[00:01] Announcer:
Welcome to Principal Center Radio, helping you build capacity for instructional leadership. Here's your host, Director of the Principal Center, Dr. Justin Baeder. Welcome, everyone, to Principal Center Radio.
[00:14] Justin Baeder:
I'm your host, Justin Baeder, and I'm honored to welcome to the program today Jonathan Farris and Tom Hirk. Jonathan has over 34 years of experience in education as a classroom teacher, principal, and education consultant, and currently serves as a field experience coordinator at the University of the Fraser Valley, where he oversees practicum placements for teacher candidates, supervises faculty mentors, and teaches courses on classroom management, professionalism, ethics, and teacher presence. Tom Herk has been an educator since 1983 in a career that has spanned all grade levels and many roles in public education as a teacher, administrator, district leader, and Department of Education project leader and executive director. He is one of our profession's leading authors and consultants with 41 total years of experience in education. And Tom is the author of 25 books, including his new book with Jonathan Farris and Kirk Savage, The Snap Solution, an innovative math assessment tool for grades K through 8.
[01:10] Announcer:
And now, our feature presentation.
[01:14] Justin Baeder:
Jonathan and Tom, welcome to Principal Center Radio.
[01:17] Tom Hierck & Jonathan Ferris:
Thanks, Justin. It's always good to be with you and to share some things with your audience. Thanks, Justin. Great to be here.
[01:23] Justin Baeder:
Well, let's jump right in to the SNAP solution. First of all, SNAP is an acronym. Tell us what that stands for and what that means.
[01:29] Tom Hierck & Jonathan Ferris:
Yeah, so SNAP stands for Student Numeracy Assessment and Practice, and it focuses in on number sense. And the key part here is that it's kind of a unicorn in a sense, because it looks at for, as, and of assessment. And the key part is that it includes practice as well within the assessment itself.
[01:46] Tom Hierck & Jonathan Ferris:
Yeah. And so we also had a little bit of a play on words, right? If you ask educators, what's a subject you struggle with the most, particularly in terms of the thing I love to teach the most in elementary school is math doesn't tend to make the top of the list very often. And so this notion that maybe it's because of how we've taught math and how we've assessed math. So what if we made math assessment a snap?
[02:11] Justin Baeder:
Well, let's talk a little bit more about the role that this plays. So, you know, typically teachers will have a pretty well-defined math curriculum. They may follow a textbook. They may follow a program with manipulatives and consumables. And often assessment is built into the curriculum. What role does Snap play alongside or in addition to curriculum?
[02:34] Tom Hierck & Jonathan Ferris:
One of the things about Snap is that what we wanted to create is an assessment, a one-page assessment that could be filled with curiosity and joy. And we wanted to make it one page, and we wanted to focus on number sense in itself because we believe that number sense is a foundational component of math. I mean, there's so much. There's measurement. There's probability. There's a lot out there.
[02:54]
But if we thought, okay, what's the essence? So in the Chilliwack school district, we designed this one page assessment a number of years ago and piloted it and it took off and basically it's a one page. It's like a puzzle and it's very inviting. So it's full of curiosity and full of wonder. And it's like a window into student thinking. And we think it's just really, really powerful.
[03:14] Tom Hierck & Jonathan Ferris:
So that ability to represent. And so, you know, the one pager that Jonathan's talking about, it's a simple document. It's downloadable. You can try it in a variety of different formats, but in essence, you know, you might have the kid put a number in the middle and then there's a bunch of different ways that they would get to that number. They could write equations for that number. They could count forward, they could count backwards, they could tell a story.
[03:37]
The key part here is in both the simplicity of the tool, it's really easy to use, but the complexity of the evidence it gives you, it allows you to then plan all of the next steps. You know, for me, a lot of my work in the past is focused on what do we do next, right? What's our intervention going to look like? And the intervention has to be as clearly and critically informed as possible in order for it to be effective. I think that's the big win of this particular tool.
[04:12] Justin Baeder:
So it's helpful if you're listening to this as an audio podcast, as everyone is, to see a little bit of a visual. And I've got it pulled up in front of me. But is the format the same for all grades K through eight or do you differentiate it by grade level?
[04:25] Tom Hierck & Jonathan Ferris:
Yeah, so kindergarten and grade one is a little bit different. It's a little bit simpler than the template you probably have in front of you. And things like mounting by five, counting up, doing some simple sort of inviting concepts that are done at a whole class. And one of the key pieces about SNAP is that there is not a lot of reading involved. And that's what sets it apart from many other assessments. So kindergarten, of course, students are, you know, they're learning to read, but the assessment itself does not contain a lot of reading in itself.
[04:52] Tom Hierck & Jonathan Ferris:
Sure.
[04:53] Justin Baeder:
And visually, in the middle of the page, we've got a number, right? Is the intent to have the teacher select a number and then have students do various things with it, like create examples and count up, count down, and so on?
[05:06] Tom Hierck & Jonathan Ferris:
Yeah, exactly. So think of the number 234. If that was in the center, we would ask students to draw an image of that number, represent it. And very often a student will go to base 10 blocks and those kinds of traditional pieces. But as Tom was alluding to a little bit earlier, there's a lot of room for flexibility here. So students can represent in animals or in nature, all sorts of different things.
[05:28]
And then what we want to do is we want to ask the students to write to describe the picture. So explain what that picture meant. Below that, we would ask them to write in an expanded form. And what does that look like? And then we would want our students to create three equations that equal that number. It could be adding, subtracting, multiplying, dividing.
[05:46]
And one of the most powerful pieces, or there's a lot here that's powerful, is write a real-life example of what that number looks like. So thinking back to when I was in school, I was never taught to think of numbers in real life. It was just, you know, do the math, do the number. But now I'm asked, what does that number look like outside? Like it could be in nature or, you know, wherever we are, happen to be in a grocery store, et cetera. As Tom was talking to a little bit earlier, we asked students to count forwards and backwards by a number.
[06:12]
Then we want students to put the number on a number line. And finally, we want students to reflect on their thinking. And this is a really powerful piece of the metacognition piece where you're thinking about your thinking. So what went well? What do I need to be thinking about next time? Did I meet my goal?
[06:26]
And what was easy? What was difficult? So that's essentially the snapshot, so to speak, of the snap.
[06:32] Tom Hierck & Jonathan Ferris:
Yeah. So, you know, and again, what number would I put in? Well, that's based on your individual progress, right? If you're not yet beyond three digit numbers, then that's probably where we're going to start. Right. But I got to tell you, as I work in high schools in particular in mathematics, more often than not, the challenges can be tracked back to number sense, right?
[06:50]
To the inability to understand in a variety of different ways what 234 really is. I know it comes before 235. but in terms of getting a sense of what that number represents. And so, you know, what we're trying to do is peel back now to building this foundational piece, because why math is such a struggle. And by the way, such an accepted struggle, you know, Justin, you could go to a social situation tonight and say, Hey, you know what? I don't do math.
[07:23]
And everybody would say, it's OK, it's only math. Don't worry about it. I don't do math either. Right. I think it's all tracked back to we never built this foundational piece. Math is not about memorizing formulas.
[07:36]
That's the application of math. When I watch my grandkids play, I think they love math. They love sorting. They love representing. They love organizing by shape. We've got to keep that joy, that wonder there.
[07:50]
And I think if we can build this foundational aspect in K-8, pre-K-8, that number sense really means something and this ability to represent that something, I think we're going to see better appreciation of mathematics in the high school grades.
[08:07] Justin Baeder:
What does number sense mean? Because I have kind of an intuitive sense of what number sense is, that it means kind of the sense that students have about numbers. Is there a more formal definition or what does number sense mean to you?
[08:19] Tom Hierck & Jonathan Ferris:
So when I look at Marilyn Burns, who's an author, one of her definitions for number sense is that students with good number sense can think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different ways, see connections among operations, figure mentally, and make reasonable estimates. These students seem to have a good intuition about numbers and see numbers as useful. And when I think about a personal example, I was recently traveling to Mexico and doing the conversion rate in my head. And I thought it was very challenging to do that. And that's kind of what NumberSense is, the ability to take an hour to be able to think flexibly, to understand it in multiple different ways. And the Snap really is exquisite with that.
[09:02]
It helps students to think about number in a variety of different ways.
[09:05] Tom Hierck & Jonathan Ferris:
We've all heard the notion of reasonableness in mathematics, right? Is the response reasonable? So if you had $20 and the item was $11, is it reasonable that you get $4 back or is it not, right? And so that ability to manipulate, to say, you know, I shared the example of walking into a math class and asking the kids what one third of 12 was. And one kid of me, he answered it was four. And I thought, wow, this kid really gets it.
[09:35]
So I thought, okay, moment for this kid to highlight. And I said, that is, you have done that so quickly. I'm fast. I'd love to hear your method. He said, those are so easy. You just add the one and the three.
[09:47]
All right. Guess what? In math, sometimes you can get the right answer the wrong way. So did he have the right answer? Yes. Now, does his number sense kick in here?
[09:57]
So, wow, that is really good. Does it work all the time? What would you say two thirds of 12 is? And immediately he says five. Oh, okay. Well, here's what we know.
[10:06]
And here's where the rub comes in, right? So I let them know that two thirds of 12 is actually eight. So now we know that one third is four and two thirds is eight. Now I need you to go back and work with one of your colleagues, one of your peers. What do you think? What might be the way we get there?
[10:24]
And that's where, again, this number sense starts to kick in rather than a simple memorization of formula. Now, to be fair, for some kids, that memorization stuff's great. Look, if you have a great memory, you're going to be aces in high school math and science. You might not intuitively understand it, but there's a lot of rote memorization to it, right? If instead you can get to that ability to say, and here's why, that's number sense.
[10:51] Justin Baeder:
So we've talked a little bit about what the SNAP approach is. We've talked a little bit about what NumberSense is. Jonathan, I wonder if you could take us into a little bit of the history of how this tool and this practice developed and how teachers use it.
[11:05] Tom Hierck & Jonathan Ferris:
Yeah, thanks, Justin. A number of years ago, maybe in the early 2000s, we were working with an assessment that Kirk had designed, actually. It was called the ANI. And it was a one-page template, and we brought it into Chilliwack. and teachers were adopting it. But then we felt very strongly that it was important to create homegrown assessments.
[11:21]
So to do something ourselves, we gathered a number of teachers and principals and our task was let's design a brand new template. Let's think about what we want. We want to create something that's one page. We want to create something that's inviting, that's full of curiosity and wonder because we know that math anxiety is very, very real. And we also know that we want students to be able to think about number. So we gathered and we designed and we came up with a number of different templates.
[11:49]
We worked with John Mighton, who's an author of Jump Math. And then we developed that and then we started to pilot it in our school district. And that was initially at grades two to seven. And a number of people were like really, really interested and really getting on board. And then I had kindergarten grade one teacher in the school that I worked at. And they said, we'd like to do this too.
[12:07]
Can we design something? Because we're seeing how powerful this is in the later grades. So they ended up designing the kindergarten grade one version. And the neighboring school districts were wanting to know about it. And all of a sudden, we've got people in British Columbia, 10 different school districts, adopting SNAP and getting on board. So that was kind of the story of SNAP.
[12:26]
And it's made its way out into a variety of different places because teachers really see the value of it. They see the value of a one-page assessment that's full of curiosity and wonder and thinking. And it's very much tied to the curriculum, not only the curriculum in British Columbia, but it's tied to sort of curriculum everywhere, so to speak. And when I say that, I think about the five strands of mathematical thinking developed by the National Research Council in 2001. where they talk about conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. And the SNAP embodies those pieces in and of itself.
[13:03]
So yes, we've designed it in Chilliwack, British Columbia, but if you're using it in a different district or a different region, you can be safe or assured to know that you're addressing mathematical thinking globally, so to speak.
[13:16] Justin Baeder:
Good deal. And I'll refer our listeners to my previous interview with John Mighton, who has developed quite a curriculum and quite a following for his Jump Math program. So glad to hear that you worked with him. Let's talk a little bit more about how teachers use what they find on the SNAP assessments that they administer to students. Because, of course, we have lots of different ways of assessing. Teachers can observe students when they're using manipulatives.
[13:43]
They can have students solve problems individually or collaboratively or on the board, you know, a variety of different ways that the teachers get a sense of kind of where students are. But how do teachers use this particular tool in the classroom?
[13:55] Tom Hierck & Jonathan Ferris:
And I think you've hit the nail on the head. Part of it is this notion of a variety, right? So it's not just one way of representation. I think, again, if we're being honest, there's sometimes a lack of comfort with mathematical instruction in the lower grades. I think if you are in love with mathematics, if that's your jam, you're probably going up to the high school if that's really what you love to do. As a result, and I know it's not a black and white statement, but as a result, if I'm not as comfortable, I tend to teach the way I was taught, which is a very limited and narrow sort of focal aspect.
[14:33]
And so I don't have any other ways of, now I pull out this document and look, you've seen it. It's pretty simple to use and it gives me a bunch of different ways of where this kid is struggling. I mean, if they don't know where 234 is on a number line, if they've got it before 100, We got some real challenges. If they can't count forward or back or they aren't able to visualize what 234 is in any sort of representative model, then I'm probably having to dial back to some of the single digit work before we get to three digit, et cetera. Jonathan, I know you've had a chance to work through this with some schools and we've seen some evidence emerging. Maybe pick it up from there.
[15:25] Tom Hierck & Jonathan Ferris:
Yeah. So as Tom was talking about, to use it for, as, and of, and it's pretty rare to have an assessment that you can use for all three. So for is it informs the instruction. So you can use it whole class. You can use it in small group. You can use it individually.
[15:38]
You can put it under the document camera. You can zoom into certain aspects. You don't have to give the full temp itself. So that provides information. Then the as is the students are learning while they're doing it. So they're becoming deeper.
[15:51]
They're understanding. They're getting stronger in each of those areas. And then the hub is you can use it at the end of a certain, at the end of the month or end of the unit or whatever it happens to be. And then that's your, that's your summative example. One of the, one of the pieces that's amazing about it is that it's low floor, high ceiling. And I had a student in a school that I worked in and for the real life example, he was an aviation expert or he loved planes.
[16:14]
And this is a student in fifth grade or grade five. And he knew how many seats there were on a Boeing 777. So if a large number was put into the middle of the circle, let's just say it's 10,000, he would be able to figure out, okay, that's 40 Boeing 777s, and then there's this many seats left over. And I was just flabbergasted by that because I'd never...
[16:36]
In my teaching career, I've worked in school, seen a student so excited about math, so able to take something and go and to explore and be curious about it. And you might see the curiosity in kindergarten where students are coming into school and they're full of wonder and they're exploring. But that wonder and curiosity kind of fades as time goes on. In the later grades. So here's a student in grade five and grade six, full of wonder and full of joy, full of like inquisitiveness. And let's now play with math.
[17:02]
And that's what we want. We want our students to be playful with it. We want them to think about it, to explore it, and to be open to it.
[17:10] Justin Baeder:
I love that. It's striking to think that the people who, the adults who love math tend to end up teaching secondary and the students who love math tend to lose that love from secondary. So it certainly makes sense that, that bringing some play into it, bringing some kind of appreciation and playfulness to our assessment and thinking of that assessment not only as assessment of learning, but as you said, assessment for learning and assessment as learning makes a lot of sense. Talk to us a little bit about what happens across the district, because certainly I can envision a single teacher using this type of tool with a single student to understand and gain some insight into where their thinking is and maybe what they need next. What are some of the bigger system level implications of using this tool?
[18:02] Tom Hierck & Jonathan Ferris:
So when we first adopted SNAP, we had an implementation process where we had helping teachers go into every school and we set aside time to do that. And as a principal at the time, it was very important to me to be a lead learner and to learn alongside. So I would join every meeting with the students, sorry, with the teachers when we were learning about it. So the implementation process took some time. What I would do as a principal is I would look at the data, I would collect it. I would actually have a data board.
[18:27]
I would write all this by hand, actually on a whiteboard. And even though there's technology available, I'd have that data board right in front of me so I could see where the students were and where we needed to provide supports in my school along those pieces. So there would be, you would look at the data from a school point of view. The school district would actually collect the data as well in May. And look at that and then we would meet and talk about how can we support and what do we need to do differently and how do we need to address pieces within. Fits beautifully within the RTI model where you're supporting students and you're having things like team time and looking at common assessments in time.
[19:01]
And I would provide time for teachers in my school to gather and collaborate and look at that. So the school district would look at that from a wide angle lens. And we also have provincial assessments called FSA, Foundational Skills Assessments, that looks at numeracy and literacy province-wide. And in fact, the Chilliwack School District has noticed, I think last year, for example, that the numeracy assessments at the FSA in grade four have been the best that they've ever been. So we've noticed a bump in the numeracy score. scores or thinking over time.
[19:32] Tom Hierck & Jonathan Ferris:
I think that those are all sort of the positive trends, right? And again, I think all of us know it's not always so straightforward cause and effect, but it's hard to dismiss that the impact of a district that's been using this very effectively, that their results are not somehow connected to this practical rollout and implementation of this view of assessment. As I said, it's more about Getting a degree of confidence, familiarity, comfort with all kids, right? I loved your analogy earlier, right? The kids who love math the most don't tend to get to the teachers who love the math the most until they stop loving math, right? And so how do we continue that joy, that wonder, that appreciation?
[20:16]
Look, I'm not suggesting for a moment that 100% of our kids are going to be because 100% of our kids don't love a bunch of other subjects. But we have to do something that dispels the notion that it's okay to not be good at math. Yeah, absolutely.
[20:34] Justin Baeder:
Let's talk a little bit about what we do with this information in the classroom, because I think one of teachers' perpetual frustrations with standardized assessments is they don't get the information back quickly. They often don't get very detailed information about what their students know and are able to do. It might get boiled down into some sort of number. So having a more frequent, more timely assessment that they actually get to look at is probably very appealing to teachers. But then, of course, there's the question of, well, now what do I do with this? Because we have to move on to the next unit.
[21:06]
We're not going to have the luxury of slowing down and taking as much time as we need to get all students to mastery. You know, there are pacing considerations. So what do we do when we find a need, when we identify an instructional need from this assessment? What do teachers actually do in response to meet those needs?
[21:26] Tom Hierck & Jonathan Ferris:
So one of the pieces when I think about is I think about the number line example. So I recently was in Alberta and we were looking at the snap in middle schools and we designed an activity called a number line, clothesline math. So we set up a clothesline in the class and we gave students different numbers and we said, okay, here's where zero is committed. Come up to the board and put where your number fits on the number line. And this is a result of the fact that their snap or their assessments would have shown that that's an area that they needed to work on. So it was an incredibly hands-on activity and students would come up and then the other students would say, oh, I'm not sure if that should be moved to the left or to the right.
[22:01]
And then there was so many teachable moments within that. So as you said, Justin, you provide the assessment itself and then where do you go next? So one of the examples, you know, number line, use clothesline math and get the students involved and engaged. And where does that, where does that fit? And you can do that with each of the areas in number sense in the SNAP, if it's counting forwards and backwards. Let's take the students outside and let's, you know, climb some stairs and move back down some stairs.
[22:26]
So based on the information that it gives you about your students, you know, the four part, where do you go next? And this is what we can do next in terms of some of the activities or some of the teachable moments that we need to go after for some of these pieces.
[22:40] Justin Baeder:
I'm hearing a ton about number lines all of a sudden, and I don't really remember using number lines as a kid. I don't know if they're something that has really come to the fore in the meantime, but it's interesting to hear that theme of number lines being powerful for helping kids develop number sense and get a sense of proportion and be able to make, have better intuitions about numbers.
[23:01] Tom Hierck & Jonathan Ferris:
Exactly. And you can leave the number line up in the classroom and you could have, you know, particular integers, you know, like one minus one and all of those different pieces. And then you can think about, let's put a number line below that. And now let's look at fractions. Where does that fraction line up in terms of the number line that's above? And then we can go below and let's draw pictures.
[23:19]
What does that look like from a picture point of view? And all of this is done to promote thinking and engagement as opposed to we're just going to do some worksheets and we're going to write out 40 practice questions and we're going to just do the math. We're going to cross off the zero, put the nine up and just do it. Just do the procedure as opposed to understanding the concept. That's where, you know, SNAP comes in in terms of, you know, Where are the students? But it's what you do next also invites that curiosity, engagement with the students and playfulness.
[23:47]
And yes, we want to get the right answer and there is accuracy, but we can do it from a growth mindset. We can do it from a playful and an inquisitive point of view, which is really, really important.
[23:57] Justin Baeder:
And you also draw some connections to response to intervention as well.
[24:01] Tom Hierck & Jonathan Ferris:
Yeah, you know, I think that's the biggest piece and perhaps, you know, one of the absolute strengths of this tool is that it does give that clarity that response intervention tier two and tier three are predicated on quality evidence being gathered at tier one. Not a supposition, not a feeling, not an, again, go back to my example of If a kid gets one third of 12 by adding the one and the three and they get it right. And all we do is say that kid's got it right. We're missing out on an opportunity to intervene because it's got some capacity, but not really quite what we need. Right? So how do we set up our tier two and our tier three based on what evidence?
[24:42]
When you've got a tool that gives you seven or so different entry points, got to believe that it's going to make what comes next much more viable, acceptable, and engaging for the student. Right. So again, the other, and you know, this probably, you know, from your own research, but you know, that Burger King trying to launch the one third pounder and how it crashed because nobody could figure out that that was actually bigger than the quarter pounder. Right. I mean, that's the clearest example of a lack of number sense, but, that we might want to, right? And so there are consequences to not having number sets, right?
[25:24] Tom Hierck & Jonathan Ferris:
Yeah. You know, when I think of data-driven instruction, this is where SNAP comes in perfectly. High quality, collective responsibility, all of those pieces, you know, the RTI, it just fits in. And when I was at my school, it was just, it was one of the foundational pieces that we used for numeracy. Literacy seems to get the priority and numeracy seems to be kind of like the second cousin And we're gonna look at that a little bit later. We're gonna pay attention to it, but literacy, we're gonna put a lot of funding towards that because, and it is important.
[25:54]
Literacy is very important, but to be numerate is also extremely important. So we use the SNAP in our school to embed within the RTI framework. And where are our students? What do we need to do next? And as I was explaining earlier, I had my data wall right in front of me on my whiteboard. So I had all the students that we were sort of wondering about, where do we need to go next?
[26:14]
And, you know, those are the tier two and the tier three. And so it was right in front of us. And we were able to design and adapt and work collaboratively around that to try to improve our students' understanding of numeracy.
[26:26] Tom Hierck & Jonathan Ferris:
You know, as I said, I think, um, you know, capacity as we keep hearing and Jonathan just shared, this isn't about, Hey, we don't want you to do literacy. This is about trying to come up with a way that puts them on par. You know, successful adults are both literate and numerate, not either or right. And so how do we help now to continue this notion of number sense, this continuation of this love of mathematics that I think is evident in our younger kids.
[26:55] Tom Hierck & Jonathan Ferris:
Yeah, just one other piece, Justin, is we want to be mindful that Snap is not just a worksheet because it can turn into a worksheet and we don't want that to happen. So, you know, you can zoom in, you can take different parts. And I have a teacher colleague who's actually designed different formats for the Snap. So instead of the page itself, he's created a pirate ship. So now students can look at where are they on the ship count backwards and forwards where they're climbing the sails and doing those kinds of things or a spaceship or students jumping a line. In that particular classroom, the students are able to go up on the windows because they have certain examples that you can draw on the windows with erasable markers.
[27:29]
So it's important for the novelty to be maintained as well because we know that students can become bored or things can become a little bit redundant when they look at the same thing over and over again. So the brain likes novelty. So it's important to embed that within this as well.
[27:44] Justin Baeder:
So the book is The Snap Solution, an innovative math assessment tool for grades K through eight. Jonathan and Tom, thank you so much for joining me on Principal Center Radio. Thank you, Justin.
[27:55] Tom Hierck & Jonathan Ferris:
Thanks, Justin.
[27:55] Justin Baeder:
It's always good to be with you.
[27:57] Announcer:
Thanks for listening to Principal Center Radio. For more great episodes, subscribe on our website at principalcenter.com slash radio.
