I don’t know what to call this

I’ve started writing a reflection on my week a few times now and then think, “I don’t know what happened in math this week!”  It’s not exactly true. If I really concentrate, I can remember, and even make some assessments about our week. In fact, I did that as I was planning for next week.

However, there are bigger things going on in my class this week that take the forefront in my mind. We had some successes with some behaviour management systems. We had some tears when kids were told they were moving to another class because our class was too full (tears from the leavers, and the stayers!) We were excited about our worms. We did some art. And we really practised walking down the hall when I had anticipated practising counting and sorting the doors in our school. 

So, our math lessons this week we’re not a huge spectacular wonderful set of lessons I want to blog about. Math was good. Math was fun. And I learned a whole lot about my learners. However, there was just a lot more going on this week that is on my mind.

I was at the grocery store this afternoon. There was a man whistling a beautiful tune. Everywhere I went I could hear him.  I could even hear him when he was a few aisles over from me. At one point our paths crossed and he smiled and said, “Excuse moi.” I answered in English, “No problem.”  But as I walked away I realized I knew how to answer him in French. I know how to respond to him in the language he had used to speak to me. And yet I did not naturally do that. I had answered him in English before I even register that he was speaking to me in French and I could answer him in French.

That is where I am with my math teaching on this Saturday. I am naturally thinking about all the obvious big successes that we had that were indirectly related to our math. Everything we did is improving our math classes, and our classroom community, and is therefore important. It is just that the math is not naturally at the forefront of my mind today.

I am diving into one of the Young Mathematicians at Work units this next week. I should have more to write about then. But the truth is teaching is all a juggling act both in the doing and the thinking.  There are so many decisions to be made. I can never just concentrate on curriculum decisions. I have to also think about decisions that affect my students socially, emotionally, and in their physical well-being. 

So, in summary, I taught math this week. It was good. I’ll teach it again next week.

Guided Math, math


Like I already told you I was going to (here), I started talking about estimation in my class last week.  We read a book called Great Estimations by Bruce Goldstone, tried out a few of the problems he posed, and then tried some of our own.

I had prepared some bags of stuff for us to estimate in advance. For each item, there were two bags: one had 10 of the thing in it, and the other had an unspecified number of the thing in it. Here you can see I used Mike ‘N Ike candy and mini marshmallows. I also had popcorn kernels, elbow macaroni, and Cheerios.

I gave a set to each table, and asked them to estimate.  They also had a piece of paper they could record their thinking on.  At the end, we shared our estimates.  We did not get an actual count of the items.  This was on purpose.  I wanted them to feel like their estimate was good enough.  Mostly their estimates were in close proximity of each other, and I complimented them on that.

The following day, I have them 2 bags and an item.  They were to put 10 in one, and count as many as they wanted for the next. I gave them Lego, glass beads, counting chips and colour tiles.  Most groups put around 30 in the bag. Just we had the day before, they traded bags with each other until they had an estimate for everything.  Then, we shared our thinking, and confirmed the count for everyone.

One group thought it would be funny to put over 100 counting chips in their bag.  They were each counting out 100, rather than working as a team, so we had a good conversation about that. When another group got that bag, they were sure it was impossible to estimate. Imagine their surprise when their estimate was within 5 of the actual number!  That group was composed of grade 3 children who are still adjusting to the idea that they are the older students in the class now, so I think this was a good confidence booster for them.

This is what I discovered:  they are mostly pretty good with recording their thinking so they can share it later.  We do need to do some work on labelling.  We also need to work on each person contributing to a group assignment or task.  In each group there was a clear leader who railroaded, or attempted to railroad, the rest of the group.

This is what they discovered: they really were training their eyes (as it says in the book) and their estimates were closer to the actual counts as we went on. In some groups, they discovered the need to label.  They had written a number, say 34, but didn’t label it as “colour tiles = 34”.  When it was time to share it was tricky to share! I like that they discovered this on their own.  I know I will need to talk about this again, but I’d say about half of them were able to identify this as an important thing to do going forward.

Using the website as inspiration, I am going to create some more provocations for my students to explore.  I want to add this as an activity for them to complete during Guided Math.  (Yes, I am still trying to figure that out!)

My hope is that these estimations activities, revisited throughout the year, will help my students develop a stronger sense of numbers.  I think they will develop a better understanding of magnitude, and that the numerical reasoning skills will improve.

Finally, here is an article from Math Solutions that has had me thinking about all of these things.

math, Number Talks

Number Talks: Week 1

I hadn’t decided yet if I wanted to start off by making this sound like I am a genius (which I totally am!) or if I was going to list all the sources of this idea and talk about how they converged into this seemingly-original idea.  But then I listened one morning this week to a podcast from Derek Rodenizer on voice.ed radio.  (You can listen to it here.  It’s only 5 minutes!)  He posted this graphic later on Twitter:

I think you can see the original Tweet by clicking on the picture.  Sorry, I can’t figure out how to post it!  

That podcast made me realize that this Number Talk idea was just that – an example of how sharpening my pedagogical sword gave me an idea that wasn’t/isn’t truly mine but is me knowing a bunch of stuff and then putting it all together and coming up with something different.

The “Introducing Multiplication” unit by Marilyn Burns starts with an activity where students are asked to work with partners to make posters about numbers.  Specifically, students are supposed to write down things that come in 2’s, or 4’s or 7’s, etc.  So this is partly that idea.  If you look on Pinterest under “math activities” you’re sure to see art projects students have made where they have written down all the ways to write a number, or what the number means to them. (If you don’t know what I am talking about, look at this.) This is partly that idea too.

On the first day of school, I told my new students I was going to write a number on the  board and they were going to tell me everything that number made them think or remember.  I then talked to them about how we put our thumb on our chest to show we have an idea, and that they could take as much time as they needed because math is not a race.  I wrote a 2 on the board.

I am not exaggerating when I say we talked about this for probably 15 minutes. Here is our result:


I have erased student names before posting here!  “(Blank) has 2 kittens.” used to be attributed to a specific student.  

It was so interesting and, I thought, successful that I couldn’t wait to do it for the rest of the week.  Here are our results:

I do not think it is a coincidence that we got more information for 2 and 5 than we did for 23.  This is a grade 2/3 class and most of the ideas on 23 came from the 3’s. Also, there aren’t a lot of every day things, like bike wheels and toes, that come in 12’s and 23’s.

There were some common themes:  each day they wanted to talk about someone who was the age that matched the number.  They know people who are 2, 5 and 12 – mostly siblings.  But 23 is too young to be one of their parents, and too old to be a friend or sibling (for most.)  When we talked about 23 as an age, it was clear they don’t really know what 23 years-old looks like. They guessed that I am 23, which I totally look like I am but I am not. They then guessed that our principal is 23, which is what she actually looks like (no this is not an evaluation year for me.) We settled on “Justin Bieber and college students” after some discussion.  Everyone finally agreed that a 23 year-old is a “young grown-up”.  But I think many of them are still not 100% clear on this idea.

My original goal was to start using Number Talk routines – mainly the one with the thumbs up instead of hands up.  I also wanted to start talking about them building on each other’s ideas, which they did.  I was busy building routines, not taking notes.  But I still feel like I got some important information from some of my new students.  This will help me going forward.  I had originally planned on doing dot-number talks for the week.  I have already prepared slides to use for this using Smart Notebook software, even though I do not have a SmartBoard in my class. I kind of chickened out because the tech-gremlins have been busy at my school over the summer and things were randomly not working.  I didn’t want to start off my school year muttering curses at them while repeatedly jabbing buttons.  I’ve saved that for the coming week just to give myself something to look forward to!

To read more about how a dot number talk can be used to start the year, check out this great blog post!


My thoughts on EQAO: Episode 1

“Where do these norms come from anyway?” That’s what Cathy Fosnot said in response to a question I asked her on voice.ed radio. I wanted to know what to do to help students who were well below their peers on the Landscape of Learning.  (You can listen to the whole thing here.)
I was thinking about this again this past week when EQAO math results were released to the public. Spoiler: they aren’t great. And now everyone is in a snit. Blame is being placed on the teachers, the “new” way of teaching math, the curriculum and even the test itself.
I did a lot of reading this summer about developmental progression of the acquisition of math skills. And you know what? None of them strictly says, “By such and such age kids need to be able to do this….and that…” Instead, the research has shown that first this skill develops, and then that one, and as problems become more complex the student folds back (as Alex Lawson calls it) to earlier strategies and skills they trust.
When my children were small, I carefully monitored the expected milestones for physical and cognitive development. My daughter met each milestone at exactly the right time. Rolling over is supposed to happen at 5 months, and sure enough within a week of her 5 month birthday, she rolled over. Same for walking, running, accepting solid food, etc. When at age 18 months she did not have 20 words in her vocabulary, I signed her up for a speech assessment. Those milestones are normed. Lots of work has been done, lots of comparisons have been made, and now we know it is developmentally appropriate for 5 year olds to stand on one foot for 10 seconds or longer, and that they could be doing it before 5, but if they are 6 and can’t we need to talk to the doctor about it because something is not right.
But none of the math research seems to be that specific. I can’t look at a student and say, “Today he turned 8, in the next few weeks fractions are going to make sense to him.” The math skills develop sequentially: the child learns to add 1 digit numbers, then 2, etc.
But large scale testing, such as EQAO, isn’t like that at all. Instead, we test kids when they are in a certain grade. At times the difference between the oldest child in a single grade and the youngest can be a whole year. My daughter turned 6 in January, but another child in her class won’t be turning 6 until December. But someday (3 times to be exact) the two of them will be expected to take their EQAO on the same day. They are not marked on their achievement as it relates to their age. This test assumes that every grade 3 or 6 or 9 student is at the same developmental stage and should be tested in exactly the same way with the same tests and same testing conditions. Maybe this is closer to true when they get to high school, but I feel like I have a lot of anecdotal evidence, collected over 17 years of teaching grade 3 students, that would suggest grade 3 students are definitely not all at the same place developmentally in a lot of different areas.
So where do these norms come from? Well, in this case, they aren’t norms. They are raw scores that reflect the number of right and wrong answers a child gave. They say, “This child is meeting the standard for a child in this grade.” Or is not meeting the standard. Or is nearly meeting the standard.
I think the problem lies in the interpretation. We jump to the conclusion that a kid is behind, lagging in skills his peers have. Most teachers would be able to tell you this sort of information about the students in their class (and do – 3 times a year in massive essays about students a.k.a. report cards.) Hopefully all of us are getting better at identifying exactly which skills to work on to move individuals along the landscape or continuum.
When I look at the test results for my class last year, it will be too late for me to do anything for those exact people. They are in somebody else’s class now. But I can see that all or most struggled with this or that and examine my own practice to see what I can do to perhaps avert this result for the current group.
However, how well my students are doing, whether or not they are meeting grade level standards, is only one piece of the puzzle. I’m much more interested in what they can do, and what skill they need to develop next than I am in comparing them to all the kids in the province. My job is to teach the 20 kids in front of me. I’m just going to worry about them.