Balance & Stamina & Time

I had a great chat with my neighbouring teacher today, who also teaches the third grade. The culmination of our conversation was all about the necessity and importance of balance and stamina and taking the time to build a skill.

You see, she thought I wouldn't agree with her when she said that it's okay to only give one thing to do, rather than options, at the start of an exploration. (We were actually discussing open-ended art, but it led into a math chat. The big idea was that if there is no skill yet built, then we should give the kids some exposure before saying "go wild and free!") I think I'm sometimes misinterpreted because I don't have desks in my classroom, but she was happy to hear me go on about it elaborately. I explained that while I'm a little out there with my ideas, they are grounded in pedagogy and research driven data.

We eventually ended up agreeing that with the proper skills, built through a balanced and thoughtful facilitation, will eventually allow the students to have more freedom over their work. Building their stamina and allowing time to do all of these things are how we can have them approach open-ended activities. This is where we are right now, as we balance inquiry and the culture of the pros and cons of our educational system.

This post is inspired by that short conversation, which was the fruits of some ideas that have been bubbling this month as I settle into a group of students far from the independent thinkers I worked with last year.

Stamina is something that is undervalued and overlooked. I realize this now. I didn't always. In fact, I hadn't thought explicitly about it until I'd read the Daily Five. When I read it, it clicked. Stamina is so important to build, in anything, regardless of being a part of the Daily Five language program or something else. The kids need to build their stamina for math problems, through repeated activities which increase in time over a period of time. They need it for independent reading. They need it for writing. They need it for art. They need it for transitions. So we started explicitly building our stamina with all of those things. Things are calming down as the kids start to see how pleasurable working can be.

Balance is the other piece to this puzzle of not wanting to jump out the window all year. Balancing through careful releasing of responsibility is such a necessity that it should be somewhere in the curriculum. Then again, I also think that successfully transitioning should also be a curriculum expectation, and I have no desks, so maybe I'm a little weird. So what?! When I'm talking about balance, I'm referring to everything from how much they are asked to do independently and how often that happens in comparison to large and small group opportunities; I'm talking about balancing my modelling with their own exploration, determining when it is a good idea to model first or to model after (thereby flipping the lesson around, which in my opinion and experience is often the best way to introduce something new!); I'm talking about balancing activities with quiet reflections and transitions. I'm even talking about balancing our "calm" through meditative opportunities, to turn down the volume inside their busy brains, and to give them an opportunity to have peace for a minute or two.

When the right combination of balance and stamina is combined, the results are wondrous.

I recognized, almost immediately, that my students had many misconceptions about numbers. I was trying at first to give them too many activities, to bounce around too much from adding to breaking down and building numbers and so on and so forth. I wanted them to be excited about math, but in my own excitement, I lost theirs. Lost. That's what they were. I could see it in their eyes.

So I had them work at numbers up to ten for about a week. We used ten frames and other manipulatives until getting up to ten was comfortable.

Then for two solid weeks we ONLY played with the base ten blocks. This was more modelled at first, and then I shared the conversation with the kids, and then they would work for a couple of minutes with a partner to build any number that they wanted. At some point, one kid noticed that he really didn't need more than nine single blocks. Once he reached ten, he could use a ten-rod. About a week later, someone connected that to the tens and hundreds. Bingo!

 


Time was so important. I couldn't rush it. These guys needed to become independent workers with these blocks, representing the numbers over and over and over. But it didn't get boring, because they were picking the numbers themselves. They owned the numbers. And, when their partners got it wrong, it was freakin' exciting! They got to teach their partners how the number should have been built, according to our agreed-upon system of using the most efficient blocks only.

So I would begin each lesson by inviting them to sit around the perimeter of the carpet (thereby sneaking in a math vocabulary word and making a connection available for them when it is time to look at perimeters in Geometry). I would spread out some blocks and have them count with me (because we need to count everyday). They would need to pay close attention because I might switch from ones to tens at any moment. Of course, I only did this in increments that they would be instantly successful with, in order to build their efficacy.

I would build a number and ask them what it was. They'd talk about it and call it out and we'd do it again. And again. Then, I'd ask someone to give me a number to build. Back and forth with me in the forefront (although I was sitting on the floor with them), they were able to successfully participate in the activity and practice for their independent time, with a partner. They'd break off and go to work. I'd stop them after 3-5 minutes and we'd come back together, cleaning it all up. Then, I would model some more and ask about their experience. I'd send them back to work. Having them tidy set their minds at ease and they were able to focus on me. It didn't matter that they'd be heading back out soon.

This week, I introduced a new hurdle to the mix. You see, I really, really, REALLY want them to understand numbers and work with them with ease. So the base tens were a great start after the ten frames from week 1, but they needed to work more with it, but with a challenge now. This week, they needed to draw out their blocks into the proper columns for their number. AND, they needed to write the number in words, giving us a language connection and words for our word wall. AND ... they had to write down the equation for the number. For example, if the number was 27, they would write:

Twenty seven

20 + 7

If it was 124, they'd write:

One hundred twenty four

100 + 20 + 4

The chart gave them a framework to organize their thinking, an opportunity to practice addition, writing, representing numbers in pictures, and a chance to see how complex the numbers are.

At first, this was a struggle. Now, I have kids flying through their own pages, even working with thousands. I'm not saying that they are geniuses or experts. I'm saying that they are comfortable and grasp the concept.

Next week, we will start comparing and ordering these numbers. Once this is established, I would like to work in some measurement and continue on down the path. It is all about building that stamina through balanced opportunities, which will drive their efficacy upward, to infinity & beyond! Then they'll be able to do anything.

Here is a link to the organizer we have been using, in PDF:

Base Ten Organizer (Hundreds/Tens/Ones)

You can make your own in less than two minutes, to suit your own needs!

Does 8 = 14?

Welcome back!

In a flurry, summer flew by and here we are, sitting back in our desks in rows.

Wait a minute.

No, we're not. We're not, because that's not how today's students learn. At least, that's not what I think!

I've been assigned to a new school, a new set of kids, a new grade - basically, everything is new again. I've been wracking my brain trying to figure out what and how to teach this group. It's only been a few days (6 to be exact), but the picture is beginning to clear up a bit.

It's funny, when you are faced with a new group of strangers, how little you feel you know. I was so confident in my Gr. 5 math class last year, but now thrown into a group of Gr. 2 and 3 students, I feel a bit lost! I've taught the grade before - but it's new every time. I know the curriculum expectations, and I know my philosophies. What I don't know include: the kids, their needs, their skills, their interests, their behaviour blips, their attention spans, and their pasts.

But that's okay.  In fact, I prefer to not know much about them. It stops me from forming ideas about them that may not be true, in my room or in general.  A mom told me today at our open house that her son was excited to be at school because he liked me. Had I known about his past, I'd have assumed that he didn't enjoy school and then we may be in a whole other mess!  Fortunately, him and I are in a good mess - a mess called learning!

I always start off more or less the same, regardless of the grade, with the same questions.  Ones like:

"How many numbers are there, and how do you know?" and "How many ways can you build the number 14?"

The kids rotate through these centres, 10-15 minutes at a time depending on their age and "vibe" (if you're a teacher, you know what I mean ... we are always reading the kids ... when it is time to move on, we move on).

From this, I get a sense of:
- what sort of learners are they?
- are they comfortable with manipulatives?
- do they naturally go to manipulates?
- how do they organize (or do they organize) their work/thinking?
- are they comfortable talking about it?
- can they stay on task at this point in time?
- do they "get" this stuff or is it too abstract?

I found out by day 2 that this was all too abstract for most.

One girl asked me if 8 was 14.

Yes, you read that properly.  "Is 8 fourteen, Mr. Patrick?"

"Sorry?" I thought I had heard wrong.

"Does 8 equal 14?"

2 years ago I would have said "No. What does 8 equal?"  And that may have been okay ... at the time, for me.  I know better now.

I said: "Does 8 equal 14?"

She just stared at me.  So I said, "Let's get some counters and see."


The trick here is to explore fully WITH them.  EVEN THOUGH I know it's not right.  EVEN THOUGH it logically to me makes no sense at all.  EVEN THOUGH!!!!!! I need her to experience the answer.  She needs to be in control.

We got the counters (she picked them, because there are bread tags and blocks and animals and so on).

I said, "Let's get eight."  So she did. We counted eight together.  Good! She can count.  This is giving me information.

I said, "So is eight fourteen?"

She stared at me.  "Yes?"

I said, "Okay ... how many are here?"

"Fourteen?"

"Let's count them again."  So we did.

"How many are here?"

She said, "Eight."

I said, excitedly of course, "Yes! There are eight! High five man way to go!! WAHOOOOEY!!!!" (Okay maybe I didn't get that excited ... or maybe I did.  I don't remember.)  I circled the blocks on our chalk table (see, it comes in handy!) and wrote the number 8 over it. Then I said, "If there are eight here, I wonder how many more we need to get to fourteen?"

I knew at this point that she needed a push in the right direction.  We probably could have gone back and forth all day about eight being fourteen, yes, no, yes, no.

So we counted, with my direction, the original eight, and seamlessly continued counting new blocks until we reached 14.

These blocks went in a different pile.  We circled it.  I asked her how many were in it.

She counted them and found it was 6.

So I asked her, "So, now that we can see this, is 8 fourteen?"

She said, "No."

I asked her, "How many more do we need to go from eight, to fourteen?"

She double checked by counting the new blocks and told me it was six.  We wrote 6 over that pile, and I showed her the number sentence: 8 + 6 = 14.

She smiled, and I could tell she felt better.

The big idea here is that she didn't have the concept of numbers being their own values.  It may have been some sort of weird memory lapse, but the understanding wasn't there.  I needed to take the time, even if it seems silly to spend so much time of 8 not being 14.  I needed to give her an opportunity to EXPERIENCE the numbers.  It would have been unfair to just tell her the answer.  It would have been unfair to shut down her thinking right away by saying "No, go find out how many more you need." She was brave enough to ask me, a relative stranger (this was day 2).  How dare I shut her down!  So I didn't. We built up an understanding together.



Throughout this first week, I've found some number sense skills all over the place.

We've started working with ten frames and number lines, and are focusing on building a strong understanding of how numbers work together, so that we can start thinking about mental math and everything else.

If you don't know how numbers work, how can you do anything else?


The first weeks are messy.  They're muddy and unclear.  It is a scary place to be.  But, it's also important.  Every word I say or don't say - every extra minute I give or don't give - every nod I nod, every smile I smile, every example I choose to give or select not to ... they ALL  matter.  I'm forming their love or hate for math; I'm determining how they will approach, organize and eventually think.  I need to be sure that I'm doing it well.