Category / math

by Beyond Traditional Math

Build It = Deep Conceptual Understanding of Multiplication

Being a math interventionist is one of the hardest jobs I’ve ever had. It’s like a constant cycle of diagnose…teach…teach…teach…light bulb on…light bulb off…diagnose…teach…teach…teach…

I’ve been working with a group of fourth graders that were just struggling BIG TIME with multiplication. They weren’t able to see how a fact like 3×7 could help them solve 6×7 by just doubling. The numbers were too abstract, and they had nothing to connect it to.

Of course as I dug deeper I found that they simply had zero understanding of what 3×7 really means.  So as usual, I tried to find a way to connect it to real life, my favorite thing ever. I was trying to think of a way to help them remember the difference between rows and columns.  And then it occurred to me as I was waiting in line at the theater, no one wants to wait in line to sit in the first COLUMN for a popular movie. We all want the best seats in the house, so we wait to sit in the first ROW.

Enter the Movie Theater Multiplication Project.  I went home over the weekend, turned off all distractions and poured days and days into authoring this project. I needed to really think for myself what 3×7 represented.  I was not taught this way and I know that it doesn’t come easily to me.  I also had to think of a way that would be meaningful and that would STICK, since that seems to be the biggest challenge facing students in intervention. The last thing that I really needed to think about was the Concrete-Representational-Abstract instructional approach. Kids LOVE to build. The second they walk into my math lab, their hands are all over my cubes, blocks, counters, etc.  Starting with building means that they can usually connect a pictorial representation to it, and then connect that to numbers.

So I made a movie theater or two or three as I wrote the project. I made theaters that were 3 rows of 4 seats, making 12 seats total (3 x 4=12). I made tickets placing them in the correct row and seat number. And finally I made some mega theater designs so they could learn to use known facts to solve harder facts.  There is a fourth stage to the project also that involves some open ended challenges to calculate profits and revenue. Say hello to my little friends:

Multiplication-conceptual-understanding

Seemed like it might actually work!

So I brought the idea to school. I got out some tools and some little tiny bears and THAT got their attention.  Tiny bears! Seriously, that is all it took?!

The first three days of the project were brutal.  They were making columns instead of rows, they were making rows of 20 instead of 20 seats total.  With probing questions they started to see what was happening.  And THEN, light bulbs turned on…and for several days now the light bulbs have stayed on! Is it sticking?! I hope so, and we’ll find out when they get to the mega theaters and can break down more difficult multiplication. Wish me luck!

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If you want to try this out, in the preview you will find three parts of the four stages of the project that are free.  You could totally continue the project by giving them your own specifications!

 

 

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by Beyond Traditional Math

Level Your Games: More Small Steps for Differentiation

Recently, I had two first grade teachers approach me about fact fluency. They were feeling both frustrated and scattered. They weren’t sure how to organize the time, how to organize the many games, or how to reach students at all the different skill levels they were at.

It is the same story we all have where every child that we teach is functioning at a different level. Some students didn’t even know their combinations to 5, many were learning combinations to 10, and even a few of the students could work within 20.  The games that we were using were just not reaching every student with what they needed…they were flat and one dimensional. WAY too difficult for the students who weren’t on level, and WAY too easy for the students that had already reached mastery.

Enter the post-it note.

 

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In “Steal the Cubes” each post it assigns each group to a level that is right for them.

Those sticky things are my savior when it comes to flexible grouping.

After talking it through, we thought that we would choose just FOUR fact fluency games that the students could rotate through daily. Once they get bored with the same four, we might introduce a new one.  Time in the day is precious, so we knew that they had to be “go-to” games that could be setup, played and cleaned up quickly. We also knew that students grow fast as they learn, and that our groups had to be easy to change in and out.

So here is what we did:

  1. We taught ONE game to the students each week.  They played them for a week until they understood the ins and outs of them. Then, once the routines of the games and the game playing behaviors/expectations were taught, we were ready to rotate through them.
  2. Each day the teacher chose the game by putting the color of the game out first, leveling the game like in the photo. Each game can be easily modified with different numbers, different cubes, etc. by just changing the post it note.
  3. We attached a third level of post it notes for the partners/groups that stayed in the same place for each of the games, the teacher can simply change up the post its when students move levels.

So once again, differentiation can truly be a little small step.  While this one takes a little bit to set up, the students aren’t bored which makes that classroom game time so much more productive!

 

by Beyond Traditional Math

Oh My! The Progression of Multiplication

Well, I’ve watched this video three times now and I think I need to watch it at least five more times. I love, love, love how this presented to the audience.

 

My take aways for when I am teaching multiplication:

  1. I need to stop stealing the opportunity to let my students use concrete tools! They should be available every SINGLE DAY.
  2. Rushing to the traditional algorithm is a huge mistake. I am thinking we need to have some serious conversations about when to introduce this.
  3. I need to let the students explore. Let me say that one again, I need to let the students EXPLORE. So many times when they hit a struggling point I feel this need to jump in and tell…I need a muzzle for my mouth!

What did you take away from this?

by Beyond Traditional Math

An Approach that Works for Struggling Learners EVERY Time

I have been reading about the Concrete-Representational-Abstract Sequence of Instruction for some time now, especially since I began working with our most struggling math students at our school.

I’m hooked and am a firm believer in this approach!

I know you know that moment… where you find students looking at you with the deer in headlights look.  In my intervention groups, I see it several times in 30 minutes! I was desperately searching for more ways to make math meaningful for them when I discovered this approach. And, I will tell you, it works EVERY time. I mean, EVERY SINGLE TIME. There has not been one single concept that I haven’t been able to master with a child when I used this approach.

If you don’t have time to read the article, the approach is summed up quite simply in three steps:

  1. When a student is introduced to a new concept or something unfamiliar, you allow the use of tools. (Concrete)
  2. When the student can perform the task, they move on to representing the concept with drawings or pictures. (Representational)
  3. When the student can master the task with a drawing or a picture they move to using only numbers and symbols. (Abstract)

    * Note it is important to keep all three of these ways visible to promote strong connections and deep conceptual understanding.

I realized that this could be even MORE powerful when students could self assess where they are in this approach. I made this poster with them and we refer to it constantly.

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They are constantly checking “where their brains are at” when they are struggling through a problem.  When the numbers and symbols don’t make sense, they actually back themselves up to drawings. If that still doesn’t make sense they back up and use concrete tools.

It has been simply amazing, and you must try it!

by Beyond Traditional Math

Common Core Help for Parents: Educators and Parents Can Work Together

A friend of mine forwarded his child’s math homework to me the other night. His son is a third grader at a great school in the community in which I live.  His son’s homework had a problem like this, and both the father and son were at a loss for how to solve it.

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Parents having a hard time understanding Common Core Math need support from educators as we make the shift together.

There are a few important things to note. Number one, the amount of attention “New Math” and “Common Core Math” has received in the media has been non stop and very negative. This leads to parents feeling frustrated with schools for not communicating this new shift in mathematical thinking. In some ways, this is a failure on our school system, but in other ways it is a lesson to not always believe everything we read/see in the media. Much of the information out there is false.  For example, many parents ask me, “Why don’t you just teach the traditional algorithm?” We do teach it, but we teach a whole lot of understanding before introducing it so they don’t have to memorize a meaningless set of procedures. Luckily this father is open minded since he did not have a great experience with math himself as a child, and he wants to do his best to learn along with his child.

The other thing that is so common when parents are frustrated with Common Core Math, is that they haven’t been taught to think of math as a problem to solve, as a puzzle. Instead they look at it from the angle that there must be only one way. How can you blame them when they were taught math this way? It isn’t their job to learn this new shift in thinking without any support from us. We all go back to what we know, and what they know is that they were taught to memorize. This same attitude is common for children in their math classes as well because teachers are trying to shift to deeper thinking activities for our students.  (Sadly, math curriculum/textbook companies in the U.S. is not there yet.) This is a HUGE shift that will take time!

So in the meantime, let’s work together with our parents about math. Actually it doesn’t matter if your school has adopted Common Core Math at all, these are positive messages for ANY parent. Let’s tell them:

  1. It’s okay that you don’t know the answer immediately to your child’s homework. Math is not fast anymore, in fact it should be both slow and messy. Many times there is more than one way to solve it or show your thinking.
  2. Ask your child questions like it’s a puzzle that you are trying to figure out together.
  3. Try to google your way through it…I was able to solve ratio tables last night with Khan Academy, something I haven’t thought about since middle school.
  4. Be open minded and positive about it.  Sometimes adult’s (both teachers and parents!) negative attitudes about math will transfer to the student, causing even more stress and anxiety.
  5. If all else fails and there is no way for you both to figure it out, write a note to the teacher. We’ve all had to learn this math differently as well, and we get it! We won’t be upset with your child for not finishing!

By the way, here is how I thought about that problem above. If you thought about it a different way, I’d love to know your solution!

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Parents, keep on advocating for you and your child.  We need to know if you don’t understand, and we can all make math meaningful if we learn together. What other positive messages would you like to tell parents so that we can work together?