Tonight I was working with an eighth grade student I have been tutoring for a while.  He recently had a quiz in math class that he got a D on due to a couple of plug and play mistakes.  I asked, “did you ask your teacher if you could fix your mistakes and get back some credit?”  He said, actually she gave me a bunch of worksheets to complete.  He then proceeded to pull out a packet of 6 pages front and back on the chapter that he could complete for extra credit.  Hmm.  I will not comment yet.

He said, we can just  breeze through them because this is stuff we already did.  I caught his meaning.  It didn’t matter if he knew how to do the math, it would never be on the test again.  Double hmm.

So we sat down to look at the mountain of snow that had accumulated before us.  We worked out a few problems on the first page and then I said, “well let’s go over the word problems because those are the ones you can’t check on your own.”  My dear student has found that he can very quickly “complete” his math homework using a math app called Photo Math.  And let me tell you, I don’t blame him.  If I was forced to complete 18 problems that were exactly alike, I would look for a more efficient way to get on with my night also.

We looked at the first word problem and I found myself having a Deja voo moment.  I’ve seen problems like these before.  As I worked to wrap my brain around the question, I realized the problem I was having was that I just didn’t care what the answer was.  And if I didn’t care, he certainly didn’t care.

Here is the first problem we looked at:

“Health Club  Currently 96 members participate in the morning workout, and this number has been increasing by 2 people per week.  Currently, 80 members participate in the afternoon workout, and this number has been decreasing by 3 people per week.  In how many weeks will the number of people working out in the morning be double the number of people working out in the afternoon?”

I’m not embarrassed to say, I had no idea how to approach this.  I scribbled down a bunch of equations, but I was limited by the fact that I knew (the game of school dictates) this word problem somehow needed to match the problems above it that we had been working out.  I couldn’t recall the format of how to set up the equation using all the information I was given and have it “match” the previous problems.  I also hadn’t solved a problem like this since math class which was many many years ago(no I’m not willing to divulge just how many).   Does that say something about the value of such a problem?

I am genuinely (what’s the word I am looking for) confused? angry? Baffled? that our students time is not more valuable to us.

But that really goes back to the question, what math do students need to know to be contributing members of a society?  That’s a topic for another time:)

To address the Photo Math app, there has been a lot of hype about “non-google-able” problems.  I agree, I want my students involved in experiences that require them to think and apply their learning.  But most of all, I want their learning to be relevant(to them now or in the near future).  This is definitely a filter we need to put our tasks through.

The problem referenced above would probably make it through the non-google-able filter, but it would never make it past the latter.

So let’s try a word problem that I might come across involving a health club:

I want to start working out, but I need to find a health club that meets several criteria:

Has childcare, Offers fitness classes, Is open late, is around $50/month or less.

I narrow it down to two.  The names are Chesterfield Family Center and the Pat Jones YMCAPat Jones YMCA.  Click on the links to go to their websites.  Compare the two clubs and provide a recommendation for which I should join.

Some things to keep in mind: Base the cost on a family size of 3: 1 adult and 2 children.  Cost difference between paying all at once and paying monthly: Do I qualify for a Corporate membership discount?  What does it cost if I want to bring a friend with me?

How many people might encounter a problem similar to this in their future?  I’m willing to bet the answer is significantly higher than if I had asked the same question about the original problem on the worksheet.

If I wanted a word problem that assessed the content in the original, I would probably go with something like this: 3 Act Ditch Diggers.  Should this be considered a word problem?  Should we re-brand that phrase?

One of my favorite math teachers/bloggers/speakers is Dan Meyer.  He really “gets it” when it comes to making math meaningful for students and I learn so much from him every time I watch a video, hear him speak, or read a blog post.

He has inspired many people to take mathematical thinking to the next level and turn students into question askers instead of question answer-ers (is that a word?).

Many elementary math teachers have began making videos to explore concepts using his 3 Act model and this post will explore one of those.

If you type 3 Act Math into Google, you get lots of different sites where educators have begun posting libraries of lessons.

I have always admired this approach to mathematics and it aligns so closely with my instructional philosophy that I decided to try it out with some students.  I went into 3-5 classrooms and introduced the lessons as “you figure out the objective” instead of telling students what we would learn in class today.  They had to figure out which questions to ask, which operations to use, and why the answer didn’t match the problem they set up.

The first lesson I tried, was from Graham Fletchy’s blog  here.  I presented the lesson in a module format with each act on a seperate page in our Canvas learning management system.  They first watched the video for Act 1 and then were ask what they wondered about the video.  Students said things like “How many skittles are in each bag? How many did it take to fill up the jar? How many bags did it take?”

So naturally the next step was to see if we could answer their questions. Dan Meyer uses an ingenious strategy to get students to engage with the math.  He first asks them to write an estimate that is way too high, and then one that is way too low.  Every student has an entry point with this approach.

We talked about what it means to estimate and what was a crazy number that they know could not be right.  Then we talked about a number that might be close.  We then talked about what we might need to know to figure out how many were in the jar.

Enter Act 2:  We opened the page that had a picture of how many skittles were in each bag, and how many bags there were altogether.  What operation could we use knowing that information to arrive at a solution?

Students did the math.  We revealed Act 3 and some students were down right mad.  How could their answers not be correct?  What factors played into that.  They did the computation correctly.  Finally we were able to talk about the fact that maybe not every bag had the same number of skittles in it or some were left over at the end. We talked about how math in our daily lives is sometimes messy, there are multiple factors that we have to take into account in addition to computation.

To wrap it up, I asked students what they thought the objective was today?  Where was the math?

Answers came as multiplying, adding, estimating.  And although we did all those things…the true purpose was productive struggle.  Engagement. Critical thinking.  Collaboration. Put your finger on a practice standard. Nailed it.

Can’t wait to blog about some of the other 3 Act lessons we used and 3 Acts with K-2!

Special thanks go to Graham Fletchy and Dan Meyer for sharing their knowledge and resources!

What I (and other educators) have noticed over the years is that student attention spans are dwindling, they require more stimulus, they give up easier when faced with a challenge and in doing so don’t every find a true sense of accomplishment.  They are afraid to make mistakes, and in turn, they are afraid to try.

I am constantly looking for ways to engage students in problem solving situations that require persistence; Opportunities for them to be meta cognitive, to reason through obstacles, and to persist in finding a solution.  I found that in code.

Anyone who knows me knows that I am a tech enthusiast, so when I first heard about Hour of Code, I had to try it for myself!  I was so impressed by the skills required to complete coding lessons, I felt like it needed to be an integral part of our daily routines.  So I asked our 3-5 teachers if I could introduce it to students and I don’t think any of us were prepared for the levels of engagement we saw.  Students were talking to each other, they were problem solving, they were helping each other…and best of all, they were proud of what they accomplished.

The experience opened up dialogue about fixed mindsets vs. growth mindsets and we got an authentic opportunity to talk about productive struggle and the willingness to fail.

After the success we saw, we decided to incorporate coding as an option in our Math Workshop block as a “may do” when daily work and individualized learning programs were complete.  Weeks later, they are still excited to complete coding challenges.

I truly believe that the opportunities that students have had at “debugging” their coding lessons will transfer into their mathematical reasoning and better prepare them for scenarios they will face in their daily lives and in their future careers.