Sunday, February 5, 2012


Today, one of my students posted to Facebook, "We're mixing food & statistics together, I'm excited."  I'm going to ignore the fact that she posted during class, without permission, and just be happy.  Pi Crust wrote about how happy she was after her class asked to take pictures of some really awesome student work and had several students change it to be their profile photo.   I totally understand her sentiment.  The student that posted is one that has had an up and down relationship with math and school and grades for the two years I've known her.  Being excited about school and showing it and posting it to Facebook is awesome.  Even though her excitement may have been more about food than the statistics, at least stats gets mentioned. 

As for the lesson that prompted the excitement, I wasn't terribly into it.  I had been feeling sick all week and  wasn't mentally all there.  So I found a lesson from a book of hands on math lessons for middle schoolers.   I didn't adapt it at all, I just made copies of the student worksheet.  I felt like a terrible teacher doing that.  I find lessons online all the time for use in my class, but always need to modify and adjust for my students.  Not adapting it felt like I wasn't thinking about MY kids, like I was just one of the many terrible teachers along the way who churn out copy after copy of worksheet after worksheet.  Maybe it was the cold talking. 

Anyways, even though the lesson was for younger grades, most of my students had forgotten the skills.  They needed to estimate how many M&Ms of each color were in a package, then calculate percent of total, make a bar graph, and a pie chart.  After opening the bag, they repeated the process, but this time for the actual number of each color.    

The number of students who wanted me to open the bag before the estimations was shocking.  Some were pretty upset that I wouldn't do it.  Others wanted me to tell them the total and then they would do the guessing.  It wasn't that they wanted to be closest to correct, they just couldn't work under uncertainty.  On the pie chart, they forgot the process, but once I showed them a sample section, they were completely capable.  I remember trying to teach the lesson to my 7th graders a few years ago and wanting to bang my head on the wall.  Figuring out how many degrees each section should be, then measuring it out was a several day set of lessons for 7th graders.  But for high schoolers, it was over in a matter of minutes.  This was one of the first times I really saw them "getting" skills that they didn't remember from earlier grades.  It was still a very procedural understanding, but I'll take what I can get. 

Next the lesson heads into whether a small vs large samples for estimating a population and accuracy.  Here's to hoping M&Ms can capture their attention for more than one day.  

Sunday, January 8, 2012

Pattern Sniffing

During my afternoon time as an EA, I spent most of the class working with an 8th grader yesterday.  The class was practicing solving single and multi step equations.  A particular student finished his sheet of 20 problems in about 10 minutes, whereas his classmates needed closer to 30 minutes.  He had a few errors and pretty consistently missed the negative sign in his final answer.

None of that is particularly interesting, but in watching him do the problems I realized he had no idea of why or what he was doing.  I know this student from last year and he has an amazing ability to see, memorize, and repeat patterns (pattern-sniffing as my PCMI peeps would call it).  He just looked at the numbers and knew "well you add this one away from the x to the one thats alone, then you divide by that other one."  He didn't know anything about "doing the opposite" or "trying to get the x by itself"  he just knew what sequence to enter into his calculator.  He didn't and in fact couldn't write any of his work down.  When he had made a mistake he couldn't see it or correct it and pretty much had a melt-down when I tried to explain and show him the reasons behind why he was doing each step.

Is this a problem?  Is it good as long as he gets the right answer and it doesn't matter if he has a concept of what is fundamentally happening when he is punching the keys?  Will it just self-correct when he gets more complex problems?  I think not.  From what I saw of him last year and from other struggling students, when the complexity rises, without an understanding of the base level, his ability to pattern-sniff is not longer as helpful and he is suddenly in the deep end without any floaties.  There isn't a base to build off of or go back to.  Similarly, when different types of problems are all jumbled together, then the pattern isn't as obvious and if the student doesn't happen to remember "oh this type of problem is done this exact way" then he is out of luck. Maybe that's part of why this brilliant boy, an others like him, does miserably on standardized tests but seems to understand everything at the time.  Had I been the classroom teacher and not had the chance to spend most of the hour sitting and watching and talking, I wouldn't have known how he was solving the problems or that he really knew nothing of the basic concepts.  

Bonus Story:  The reason I know this kid is an excellent pattern sniffer is because he is the fastest to ever beat me at the "Block Game."  I put out 15 pieces.  My opponent can choose to go first or second.  On each turn, we can choose to take 1, 2, or 3 pieces.  The person to take the last piece loses.  Over time students realize that I have a "strategy" that lets me win almost every time.  If a student wins, it is typically by dumb luck.  Using backward deduction will reveal that there is a set of moves that allows the first player to win 100% of the time.  The second player is able to win as long as the first player doesn't know the string of moves.  

Most kids take a few days and many many rounds to figure out how to win. This student figured it out in about 30 minutes.  When I asked him to explain how he knew what to do he explained that he just watched me.  All the other students watch the pieces, or their own plays.  He knew enough to watch the person who controlled the game.  From there, he memorized and analyzed every move I made to figure out what to do in each situation.  He didn't know the nice "summary" of the moves or realize that there was a particular string that I was playing each time.  He just knew that if my opponent pulled 3, then I pulled 3 and so on.  I was very impressed by him and his ingenuity.  He has become very adapted to finding and exploiting patterns, but isn't yet capable of taking the next step and coming up with a clear set of rules.

Back from Break

Last week was the first week back from break and we only saw each class three times because of having Monday off.  Thank goodness it was a short week.  It was fairly easy week, but draining.  Even though I kept a similar sleep schedule over break, by 7PM I was exhausted.

In my statistics class with the juniors and seniors I did two longer application problems. One (found here) on misleading graphs and statements.  I was a bit nervous with the political tone of the assignment, but no one really noticed it.  Only one student picked up on the fact that the ACS might be trying to mislead with the graph in order to help out Giuliani.  On one hand, it was good because there were no political battles in class, on the other hand, it meant that the students still aren't totally thinking.

My biggest issue with my statistics class is that the students are so used to being led through problems and worksheets that anything requiring actual thought is really difficult.  One girl even commented, "You really come up with good questions.  I have to think.  I don't like it.  Why do you do that to us?"  My whole goal is for them to think, especially when it comes to presentation of graphs and data and arguments.  I've been pretty disappointed in this unit and haven't figured out how to remedy it.    They still can't tell the different between a causal and a correlational argument unless the title says "X causes Y."  They only see the articles at face value.  I gave them a series of 5 articles on soda and teen violence where some articles said soda caused it, others explained a correlation, and the last put down the articles that claimed causation.  On the whole, the class didn't see the differences between the articles and thought it was all totally dumb because adults were trying to say that soda made them violent.  Even the attempt at a discussion after went no where.  The one or two kids that "got it" didn't really say anything and the others just stayed with their own initial perception rather than evaluating the article.

I think the biggest issue with my lessons on them identifying inappropriate causation in articles is that many of the students do not read well.  They only had to read two of the 5 articles and each article was a page or two, but it was still tough for them.  Others probably never did the reading.  I want to do an interdisciplinary math class, but how can I get around, differentiate, scaffold, or support the low levels of reading?    The students want to do well. They want to learn.  They like the class and they try.  But without the ability to read, interpret, and analyze newspaper articles they are at a big deficit.  I want to say "I can't correct it all" and "It's stats class, I don't have time to teach reading too," but I can't have it both ways.  I can't demand reading skills and ask them to apply knowledge they don't have.  I need to make time for it.