Ever-loving Evernote – #ExploreMTBoS 6

When I started discovering the math teacher amusement park that is the MathTwitterBlogosphere, I quickly found myself so excited about what I had discovered and so overwhelmed about what I had discovered.

My first instinct was to bookmark, bookmark, bookmark.  I made bookmark icons on my ipad, bookmarks on my web browsers and bookmarks on my desktop.  I had bookmarks inside bookmarks inside bookmarks. The problem:  I couldn’t find resources when I got ready to use them and I now had more bookmarks on my ipad than I had actual apps.

Then an angel appeared in the form of Kate Nowak at a Global Math Department session last spring.  Kate suggested Evernote as a method of organizing all of the resources I had found.  I had a few things in Evernote and had used it very infrequently as a medium for holding a few PDF files or interesting articles.  Kate Nowak uttered the words I was waiting to hear when deciding how to organize my mountain of resources:  Tagging and Searchable PDFs.

Many of you might be thinking “there are plenty of sky drives that are searchable.”  (Maybe you are now wondering what a sky drive is.)  Anyway, none of the online storage platforms have been as versatile, flexible, and easy to use.  I’ve tried Adobe Reader, Dropbox, Google Drive, iCloud, the works.  Evernote surpasses them all.

A bonus:  Evernote and Adonit joined forces and created Jot Script, a one-of-a-kind stylus for note-taking.  Now, I can handwrite notes into Evernote and they are searchable as well! It’s like Christmas and my birthday!

Vegan Teacher Crazy about Cheeseburgers

A year and a half ago, I made the best dietary decision of my life and decided to try a vegan diet for 30 days.  Fast forward to now, I love the vegan lifestyle and I’d never go back to a diet filled with animal products.  I know too much.  But that’s a story for another post.

A couple of weeks ago, I logged into Robert Kaplinsky’s presentation on Global Math Department.  He started off with a visual, which is usually good to draw listeners into the presentation.  However, this visual was a cheeseburger.  And he went through more and more visuals, and the cheeseburgers kept getting bigger and bigger until finally I’m face to screen with 100×100 cheeseburger from In N’ Out burger.  I try very hard not to be one of those ‘enlightened and superior’ vegans who constantly judge the dietary choices of others, but these burger pictures were not how I envisioned spending my Tuesday evening.  His methodology had my attention however.

After explaining his problem solving process and distributing his problem solving template, he threw this photo into the mix and asked,

“How much would that 100×100 cost?

Now I was hooked and needed to figure out how much that 100 x 100 cost.  I didn’t care if it was a cheeseburger or a truckload of kale.  The wizardry of Robert Kaplinsky drew this vegan teacher into the problem solving process and made me care how much this monstrosity of a cheeseburger cost.  Brilliant.

Then Robert Kaplinsky threw down the dynamite:

That’s right.  The actual receipt of this 100×100 cheeseburger.  A boatload of kudos to Mr. Kaplinsky for presenting something that was simple, with some great mathematics to go with it.

I’m glad this weeks ExploreMTBos mission was LISTEN and learn.  This was a great presentation, a great lesson, and a great resource.  I’m glad I took the time to listen to Robert Kaplinsky’s presentation, even if it wasn’t so appetizing on the outside.

The Mr Barton Gem

Over the last year, I’ve looked at hundreds of awesome math resources that have truly helped transform my teaching practice into something I’m really proud of.  I’m so grateful to the truckload of great math teachers out there who willingly, freely, and eagerly share the wonderment that happens in their classroom.  One of my favorite things to do is to talk to other teachers about what they are doing in their classes.  How fortunate am I that I get to also do this collaboration with teachers across the globe.

One of the most fantastic collection of resources that I’ve have the pleasure of stumbling upon is that of Mr Barton.  The link is easy to remember, and I’ll post it again because you won’t want to miss this guy’s stuff:  www.mrbartonmaths.com.  He’s compiled websites, activities, and videos exploring all kinds of fun math stuff for all levels of the classroom.

One of my absolute favorite things that Mr Barton does every month is his TES Maths Podcast. This podcast is where I first learned of Nrich, and I’ve been in love ever since.  He’s done many excellent interviews with math professionals across the globe, and it’s my favorite day of the month when the podcast becomes available.

I hope you’ll take some time to check out his stuff.  He really does a great job of compiling some of the best resources out there.

 

Olympians, Tweagles, & Friends in my Phone

I started tweeting in 2008, around the Beijing Olympics. It was cool that actual Olympians would respond to my tweets.  When Summer Sanders responded to one of my tweets, I about fainted. Twitter was new, they probably didn’t know any better.  

I followed a few celebrities. I found some of their off-color honesty hilarious and sad at the same time.  In the meantime, my hilarious brother managed to rack up tens of thousands of twitter followers. (@sucittam if you are looking to add some hilariousness to your timeline). Here’s one of his tweets being featured on Ellen:

He opened my eyes to the idea that following actual REAL people is more entertaining and fulfilling. He was absolutely right.

I went through a phase where I followed a bunch of people who tweet as their beagle.  I’m pretty sure I was the first one to use the term Tweagles, although I have no proof of that. 

Then in January 2013, my indifferent view of people on twitter changed forever. My 29-yr old sister in-law, Danielle, suffered a massive brain aneurysm and it wasn’t certain she would recover.  She was in the ICU at the University of Iowa for almost 6 weeks, and while my brother stayed by her side every day, his twitter followers rallied support that went viral. All of these people, most of which he’d never met, wanted to reach out to help. Benefits were organized, gifts were donated, and memorabilia was auctioned all to benefit Danielle whose recover was slow, but steady. 

Rex Huppke (@RexHuppke) wrote a beautiful article illustrating that the people we interact with on twitter are not just cyber-acquaintances.  Danny Zucker makes the best point:

 “We’re willing to accept the concept that cyberbullying is real, and it is. But if you can accept the idea that the negative is real, then you have to accept the idea that the positive is real. If strangers can hurt you, they can be friends as well.”

And just like that I leaped head first into the T of the MBToS. I realized that people like Fawn Nguyen, Andrew Stadel, Kate Nowak, and Christopher Danielson were real teachers just like I was.  They had great blogs, and they were on twitter too. And if I wanted to get a real benefit from all of the resources I had found online, I needed to start posting feedback of how I incorporated them into my classroom.  And then tell the creator of the activity about how it went. Through this I’ve really been able to experience the genuine human behind all of these @ symbols. These are not only great teachers who don’t just shine on their own. They want to freely share what they’ve done so that others can shine just as brightly. 

A Visual Patterns Trifecta

This is my third (and most exciting) post about my new found love for Visual Patterns.  My enthusiasm stems from a growing appreciation of how these patterns can be used in such a wide range of grade-levels, including advanced algebra.  The use in an elementary or lower-level secondary classroom is easy to see.  However, the teacher and student need to dig a bit deeper into the make-up of these patterns in order to generalize them.

For example, here is Pattern #8.  Kudos to Fawn Nguyen on this one.

It’s not immediately apparent what step 4 should be.  But even more so, the quadratic nature of this pattern is not necessarily simple to comprehend.  From yesterday’s pattern #5, the students had a method for finding the number of penguins in the nth step by converting the penguins into a table and creating a system of equations.  I didn’t want to encourage this method, as it is very procedural and tedious.  However, it was a good place for students who liked to work in a more algebraic way to feel successful.

Also, the table allowed them to explore what the difference of differences really told them.  I had a student, let’s call her Kay, ask “I wonder what the constant difference of differences represents in our equation for the nth step.”  She came up with a conjecture by comparing it to our problem from pattern #5.  Kay concluded that the “a” value in the equation ax^2 + bx + c = y is half of the constant difference of differences.  I challenged Kay to continue to examine these values in future problems to see if her conjecture holds true.  I had another student, Em, wonder if that meant that the “a” value in a cubic function is equal to one third of the difference of difference of differences.  This she will investigate as well.  What is very exciting about these questions is that they were non-existent 5 weeks ago.  It wasn’t that the students didn’t WANT to be mathematically curious, they just didn’t know HOW.  It was a huge thrill for me as a teacher to see these kids move from looking at a math problem with a single solution to being able to ask new questions.  A nod to Christopher Danielson for helping me realize that learning is having new questions to ask.

  Back to the problem at hand:  How many penguins are in step n?  A few of the students were able to get the answer without using a table.  These were mostly the students who like to do things in their head.  The ones who want to fully process the problem in their brain, but not write any of it down.  [Side note:  these are usually the ones who are brilliant with numbers but get lower grades in traditional math classes because they don’t want to “show their work.”] Anyway, I wanted to challenge those who used the table method and set up a system of equations to relate their model back to the picture.  Spoiler alert!  The answer is 1/2n^2 + 1/2n + 1, but I wanted my students to be able to relate that back to the picture.  What do the individual pieces of the expression represent in penguins? This way, the students were able to make that connection of a picture or pattern that didn’t seem quadratic to begin with and flesh out its quadratic properties.

When the students figured this out, it was a magical moment.  I had to capture it:

IMG_2993

Another cool experience with this problem:  the same evening that I did this problem, our school hosted parent-teacher conferences.  One of my students came into conferences with her parents and her three little sisters, ranging in age from about 5 to 10.  One of the little sisters sat down and wanted to be part of the conference.  I pulled up the visual pattern and asked her how many penguins would be in the next step.  It was a validation of my initial thoughts of how open and accessible these problems are to all levels of mathematics.  Here was an 8? year-old looking at the same pattern that her 17 year-old sister explored earlier that day.  And it was mathematically applicable to them both.  Beautiful.

Visual patterns with a side of awesome sauce

Regular old Wednesday turned amazing today when I posed pattern #2 to my math recovery class, a remedial math class for kids to recover credit from a previously failed course. It may not need mentioning, but just to be clear, these kids hate math and think they’re no good at it. In pattern #2, the kids need to find how many cubes are in step 43 and the surface area of step 43. Side note:  My kids wondered, why 43, Mrs.Nguyen?


Anyway, finding the surface area was where the magic started to happen. I had 4 or 5 kids out of this class of about 15 get seriously invested in finding out the answer. They were drawing pictures, explaining their thinking to one another, figuring out different ways to think about the problem. It was inspiring and motivating for both them and me.

As if that wasn’t enough to make it a great day, I decided to pose the problem to my College Algebra class as a starter and try my hand at the 5 Practices for Orchestrating Productive Mathematics Discussions. My expectation was that they found the number of cubes and surface area of step ‘n.’ What was gorgeous about this problem was not necessarily the answer, but the numerous ways they came up with to arrive at the nth step. Here are a few:

n + n + (n-1) + (n-1) + n + (n-1) + n + (n-1) + 2

4(n-1) + 4n +2

4(2n – 1) + 2

6 + 8(n-1)

4[n+(n-3)] +10

6(n-1) + 2n + 4

8n – 2

What was even more powerful was, as Ben Blum-Smith calls, an effing game changer.  He’s right, and this was beautiful.  I used the tactic he lays out in his blogpost where students are asked to summarize the ideas of someone else.  I had a few try to slyly summarize their own ideas, but alas, I would have none of it.  As a result, I had more engagement, more involvement, and more buy-in that this problem solving process is helping them to understand the mathematics more deeply.

Here is an exchange between two students (T and C) that is worth highlighting.  T is the student who came up with 6 + 8(n-1) as the surface area for step n:

C: Oh, I see.  T just used the arithmetic sequence formula.  The first term is 6 and it goes up by 8.

T:  Actually, that’s not what I was thinking.  I thought that there were 8 sides of the figure that had ‘n-1’ squares and then 6 squares left over, two on the caps and 4 in the corner.  OH, you’re right, it is the formula.

Then the lights came on.  This girl who had probably only known mathematics and algebra to be a long list of rules, procedures, formulas, and practice was able to experience that developing a conceptual understanding of this pattern help her to create the arithmetic sequence formula.  It was the bottom-up approach that I’d been talking about all trimester where developing conceptual foundations are where real math learning happens.