## We can make our own number lines!

I’m not going to lie:  making the jump to drawing number lines independently has taken a while!  All the grade 2s can explain what I am doing on a number line, and all of them (ok, most of them) can describe a strategy and when I draw it on a number line they confirm I have drawn what they were doing in their heads.  But to make their own?  That’s been hard.

We had completed all of the activities in “Ages and Timelines”, one of the Context for Learning Units, and people were still referring to tools (hundred chart mostly, they they tried to use math racks unsuccessfully) so I wanted to spend an extra week just talking about how to use that number line AND draw it independently.

One day last week, I created some Smart Notebook slides and we all sat down the chalkboards.  Here’s the first one,along with some notation to show that people were flexible with strategies…they used both addition and subtraction to find the answer. I will say that those who added were surprised some had used subtraction, and those who subtracted were surprised that addition could be used, so we had a great conversation about this slide! (Oh, and we are collecting paper towel tubes for science! 🙂 )

Here is another of our questions:

I wandered around and captured some number lines.  Now, this might not be beautiful to you, but darn it!  It is gorgeous to me!  Look at the line, the iterated jumps, the acknowledgment that 4 jumps of 1 is the same as 1 jump of 4…*sigh*  I’m smiling again just thinking about it!

I caught one person who was struggling, and handed that child a hundred chart, with a 25 chart on the back.  For this problem, this child was able to use the 25 chart, but for later problems, had to use the 100 chart, and did!

Another beautiful number line… Another great demonstration of the iterated units drawn evenly and there even arrows on the end!

One of the most amazing things that happened is shown here.  One child had a 100 chart and was using it well.  Another had no strategy and was looking around the room to see if she was alone in this dilemma.  As soon as she spotted the 100 chart, she scooted over to it.  However, upon arrival, she realized she wasn’t sure what to do.  The other child showed her!!!  (There is a sock on one child’s hand because we use them to erase the chalkboards!)

So, it took us an extra week, and I am quite sure the number of grey hairs on my head has doubled since March Break. Next week, mixed in with some probability to math workshop centres, I am going to be sitting at a table interviewing these lovely grade 2’s to see what they can really do all on their own.  Can’t wait!

## Finding Connections

A few weeks ago, I sort of made my husband famous when I wrote about how he and I had each solved a problem about a good deal.  I had used an elegant solution, to quote Cathy Fosnot, and he had used the long division algorithm, which was just fine, also to quote Cathy Fosnot.  (You can hear the whole thing here.)

I had occasion to ask my husband to solve some math problems again this week, and I thought I should make sure that everyone knows he is my go-to double-checker. His methods may be old-fashioned, but he gets the job done.

I have applied for a Teacher Learning Leadership Project grant (TLLP) and am pretty close to getting it approved (I HOPE!!)  At the beginning of the month, I received a request for some clarifications about the project, which is apparently what they do.  Makes sense.  I am asking for just shy of the maximum allowed amount of money, so I’m actually glad to know they are making sure people are being fiscally responsible with this money.

One thing  I was asked to do was to make sure my budget aligns with the project goals.  I went over the entire thing with a fine-toothed comb, making sure I had the right number of days, and had figured it all out properly.  I have to account for the number of days each member of the project will be out of the classroom, and how much it will cost to provide coverage for the class.  My principal is joining, so I have also had to account for the extra money paid to a “teacher in charge”.  One member of our group doesn’t actually teach at my school, so I have factored in some mileage for her.  Even though I’ve been over it a few times, I needed someone to double-check it all for me.

I suppose you could say we worked as a team here.  I gathered the information we needed, and organized it into problems.  My husband, new to using an iPhone took one look at the work I needed him to do, pointed at his phone and asked, “Does this thing have a calculator on it?”  I showed him, and he proceeded to answer each question  on it’s own.

Again, the interesting thing here is that he didn’t see that he could solve one and use it to solve the others.  The 4 day option is double the 2 day option, but he didn’t use this. I think I am paying extra close attention to this right now because in my class we have been talking about splitting.  If we know that 40 + 50 = 90, then we don’t have to start over to solve 44+50.  We know it is 4 more than 90!  For some people, this might not be a huge revelation.  But for me, when I first learned to do math without using algorithms, these important connections between problems were completely missing. The only time I used anything like this was when I figured out 3 x 7 = 21 (for example) and then found all the 3 x 7 or 7 x 3 on a Mad Minute and wrote 21.  But I wouldn’t, for example, notice that if I knew 3 x 7 = 21 I could use that to help me with 3 x 8.

Connecting is one of the 7 mathematical practices in the Ontario Mathematics Curriculum: Grades 1-8 (2005).   On page 16, it says:

Experiences that allow students to make connections – to see, for example, how concepts and skills from one strand of mathematics are related to those from another – will help them to grasp general mathematical principles. As they continue to make such connections, students begin to see that mathematics is more than a series of isolated skills and concepts and that they can use their learning in one area of mathematics to understand another. Seeing the relationships among procedures and concepts also helps develop mathematical understanding. The more connections students make, the deeper their understanding. In addition, making connections between the mathematics they learn at school and its applications in their everyday lives not only helps students understand mathematics but also allows them to see how useful and relevant it is in the world beyond the classroom.

Since I have started to focus on teaching students to see the connections in math, I have noticed an increase in their over all number sense.  For many, as soon as they see a connection, it’s like a switch was flipped and they “get it”.

## They heard me. They really did!

Last week, I was ending the week feeling like I may have spent a few days talking to the walls. (You can read about it here.)   This weekend, I feel much better.

We spent the week working on building an understanding of number lines. After making a measuring strips, in groups of 5’s and 10’s, and measuring some things, we needed to start thinking about how a person could skip around on that number line and use it for adding.  When I taped a 100 strip to the board and started asking kids to tell me the number of a certain cube on that number line, it was like a miracle had occurred.  Because nobody could reach the number line to touch each square, and because we’d talked a lot in our math congresses about how we could use the 5 and 10 structure of the paper number line to skip count, they started actually using the number line tool and the skip counting strategy to find the answers I was seeking.  THEY ACTUALLY DID!

Oh, and no big deal, but they were finally counting on from a known number instead of starting back at zero every time.  Seriously.  I’m not even exaggerating to make myself look/feel better.

Here’s the lesson for me:

1. Trust Cathy Fosnot.
2. Sometimes moving forward helps some kids who appeared to not be ready to move on.  I thought I would do a quick number string, sort out who needed some more help with skip counting and counting on, and then make up some Math Workshop groups.  But, low and behold, some of the kids who haven’t been counting on started counting on!  And many who had been fully committed to counting by ones were using the 5s and 10s.

So there you have it:  Valentine’s Day, Winter Electives, and a field trip, all in the same week, and we still moved around on the Landscape of Learning!

## Use the 5’s and 10’s, PLEASE! I’m Begging You!

This week I started a new Context for Learning unit with my grade 2/3 class.  Prior to this unit, we have completed the “Collecting and Organizing” unit, which encourages the use of the 5 and 10 structure to organize and then count large groups of items.  We counted books in our classroom because that was a meaningful thing for my class.  The parent council had recently offered up money to buy more books, so I tied that all together. After that, we completed the “Double Decker Bus” unit, again using 5’s and 10’s and thinking about adding and subtracting.  Simultaneously, my grade 3’s – who were already doing well with the models and strategies taught in the bus unit – were working on “The T-Shirt Factory” unit.

Measuring for the Art show comes next on the recommended order list.  I should be starting “Grocery Stores, Stamps, and Measuring Strips” with the grade 3’s.  However, I really want to solidify this number line business, so I am not going to go forward with that unit for another week…maybe two. I am going to extend the numbers well past 100 in this unit so the grade 3’s are still challenged. Picking the numbers is my job this weekend.

So…here we are, measuring for a fictitious art show, and also thinking that we will run this year’s school art show.

I gave groups of children baskets of cubes in 2 colours and set them the task of using the blocks to measure the papers.

As you can see, there was some great measuring going on!  We even agreed on the measurements!

Despite all the work we have done with counting things in groups of 5’s and 10’s, some of my little friends really can’t stop counting by ones.  I asked myself, “WWCFD?” (What Would Cathy Fosnot Do?) I finally had a serious talk with them about it.  “WHY?????”  I screamed. But out-loud I said, “I know you guys can count by 5’s and 10’s, but you keep counting by 1’s even when we have a lot of things to count.  What’s up with that?”  They gave me the blank stare.  “Here’s what I think,”  I continued.  “I think you know how to count by 2’s, 5’s and 10’s, but you’re not sure you are getting the right answer so you always count by 1’s because you are sure that will give you the right answer. Am I right?”  There was a lot of vigorous nodding.  “What I want you to do is keep counting by 1’s.  But do it after you count by 5’s or 10’s. Do it to double check your work.  But challenge yourself to grow your brain and do it the harder way.  I know this is going to help you feel more confident!” So now we are doing that, except a lot of them quickly realized they were getting the right answers the first time, and it was a lot more efficient to skip count.

After 2 days of this, including a congress when we had the above conversation, I asked them to help me make a number line, organizing the cubes into groups of 5.  Believe it or not, there was magic!  As soon as I had a long string of cubes up on the board, out of everyone’s reach, 15 out of 18 immediately saw the value of using the 5s and 10s.  We worked on related Number Strings for 2 days, and then I asked them to make a number line like I had been making using their own cubes and a piece of adding machine tape.

The group pictured on the left kept counting  by 5s, but when they got to the mis-matched groups of 5, they realized that maybe I am a genius after-all and they should have listened when I said, “Make all 5 the same colour!”

So everyone make beautiful number lines, with mostly iterated units.  We put the cubes away and I didn’t get them back out. When I asked them, the following day, to figure out where numbers like 13, 23, and 33, should go, they did a great job of reasoning their way through the problem.  I can look at these and see some immediate needs I need to address on Monday or Tuesday.  But I feel like we are on our way!

In a VoicEd.ca radio broadcast (You can listen here!) , Cathy Fosnot said she hoped that teachers who were listening would stay curious and keep wondering about the things their students are doing.   For me this is some of her most valuable advice.  Being curious about why my students are doing something, especially if it is something that makes no sense to me, has paid off so many times.

So…there you go, Cathy Fosnot.  You were right again.

## Equal Playgrounds?

Believe it or not, playground equity is something my students have talked a lot about.  At my school, we have a “Primary” playground and a “Junior” playground.  The Primary students think the junior side is better, and the junior students agree, but sometimes wish they could go back to the Primary side to play. I mention this because the context of a community playground and having equal play space is something I know they could relate to.  This week’s problem can be found in detail here.

Trying to solve this problem reminded me how much I still struggle to see and draw a model of my thinking.  I really didn’t have any trouble with those rectangular subs!  But 3/4 of 2/5 and 2/5 of 3/4 sort of messed with my mind.  I wanted to work it out with some manipulatives at school today.  I was going to use colour tiles. Unfortunately, I have this thing called a “full time job” that tends to interfere with my blogging life and I didn’t get to it.  Add to that the fact that we are right at the beginning of the “Measuring for the Art Show” unit and any spare time I have to work things out for my own understanding is being devoted to that right now.  (I’m going to blog about that unit at the end of the week! Or I’m going to work on report cards.  Or maybe both.)

I was able to work this one out with the numbers though. This is my first attempt at drawing a model:

I was confusing myself, so I went back to numbers. After, tried to model it again (on the top sheet.)

Working this problem took me right back to school.  I was forever answering the question I thought was being asked instead of making sure I understood the problem.  Time and again I would have a test returned to, read a problem to see if I could figure out what I had done incorrectly, and discover I simply hadn’t answered the right question. With age comes wisdom and this time I went back and listened to the teacher set up the problem a second time before I tried to solve it.  The first time I thought I was to find 3/4 of the whole and 2/5 of the whole and compare to see if the playground and pavement were equal.  Now I know what I have to ask myself if the question makes sense, and this one did not.  After listening  the second time I knew I was to find 2/5 of 3/4, and 3/4 of 2/5 and compare which is a different question!

Without going into too much detail, I’ll tell you that this turns out to be a common concern amongst my colleagues. Students answer the question (in reading, in writing, in math, on the provincial assessment) they think was asked, not the question that was asked.  I love the way putting the problem in an understandable context, and presenting it in a way that encourages students to really discuss the problem until they understand what they need to figure out, helps us make sure we are really assessing what the students know about math, not about following directions. And I also love that the conferring process can focus on straightening out misconceptions so the student can go forward with a set of skills that help them make sense of problems, not just find answers.

And I love that if I was actually going to teach this unit (I won’t because I don’t teach the grades these units are recommended for) there are some models modelled in the books and I could learn how to draw them before I teach the unit to my class.

## Is it a good deal?

Perhaps the only thing worse than being a teacher’s kid, is being a teacher’s spouse. My husband is both.  His mom and dad were both teachers when he was growing up – and  his dad was teaching at his high schools!  The worst possible fate, right?  His dad was also a principal, but luckily after my husband graduated, and in another town.  So, yes, it could have been worse for him.

He doesn’t remember this happening to him, but I am always experimenting on my children.  I try out new games, and practice my mini-lesson and conferring language, and I read them the books I am previewing for lessons planning.  This week, I decided to give them a break and experiment on my husband.

The next conversation with Cathy Fosnot and Stephen Hurley on VoiceEd.ca takes place tonight.  We were challenged to solve a problem in preparation for the learning we are doing.  I teach grades 2 and 3, and thought this was a problem that would not be appropriate for them, but I wanted to try it out myself.  Here is the problem:

A neighbourhood store is selling 12 cans of cat food for \$15.  Another store is selling 20 cans for \$23.  Which is the better deal?

You can watch a teacher introducing this to some students here.

My first thought was, “Division algorithm”, but I am pushing myself to think in new ways, so I did it like this:

I found halves of each side, until halves no longer made sense.  Then I found 3rds for the first store, and 5ths for the second store, all in order to find out the price per can of food at each.  I feel confident I am right. (Which I only mention because I don’t always feel confident when I don’t check my division with the standard algorithm.  I’m getting better! I teach primary students, and haven’t taught anyone older than grade 4 for a really long time, so division isn’t something I’ve had to think about as a teacher in a really long time.  I have taught basic, beginning division of course, but mostly I’m focused on adding and subtracting – the Number Sense, Addition and Subtraction Landscape skills.)

On a whim, I decided to ask my husband to do the same. He is not a teacher, so hasn’t done any learning about math since he was a kid, unless you count the stats class he barely survived when he was working on his master’s degree.  Here is what he did:

I conferred with him after, and you can see how well that went.  🙂

Here is the interesting part for me:  He has always been good at math.  He plays cribbage too quickly for me to learn from him, and has done so forever.  He calculates in his head really quickly, and can seriously look at numbers and just know (as he indicated in our conference!) He is a social worker and has to do math all the time, but all of it is calculating, and all of it the same week after week.  He calculates mileage, works with money, figures out time sheets for the people he supervises.  He’s had this job for 15+ years though, so he doesn’t ever have to problem solve with math.  Or at least he rarely has to. Mostly, he figured out how to do this 14.75 years ago, and now he just does the same thing week to week.  And he does it every day/week/month – so lots of practice.

The problem really came for him when I asked him to explain.  He was so irritated with me for pushing him to talk about his strategy, how he knew what he needed to figure out, why he needed to divide. He had trouble putting his thoughts into words, and that is not typically a problem for him at all.

This is one of my favourite things about teaching math now:  I’m not just training kids to do math tricks.  I’m teaching them to be math thinkers, and math communicators, and math users.

(Update:  Click here and you can listen to Cathy Fosnot and Stephen Hurley talk about the math in this problem, including my solution.)

## WWCFD: 3

I already blogged earlier today, (here) but I want to talk about another amazing math moment, so here I am again.

A few weeks ago when I went to a Cathy Fosnot learning session, someone new to her Number Strings called her work magic.  Specifically, seeing how one problem helped solve the next problem and the next seemed like magic.  He said something like,  “Now that I see what your doing with your magic, I can figure out this problem.”  She countered by explaining that it isn’t magic, it’s math!

Problems don’t exist in isolation.  The connections we find in math  help us solve problems. We can use familiar and known problems to solve unknown problems.

Because I am just like Cathy Fosnot, I had a similar moment this week.

We (me and the grade 3’s) started with 3+6 = 9.  You can see where we went from there!

See that note on the side?  After 56+43, One of the students said, “That’s (pointing to 3+6=9) spoiling this answer. It has 6+3 in it!”  I got to say, in my best Cathy Fosnot impression, “I’m not spoiling it!  That’s math!  Math is all connected and knowing how to do one problem helps you with so many other problems!”  And then we talked about a bunch of other answers, and made some connections and found out that math is actually kind of magical.

A few years ago, long story short, I figured out that my students were not making connections in math.  They were thinking about each unit, each skill, each day in isolation.  I started to explicitly talk about connections between big ideas, strategies, models, numbers, etc.  I feel like it really pays off and helps to build understanding.

## Guided Math: part X (I’ve lost track)

This past week, predictably, was crazy.  Halloween in the middle of the week?  Seriously.  Why even bother having school that day?  I know people think it’s important for kids to have good memories from their childhood associated with fun things, like a costume parade on Halloween at school.  But I think we can all agree it’s gone too far.

It’s also been a weird time for our math class.  As you may recall, 4 of my grade 3 students were my students last year.  Two of my grade three students were in a 1/2 split, and the rest of my class are grade 2 students who are all new to me.

My grade 3 students are solidly moving along as a group.  They make a beautiful cohort – teaching important things to their younger, less experienced classmates. Up until now, I was satisfied with how they were helping to scaffold the class through Number Talks and Number Strings.  I was happy with what they were teaching the grade 2’s about communicating their mathematical thinking.  About mid-week last week, the tide shifted.  I started to feel that the grade 3’s were dominating the conversation too often.  They were figuring everything out way before the grade 2’s. If I plotted the 2’s and 3’s on a Landscape of Learning, they were in two very different spots.  So different in fact, that I felt I had to do something about it.  That something, I decided, would be to split the class into two entirely different Context for Learning units.

Now, I have taught split grade classes for most of my career. I have, many times, had the kids in one grade working on something different from the kids in the other grade.  In math, this usually looks like one grade continuing on in a Context unit that we started together, while the kids who are not ready to go on work on something else to help them solidify the part they are A) ready for, and B) required to learn thanks to the curriculum. You’d see this, for example, when it comes to multiplication and division.  3’s and 4’s have a similar starting point, typically, based on their needs.  But 4’s need exposure and practice with dividing that 3’s don’t.  To be clear, if I have some 3’s who are developmentally ready to move forward, and keen to move forward, I would take them along on the trip.  But if they need to hang out at “multiplication up to 7×7” for a while, I let them.  This would probably include them repeating some games we had played, or something like that.

But this time, I was feeling strongly that I needed to be pushing both groups, not just letting one group sit in one place for a while.  Here are two of the Number Sense and Numeration Big Ideas for Grade 2:

• demonstrate an understanding of magnitude by counting forward to 200 and backwards from 50, using multiples of various numbers as starting points;
• solve problems involving the addition and subtraction of one- and two-digit whole num- bers, using a variety of strategies, and investigate multiplication and division.

• demonstrate an understanding of magnitude by counting forward and backwards by various numbers and from various starting points;
• solve problems involving the addition and subtraction of single- and multi-digit whole numbers, using a variety of strategies, and demonstrate an understanding of multiplication and division.

My grade 3s have mastered the grade 2 concepts.  (As they should have last year by June.)  My grade 2’s, however, are still needing a bunch of work on this. (As they should until this year in June.)

So what was I going to do??

Well, I started two Context units at the same time. Seriously.  In the same week when Halloween was on a Tuesday.

As part of my evolving thinking about Guided Math, I thought I could have one group working independently each day, while another group was mainly spending time with me and getting my attention.  So far, it’s been chaotic.  But I feel like we are accomplishing what I want to accomplish.  I’m really wishing I could do more observing and conferring, so I will be addressing that in my planning this week.  I don’t want to be occupied with whole-group teaching and missing out on the conversations kids are having while they do their work. I did throw in the towel and have a “Fun Friday” during math because I felt that instead of moving on I needed to regroup.

Grade two’s are still working on unitizing single digit numbers and using the 5 structure to help them add.  They are working on the “Double Decker Bus” unit.  We ran into some problems because I am a paper-saver and had given them one day’s work on one side of a page, and the next day’s work on the other side.  I know: rookie mistake.  Even though I clearly told them and showed them were to start, 3 out 5 groups tried to do the wrong side.  Learning experience for all of us!

Grade three’s are working on the same things, but using the “T-Shirt Factory” unit to move into hundreds, using the 10-structure, and building a deeper understanding of place value into the hundreds.  They need more help with the use of a T-Chart to organize information.

I congressed with both groups on “Not-So-Fun Thursday!” as I am now calling it.  One group was working  on something while I congressed with the other.  I think I’ll keep this.

Moving forward, I am going to continue in both of these units.  After Fun Friday, I discovered that there are still some counting issues for grade 2s. I think they can have a “Count-Everything-in-Sight Monday” or maybe a “”Put-All-These-Numbers-in-Order Monday” while I get the 3’s started on the next part of their unit.  Then on Tuesday Grade 3’s will be able to work independently while I get the two’s started on their unit, and then I can wander and confer.

And it is going to take me the rest of the day to figure out how I can work Number Strings and Talks into it all.  Cause we have different needs there, as you probably guessed.

Thankfully I have lots of Halloween candy to get me through!

It’s such a big week in math that I’m blogging twice!! See the other post, about a Number String, here.

## WWCFD

Today was the day that I was going to “do something different” based on all the learning I did with Cathy Fosnot last week.  I sat down carefully on Sunday night and planned out the Number Strings I wanted to do each day this week.

I started with this goal:  Guide my students to discover the Big Idea of “Part/Whole relationships”.  I feel like this is one thing we can work on in our Number Talk time that will help everyone understand numbers a little bit better, and help us understanding adding and subtracting.  I also feel that too many of my grade 2s are still having trouble counting on from a whole number, and are struggling with hierarchical inclusion.  There’s is too much “counting 3 times” and starting at 1 every time something is counted.

I started with 4+3 = on the board.  Through conversations, we ended up with this:

So far, so good, right?  One of my grade 3 students said he’d found the double then added in the “extra” one.  Right there I thought this is the difference between Number Talks and Number Strings.  I could have written more problems that let everyone practice the “find the double” strategy.  But I was really looking for the “part/whole relationship”.   We started talking about other ways we could make four.  I made a list.

Here’s something I have decided:  The goal doesn’t have to be completed in just one day. I have the whole week to explore part/whole relationships.  And maybe it’s stretching it out over a few days that really helps the kids to see some ideas.  I could have easily turned this into a full 1 hour conversation.  But after 10 minutes people start to get restless and stop really listening, so I ended it.  We’ll pick it up again tomorrow.

One of the things that really struck me in Cathy’s lesson on Saturday was that she displays all three parts of her conversations (the question, the model and the conjectures) at once.  One is not behind the other.  She said that this way kids can see all three and each helps to strengthen the other.  This is one of the main things I want to really do this week (and beyond.)  I am going to start to do these talks on the large white board instead of the small one so I have room for everything.  I also, as you may have already thought when you looked at my pictures, need to make sure I am organizing this better as I go.  But I’m okay with admitting this is going to take some practice.

math

## PD Saturday

A few years ago, I read a book by Burkins and Yaris called “Who’s Doing the Work?”  It’s a fabulous book.  I now follow a learning community they have created on Facebook.  The other day, this photo was posted.  It was captioned:  We had such a wonderful time filming next generation shared and guided reading lessons this week! Stenhouse Publishers is accelerating the production process so that we can debut the videos at our full-day workshop in Hurst, TX on November 3rd! We are so excited! Come see! https://buff.ly/2gsHVgd  (I pulled that directly from their Facebook page.)

This photo has been alternately bothering me and making me feel vindicated.  You know when you watch a demonstration video and the whole time, instead of thinking about how great the teaching is, you’re really thinking, “There’s no way that could happen quite like that when there are 23…25…37….kids in the class.”  Well, here’s proof that the videos aren’t actually set up in a “real” classroom setting.  I mean, I already knew that, but it feels good to have it validated.

I spent a few days this week learning from Cathy Fosnot. What I mean is Cathy and I hung out and talked about math.  There were about 25 other people there on Tuesday, and maybe 125 there today, but I still feel like it was me and Cathy getting together to talk about math.

Cathy had a variety of videos to show that showcase her work, and to help me (Ok, “us”) learn from her methods. One of the very first things I noticed was that there was so much background noise.  There were actual other kids in the classroom also having math discussions.  Cathy was talking to a small group of kids while the rest of the class was also working on their investigation.  This is how it sounds in my class too!  I am chatting away with a few kids, and brilliant things are happening, but I’m also using my peripheral vision to make sure naughty things aren’t happening, and once in a while I have to sort of tune out of the conversation, or say, “Hold that thought…X!  SIT DOWN AND DO YOUR MATH!!…ok..go on.” That’s reality.  What this showed me is that it’s okay that sometimes I am giving a group less than my full attention during a conferral.  That doesn’t mean great things can’t happen in my room.  It does mean I need to remember to turn on the voice or video recorder when I sit down for an important conferral because I just might miss a bit of it. It also showed that brilliant math conversations happen spontaneously in lots of math classrooms when the situation has been properly set up.  It doesn’t just happen with a hand-picked group of children in a quiet one on one setting, which is then edited to highlight the moments of brilliance. I feel like I am probably going to be able to pull together some examples of how this has happened in my own classroom in the past few weeks, and I’ll be able to do it easily.  (But I will probably have to wait until next weekend because I was away all day and my house shows it. But I might also decide to just throw out all of our dishes and clothes and just blog all day tomorrow.) My point is, it’s happening in my real life!