Stringing Students Along

If I’ve done one thing consistently this year, it has been Number Talks in my Probability and Statistics classes.  I have seen students who, at the beginning of the trimester, told me flat out, “I can’t do math in my head.” Now that Trimester 1 is coming to an end, those same kids are volunteering multiple strategies in these mental math challenges.

During the trimester, we started with the dot image below and have moved through the four operations, onto decimals, and even dabbled in fractions and percents.

How many dots are there?  How did you count them?

What’s important to me with these number talks is the visible improvement I saw in my students’ confidence and flexibility with numbers.

I’ve shared before about my experience with number talks and I plan to continue these throughout the rest of the school year.  But at the NCTM Regional conference in Minneapolis a couple of weeks ago, I had the pleasure of attending Pam Harris’s session on Problem Strings.  I found that problem strings are very useful when wanting to elicit certain strategies or move toward generalization of a strategy.

Here are my notes from a problem string I did recently with the same group of students I have been doing number talks with.

I noticed:

• Many students did not use “17 sticks in a pack” to figure out sticks in 10 packs
• Many more strategies than expected were shared to find the number of sticks in 6 packs of gum.
• Most students were able to generalize about number of sticks in n packs.
• Participation increased with the multiple opportunities to volunteer their strategies.
• Students could see relationships between the numbers and find the solution in multiple ways because of that relationship.
• There are many implications of these problem strings in secondary mathematics. In this example, the slope formula can be easily elicited through further exploration of the table we made.

I’ve read all of Pam’s books, but getting to see her present problem strings in person really illuminated how these can be useful in my classroom. Thanks, Pam, for opening my mind to this and letting me fangirl you.  I’m looking forward to doing more of these, including recording them.  Stay tuned.

Regional Reflection – Releasing my Grip

As humans, our complex brains are able to create such detailed visions of the future.  We build things up (or down) in our minds that reality can’t possibly compete with.  Until we let go of what we believe should happen, we are unable to fully experience the beauty of what actually is.

Proposals for the NCTM Regional Conference here in Minneapolis were due in September of 2014.  This means I have had over a year to continue to wind the anxiety yarn into one giant ball of stress.  But sweet relief occurred when I released my iron grip on my expectations and began to appreciate the phenomenal power of educators coming together.

First off, thank you, from the bottom of my heart, NCTM, for  your support of the MathTwitterBlogosphere at the NCTM conferences. I spent much of my time at the #MTBOS booth in the exhibit hall.  Sharing this wonderful, supportive, organic community with other math educators has been as fulfilling as it has been fun.

East Coast meets Minnesota Nice

You guys have something called the “Trap Team?”

Woman: You didn’t say there would be math. Christopher: Actually, I said there would be nothing BUT math.

When Nicole Bridge gets fired up, the magic happens.

When asking people in the Exhibit Hall “are you on Twitter?” the most common response was “yes, but I don’t tweet.  Think of the student in your class that thinks very deeply, submits very thoughtful work,but doesn’t raise his/her hand in class to volunteer his/her thinking.  I’d hope that most teachers would agree that these students are still valuable members of the classroom community.  It works the same with the online edu-community.  Plus, I’d venture to guess that many people who actively tweet with other math educators started by diving down the rabbit hole of math blogs.

Max Ray-Riek led a panel where we discussed this problem and blog post of mine.  Next week we venture into rational functions in college algebra and I anticipate good times to be had once again.

An hour later, Carl Oliver and I spoke on statistics, social justice, and how to have safe, productive conversations with students around the issue of race and equity. Here is the link to the slides.  The discussion centered around these data sets:

I really enjoyed giving our presentation and a lot of great discussion ensued.  But ultimately, I’m thankful to the MathTwitterBlogosphere for being the catalyst of the great discussion we get to take part in, day in and day out.  I had never met Carl Oliver in person before Wednesday.  But the powerful connections we (all of us) have made with one another, make it possible for an algebra teacher in New York and a stats teacher in Minnesota to get together and share their passions with fellow educators. It allowed a teacher in Massachusetts to spread the fire she started in Boston on to Atlantic City, Minneapolis, and Nashville.  And that fire is continually kindled as we welcome, share, engage, and support over and over and over again.  Thank you, #MTBoS for being the genuine, authentic community that has naturally produced so much awesome for so many teachers.

But Would You Put Money On It?

I have felt one of two extremes every day this school year:

1. My students aren’t learning anything meaningful, it’s impossible to do everything I need to do well, and my brain is on fire.
2. Cheers!  My students had fun while making meaningful mathematical connections.

Today was the latter kind of day so I thought I’d take a few moments to embrace it.

I proposed this scenario to my non-AP probability and statistics class:

I had students discuss their initial reactions.  Many of them mentioned specifics like “1 out of 6” and “36 possibilities” but for the most part, the students were willing to put their hard earned money on the line for a chance at avoiding doubles.  (To be clear, no actual betting went on in my classroom)

Then we rolled until we got doubles.  And rolled again and again and again.  I have one computer and a class set of TI-84s.  So, naturally, we made a class dot plot of our average number of rolls to get doubles.

Now that our data was collected, I asked them again if they would take the bet.  Since \$5 didn’t seem to be enough money for them to really consider the probability, I upped the wager to \$100.  That seemed to be enough money for them to consider the results of the experiment and think twice about putting up \$100 because they feel lucky.

Thanks to Chris True, Mathematics Professor at the University of Nebraska, who proposed this scenario at an AP Statistics training I attended this summer.