>> Marian Small: I was talking to a grade one teacher yesterday, and she was telling me

Marian Small transcripts Leadership Matters >> Marian Small: I've been asked by lots of leaders of boards, I've asked by teachers, you know, "What's the most effective thing to help us? Is it -- you know, is it working with junior teachers, is it working with primary teachers, is it working with whatever?" And so I've thought lots about what is effective and what isn't. I actually think there is, of course, no magic bullet answer because there never is. So I don't think there is a most effective way for everybody. I believe that the collaborative approach that has been used a lot in Ontario has lots of merit because most teachers -- not all -- benefit from collaboration. They grow more, they learn more, their minds are open to more. So I actually think collaborative work is great for most people. I do know that there are lone rangers, and we have to love and respect them as well. I think that you need a combination of people who really shake you up; and living it in your classroom as a result of that shakeup; and then going back to be shook up some more; and then living it again. So I actually believe professional learning needs a combo of people who have that expertise that can shake things up with people who are closer to you, and your work, and what you do and kind of straddling those two spheres. My experience has been when all of the work is in a location where there isn't real expert leadership, it doesn't really move very much. But I would equally agree that going to a big talk once a year is pointless as well. So I really think the world is in between. The other thing that I've decided at this point in my life is that the people who really need the work are the principals first. So I think teachers do -- are the people with the kids, and we have to do a lot for them. There have been before and there always will be wonderful teachers who don't need any of us to help them with anything; they just figure it all out. All of us benefit from these interactions we have and they get better. I've been telling school board officials at the higher end of the chain that schools won't change until principals and vice-principals are truly instructional leaders; otherwise, you can change three people at a time but you can't change a school. So I've been -- I was working in one board and I actually shared with them that I felt some of their money has been sort wasted because the principals weren't involved. And so they could help a few teachers. And that, of course, is a good thing because you're helping hundreds of kids. But it's just not as effective as -- so if I had to choose in a board, like, where to put my eggs right now, it's in the instructional leadership basket. And that's where I think we need to do more work. And I've told people who are at the supervisor/director level that the only way that can happen is if they choose to focus their leaders on being instructional leaders and not managers. And until they give them the say so to do that, until they say, "I care more whether you're at that meeting with this instructional leadership than whether the report is in at 3:00 o'clock," nothing will change. We want culture change. And the truth is in Ontario we've been -- there's an enormous amount of money being spent to create a culture change, so you may as well do it right. Representing: Purpose guides the way >> Marian Small: I was talking to a grade one teacher yesterday, and she was telling me

about data management work that she was doing with her grade one kids and they were learning to do surveys. And she said, "What do you think?" So I said, "I think you're missing one." And she said, "What am I missing?" Like, "Why are you doing this survey?" Because there is a big idea that says the reason we collect data is because we want to know stuff, and the only way you can find some stuff out is doing a survey. If a child doesn't know that, what's the point of him being able to do a survey? So I think teachers are missing those big connectors all the time. Here's another example that I've done with lots of teachers. There's a big idea that I've written about and others have, as well. And it's implied in the expectations but not quite. So there is an expectation -- a process expectation -- that talks about representation. Teachers know in Ontario, like everywhere I go, that multiple representations are good. And then you say, "Well, why?" And they say, "Because multiple representations are good." And then you say "Why?" again. And then eventually, you get them to understand that the real big idea is that a kid understands that a different representation reveals different things. And that sometimes you want this revealed, but other times you want that revealed. And so a different representation would serve you well. So I do an activity with lots of grades, but here's what it would look like in grade one. I ask them to have kids represent the number seven in a lot of ways. And then I say to them, "And that's not really the activity. Here's what's coming, and this is the activity." The activity is to tell kids, "So look at all your representations; which of them help you see that seven is less than ten, which don't?" Look at all your representations; which of them help you see that seven is five and two; which ones don't? And you train kids to see, "Oh, yeah. Different representations show me different stuff." If a teacher doesn't know that, all she does is have kids, like, make representations and they look at them. And I don't think that's math. Creativity and Mathematically Interesting Problems >> Marian Small: I'm asked by a lot of teachers what kinds of problems they should use in their work with kids, what makes for a good problem, what do problems look like? One of the interesting things is that there are always miss. So one of the miss now is that a problem is only good if it's real life. And I respectfully disagree, is the way we say it these days. It seems to me that there are some really important, really valuable, great real-life problems -- contextual problems -- to do. But there are equally mathematically interesting problems that engage students completely that have no context. So in this proportional reasoning project I've been involved with, my mission in several of the boards that have engaged my work is to focus on these manipulatives in math classes with their teachers who are less comfortable with them. And so I've created problems that work completely around manipulative but had no real context. So here's an example. There would be a problem, the children would have pattern blocks, and I would say something like "There are twice as many reds as yellows, there are three times as many blues as reds; tell me how many blocks you might have, tell me what fraction of each design is yellow." There is no context whatsoever. There has not been one single kid who was not fully engaged -- like, not one -- because there's stuff that you want to find out about. There's tons of mathematically important questions to ask them. So for example, since I said, "There were twice as many reds as yellows," I said,

"So how many red blocks did you have? And how many did you have? And how many did you have?" And when we make the list, we only see numbers like two, four, six, eight. Like, there's no fives -- like, where's the five? And then we start talking about "Why couldn't there be five?" And the kids tell me, "It's because you said 'twice.'" So all these important mathematical ideas come out. And because it's what I call an openended problem and kids could go in many directions with it, our conversation is super rich. If I give them just a straightforward, like, "I went to the store and I paid for, how much change did I get?" Like, there's not a heck of a lot conversation. So I think that I could make contextual problem that have lots of conversations, and I often do. But I think a problem means, "Hey, I don't know what to do. I got to figure this out." And frequently, if you use the same kind of word problem you used seven other times, it's not a problem anymore. So I think that there are contextual problems that truly are problems because "I've never seen anything like this; I really have to think about it." And then there are contextual problems that are so routine that you can't even call it a problem anymore. It's the, "Yeah, another one of those. Remember when I did?" "Yeah, do it again." So it's not like you should never do those, but those are not problems. I think kids want a mix of those problems. A lot my work is about creating divergence rather than convergence in math. So I often tell teachers -- and I tell others -- that math is sort of a double edge, that there are questions to which there is one answer. And, like, you better get it. And four and three is seven, and like, that's all it is. But there's a lot the divergence that I want to create. And for me, I think -- I guess it's about creativity to a certain extent that I'm looking for your unique spin on things. So when teachers read the curriculum document, and read the words in the document and they see words like "add and subtract these numbers," they don't see creativity words. So we have to do a better job of messaging from on high that creativity truly is valued, and you can't just say it in one breath and then do this other thing in the other breath. It has to live in the things you ask teachers to do. So I actually believe that creativity is for all kids. But I don't think creativity means that you sang a song about the number three or that you wrote a poem about the number eight. I think creativity is you have your own spin on this idea, and this is what it sounds like for me. And I think teachers are not really seeing math as creative anyway, so that the only way they can deal with developing creativity in math is to actually do the arts and not really do the math. The math is just, like, in there, but it's not really what the creativity is all about. So I feel a need for kids to do creativity that has to do with the math. So you can use the arts, but it's just as creative to not go all fancy like that and just to say something like, "You know, I was thinking -- here's a question, like, why did you do it that way? Or what made you do it that way? I like your way. What do you think about his way?" Like, I think creativity is about the divergence as much as it is about this, like, big fun stuff. I think we all need big fun stuff in our lives. So I think we need a balance of those kinds of things. But I think the creativity needs for teachers to be in the math, not the math is, like, stuck in it. The Art of Mathematics >> Marian Small: And so I had an interesting experience the other night. I did a parent night at a school. And one of the parents -- one of the dads -- asked me, "Well, isn't

math really just application?" Like, "Why are you doing these other things because it's, like, to learn how go to the store and whatever it is." And I shared with him and he seemed to accept it nicely that there are two sides of math: There is the side that math is a tool to help you with science, or to help you live your life, or to help you with, you know, if you're in the social sciences, interpret data; and there's also, like, math is an art form, just like music is an art form, and visual arts are an art form. And there's this beauty in that, too. The truth is that most people who become mathematicians do it for number two, not for number one. The number one people become engineers and the number two people become mathematicians. So I want kids to experience that and to realize it's just, like, fun to figure this stuff out. And I like that. So it comes back to -- I figured out -- what you believe school's about. So some people believe -- I think a lot of people believe that school is to accomplish that list of expectations that's in the curriculum document. I see those as a means to an end. The end is I want kids to love to learn and love to think. A lot of the way we behave as teacher, a lot of the way the systems behave depends on what we see as the goal of education. So for me, the goal of education is not really the accomplishment of that set of expectations. That's important as a means to the real goal. And for me, the real goal is I want kids to want to learn, find it interesting; want to think, find it interesting. And so I don't need to always be thinking about what's practical because that's not my goal. My goal is I want you to, like, want to learn stuff. I want you to be curious about stuff. It is our main mission to want kids to be curious and want to figure things out. And it doesn't always have to be practical. So I'll just say one more thing I think about this, which is that teachers often say to me, "But kids say 'Well, why do we have to do this?'" And what I say back is, "The only they're asking you that is they're bored out of their trees and they want some reason to have to be doing this. If they were curious, there would be no reason to even ask that question." Math Curriculum: What teachers need to know I'm asked in a lot of boards about the Ontario math curriculum and what they're hoping for in a new version. What people admire. I was in a fortunate position, probably 20 years ago now, of actually writing the curriculum for New Brunswick. So I actually have a pretty firm idea in my head about what curriculum should look like. And one of the things I've noticed in particular is that I think that curriculum is too open to interpretation now. And teachers need some more guidance on the intentions underlining the expectations through teachings. So when we wrote the curriculum for the Atlantic Provinces, what we did is we ensured that with each expectation, we talked about why are you doing this expectation? Like, what's important about it? What are the important ideas to emerge? What kinds of assessment things should you do? There's real background. And I think Ontario teachers are craving that background. And I think that's an important piece. Another piece that I think is important is to get somewhat away from, this is what I want kids to do to and this is what we want kids to know. And I frame that in talk about big ideas and essential understanding and medium ideas and whatever. Teachers are too focussed, I believe, on just do this instead of why are we doing this? And what ideas do I really want kids to have? So my experience talking to teachers on a regular basis is that when they read a curriculum expectation, there's a lot

of interpretation to be done because these tend to be very succinct phrases. And you have to interpret, what does that actually mean? My experience is that teachers are even unaware that different teachers do interpret it different ways and have very different ideas about, what's the point of this? What is the underlying reason why that expectation is there? And based on the experience I've had and the knowledge most teachers in the elementary grades, particularly, come to in math. It feels to me that we need to give more guidance. Why is this expectation there? How important is it? What ideas underneath it should they be aiming for? Rather than: can kids add these numbers? So teachers are focussed on: get the adding done. Instead of: what ideas about adding should kids think about? And I think most of the work I've been doing- in fact, in the last- I mean, actually my whole life, but particularly in the last year- has been focussed on getting teachers to go deeper as to what's the point of this? How do you make ideas clear to kids? How do you focus more on what the point is? So I think that's a huge part of the curriculum piece. I think teachers need to know how ideas develop. In particular, bigger ideas. So there are big ideas that go from K to 12, K to 8, K to 10, whatever they are. Teachers need to know that kids are meeting those same ideas in grade 3 this way. But they're meeting the ideas in grade 10 this way. And they have no knowledge of that, and the curriculum doesn't help. So if we are worried as we tend to be in Ontario about teachers content knowledge in math and how that's helping them or hindering them from helping opportunities. Then I think the curriculum document has to do a little more for them in helping them see how those ideas play, how they play differently, what to focus on, what to let happen but not really focus on? All of those things are really important. So the word I've been using lately is intentions. So I believe every teacher should teach a lesson with intention. This is what it's for. And I think the curriculum document should help them with what those intentions might be. And then they could reframe them their own way. Another piece that I think is important is somehow to embed the process expectations more visibly with the content expectations. Right now, they sit as stand-alones. And we know that there are wonderful teachers who do embed them. We also know there are teachers who didn't even know there were those pages in the front. So I think we need to do a better job of that. And so front matter, I don't think in this day and age front matter can be front matter anymore. I think it needs to be integrated into the things you're doing. So I think that piece is important. And another piece that I think is probably important right now is there is a lot of talk about mindset. And I have a different version of mindset than most people are talking about. And so for me, I want teachers to believe that the ministry is okay with the purpose of teaching math is not to create convergence. It's to create thinkers who might be divergent. And I believe most teachers I meet actually believe strongly, everybody should eventually get here. Like you can fool around for a while, but like this is where we're going. And I think until somebody gives them permission to say that we would be thrilled if he got here, but she got there, but they both got good places, they're always going to be insecure about that. ^M00:04:48 Responding to Students

Marian Small: One of the things that frustrates me, I guess, is that teachers believe that if there's a name for a strategy, it's good and if there's no name, like, it isn't anything. So people are telling me, "Well, I use blah-blah-blah." They can use it well or they can use it poorly. Like, I don't care if you use blah-blah-blah. It's like, "What are you really, really deeply doing?" So I think it's great that teachers have what they call "talk moves" I think it's great that they do things called "gallery walks." I think all that. But you could do a gallery walk and do good stuff with it or not good stuff with it. So I don't think it's about naming anything. Essentially, I think the most important thing a teacher needs to learn to do is ask the kid important questions. So, "Tell me about this, and follow up with that." Like when he says this, you've got to figure out: what do you say now? And it's that - I mean, in the end, teaching is an interactive activity. And all that matters is the relationship between those two human beings, or three, or four who are interacting. So until teachers develop skill at responding to students in meaningful ways- asking the right kind of probing questions, not just ones that are on a popsicle stick somewhere, but ones that make sense in this situation - we're going to make relatively little progress. So I was working with a group of teachers and we were looking at a number of student pieces of work in response to the same question. And I gave them a little bit of time. They wanted me to tell them what to do, and I wouldn't. I made them talk to me about what they would do, which is, again, an important strategy for teachers to learn. And they shared with me how they would deal with them. And one of the things that I noticed is they were fixated on ranking, you know? "I like this one better than this one. I liked hers better than his." And I actually asked them: "Could you get past ranking and just talk about what could you say to the kid? When you look at this one, how do you know he didn't really have great things to say, he just didn't, like, write them all down?" So one of the things I think we have to do a better job on is helping teachers learn not to evaluate everything and to truly learn to probe without all that baggage on it. Medium Ideas >> I've been able over the years to create documents that talk to big ideas and I've come to a new place with that actually. So I do think that it's important for teachers to understand what are the big, big ideas that are in mathematics, that frame mathematics that kids will need from grade to grade to grade and I think that's important information. I'm now into layer 2. So layer 2 is I'm a teacher, I read a curriculum expectation because that's my job to teach this thing and when I look at that thing, sometimes stretching all the way to the big idea is too big a stretch for me to suit me in this lesson. So I've been talking...in some words I call the "medium ideas," it's weird but what I really mean is that there is something else. I guess lately I've been calling them "essential understandings" which are somewhat smaller than big ideas but really particularize the big ideas. For example in this strand or in this context or whatever it is and I'm asking teachers that I work with to use that as their learning goal. So their learning goal becomes the "medium idea" which is marrying the expectation to an appropriate big idea which particularizes it for a piece of content. And as I've been working with this with teachers, I've been spending a lot of time saying, "So if this were the expectation I wanted, which of these big ideas might it feel right with?" And sometimes there's more than one. If I decide to go here, what is the interface? What goes between this expectation and the big idea? How could I make this my learning goal and how could I

emerge this learning goal for kids so that they'd actually see this idea? So I don't know if medium idea is a very good word, but it definitely is the interface between expectations and big ideas. So I don't want a teacher just to fit a big idea on a board and let it sit there all year and keep saying to the kid, "Remember that big idea? Remember that big idea?" I want it to live by particularizing it into a context which relates to the particular expectation. So I guess that has changed me some. It changes how I'm suggesting teachers deliver lessons. It doesn't change my belief that they should know that these big ideas really do recur over and over and how they recur over and over, but then I want them to say, "But then how does it sound at your level in this strand?" And I think my experience is teachers need help to make that bridge. So I think a lot of professional learning if I were choosing it would deal in fact with that; how do I take an expectation, bridge it to a big idea, look at what those medium ideas are, and how would I bring kids to those ideas?" ^E00:02:35 A Tool, Not a Rule >> One of my experiences in Ontario, which is by the way the only province that uses the phrase three part lesson. If you say that in Alberta they just look at you, what are you talking about? One of the things we've done is we've turned it into a buzzword instead of focussed on what were the intentions of the parts of a lesson? So lots of teachers know they're supposed to do a three part lesson but they don't know like what it is. So it seems to me that our goal is to help people understand here was the game. The game is before you give students a problem where they do the thinking instead of you, you have to get them ready for that problem in one way or another and that activation can take many different forms and there's no right form and wrong form but you have to get them ready for the problem. They work on a problem probably collaboratively but not necessarily. Maybe with chart paper but maybe not with chart paper. And then in the end the big part is consolidate. I believe that the intention of consolidation and this is just my spin, is that consolidate usually means like pull it all together. So for me it's the notion that I teach a lesson for a purpose, I picked a problem to accomplish that purpose, and my consolidation will bring that purpose to the surface. And no child will leave that room not knowing what this lesson was about. And that's my goal. It's not like this is what Sara did and this is what Marshall did, it's like this was the math idea I learnt today. So until we get that to teachers, I don't think the words thee part are accomplishing much. And the truth is, I don't think it's about how many parts anyway. So one day I deliberately, I announced that I was going to do a five part lesson. I gave no, you know, I didn't feel guilty, it was all good. And the reason I did it was instead of having one long problem I had two smaller ones that accomplished goals that were related that I wanted to accomplish in the same lesson. And I said I really think it worked, you know we had five parts. And I still did the pieces that the intention of the three part lesson is about. So for me, I think teachers have to be much more thoughtful about why am I doing what I'm doing? Is this structure the best way to accomplish it today? Would I have a mix of three part lessons some days but games other days and some other, like some kids are working on smaller problems in stations but I'm working with a guided group over here sometimes. My answer is yes. So a

whole whack of teachers say well should we do a three part less one day a week, two days a week, three days a week, and I kept saying like I don't know. It depends what you're trying to accomplish which means is best. So if you're getting, if your focus on a particular day is for kids to practice a skill, often unless you pick the right problem, a three part lesson's not going to do it for you. There are three part problems, lesson problems if you want to call them that, which probably do require a lot of practice and then it might work. But you have to know why you're doing things. So I worry that we're selling slogans and we're not selling ideas. So I really hope we get away from, I know you're supposed to do three part lessons and I want teachers to say so this is what I want to accomplish today. ^E00:03:06 Skills in the Technological Society >> Marian Small: One of the things I've had an opportunity to talk about a lot lately is computational skills. There's been a lot of media talk about this lately. And so it comes up all the time. And one of the things I want teachers to know is that you have to think about what kind of skills are really useful to kids in the society in which we live now and in which they are going to live in. And we live in a society where there is a lot of technology. And that didn't exist, you know, 25 years ago. So even though you could argue not everybody has a calculator with them all the time, I'm betting in about three years everybody will. They will be embedded in your skin by Google somewhere, and you will have technology. And then even now any adult has a cell phone and it has technology. So I actually believe that we should be devoting way less energy to calculating with large numbers and way more energy with calculating with small numbers, doing mental math with friendly numbers, and estimating. So I want a kid not to spend a lot of time mastering 23 times 58; I went them to know that 23 times 58 is sort of like 1,200. And then they can use their little tool. And it didn't come out near 1,200, oops, I should worry; and if it did, I'm happy. I think the only way we can do that is not to ask kids to do the calculation as well as the estimation because they won't do it. They'll just do the calculation. So I'm saying: Don't ask them to calculate. Like, stop. And the only kinds of numbers you should ask them to do are numbers like 20 and 60, and 40 and 50, and 32 and 10, or things where you're actually cultivating mental math. So if I were rewriting the curriculum, there would be way less calculation, except with small numbers. There would be way more estimation. And my estimation questions wouldn't always sound like, "Here's a calculation, please estimate it." It would be something like, "If I were multiplying 43 by 82, do you think the answer is probably closer to 2,000; 3,000; or 4,000? Tell me why." So I would ask tons of questions like that, not just say, "Here is secretly a calculation but I'm asking you to estimate like there is no calculation." So my question is, "Would you pick this one, this one?" And I think that is the skill people really use in their life. And the other skill -- get a machine out for them. So you get a machine out for any other skill. So I believe that the curriculum document -- I'm hoping in some revision of it -- will make estimation a bigger piece and calculation a smaller piece. ^E00:02:31