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This month, some of my Twitter Math Camp friends are hosting a fun, month-long event called “Explore the MathTwitterBlogoSphere”.  You can check out the website for more details, and each week promises a new task designed to encourage math teachers to reach out via blogs and twitter.

For the first weekly challenge, Sam Shah has asked participants to share their favorite rich task.  Even with having taught for 17 years, it was not easy to come up with one task which I felt summarized my philosophies, but here is what I feel is my best question.  It is one I have given many times in algebra 2, and our freshman-year prob/stat course:

How many zeroes are there at the end of 200! (200 factorial)?

That’s it.

Here’s why I like this problem, and why I enjoy giving it:

• It’s has a simple premise.  Sometimes I need to embellish with “think about multiplying out 200!  It would be a really long number.  That number has a lot of zeroes at the end.  How many are there?”  But besides having to know what factorial does, it is plain and simple in premise.
• It requires thinking about the nature of numbers.  Brute force doesn’t work well here.  When I first started giving this problem, I think I used 25 factorial, but then technology started to catch up with me.  One year, a few students used Excel, which gave a wrong answer, as it began to konk out at bigger numbers.  Even if students can now find an “answer” through some tech means, the challenge to explain the “why” remains.
• The answer is secondary.  Communicating your reasoning is king.  This problem present great opportunities to utilize math vocabulary: factors, commutative property, grouping, etc.  I grade this task almost exclusively on communication, and students are often surprised to find that a math task can require such a level of revision and reflection.
• I can move towards a generalization if I need to put my foot on the gas more.  If a few students seem to have the answer and communicate a solution, I can challenge them to develop a formula which works for any number factorialed (is this a word?).

Rich problem solving experiences have always been a part of my classroom culture.  This problem is one of my favorites.

If I could change the MTBoS to make it better, I would make it less of an “underground”, almost secret, society and work to make our ideas more mainstream.  Let’s co-write articles for NCTM.  Let’s share beyond the 140 characters.  Let’s begin to become a force for change beyond our followers.  I look forward to the day where my colleagues don’t look at me with strange glances when I mention a great activity I found on a blog.

In the last few week’s, there has been a lot of back and forth discussion regarding the present and future of the “Math-Twitter-Blog-o-Sphere”.  The MTBoS is the community of math educators who share ideas, stories and friendships through Twitter and blogs.  Its a wonderful and growing community of diverse educators, many of whom have formed real relationships through the love on online math sharing.  But it’s also a place which can be intimidating to new tweeters and bloggers.  To be honest, until about a week ago, I had to keep looking up “MTBoS” to remind myself what it stood for.

Last week, discussion of the MTBoS was featured at the weekly online conference at the Global Math Department. The “If I could change” prompt I completed above was one of the closing activities from the hour of sharing.  Some quotes which struck me from the discussion appear below.  I apologize if I don’t cite names here, as it was hard to follow who was speaking all of the time on the playback.

“I feel very isolated in my own department” – I could not agree more with this.  More than anything else this community not only makes it safe for me to share new, perhaps game-changing, pedagogical ideas, but lets me hear from educators I respect and admire on a daily basis.  There have been times when I felt   uncomfortable with sharing ideas locally, for a number of reasons, and the MTBoS makes it safe to be creative and different.

“I know stuff, and I am obligated to share it” – this sums up nicely my rationale for the blog.  I’m often surprised when I look back on the lessons I have developed over 16 years, and more surprised when other teachers find them unique, when it never really occurred to me I was doing anything special.  There’s such a great feeling when I read someone else’s blog, see a lesson and think “man, why didn’t I think of that?”, and immediately share it with the 40 math teachers in my department.

“What’s relevant is that it is for the kids” – perfect!  There are a lot of bells and whistles is teaching ideas, including an avalanche of tech tools.  Sometimes it helps to take a step back and think “how does this improve anything?”  If there is a MTBoS mission statement to be written, it must be written around the idea that we all want to help kids learn math better.

It seems like a good time to evaluate my personal mission as part of the MTBoS. I can’t state that I am a “primary” member; rather, I tend to hover and grab ideas or join discussions when time allows or interests dictate.  So, who am I, what am I doing here, and how am I contribtuing to the good of the cause?

WHY I BLOG

I started blogging about 2 years ago because I felt like I had a lot of math stuff worth sharing.  I had always enjoyed sharing teaching ideas and lessons with colleagues in my building, and blogging just brought it to a whole new level.  There really isn’t a rhyme or reason to my posting schedule.  When I come across something neat, or a great experience occurs, I blog about it.  I also have a backlog of a lot of drafts of incomplete ideas, which I hope to get to…someday.

The blog has been helpful in that it is now a warehouse of some of my teaching experiences.  When a collegue now comes to me looking for an idea, or wanting more info on something, I can now send out blog links.  I am sometimes disappointed when I don’t get feedback on ideas, but then I can look at my blog stats and see which ideas are being “pinned” on Pinterest, or linked to from other places.  It’s often suprising to me some of the activities, which I never thought to be special, get picked up and shared by new teachers.  It’s a good feeling to help out new educators in building their filing cabinet of teaching ideas.

WHY I USE TWITTER

I now get my best classroom ideas primarily from items I see on Twitter.  From articles to videos to classroom lesson ideas, I am constantly looking for something new to share with colleagues.  My advice to my local math teacher friends is to join twitter and follow just a few primary folks at first.  You don’t need to check in every day or every hour.  The beauty of twitter is that will all be there when you have time to look.  There seems to be a fallacy out there that twitter is a time-consuming intrusion.  And it can be, if you want it to be.  It can also be a wonderful, low-pressure way to think outside of your building.

I use twitter to participate in chats.  During the school year, my favorites are #sbgchat (standards-based grading) and #statschat, along with #mathchat.  Where else can you rub virtual shoulders with authors and national experts?

PERSONAL CONNECTIONS

I actually have met very few of the people I follow on twitter.  At the AP Stats reading a few weeks ago, it was my pleasure to meet Shelly (@druinok), and touch base, and I look forward to meeting many more at TMC13 in Philly later next month.  Twitter’s great, but there is no replacement for a real, face to face, argument over how to teach complex numbers.  I look forward to it over a few beers.

SO WHAT’S NEXT?

The end of the school year bring with it the end of my tenure as an instructional coach in my district.  By choice, I am heading back to my high school classroom.    Part of my decision is based on all of the great ideas I have acculumulated and hope to bring to to my classes.  It’s a bit overwhelming really.  The blog will continue, but maybe with some more classroom focus.  I doubt I will change the name of the blog, as many people have it linked.  But a new tagline should be coming.  Suggestions encouraged!