Asides

Yesterday:  As much as I get frustrated by the attitudes and actions of my 5th hour, much of my resentment stems from the fact that I believe the situation in my class is my fault.  I feel like I’ve conditioned them by accepting disrespectful behavior in order to keep kids in the classroom.  As a result, the entire learning environment has suffered.

Today: So that was the beginning of yesterday’s post. I was concerned going into today’s class. Last Friday of the year and the fact that the school has been a circus compounds the issue. I was expecting chaos, but what I got was mathematical success. The difference was I demanded their attention in a more respectful way. I was firm, but polite, and it payed it’s dividends in student engagement.
We began with a simple math talk that I modeled from Fawn Nguyen’s March 21st math talk:

Today is the 30th day of the month.  Write as many equations you can that equal 30.

I gave them about 5 silent minutes. Then I let them use their calculators to come up with more gems.  At the end, I had them share their favorite or most complicated equation on the whiteboard.

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Here’s where the real magic happened.

Me:  Look up here and see if there are any equations you disagree with

Lots of discussions ensued about order of operations, square roots, rounding, parentheses, etc.  Overall, the activity lasted 30 minutes, which was about 29 more minutes of math than we did yesterday.

But the fun doesn’t stop there.  To boot, I introduced the Mathalicious Decoder Ring Lesson.  We watched the Christmas Story clip and talked about what a decoder ring does.  What I liked is that most of them were trying to figure out how the decoding worked, rather than just “get the worksheet done.”

Justin Aion stated poetically on his blog today the exact way I feel about this class:

We teach students long-term strategies to accomplish short-term goals and often don’t see any progress.  If we are very lucky, we’ll see the kind of growth we want by the end of the school year, but the growing season on students isn’t as regular as it is for other crops.  Each seed needs its own time to grow.We desperately need to get away from the notion that if it hasn’t sprouted by the beginning of June, then it must be a defective seed.

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Thanks Ashli for the spectacular idea of sharing what adorns our classroom walls.  I’ve got the regular math posters, sports schedules, school policies, and motivational cliche’s, of course.  A classroom would not be complete without a stock photo along with transformational words like, “the key to success is self discipline.”

What really brings me the most joy in my classroom and truly makes my classroom mine is my dog wall.

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Ok, it’s actually two walls.  Backstory:  I love dogs, beagles in particular.  Duh.  But the reasoning behind my dog wall runs deeper than that.  Yep, the dogs are adorable and the kids love that they can put a picture of their own dog in my room.  I love it when I have younger siblings of former students, and they ask “hey, you have a picture of my dog!”

The real power behind the dog wall is acknowledging what dogs can teach us about love.   In short, no one on earth is capable of loving you as much as your dog.   Oprah gives us a nice example when remembering her cocker spaniel, Sophie.  If you have a dog, you know what I’m talking about.

I recognize that not all students are lucky enough to own a dog.  I also let them bring in a picture of any dog, but I make sure to mention that I like beagles best.

My plans for the expanding dog wall include using them for some estimation and data exploration.  Someday.

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If you’re decently competent in the area of probability, you might know that your chances of winning fall below things like “death from a vending machine” and “having identical quadruplets.”  This doesn’t stop many people from playing.  I think playing the lottery is more about the chance to dream of what our lives would be like with that much money rather than actually believing we could win.

In the UK, the lottery consists of picking 6 numbers between 1 and 49.  Any player to match all 6 numbers is the grand prize winner.  The chances of this are certainly astronomically low.  A fun question to ask a class of students:  If we bought a lottery ticket for every different combination of 6 numbers to ensure we’d win, how high would that stack of tickets reach?

In the task Do You Feel Lucky, Nrich tackles the idea of evaluating advice given on raising your chances of winning this seemingly impossible lottery. Students are asked to comment on the validity of the advice given and one in particular caught my eye:

When picking lottery numbers, choose numbers that sum between 100 and 200 because the total is rarely outside this range.  

Whoa.  There are so many ways we could evaluate the validity of that claim.  So I sent my students off to the races. Most of them wanted to use a random integer selector and then gather the data from the class’s trials.

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GeoGebra Results:

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Lots for them to talk about here.  Lots of questions for them to ask as well.  Does the range seem too wide?  Do we have enough trials?  What do we make of the dip in the middle?  Should we change the bar graph to have different class sizes?  Would a box plot have been more appropriate?  What about the descriptive statistics?  Would those help us out?

I’m hoping next year to extend this into more of a class activity rather than an impromptu discussion.

 

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It’s probability time in my 9th grade prob and stats class.  Call me crazy for giving 9th graders dice and pennies with a month left of school, but it’s how I roll.  (Ha! I’m cracking up over here!)

I like to start with the Game of Pig, similar to the game used in the IMP curriculum.  I adapted it a little to have kids compare strategies for when playing with their own dice (or separate from their partner) to playing with the same dice as their partner.

It’s interesting to see their strategies develop here.  Some use very solid ideas like “I stopped when my round score reached 20.”  But I also get to see misconceptions like believing that a “one” will be rolled relatively soon after a “two” is rolled.  Having them share their strategies helps me to see where these misconceptions lie and deal with them before we start calculating any concrete probability.

Tomorrow, we’ll start by discussing which of these are legitimate strategies and which of them are not.

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Class: 9th grade prob and stats. Topic:  Linear regression.  Enter: the Laundry Data.

The data sheet seemed to spark a LOT of curiosity.  In retrospect, I wish I would have given them some time to Notice and Wonder about the detergents.  Probably I’d also add some estimation first about these bottles of detergent rather than just handing them the data.  I should have known better.

Still, an interesting discussion ensued about ounces of detergent and loads of laundry.  We plotted the points on Desmos and wanted to choose two of them to create our linear model.  I teach three sections of this class and all three classes picked different points to make their equation.

One class picked (50, 33) and (200, 140), and after determining that they needed to find the slope in order to write the equation of the line, I posed that question to them.  How would we find the slope between these two points.  Crickets.

I want to note that a good minute of silence and eye-contact avoidance went by before one brave student spoke up.

S:  You FOIL them.

Me:  Can you explain what you mean by that?

S:  (coming to the board) You multiply them like this.

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Me:  What do we think of what S just wrote up here?  (at least 8 hands shot up in the air)

Me:  Please put your hands down and let’s discuss this.  What I like about what S just did here is he got us started somewhere.  He was willing to take a guess and risk being wrong.  Before S showed us his idea, no one was willing to volunteer their method.  Now that S has broken the silence, lots of you seem ready to discuss.  Thank you S for starting us somewhere.

After this student broke the ice, we came up with about 4 ways to determine the slope of this line and about 8 ways overall to figure out the equation of the line between these two points.  In the past, I would have said to this student, “No, we don’t FOIL, who has another idea?”  Now I know that allowing this student to explain his method does multiple things.  First, it helps the other students practice patience and courtesy when listening and responding to this student whose solution they know is incorrect.  Second, it is a great opportunity for students to engage in SMP #3: Construct viable arguments and critique the reasoning of others.  Third, it provides an opportunity to praise the value in providing the wrong answer.  So much of math class for these students has been about getting the right answers.  I’m glad this teachable moment came about for students to learn from the wrong one.

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