I hadn't seen before, the first was the idea of the "fair game".  This concept basically looks at games of chance and compares the cost of playing the game to the payoff of each game.  If the payoff is equal to the buy-in the game is considered fair.  I wish I would have known this about 15 years ago when I turned 18 and went to a casino for the first time.  Those games would not be considered "fair" by a long shot.

A concept I struggled with this week was the idea of permutation versus combination.  It's actually a pretty simple concept, permutation is a data set in which the order of the elements is specific, whereas combination is the same idea except the order doesn't matter.  For some reason I really struggled figuring out when to use the correct algorithm to solve each type of problem.  The question I missed on last weeks test was about home builders with 6 lots to build but 12 model's to choose from that they could build.  I solved it as a permutation, but of course it was a simple combination.  My answer was only off by about 650,000 but I still got it wrong, talk about nitpicking.  Check out this great video on permutations!

I really like statistics, one of the first online classes I ever took was a statistics class back in 2002.  As a computer programmer I use different algorithms and formulas for creating passwords for security issues.  As an Analyst I compile user data and use that data to understand usage patterns and look for areas where there can be improvements.  I still struggle with what I consider are abstract ideas of probability, the calculation of dependent events when there gets to be three or more events still doesn't make a whole lot of sense to me, but I'm getting there.

There's laws in them thar standards!

I thought the frequently asked question this week that covered the standards for Minnesota was a great way to get some background info on why we have standards and benchmarks and how they affect the classroom. There was actually a time last year when I was speaking with a middle school math teacher who said all eighth graders must take algebra, whether they're ready for it or not.  I thought it was counter-productive, and it didn't seem to make much sense to introduce students to a subject they weren't prepared for.  The state legislature actually passed a law that says all students must have an algebra I credit by the end of eighth grade.  I understand the necessity to keep students moving forward and challenging them, but it seems those decisions should be made by educators and researchers, not lawmakers.  I would like to see a progressive increase in skill required, rather then such a simple answer to a complex question.

I think the requirements for math in high school are a good thing, but dictating what math courses students take (like algebra in eighth grade) treats students like commodities and tries to fit what may be square peg in a round hole.  I, unfortunately, opted not to take math my senior year, because it wasn't required, and I paid for it later when I had to take remedial math classes in college.  I had completely forgotten any advanced math concepts I had learned in high school.  I would like to see the legislature require math for all four years of high school rather then just three.  Even students who enjoy math, like myself, the temptation to skate through their senior year of high school might be too great to pass up.

Another reason the requirement for grade eight algebra seems odd is that the standards and benchmarks for grades 9-11 are combined.  If the legislatures goal by passing the law to require eighth grade algebra I was to push students and teachers to meet a certain goal at a certain time, it would make sense for them to legislate what appears in the other grades as well, especially subsequent grades.  It makes me wonder if the state just wants to make sure students complete algebra I, and if they need to they have their entire high school career to do so, or if the decision was simply based on the idea that most students take algebra in eighth grade anyways.  Regardless, I think there are inconsistencies that need to be remedied in the standards that have been handed to students and teachers.