Division Day 1

As I previously blogged about, we've had some disagreements about math.  

Today was day 1 of division in my classroom and it went really well.  They really liked using manipulatives and working together.  We went over the vocabulary for the unit (dividend, divisor, quotient, remainder).  They worked on problems and generated their own strategies.  

It was nice to see them struggle and problem solve.  I did have to talk to a few students who immediately saw the connection between multiples and division. I pulled them into the hallway and shared that they need to observe, letting others make their own discoveries to take ownership.

I was pleased to hear how well the lesson went in other classrooms as well!

I think my students' favorite part was when I told them they could write on their desks with the expo marker.  

But...that was intentional...

It's okay to disagree with a fellow teacher.  It's okay to not want to deliver a lesson the same way as another teacher. It's okay to put your own spin on things.  Some things should be the same (the assessments, the vocabulary, the definitions), but we aren't going to teach the same way.  That's okay. I have a difficult time following instructions or lesson plans verbatim, even when I'm the one who wrote them.  Don't get me wrong, I am always meticulously prepared for my day.  I just also take advantage of teachable moments.

However, I do get a little frustrated when it seems almost every instructional decision I make is questioned.  I've got a lot of background working with special ed kiddos and with the pacing of units.  Things are sequenced intentionally to help students make connections between background knowledge and new content.  The use of manipulatives (hands-on materials) during the first few days of a unit is quite necessary.  Students, even my fifth graders, need the concrete examples to investigate a concept.  They need experience in the concrete before moving to representational and abstract understandings of content.

We are starting division on Monday.  The standards quite explicitly state do not teach the standard long division algorithm. This is not to be introduced until sixth grade because students don't have the number sense nor mathematical understanding to reason through what is occurring.  

Here it is, straight from our professional development department:

I'm not really sure how much more clear this could be, but there were still debates about what it means.  

The first few days in our math unit has a lot of investigation by the students.  I'm giving them a bunch of paper clips to sort into smaller groups.  Some problems will divide evenly, some won't.  

I want them to tackle it. I want them to struggle.  Some kids will count those 48 paper clips into the groups one at a time, driving their partners bonkers in the process.  Some will make the connection to multiples and give away larger groups.  Some will use their multiplication facts to estimate the quotient.  Some will see division as repeated subtraction while others will see it as repeated addition up to the dividend.  

That's okay.

I want my students to understand what they're doing.  I want them to make connections.  I want them to discover how division is related to the other operations and take ownership over their strategies.

My math unit is scaffolded intentionally.  The first day is exploration.  The next introduces vocabulary terms, goes over making sense of the problems (hello math practices), and has student generated strategies.  Direct instruction doesn't begin until day 3 after students have had ample time to investigate sorting and making groups with paper clips and cubes.  From there, we'll move to hundreds grids and talk about regrouping.  We'll make the connection from the physical orange flats, rods, and cubes to the paper versions and drawings, thus moving from concrete to representational. From there, we'll move into number based strategies that build upon other operations, powers of ten, place value, and multiples.  Again, scaffolded from representational drawings and grids to strictly numbers (abstract).  There's a plan.  It took hours to design, but I'm really excited about it. The plan, which spans thirteen instructional days, scaffolds so students will feel successful and anticipates common misconceptions.

However, another teacher entirely disregarded the plan...and told me about it, gleefully.  She had them try one problem with manipulatives and then gave them the algorithm.  I'm so disappointed and feel sad for her students.  I'm sad they lost the opportunity to make their own discoveries. I'm sad they lost the chance to feel ownership over the concept. I'm sad they lost the opportunity to have a meaningful struggle with the tasks.

Her justification? They'll learn it next year and she's doing the sixth grade teachers a favor.  Besides, the standard algorithm is just faster.

I'm aware it's faster.  Faster yet? Whipping out my phone and using its calculator function.  But what's the point in that?  What do they learn when they're just handed the short cut?

I'm standing my ground on this one. My goal is not to teach math.  Yes, you read that correctly.  My goal is not to teach math.

My goal is to have my students understand math.  I want them to know what they're doing, why they're doing it, what happens to their numbers, and why their problem works out mathematically.

I'm making critical thinkers and problem solvers, not robots.  I'm aware it takes more time, but this mindset also encourages stronger students and that's my ultimate end goal.

Division Strategy

With the Common Core State Standards, traditional "long" division isn't taught until sixth grade. 

 Because this strategy relies on an algorithm with no concept of place value, it is no longer taught in elementary school.  

  While this was a struggle for some of my colleagues within my school district, we were fortunate enough to have an awesome coach last year who helped us with different division strategies that helped build students' number sense and relied on place value.

One of my favorite strategies was recently featured by NCTM on their website :)

Not only is this strategy  easy for families to understand because it does look similar to the traditional algorithm but it helps students make the connection that division is subtracting in equal sized groups.

Happy dividing!