Ep 43: Standardized Tests

Pam Harris  00:01

Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able! I'm Pam.

Kim Montague  00:08

And I'm Kim.

Pam Harris  00:09

And we're here to suggest that mathematizing is not about mimicking, or rote memorizing. But it's about thinking and reasoning. It's about creating and using mental mathematical relationships, That mathematics class can be less like it was for so many of us and more like mathematicians working together. We answer the question: if you're not teaching algorithms, then what are you doing? Alright, so in today's episode, we're gonna turn the tables just a little. I'm gonna ask Kim to talk about everybody's favorite topic, high stakes tests. Wahoo! Yeah! Boo...So we're actually not a big fan. So Kim, when you teach Real Mathematics and spend the time and energy to really mentor students, as mathematicians, everything we've been talking about, you just have to acknowledge that you're not going to get to all the things you should. Right? And your students are just not going to do well on the high stakes test. Right? 

Kim Montague  01:13

What? Oh my gosh.

Pam Harris  01:17

Okay, so actually kidding.

Kim Montague  01:20

I know, you're kidding here. And I'm laughing because I know you.

Pam Harris  01:24

Yeah. So totally not. Right? Like, we don't believe that at all. But Kim, there are actually a lot of people out there who actually think that's what we're saying. They think that we're saying, if you teach Real Mathematics and mentor mathematicians, you're not going to get to all the things, cause you're spending time, you know, trying to get the kids from where they are to really think and that's not predictable. And so the kids are not going to do as well. So you're just not going to get good scores. Or they think that if you do what we are advocating you're doing, kids just can't perform on those tests. Because the tests are asking specific questions that are in specific formats or something. Whatever they're thinking, they think that we're just like, throwing our hands in the air and saying, therefore, your test results are not going to be good. So Kim, how do you speak to that?

Kim Montague  02:13

That would be a really unfortunate predicament to be in, right? To feel like you have to choose between teaching Real Math and also having to decide, do I want the scores or the results to reflect the work that you're putting in and your students are putting in? But it doesn't have to be either or.

Pam Harris  02:31

And it doesn't, and you've proven it. Kim, you're not in the classroom at the moment. 

Kim Montague  02:36

Right. 

Pam Harris  02:37

But tell me about your students when you were in the classroom with your students. Tell me about that.

Kim Montague  02:43

So I started teaching in a school that I absolutely loved. It was a Title I school in the district at the time. It was one of the lower SES schools kind of, we kind of live in a rural-ish area. And the campus was pretty diverse, great kids, great families. A lot of my kids didn't always have the most support at home, because parents were working at a couple jobs or maybe taking care of several other smaller kids. And I remember when state testing changed. We went from one that was kind of like, yeah, you just had to do it to a massive transition to - I was teaching third grade. And it was all of a sudden, if kids don't pass the reading and math section of this particular test, then they were held back in third grade. And it was super stressful to a lot of families and kids, and teachers. It was kind of a swift transition.

Pam Harris  03:41

Lots of pressure, lots of stress, lots of sort of parents not kind of understanding. And the kids were kind of freaking  - like everybody was sort of freaking out. 

Kim Montague  03:50

Yeah, we didn't know all the, you know, rules about how that worked. 

Pam Harris  03:54

Yeah all the ins and outs. And third grade was the first grade where all that pressure was on. And so all of a sudden, this is the first time kids have really taken this kind of test. And now what? What I can't go on to the next grade if I don't pass it? And parents are aware of that. And that was kind of made a big deal. And it was pressure, right? Okay, so you said -

Kim Montague  04:15

You know me, and so you know that I taught at another school, right? So I taught at that school for, I don't know, 10 or 11 years. And then I had a phenomenal principal that I love, love, loved at that school. And then she decided that she was going to open a new school in our district. And so I decided, my favorite teaching partner and I decided that we were going to follow her and open this new school with her and it was on the other side of town. And the demographics were quite the opposite. Same great kids, great families, but it was a little bit different. 

Pam Harris  04:46

You know, it's funny when you said great kids before, I thought to myself, you would say that no matter where you are. 

Kim Montague  04:50

Oh, yeah. 

Pam Harris  04:52

Kids are great, families are great.

Kim Montague  04:53

They were though!

Pam Harris  04:53

Yeah, of course. Kids are great, families are great, but the demographics were quite different on the other side. So, you've taught in very different circumstances. And sometimes we hear people say things like, "I mean, Pam, but you don't know my kids." 

Kim Montague  05:11

It's pretty common, right? And, of course, we don't know their exact kids. And I'm not going to pretend that we have the answer for every situation. But we have had, you and I have had struggling students who have little support. They're behind grade level. And yet you and I both believe that all kids can learn more Real Math than fake math.

Pam Harris  05:33

And let me just say that, again, all students can learn more Real Math than fake math, everybody has the capacity to do more Real Math than fake math and go further, farther, deeper, richer, Real Math, then this sort of rote memory mimicking kind of stuff. So did your teaching, the way that you taught Real Math, did it change in those different circumstances? Like you said, you had this Title I school, and then you had kind of the opposite end of the spectrum. So therefore, your teaching had to change, right?

Kim Montague  06:05

No, no, no. And to be honest, I didn't find that I had any more students who struggled in any of those two situations. In every class, every year, there was always a range, right? It's not like you walk into a school, and magically, everyone's on grade level, and does exactly what you want them to do. Everyone had needs that needed to be met. And it's the job. It's just that's how it goes. And actually, in my newer school, I found that I had a more challenging time, because we needed to convince students to think and reason. And they had spent a couple years before me just finding answers to problems. And they weren't really mathematizing. They didn't know that that was a thing. So it's not really about a demographic for me. It's about experience that kids have with Real Math.

Pam Harris  06:53

And by that you mean like in the first school, which is actually my kids school, I spent quite a bit of time working with teachers and with students, and sort of overhauling things and I've been doing a lot of professional learning. So by the time you got those students, they've been thinking and reasoning and mathematizing for at least a couple of years, if not a few years before that. So when you got them in third, fourth or fifth grade, you could just sort of run with them. They were already clear that math is Figure-Out-Able, and so you just kind of continue to figure out math. But in your new school, even though the demographics changed, and all of a sudden, you sort of had more on kind of on the higher end of the income level, you had to start fresh. And you had to begin giving them experiences that build mathematical relationships in their minds that made math more Figure-Out-Able.

Kim Montague  07:42

Yeah, and we still had state testing. My favorite.

Pam Harris  07:46

Crum! Still had that state testing. So I know you're a little reluctant to toot your own horn. You don't do that well at all. So I'm gonna do it for you. I am aware that your scores at both schools were not only good, they were exceptional. Both schools, both schools. And not only was your pass rate unreal, but in our state there's a measure that the state does for students who are excelling. That was also off the charts. Your rates were amazing. Yet you were teaching Real Math.

Kim Montague  08:24

Yeah. And I think when your goal is for all students to make significant growth, right, for all of them, it's not going to be just a high pass rate. It's not a goal for students who come in just to kind of stay and keep passing, everybody needs to progress.

Pam Harris  08:41

So in order to get those kind of rates, and I know you're dying, that I just told everybody that. Thank you for letting me toot your own horn a little bit. But in order to get those kinds of exceptional pass rates and excelling rates on a high stakes test like that, you must have spent a ton of time on test prep, right? Test preparation, you must have taken lots of practice tests had your students practice with sample items all year long. You must have taught all the content by March and then spent weeks reviewing right? Right?

Kim Montague  09:11

It sounds so bad. It sounds stressful to me. We have some required benchmarks given to us -  

Pam Harris  09:17

You're saying no, basically,

Kim Montague  09:18

I would say no. No. 

Pam Harris  09:19

No, you didn't do all that? Okay.

Kim Montague  09:21

So we had some required benchmarks given to us by our district. You know, tests along the way. But the goal for me was to teach as much Real Math as possible. And so I absolutely took some time to work with students on some released items. Some time. No one wants to be shocked by like weird wording or something that's kind of social knowledge. I wanted them to at least see what they were going to be experiencing. But the idea that I was going to cram it all in by March, you know, right before spring break so that I could get a month of review of test formatting was never gonna happen.

Pam Harris  09:59

That's not what you did?

Kim Montague  10:00

No.

Pam Harris  10:01

So you did do some work with some released items. Meaning our state will give the high stakes test and then a year or two later, they'll say here are some of the items that were on that test. And so that gives teachers an idea of what the items could look like and what kids might be expected to answer. And so if you would use those sometimes a bit, but often you use them kind of nicely, right? You would often leave off the answers, and kids just solve the problem. 

Kim Montague  10:26

Yeah.

Pam Harris  10:26

Sometimes you would look at the answer choices and help the kids choose between them just to sort of - like, there's lots of really nice ways. But again, you didn't do that, like tons. 

Kim Montague  10:36

Right.

Pam Harris  10:36

I didn't see that very often in your classroom. Enough that kids were sort of comfortable, that was kind of your idea. Yeah, just to give them a little exposure, right? We do some Real Math, a lot. And then I would say, "Hey, this, maybe these things that we've talked about like this, this is how somebody might ask you that." Yeah, give them a sense and a feel for I might be asked to show my understanding in this way. So one of the reasons I mentioned this idea of like cramming it all in by March is we see that around our state. And I don't know if anybody else is doing it around the nation. But we see a lot of teachers that manage their scope and sequence, the district's manage the scope and sequence so that teachers sort of get everything in early in the year, we consider it early in the year, so that then they have this inordinate amount of time before the high stakes tests to just review. So I've gotten it all in and now we're just gonna review review review, because we got to make sure it's all fresh and everything. But that's definitely less your perspective. So let me ask you this. Was it ever true that in teaching Real Math and not like trying to cram it in really early so you get all this review? That the as you were doing that, was it ever true that you didn't get to all the standards that the content you were supposed to teach in that grade level that you just didn't? You didn't make it? By the time the test came around? You're laughing.

Kim Montague  11:51

I don't even know how to answer that. No, no, that's not a thing. In our state, right, we have required standards, and it's my responsibility to know what they are and to teach them. So, um-

Pam Harris  12:07

So you did. You were clear what your standards were, and you were really clear you were gonna make sure you exposed students to those standards, that the kids had experience with them.

Kim Montague  12:19

Yeah, yeah. The job is know your standards, or your content, and know your kids. Right?Those are the two big things for me. Know your content, know your kids. So what I did do rather than treat it like this individual list of a ton of things to work on, because that can feel like a lot. I did spend more time on some of the meatier ones, the overarching standards. And as much as possible, I made sure it wasn't teaching one single standard in isolation. We're bundling things. It's not a series of unconnected ideas. And it's not a checklist of did that one, did that one, did that one.

Pam Harris  12:55

Yeah, it's more about helping students develop as mathematicians. So you use these big overarching ideas, and sort of slide the little ones in as you go. And the better kids get at those overarching big huge things, then everything else kind of fits in more naturally. So what are the things that you did to help students get ready for the high stakes test?

Kim Montague  13:15

We mentioned this a little bit. But when I needed to give kids a kind of a feel for, hey, we've done some work on - pick a bundle, and I want them to see what something might look like on a high stakes test. There's a couple of different ways, you know, I might put up a question and without any answers. And just have a conversation about how would you think about this problem? How would you solve this problem? What's it even asking? So no answers, right? No ABCD format. I might give them the question with the answers. And we have a conversation, or they do some work around where did these ABCD answers come from? How could a test writer come up with these other choices? 

Pam Harris  14:02

Oh, nice! 

Kim Montague  14:02

So that we can kind of analyze a little bit. We definitely did a lot of time estimating first. And then eliminating choices based on if you just estimated and didn't even dive into some of the work. Then some review of like social knowledge, some of the terms that they might have seen. 

Pam Harris  14:23

And one of the things we've talked about before was also the idea of numberless word problems where you could like blank out the numbers. And ask the kids, "Like what's even happening here?" Let's make sense of the problem. And then what numbers could make sense in here? And so then if we threw those in, oh then what would this one. And so if you've ever looked at numberless word problems, we'll put that link in the show notes. We really like some work that our friend Brian Burchard has done with numberless word problems. We'll stick that link in the chat.

Kim Montague  14:54

Yeah, I was actually, if you don't mind, I was in a second grade classroom just the other day and we were having this conversation about are the numbers what the kids are struggling with? Or is it the the ideas that are happening in the problem? And so you know, we just like: close your eyes, visualize what's happening, don't have any numbers in it. And the kids really understood what was happening in the story. And it was the numbers. But for some other kids, it was the numbers, or the other way. I don't know which one I just said. But it was the reverse. They didn't understand what was happening in the story. And so a lot of work to just get kids to make sense of things first. But here's the thing - 

Pam Harris  15:32

So you're saying that that's actually important as a teacher? Like you just said, know your content, know your kids. That to me sounds like an excellent example of know your kids. Is your student right now struggling with this particular question, because they don't understand what the question is asking? What's happening? What's the scenario? What's going on? Or is it the numbers in the problem that are tripping them up? They're, doing the multiplication a little bit wrong, or they're like, whatever? Is it that the numbers tripping them up? Or do they need to understand the scenario better? And that, like hugely points to your mindset of know your content, know your kids. If you know your kids, now I'm not trying to help them solve this crazy problem in a way that they don't need. I'm really diving in, I'm dialing in and helping get like really clear, "Oh, this is what you need more help on?" Yeah. It's a different conversation. So the thing that I think we talked about earlier that I want to emphasize is that sometimes we see teachers say that they don't care about the test, and that the scores aren't important, right? They want to give that feel to their students. And they say, "Hey, students, you don't need to worry about it, because they just tell me about you and what you need and what I've done and how I can help better." Which is a good message, right?

Kim Montague  16:46

Right. It's a great thing to share with kids that it's just this one snapshot of one day. But we also sometimes see some of those teachers practice over and over and over. And they put emphasis on correct answers and not the thinking. And the kids are really clear that based on the actions of the teacher, that's something to freak out about. So...

Pam Harris  17:12

If you say one thing, like, "Hey, guys, you don't need to worry about this. It's just a snapshot. It's just a one moment, but now we're gonna practice forever." And you're filled with anxiety. Yeah, that's gonna come through.

Kim Montague  17:28

So I really feel like one of the things that my teaching partner and I worked really hard to do, when kids would ask me about it, especially in third grade, right? It's the first test year and so they would ask about it. And we would say things like, "Oh, heavens, I'm not like, super concerned about that. We're gonna do Real Math this year." But we tried really hard to make our actions match that.

Pam Harris  17:52

Yeah. So it sounds like your attitude towards high stakes tests is really important. But also how your attitude plays out in your class is actually the most important. Like that's totally interesting. Okay, so how did you deal with other pressures, like your principal and coaches? How did they deal with your unique ways of teaching?

Kim Montague  18:15

Well, I think part of the thing that helped was that my scores were pretty good. And so they left me alone a little bit. And I also knew my kids really well. And so when they asked me pretty pointed questions about a particular student, or particular, you know, score, that was not quite where we wanted it to be. We could dig into that. And we knew exactly what that particular student needed. And I could give some evidence of these are the things that we're working on.

Pam Harris  18:44

Yeah, because that's the goal, to help each individual student. It's not about, hey, you've got 5% of your students that aren't performing or whatever. 5% like, let's dig in, who are those kids? What can we do to to help them? And then I'll just mention, they actually hired you to be the coach at that school. Like, you know, it played out. Your success and the way that you were sort of handling everything was very attractive to leadership. Where they're like, "Yeah, we want you to help other teachers to be able to get results like you're getting." So I'll just add in a little bit that when I taught in Michigan, I found that I had the same experience. Because my scores were good enough, they kind of couldn't argue with me. They couldn't tell me to stop. Like they couldn't sort of look at what I was doing, teaching Real Math and say like, "That's not working, you must, you know, cease and desist and do more of this rote memory stuff." So teachers, leaders, parents, we are suggesting that teaching Real Math will actually help your scores. But be smart about it, right? Do some test prep. We don't want students to be shocked by the way questions are formatted or other social things. Really mean it when you say that the results are not the measure of a student's worth. Really mean it when you like don't want the pressure and all that thing. We submit that if students believe that math is Figure-Out-Able, then they'll just do their best to figure out the math on the test.

Kim Montague  20:06

And that's what we want, right? We want our students best and that's enough.

Pam Harris  20:09

And that's enough. Alright y'all, thanks for joining us today. Don't forget to send us your questions for our really cool 50th episode that's coming up. Send them to Kim@mathisfigureoutable.com because on that 50th episode, we are going to answer your questions. A Q&A episode. So get those sent in and we'll get right at answering them.

Kim Montague  20:29

We would love for you to join us on MathStratChat on Facebook, Twitter and Instagram on Wednesday evenings where we throw out a problem to the world and share strategies. If you find the podcast helpful, would you please rate it and give us a review? We would really appreciate that.

Pam Harris  20:45

So if you're interested to learn more math and you want to help yourself and students develop as mathematicians, don't miss the Math is Figure-Out-Able Podcast because Math is Figure-Out-Able!