Then again…

I taught 2 fractions lessons, and they went really well.  I came away from them thinking, “This is going so well I could probably stop right here!  They get this!!!”

And then we did a few things, like had a long weekend, and when we got back to our math I realized they didn’t have it after all.  I mean, they probably could have done a few worksheets, and probably would have coloured them in correctly, but I am not much of a worksheet teacher.

Instead, I asked them to do some drawing. I wrote this on the board.  A decided to just give them paper and set them to it for two reasons:  1)  I thought they thought fractions were easy-peasy. 2) I wanted them to do more of the thinking that I did.

I wrote this on the board:

The bottom line, circled in green, was there as a challenge for anyone who actually did find the work easy-peasy and needed a challenge.

The little people were my feeble attempt to get them to focus on the math, not the art.  (When will I learn?!  Everything is art, right?)

Here are some examples of what happened:

Most did not take the challenge.  It was too challenging.  Fine. I can live with that.  We haven’t done that much work with equivalent fractions, so it makes sense.

The picture with the  pink dresses belongs to a child who wasn’t sure how to sort out the eye issue.  He kept repeating, “I just don’t get it.” and he kept repeating the question: 1/4 blue eyes. Finally I said, “Well, you know, 1/4 have blue eyes, and the remaining 3/4 have eyes that are a different colour.  Like green eyes, or brown eyes.”
That was all it took.  I felt like that was a good prompt that didn’t give away any of the answer.  I know him as a mathematician, so I knew that what he was really trying to say was, “This question doesn’t make sense to me.” And I knew that he probably didn’t need a math hint.  Luckily, the first thing I said to him, that green and brown are also eye colours, happened to be the thing he needed.  If only I was always this lucky!

As a follow up, I sat everyone on the carpet the next day.  We were in a big circle, and I put 4 people in the middle.  I started describing them using fractions.  “Half of these people are boys. 1/4 of them have a pink shirt.  2/4 of them have long pants.”  Then I invited others to come up with fractions to describe the group.  After a few, we switched to new people in the middle.  After 4 or 5 things were said about this group, we spotlighted a different group, and so on until the whole class had been in the middle once.  They started to get more creative with their noticing as we went along, and after the first group, I didn’t give any more answers.

I sent them back for more drawings.  I gave them three options, and told them to pick two.  Some picked all three.

Draw a group of people.

1. 1/2 are tall.
2. 1/3 have hats.
3. 3/4 have long hair.

They did OK.

My point:

Here are the grade 2 math expectations that mention fractions:

• –  determine, through investigation using concrete materials, the relationship between the number of fractional parts of a whole and the size of the fractional parts (e.g., a paper plate divided into fourths has larger parts than a paper plate divided into eighths) (Sample problem: Use paper squares to show which is bigger, one half of a square or one fourth of a square.);

• –  regroup fractional parts into wholes, using concrete materials (e.g., combine nine fourths to form two wholes and one fourth);
• –  compare fractions using concrete materials, without using standard fractional notation (e.g., use fraction pieces to show that three fourths are bigger than one half, but smaller than one whole);

I felt like we had done that on the first day.  I felt like all of my grade 2s and most of my grade 3s were good with this.  Except when I looked closer, especially after the second time around, I realized they didn’t understand “the relationship between the number of parts of a while and the size of the parts.”  I mean, they seemed to get that when it came to fractions of a whole, but NOT for fractions of a set.

Here are the grade 3 expectations that mention fractions:  (I am looking at number sense only.  There is related stuff when you look at time and money.)

•  divide whole objects and sets of objects into equal parts, and identify the parts using fractional names (e.g., one half; three thirds; two fourths or two quarters), without using numbers in standard fractional notation;

I feel like we have this now.  If I took them outside and said, “Fill this bucket half way up with water.”  They’d do it.  And if I said, “Do you want 1/4 of the pizza, or 2/4 of the pizza?”  They could give me a reasonable answer like, “2/4.  I am starving!” or “1/4. I have other stuff in my lunch.”

 

Guided Math: Where to start

I’m going to write tonight about September.  In part because my brain is already thinking about how I will do this whole teaching thing better next year (I think that every year.) and in part because I don’t want to share too many more things that will alert everyone to the fact that I kind of got hung up on a few concepts earlier this term, leaving us scrambling to finish a few things at the end of May. *sigh* (This happens every year, and every year I think, “I will not let that happen again!” but then we get waist deep into learning something that I think is really important for us to learn really well and I keep saying, “I’m just going to do this for one more week.” and then at the end of May I am covering something like probability by teaching math all day every day for a while and…well…you’ve probably done it too.) (But, honestly, when we spend a whole day on a certain concept, the learning can be pretty magical too.  And something like probability is fun to do that with.)

But…back to where I wanted to start.

Guided Math.

After doing this for one week in my class, you may recall that I thought I’d try it for another.  However, as I sat down to plan out that week, I realized there were way too many things that I needed to put into place to make it successful.  See, I will be teaching many of my grade 2s as grade 3s next year.  I felt/feel that if I go about it all haphazardly I might be setting us all up for some trouble in the new year.

I had a table set up where the students were to take a survey and create a graph.  We have done this so many times over the course of the year, I assumed they could do it independently over the course of a few days.  I gave them the topic: favourite holiday.  I gave them the paper and graph templates they would need.  I asked for their completed graphs on Friday.  Now, I feel I should say that I was monitoring what was happening at that table.  I really was!  So I know some surveys were taken and some graphs were made.  Here’s an estimation question for you:  Approximately how many students do you think actually had a graph to hand in to me on Friday morning?  If your answer is near 2, or roughly 10% of my class, then you are correct.  They had parts and they had papers and they had apologies and excuses.

Every student already has a 2-pocket folder for their writing.  I laminated them last June in preparation for this school year, and they have lasted the school year.  (Hooray!)  ON the back, every child has a personal word wall.  I have labeled the pockets “drafts and ideas” and “work in progress”.  It’s a good system, if I do say so myself.  This June when I am making my red writing folders (because I love how it sounds close to “Red Riding” haha) I am also going to make some math folders.  I think that I will keep the word wall, and use it exclusively for math words.  Actually, it is highly likely I will do that.  (see…probability…it’s everywhere!)

1 system, used 2 different ways will = success!  I am sure of it.  I think a way to keep track of their papers from day to day will really help them start and finish something, and give them something they can turn in at the end of the week (accountability).

I am going to borrow another writing-related idea.  I think that at the end of each week I’d like my students to write a reflection about their learning.  I am going to give them a math journal….let me just stop there.  I have seriously tried this before and hated it. But I am thinking that I have evolved a bit.  I think the written reflections will be useful in helping them consolidate their thinking.  I also like a written record they can refer to and see growth.  AND it will give me some interesting anecdotal comments when it comes to report card time.

In the book “Making Thinking Visible” by by Morrison, Church and Richart, there is a thinking routine called “connect, extend, challenge”.  I used it a lot in math last year with my grade 3/4 class, and have used it somewhat with my grade 2/3 class this year.  I discovered that having students find the connections between math ideas, and within math ideas, was really valuable.  So, if I teach them this routine early on and have them use it to write in a journal, I think we’ll get some interesting stuff.  Basically, they need to thinking about how the learning they have done connects to other things they have learned, then try to extend that learning, and finally talk about what is still challenging them.  Here’s how it might look. Pretend I am 7 and we have been making graphs all week.

Connect:  This is like when we took surveys about things people like last year in my other class.

Extend:  I could use it to find out what people want to play at my birthday party.

Challenge: I want to know how to organize my work better.

The challenge part is a big challenge for the little people, so we might not add that in until after Christmas.

And that will be easy to do because I am going to be completely on track and following my long range plans perfectly.

That’s where I am now with Guided Math.  I have other thoughts too, but I am not ready to write them down yet.  I need to keep exploring this idea.

#notabookstudy: Constructing Fractions

OK you guys!  I am so excited about my math class on Friday.  Perhaps too excited??  IMPOSSIBLE!

First, I’ve been thinking a lot more about the learning that takes place when students develop a model on their own.

Second, last year I worked a lot on the open number line with my grade 3/4 class.  I thought we were doing so well!  Then we started working on fractions and they didn’t know where 1/2 fit on the number line.  They could identify 1/2 of a set, or half a whole, but 1/2 of a distance was too much. I was going to say “at first”, but I never really felt like they owned that piece of information.  They just sort of borrowed it from me for a while and then silently put it back on the shelf, I think.  Though this is giving them some credit for putting things back where they found them, and that might also be misplaced. So…this year I wanted to add fraction of a distance to our study of fractions.

Today I wanted to start talking about fractions.  Yes, this is a bit last minute.  (I’m not going to tell you the whole story of why this happened.)

So how to develop the context and ask everyone to develop their own model?

Typically, I would gather the class, show them a half, and them let them go make some halves. Then we’d do fourths and thirds, and then we’d try out other things that make kids happy like 5ths, 6ths, etc.   I would do fractions of a set one day, then fractions of a whole another day, then practice them a variety of ways – sometimes alone and sometimes side by side. Then we’d make some connections to half of dollar, or half of an hour, and then we’d be done with fractions. We are a grade 2/3, so equivalent fractions would show up in there, and so would mixed numbers, but that is not our focus.

But new-me wanted them to develop more of this on their own.  All of it, I hope.

Students in my class sit at tables.  There are 4 of tables, so 4 groups.  I put colour tiles on one table, pattern blocks on another, LEGO on the third, and snap cubes on the last. I told them to go play with the blocks for 5 minutes, and then we’d start.  It’s May, and we’ve used the math tools a lot, but they seem to still need to just play with them for a few minutes every time.  If you can’t beat them, meet them where they are, I always say.  Or at least I say that sometimes.

After 5 minutes, I had them all join me on the carpet.  I wrote 1/2 on the board. (I had 1 on top of 2) “What is that?” I asked.  I got a variety of answers.  The 4th or 5th student called it “half” but others called it 1 divided by 2, 1 out of 2, a 1 and a 2, and 1 = 2. I decided to give it to them.  I wrote “half” under the fraction.  “Oh, half, right,” a few responded.  “Now, go to your table and use the tools I put out for you to show me half.”  Away they went.

Here are some responses:

I was surprised at the number of students who weren’t sure what to do.

One student had this:

I asked, “Is this half?”

She said, “I’m not sure.”

I turned to her neighbour who had this:

I asked, “Is this half?”

He said, “Yes.”

I asked, “Can you explain to (her) how you know it is half?”

This was really interesting.  He kept saying, “Well, it’s half. See?  It’s half.”  Then after a few repetitions for this, he used his hands to separate the two halves and said, “See?  Half are here and half are here.”  He’d separated them by colour.  He wasn’t sure how to explain it, even though he knew he had half.

I asked her if she could see it, and she could.  So I challenged her to make her own.

At the pattern block table, I took this picture:

“No,” the student said.  “You have to take the picture from above.  Then people can see that half is  yellow and half is red.”

“What about this one?”  I pointed to 2 red trapezoids.

“It’s cut in half by that line.”

Here was a very interesting one:

When I asked him to explain to the class, he said, “Well I have 4 blocks.  2 are over here, 2 are over here, so half are in each place.”  I was really surprised by this because I thought he was showing me two models: one half orange, half red, and another that was 2 halves making a whole. I explained this to the class and they got it both ways.

His way: half the blocks in one place, half in the other.

My way: 2 models, each show half.

One of the people at the connector cubes table had this example:

I use the Show Me app and the Apple TV to project pictures during an activity like this so we can congress what has taken place.  Sometimes I write within the app, and sometimes, like in this picture, I write directly on the whiteboard.

He had set it up two ways. First he said, “Half are here and half are there.” Then he changed it and said, “I mean half are yellow and half are something else.”  I think he was surprised when I said that each was a different way to show half and he’d been write two times with two different answers.  They are used to me saying this kind of thing, but I think he thought he was wrong the first time.

After we congressed this, I sent them back to their tables.  “Now that you have seen some other models, go show me 5 ways to make half.”  And they did.  I mean, AND THEY DID!!!!!

We had to skip math on Thursday because of an assembly, so I decided to do double math today. I told them that after recess I’d have different blocks on their tables and they could use a new tool to show me half.  They came in and got right to work.  That’s a lie.  They got to work eventually.  But they all showed me half in a few ways with a new tool.  Photographic evidence:

One child had this, which she explained like this, “When my mom says, ‘Eat half.’ this is how much I would eat.”  I was happy to see that connection to fractions in her real life, even though she didn’t quite understand that each of her piles should have an equal amount in them.  In reality, who counts every exact pea?  But I think that might start happening, and I should probably call her mom and apologize in advance.

I then read them a great book called, “The Cookie Fiasco” by Dan Santant.  It’s part of the “Elephant and Piggie Read” series.  It’s funny!  Four friends, 3 cookies, how can this be solved? I read up to the part where the friends are completely befuddled about how to solve this problem.  Then I gave them 3 square cookies made of paper, and asked them to figure out what the friends could do.  In the book, the nervous hippo had already broken the cookies in half, but there still weren’t enough cookies for everyone.  So, all of my people cut their “cookies” in half. Most of them cut them again, and within a few minutes everyone had figure this out.

Congress:  “What did you find?”

Everyone agreed that everyone got 3 pieces of cookie.  I asked, “Ok, so how much cookie did they get.”  This took some discussion.  I had to reassemble them into wholes, then move them around until someone said, “Well, they are quarters.” and then we counted by quarters, “1/4 + 1/4 + 1/4= what?”  Finally someone said, “Well, it’s 3 quarters.”  and the lightbulbs that flashed on above all the heads nearly blinded me! It was awesome!  They got it!  I mean THEY GOT IT!!!

Then I showed them how some of our classmates had cut the “cookies” into squares and some into triangles and some into rectangles. It took a bit more discussion, but we all saw how they all ended up with 3/4 as the answer to how much cookie each friend got. I told them they could put the cookies in the trash, and about half of them put the in their backpacks instead because sometimes trash = more important to take home than our actual work or, you know, report cards.  You’re welcome, Moms!

Finally, fraction of a distance  Last week in gym I asked everyone to run halfway across the floor and stop.  It was trickier than you might think, especially given the fact that there is a giant black line halfway across the gym. But then I said, “From there run halfway to the wall.” and this time there was no line to signal halfway.  Some of them did it, and some of them didn’t.  We ended our super day of math by going outside into the glorious sunshine.  I had two hula  hoops and asked kids to stop halfway between the two.  More of them did than didn’t.  Of those that didn’t, most overshot the mark by a good amount. We’ve obviously got some work to do around fractions of a distance.  I’m thinking they need to do it in a place where they can’t really run.  I think they are going too fast and 1 meter into the full out sprint they have forgotten they are supposed to stop halfway, then one classmate stops, or they see the end goal, and something deep inside them says, “Wait? Was I supposed to stop somewhere?” and by then they’ve gone more than half way.

Tuesday we’ll do some work with writing down fractions, looking at the models and pictures and writing the number.  Then on Wednesday we start EQAO with the math section and I am super paranoid about being accused of cheating so I don’t teach math during the 2 days when we are doing the math sections (which is where we begin this year.)  That gives me some time to think about a few more ways to connect their  fraction learning to their past learning.

Guided Math: #2

I started out last week with a plan to do Guided Math for one week.  I KNEW I would hate it, but that I might be on my way to hating it less.  So, really I should be proud because MISSION ACCOMPLISHED!

We made it through the week, with just one interruption. Junior track and field events on Friday left us with some extra students for the day.  They were grade 3 students from a 3/4 split. (Primary track and field is another day.)  Because of this, our routine was quite out of whack.  Friday was supposed to be the day that my class and I sat down to go over, in a congress-y kind of way, the math that we did this week.  I will have to do this on Monday.  I think that my class actually liked the Guided Math activities, but I am anxious to hear their thoughts and ideas.

Highlights:

• I had 10-15 minute rotations going, with one grade staying with me for about 40 minutes while the other grade rotated through 3 activities. I think the timing was right.  Keep in mind that I have a grade 2/3 split, so though our stamina would probably allow for them to stay with the activities longer, our wiggly butts were happy to move along after 10 minutes.
• If I were to start this in September, I think a math folder would be necessary.  I had them putting away work in their cubbies at the end of the rotation, but a folder would have kept it all more organized and easier to find the next day.
• If I spent September training the class, as I did during our literacy block, they would know that they need to work quietly and not interrupt the group meeting with me.
• I met this week based on skills I wanted to teach. Grade 3s needed to work on multiplication, and I wanted my grade 2s doing some more addition/subtraction work.  I had different curriculum expectations to focus on.  This week, however, I am going to be teaching fractions to everyone, and I think my groups will be divided based on abilities rather than grade assignment.
• Yes, you read that right. I am going to give it another go this week.

Over all, the thing that I continued to reflect on is Guided Reading.  I did my student teaching in a school that really strongly believed in Guided Reading. The district where I worked, however, believed in basal readers.  There were no guided reading supports in place.  So the teachers used the basal readers in Guided Reading groups.  Instead of using leveled readers, they used the basals to do small group instruction. They used the quizzes in the readers to decide which group each child would be in.  It was not strategy based instruction at all; it was really focused on fluency and comprehension (retelling mostly.) There were lots of worksheets for the students who were not with the teacher.  And spelling from a spelling book. Guided Reading has come a long way in the last (almost) 20 years, but teaching reading in small groups while the rest of the class is engaged in meaningful, independent literacy activities is where I started as a reading teacher, and where I will end my career.  I would never base my entire literacy program on whole class instruction.  NEVER.  I am a zealot when it comes to Guided Reading.

When my current school board started pushing people to use Guided Reading (that’s about the year I started here), there were many people who resisted this style of teaching.  They didn’t know what to do with the rest of the class.  They didn’t really know what to do in meetings with small groups.  They weren’t sure they had the resources they needed to really teach the program.   I spent a lot of time trying to use my zeal in my role as a literacy coach, hoping to convert as many people as I could to Guided Reading.

Now I am faced with some zealots who believe in Guided Math.  I have concerns:  What does the rest of the class do?  Do I have the right resources at my disposal, or will I be up until midnight every Sunday night inventing the wheel?  What am I supposed to do, exactly, with my small groups?  (Sound familiar?)

And all of those are legitimate concerns, I think.  BUT – I don’t want to be the teacher who is still teaching a “Mrs. Frisby and the Rats of Nimh” novel study every October to my 5th graders because when I was hired in 1999 that’s what they told me to do with 5th graders in October.  So, do I want to keep excusing myself from trying Guided Math because I am satisfied with the way I do math now?  Well….kind of I do. Change is hard!  But I can do hard things, right?  (I’m asking…please reassure me!)

This is how the math block looked last week, basically, and I am going to try it for another week.

M/W:  Grade 2 students at activities.  Grade 3 with me working on multiplication.

T/TH: Grade 3 students at activities.  Grade 2 with me working on adding and subtraction (skip counting on the 100 chart and number lines by 10s.  I think they all have it this time around!)

Friday:  The circus came to town.

Activities:  Students had 3 –  Take a survey and make a graph about favourite holidays, Dreambox on the class iPads, play a game to practice adding up amounts of money.

Number Talks:  Getting ready for EQAO!!!  (I know, so exciting!!!)  so our Number Talks this week were really reviews of math skills.  I pulled out the EQAO from a few years ago and picked out a question on 3 days.  We reviewed patterning, telling time, and I forget what else.  A few times I did this at the end of the math block for about 10 minutes.  Typically I start math with Number Talks, so this was different.  It was a good way to settle the class at the end I think.  Usually I use a Number Talk as a warm-up. However, last week I was using the first few minutes of class to explain the centres, and to remind everyone to just please, if they had any compassion for me at all, to work quietly at the activities, and solve their own blasted pencil problems on their own!

This week:

Activities:  Reflections/Rotations/slides, graphing, and Dreambox.  Monday well will talk about last week, and I will read them a book and do a quick activity that sets them up to do the reflection/rotation/slide work.

Lessons:  Fractions.  I did a quick assessment in gym the other day when I asked them to walk/run a fraction of the distance between walls.  Interesting results! So I know a few of them, not necessarily all in the same grade, are going to need more support at the beginning level, while others are ready to try working through an investigation of some sort.  We need to work on naming fractions of a set, and fractions of a whole.

Which I better go plan right now. 🙂

Multiplication Models

I wish I could remember how I was taught to multiply.  I have absolutely no memory of who first taught me about multiplying…which is kind of weird because I remember all of my elementary school teachers. I do remember doing “mad minutes” in Mr. Goodreau’s 6th grade class. I would bounce around doing all of the 1s, 2s, 5s, and a few other random problems that I actually had memorized. And I remember being in high school algebra class and writing down my skip counting for problems with 6s and 7s. Heaven forbid Mr. Creager should ask a question that involved 8s or 9s.

Excuse me while I go deal with some residual anxiety related to multiplying.

As a teacher, I’ve often wondered what would have been different for me had someone along the way pulled out some manipulatives, or showed me an array, or, you know, explained that there’s more than one way to answer a multiplication problem.

I introduce multiplication to my grade 3 students using a “groups of” model. Using lessons from Marilyn Burns “Lessons for Introducing Multiplication” book, I let them investigate (though I’m not now 100% sure I have been allowing them to investigate enough…topic for another night!) ways to figure out how many legs there are in their group, or how many pencils we’d have if I bought 4 boxes, or any number of other questions designed to push them to use skip counting or repeated addition and then connect that to multiplication.

I also teach my students about arrays. I get out the colour tiles and ask them how we can arrange them to show 4×3, for example, and we move on from there.

Why arrays?

Well, because Marilyn Burns told me to, at first.  Then I stuck with it because it made so much sense to me.  And years later I am still doing it because I see it as a model that makes sense to kids.  There are arrays everywhere, so it is easy to find ways for them to practice using them, as well as a way to connect them to why multiplication is meaningful.

Today I wanted my grade 3s to work on arrays.  Usually, I would show them an array and then we’d practice them together and we’d all walk away pretty happy.  However, today I decided to let them discover the array on their own.

I pulled out the colour tiles and put them in the middle of the group.  “We’ve been playing “Circles and Stars” and I am wondering if that always has to be played with chalk and a chalkboard, or if we could play it with these colour tiles.”  The colour tiles were our manipulative, and the array was the tool I wanted them to work toward understanding.  I am going to admit to being a bit nervous about this, and thought it might be a disaster.  But who am I to question Cathy Fosnot, right?  So I kept going.

A few of them suggested that they could use tiles to make circles and then fill the circles with other tiles.  That would be like circles and stars.  I asked them to show me, and they started arranging the tiles into circles.  They soon decided  that it is hard to make a circle out of squares.  Then one boy said, “You could think of the sides.  It has 4 so you could do 5 x 4.”  This is what he made.

“That’s a Minecraft circle!”  someone said.

I asked, “You think we could do it like that?  For every problem?”

A students said,”That would be hard.  That would be a lot of work!”

Another student had been watching the whole thing.  She finally said, “I have 2 plans now.  You could use the tiles to make dice….wait…you could have imaginary circles.  You don’t actually need the circles, just the groups of tiles.”  HOORAY!!

We took turns modelling that:

I asked them to count what they had, and some interesting counting things happened.  I know Melissa will be sorry if I don’t explain that, but it is kind of a tangent. 🙂  Let’s just say that even though they had groups of 4, they still counted by 2s and 1s.  (sigh)  But then another child said, “Well if we put them in lines, we can count by 2s.”  and he made this:

Someone counted by colours in groups and then they started, on their own, talking about other ways to arrange the 16 tiles we had randomly started with.  Like, seriously, they started making the division connection ALL ON THEIR OWN!

(By now I had switched out all the tiles so they were the same colour.  I wanted them to think about organizing the arrays without worrying about making designs with the colours.  This is a real problem with colour tiles and can often get in the way of the math learning.  I mean, patterns are important too, but making checkerboard patterns for everything doesn’t seem to help with the counting or understanding in anyway. It just slows kids down and causes them to hate one another because someone is always hoarding the good colour that everyone else wants.)

We talked about how each of the arrays we had made matched with the dice we use in “Circles and Stars”. Then I asked, “Now do you see how to play ‘Circles and Stars’ with colour tiles?”  And they did!

So I sent them off with a partner and a pair of dice.  We are now using a 10-sided die to show the number of groups and a regular 6-sided die to show how many in the group.

Here are some highlights:

• On their own, one group found out about ones and zeros and what happens with them in multiplication.  🙂
• On their own, each group figured out that organizing the groups into straight lines made them easier to count, and easier to count without having to go back to ones.
• One girl started counting by ones.  I stopped her and encouraged her to try a bigger number. (Array pictured below) “I can’t count by 2s because I get confused!” I said, “Then try something besides 2s.”  I thought she’d do 5s, but she counted by 4s.  🙂
• Slowly 2 of the 3 groups moved to this sort of group arranging:

I feel like my goal today was accomplished, and then some! The students discovered the array.  I felt like I was scaffolding, not rescuing them.  (A personal pursuit of mine.) And I think there was a healthy bit of discovering things that can lead to other things for us.  (Division, for example.)

I have an idea for my lesson tomorrow.  Two of my grade 3s were away today, and should be back tomorrow.  They will need to be in on this discovery.  And I want to really solidify what we did today.  BUT…instead of sharing my idea, I’d love to hear ideas from others.

And by the way, the grade 2s were all doing their Guided Math rotations while the 3s and I did this.  I blogged about my experiment with GM earlier in the week. I am still on the fence about it, but will finish out the week before I talk about it again.

Finally, because I know that many people visiting this post are new to blogging, I want to mention that it’s great to leave a “drive by” comment.  But the best conversations happen when people return to read comments left after their own, and then comment again!  After you write a comment, WordPress blogs allow you to click a box that will “subscribe” you to a post.  Every time someone comments on that post you’ll get a notification that will keep you in the conversation.  I recommend it!

You’ll have to log in to comment on my blog, leaving your name and e-mail address.  Rest assured that only I will be able to see your e-mail address.  It won’t be visible to anyone else.  I have this setting on because it helps to eliminate many spam comments.

Guided Math: #1

I first heard of guided math too long ago to have a story to go with it.

I have resisted this classroom management strategy in all it’s forms.  Like guided reading, there is a lot of “behind the scenes” organizing that has to take place.  In reality, I felt like have done a fine job of differentiating the work we do in math class, so this strategy for further differentiating has seemed very overwhelming to me.  I’m already teaching 2 grades, so there is a multitude of curriculum expectations that I need to be looking at (sometimes they criss-cross, but not always) and then there is the range of differences in ability that needs to be covered.

I use Writer’s Workshop, and mostly Reader’s Workshop/Guided Reading.  I don’t do centres or stations in literacy  because I want my students to have authentic reading and writing opportunities.  And I want to be available to work with them, not managing the “job’s board” or the Station Rotation. This prejudice has also stopped me for doing guided math. I can only be in one place at a time, right? I tried Daily 5 a few different years and always felt like it was going to push me over the edge into a yawning, black abyss.

But….suddenly the idea of guided math seems to be haunting my subconscious.  I keep hearing about it.  Last year the range of ability in my classroom was especially wide, and this year it’s even bigger.  And I am not talking about the few outliers that are always at either end.  I’m talking about a full range and it’s WIDE!

In the collaborative inquiry I have been participating in, guided math keeps coming up.  All my usual reasons have been checked off my list every time we have talked about it:  I am not doing it because it is:

a) overwhelming

b) hard work

c) a time sucker

d) all of the above.

Except…for the second year in a row I am sort of realizing that even without doing guided math, I am feeling overwhelmed, and over worked and out of time.  I’ve started to consider that guided math might be a solution to some problems, instead of something that will exacerbate the problem.

So this week I am trying it.  Not for just one day, but for the whole week. I’m going to report back on Friday.  We did some GM on Monday, and I will reluctantly admit it was ok. And I have started to think about not needing 40 different games and activities to use during “stations” (or whatever I decide to call them) and maybe only needing a few that we can circle back to throughout the year.

That’s where I am with it right now.  And it helps that a few other people in my building are trying it out and talking about how it will look and how we can make it work and how we can support each other. I think the reason the literacy stuff is so successful is because we have so many similar management systems in place throughout the school.  Maybe this could happen in math too.

I’ll be back on Friday with a report on the week.

#notabookstudy: Research-smesearch

There is a lot of research in education. People literally devote their lives to it. Most of those people have not spent many days in the trenches with children, or at least that part of their lives was years ago. I trust educational research, and I think it is important. But I also remember to take it with a grain of salt, as they say, keeping in mind that there is not  a one-size-fit for every classroom.

I was more interested in the research when I first started doing things that deviated from the cultural norms in the buildings where I have taught. When I was trying out Running Records, for example, I had seen other, alternative assessment approaches and knew people who were absolutely committed to using them. Even though Running Records made sense to me as an assessment tool, and even though I wasn’t using them with nearly as much proficiency as I do now, I just felt in my teacher heart of hearts this form of assessment was going to give me so much more than a score that I could turn into a letter grade on a report card.  And I read Marie Clay’s book and all the research about Running Records that I could find.

Early in the week when a fellow teacher jumped onto the #notabookstudy hashtag and “attacked” (yes, I know that’s an exaggeration, but it sounds so dramatic!) the notion of “project based learning” in math, and it’s effectiveness, I was offended. “How dare she attack Cathy Fosnot and her work!” I thought. “I ❤ Cathy Fosnot!” She tagged in a friend (I am going to be honest here and say I don’t actually know what their relationship might be) who had, like Cathy, started his own business focused on encouraging teachers to read actual research and use that as a basis for classroom practice. The two of them carried on for the day, and you can probably pick up the pieces by going back through the Twitter feed if you are so inclined. If you are not, the upshot of it all was they didn’t feel PBL belongs in math, that there isn’t any research to back it up and that EQAO scores continue to decline even though more teachers are moving away from lecturing in classrooms.

There are about 12 different topics I could write about there, not the least of which is “THE WORLD SHOULD NOT BE DRIVEN BY EQAO PERFORMANCE!”

So I started looking for some research. I found a few articles, but was honestly too busy teaching to really spend a lot of time on it. I’m glad for that. I will probably spend a bit of time looking for a few things. But, at the end of the day, I decided that my teacher heart is trying to tell me something again.

I have used the Fosnot math units for many years. I have also used similar units from Marilyn Burns, and of course Super Source. There is always a mix of stuff across the school year in my classroom, and I try to be really responsive to student interests (because it helps with setting context) and student ability. I feel very committed to using inquiry based math lessons. I might not have a stack of research articles to support it all, but I know it works because I have seen it work.

Many years ago, I had a university level math course. It was calculus and yes, I just had to spend a full minute trying to remember that word because calculus hasn’t really been a part of my life since. My professor was a disaster. He knew everything about calculus and couldn’t understand why it was hard for people like me. He explained things one way, and that’s it. But there was a woman who sat next to me and we started talking about the math. I will admit that sometimes we talked during his long lectures, trying to make sense of what he was saying and showing. She and I learned more calculus from those conversations than either of us learned from the lectures. I could say the same about my statistics professor who insisted that we use his methods and even the math majors who were taking the class couldn’t figure out what he was talking about half the time. Thank goodness for open book tests!

Over the years, I have watched the proverbial light switch turn on for children in my class as they worked their way through project based learning math units.

I feel confident that there is research to support project based learning in math, and probably specific research that supports the work of Cathy Fosnot. Do I need to read it right now? Nope. I don’t. It does not bother me that John Hattie originally did his work with university medical students and now I am using it with 7 and 8 year olds cause I have seen it work.

Don’t get me wrong…I don’t think we can blindly accept everything that the Ministry or the Board of Ed throws our way. But when people I know and trust encourage me to try something they have researched and are recommending, I try not to resist it. I give it a try for myself and take it from there. That’s the only research that I need most of the time.

#notabookstudy: What Next?

We are still working on the “Ages and Timelines” investigation.  We worked out the difference between the ages of Carlos and his family, etc.  Next, it was time for everyone to calculate the difference between themselves and their family.

I expected, anticipated, that some would have a tricker time than others.  Given the ages of their siblings, which are not always nice landmark numbers  like 10 or 15, I knew some would struggle a bit.  I also anticipated that because this part of the investigation is more for individuals some would struggle without a partner to talk through the work.

I was right.

But what I didn’t expect was the number of children who came with the answer.  I said, “How old is your mom?” and they said, “She is 33, and she was 25 when I was born.”  I didn’t expect so many children to then have trouble putting this together as a number line.  I mean, if you know where to start (8) and where to end (33) and you know the number of jumps in-between (25) then making the number line should be easy, right?

It wasn’t.

So my next step feels like a backward step, but I have decided it is a sideways step.  We need to go around this obstacle, learn a little bit more about number lines, and then move forward.

ALSO:  I didn’t anticipate the halves.  As in, “I am 9 and 1/2.” or “My brother is 14 and 1/2.”

I feel like this week, so far, 2 days in, has been all about being responsive to student understandings.  In the example above, I felt I had two choices.  One would have been to teach that child how to deal with the halves.  We could have talked about using a decimal, or about using the fraction to figure out a more accurate answer.  My other option, the one I chose for this child at this time, was to say, “We are going to forget about the halves for now.” He has a tentative grasp of this whole “finding the difference” concept.  Letting him stick with the whole numbers will help him solidify.  Talking to him about the decimals or fractions would muddy the water.  He’s in grade 3, the curriculum doesn’t require us to talk about the decimals or adding/subtracting fractions.

For the next two days I am going to do a part of this unit that my colleague skipped with her class: creating a timeline.  She felt it was confusing her class, but I feel like it will be useful to mine.

And at the end of the day, isn’t this responsive teaching what ditching the textbook is supposed to be about?