Episode #217: What Should “Count” With Standards Based Grading? – A Math Mentoring Moment

Jan 23, 2023 | Podcast | 1 comment



In this episode, we speak with Guillaume Paré, a high school math teacher from Quebec City, Quebec. Guillaume has transformed his assessment and evaluation practices over the years to move away from overemphasizing grades and focusing more of the attention on growth. 

Guillaume is struggling with how to determine what should impact and influence both the feedback and grade for a specific standard when an error or misconception is not directly related to the learning goal of focus.

Listen in as we help Guillaume weed through what really matters in his assessment and evaluation process by breaking things down and building it back up again.

This is another Math Mentoring Moment Episode where we speak with a member of the math moment maker community where together we brainstorm strategies and next steps for teachers to overcome pebbles they have in their shoe.

You’ll Learn

  • How evaluation practices can affect student perceptions of mathematics regardless of how “high” the grade might be;
  • Why feedback is more helpful (and less hurtful) than assigning grades on student work;
  • How much impact or influence mistakes should have on a final grade when using standards based grading (SBG);
  • What areas of mathematics should we assess that are NOT standards in my course?



District Math Leaders: 

How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge? 

What about opportunities for those who are eager and willing to elevate their practice, but do not have the support? 

Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning. 

Book a short conversation with our team now

Start your school year off right by downloading the guide that you can save and print to share with colleagues during your next staff meeting, professional learning community meeting or just for your own reference!


Guillaume Paré: That's where my pebble is. What he's asked of me is, is that kid good in grade 10, or the grade 10 skills, this kid is perfect, but he gets no right answers. That's what I'm trying to get the kids to figure out. If you would like to go back on those skills and make sure that you get them and you are able to work with them, it's going to show up with getting the right answers every time.

Kyle Pearce: In this episode, if speak with Guillaume Paré, a high school math teacher from Quebec City, Quebec. Guillaume has transformed his assessment and evaluation process over the years to move away from over-emphasizing grades and focusing more on the attention for growth.

Jon Orr: Guillaume is struggling with how to determine what should impact and influence both the feedback and grade for a specific standard when an error or a misconception is not directly related to the learning goal of focus. Listen in as we help Guillaume weed through what really matters in his assessment evaluation process by breaking down the things that he's doing in his classroom so we can build them back up.

Kyle Pearce: My friends, this is another Math Mentoring Moment episode where we speak with a member of the Math Moment Maker community just like you, and together we brainstorm strategies and next steps for teachers to overcome those pebbles that they have kicking around in those shoes. Let's not waste any time. Let's dig in with Guillaume. Welcome to the Making Math Moments That Matter Podcast. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr. We are two math teachers from makemathmoments.com, who together.

Kyle Pearce: With you, the community of Math Moment Makers worldwide who want to build and deliver problem-based math lessons that spark curiosity.

Jon Orr: Fuel sense making.

Kyle Pearce: And ignite your teacher moves. Welcome everyone to another Math Mentoring Moment episode. These are some of our favorite, favorite episodes because we get to sit down with friends just like you and we get to chat about those pebbles that are shaking around in your shoes. Before we get going here, I want you to just take a moment and pause. And if you've got a pebble in that shoe, head on over to make mathmoments.com/mentor so you can share a short couple lines about your current pebble and hey, maybe we can get you on so we can have a conversation about that one.
Jon, this discussion here with Guillaume is great. First off, my thinking here after just hanging up the call with him is that first of all, super committed, dedicated and really wants obviously all of his students to grow and shine as mathematicians in his math class. What are your thoughts here to just set us up for this episode as we dig in?

Jon Orr: He's made some great changes in his classroom practices over the course of his career, getting to this place where he's focusing on feedback for growth. He's taken the ideas of a standards-based grading and applied them specifically to help his students see that growth is important and he's eliminated his grades to help do that. Now, the interesting thing here, Kyle, is that a lot of the practices he's put in place is actually what we teach over in the Assessment For Growth course, which we built a course on how we use assessment in our classes to do the same thing that Guillaume is doing.
That course we'll share after the episode is over, but he's doing a lot of the things that we teach, which is amazing to see that he's come a long way with those things. But let's get into it. Let's let our listeners here hear Guillaume talk about his struggle around how do I filter out the real thing I want to look at versus all these other things that contribute to success in the math class. Let's hear Guillaume and let's get right to the conversation.

Kyle Pearce: Here we go.

Jon Orr: Hey, there, Guillaume. Thanks for joining us here on the Making Math Moments That Matter Podcast. How are you doing today?

Guillaume Paré: I'm doing fine. Thank you for having me.

Jon Orr: Awesome, awesome. We are honored to have you and chat with you, and we're excited to dig into some of the ideas, what's going on in your classroom, and hopefully we can brainstorm some stuff here. Guillaume, fill us in on some details here before we get started. Let us in our listeners know where you're coming from. I know some of them are like, "Oh, I heard an accent. I heard an accent." Let us know where you're coming from and what your current teaching role is, and then maybe a little bit of backstory of how you got into that teaching role.

Guillaume Paré: Right. I come from Quebec City in Quebec, so English is not my first language. I hope that everyone's going to understand if I do some mistakes when I speak. I teach what would be grade 10. In Quebec, in each year we teach every subject, so that means that there is not only one subject for the year. I teach in a special program where I teach both math, basic science and advanced science to the same kids.

Jon Orr: Oh wow!

Guillaume Paré: I see the kids 12 times every nine days. Sometimes I have half a day with the kids. That allows me to do more stuff that we don't want to do because it takes a lots of material or lots of time. Because today I was having a two period class with my students, so that means that two hour and a half class with them. We were working on ballistics, so they were using a ramp and they had to calculate where the marble would land exactly when it was using the ramp. It needs more stuff than what we used to in the math class. But since I had two classes in a row, it was easy for me to have them work on those ramp and use them afterwards.

Kyle Pearce: I love it. I love it. That sounds so interesting. It's such a unique structure for your classes. I'm sure probably you're used to it, but in my head I was picturing you see them I think you said 12 times every nine days or something along those lines. I'm sure there's a bit of a rotating schedule going on. That's probably a little bit hectic for you and maybe even the students to keep track of. But once that routine gets going, I'm sure it's really helpful just to have it sounds like different block lengths, right? You had those half days. And then what would be your shortest period, out of curiosity, the shortest time length that you're with students?

Guillaume Paré: 70 minutes or twice 70 minutes.

Kyle Pearce: Got it. Got it. Awesome. Here in Ontario, we do 75 minute periods, so that would be like one or two periods together we would call them or two classes together. That's a really interesting structure. And like you say, it gives you a little bit of freedom. In that marble activity, immediately what comes to mind is a colleague in my district, Dylan Langlois, who I know sometimes listens to the podcast, he used to do some catapults and he used to have a marble activity. It sounds like you and him would probably really hit it off with some of that work. That is fantastic. Thanks for giving us some context.
I think I've said it before on the podcast, but I was born in Quebec. I don't have the awesome, awesome accent sadly because I moved away when I was really young, but what a beautiful city Quebec City is. Before we go any deeper though, we're wondering, can you help us take us back into your own experience as a math learner and tell us what is that math moment that resonated with you or pops into your mind when you think of math class?

Guillaume Paré: I would have to use two moments. The first one is when I was in that would be eighth grade, during my time there, every time before the end of a I would say a semester, like a three months period, we have a report card every three months. Within those three months, I would always get one answer wrong. But only one every three months. And because of that, at the end of the year, I would not even want to look at my report card because I was always saying, "Well, I could have done better." But in fact, would I have really done better? Was I really not a perfect scorer? My score was not perfect, but I think that I did understand everything correctly.
Sometimes I was wondering why would one small calculation mistake stop me from getting an A in my class. Not an A, but a 100% in my class. I remember that the last semester or three months period of the year, I just took the report card and just threw it on the garbage because I was tired of always getting a near perfect score, but not getting it because of a small mistake. When I decided to become a teacher at the end of high school, I didn't choose math because of that. I was supposed to become a chemistry and physics teacher.
Just because of that relation that I was developing with math, with always trying to get the perfect score and never being able to get it, that is something that I'm trying to get as far away as possible with my students right now. Now, I'm not evaluating with percentage anymore. I'm using A, B, C, D and E as a way to show the kids, well, you may have done a little mistake, but I can understand that you are in control of that concept and you're really, really good using it even if you are not perfect using it. That would be one thing.
The other thing would be, it's funny because it's not even a math class, but the person that helped me become what kind of math teacher I'm now is an economics teacher because she was always trying to have us do real hands-on things with the maths and with the different concept that she was teaching, and that's what I like to do with math. Because I'm teaching grade 10, and I don't know if for you in Ontario, but here starting at grade 10, we have lots of abstract concept.
Sometimes it's pretty hard for the kids to be able to see where that could be useful. I like to do activities, like the rent activity I just talked about, to make sure that they know that not exactly who is using that knowledge in real life, but there is application of that knowledge.

Jon Orr: Very interesting. Very interesting. I like those two different memories that are sticking with you for those two very specific reasons. I think you've very nicely articulated how they've impacted your style, your philosophy of teaching. I think we all do that a little bit by taking our memories of what we've experienced and using that to shape what we like and what we don't like about the education system and how math is taught or how we believe math should be taught. Guillaume, I'm curious a little bit here, you said in the assessment piece memory that you're trying to grade in a different way.
I'm curious what your old self would've felt like in that class. Imagine taking your old self who's shooting for the 100% report card and throwing it in the garbage if it doesn't get 100%. That student is sitting in your class right now. How do you think that student is feeling right now?

Kyle Pearce: Oh, interesting.

Guillaume Paré: I do have students like that in my class that are always aiming for the perfect thing. But sometimes when they do small mistakes and I can as a teacher show them that I do understand that it's minor mistakes, that maybe in another problem they would not have done it, and that doesn't really matter with how they handle that mathematical concept concept. So they're able to get an A.
If they get all A's during the semester, at the end of the semester, I give them 100% anyway. We always say that, that we need to allow and even make sure that kids that they know they can do mistakes. What I do now is I make sure that those mistakes are not what is showing on the report card at the end. If they have understand, even if they had some small mistakes, they can still get 100% at the end.

Kyle Pearce: It's interesting, because when you were sharing that memory, what resonated with me, I started to think about how we often really think about those students who are struggling in math as why reporting and evaluation and a lot of the things, the practices that we use have maybe hindered some students' perceptions of themselves as mathematicians and so forth. You've opened my eyes to the other end of the spectrum that I don't think most would think. Hey, listen, you almost got perfect. What's your problem? Aren't you happy with that? But in reality, it's like every student is looking at that and they're perceiving it differently, right?
If you're a student who has always received a 50% or has always received an 80% or has always just been just short of that perfect, it's like it has a different effect on your interpretation. It was almost like I was imagining your situation where it was like you threw it out, you knew what was coming. How helpful was that for you? It was almost unhelpful. Because you knew what was coming, it didn't help you push your thinking further. If anything, it actually hindered you. It actually sounded like maybe you moved away from mathematics, maybe thinking it just wasn't right for you.
That for me is a big epiphany that I've had here and it really pushes towards this idea of how we as educators, not just in mathematics, but I think specifically in mathematics, we tend to struggle with assessment and evaluation policies more so than some of the other subject areas. I'm wondering, before we dig in and dive deeper here, I'm wondering what would you say would be maybe a quick win for you in this area of assessment and evaluation? It sounds like you're thinking differently about it, and I think we're going to be talking about a pebble that's related to assessment and evaluation.
I'm wondering, any quick wins that you can share, maybe something that you've tried or something that has worked well for you either in the past or maybe it's something more recent.

Guillaume Paré: Well, I try often not to use marks at all with the kids. They get evaluation. It's full of comments, but there's no marks. That way they can focus on what they did right and what they did wrong instead of only focusing on the percentage at the end. I got an 80% and I don't look at my work anymore. Lots of times I'm doing that with the kids. I'm just giving them their exams and they're asking, "Oh, can I know how much I got?" No, I cannot tell you how much you got. How much do you think you should get for that work that you just did? Most of the time they are pretty hard with themselves and give them lower score than what I wrote in my grade book, but it helps them focus on what is important.
What we want to do is to learn, not to get high scores. That's something that I do often with the kids. I'm not saying that it's easy, because some of the kids are working for the grades and wants the grades. Parents are writing me, "I want to know how much did my kid get." But I said, did your kid present you the exams with the comments on it? Yes. Well, that's what they have to work on and that's what is the important thing. In my classroom, a kid can always retake an exam or show me that the marks they got is not a good appreciation of what they are able to do.
Without having any marks, they can say, "Well, I did a lot of mistakes in that area. Let me show you that I can do that. That way, I don't know what my mark is, but I know that I can improve it." That's something that I like to do. It's not easy, like I said, because some parents are not for that way of thinking in working with the kids.

Kyle Pearce: Yeah, no, totally. I was just going to mention that it's so interesting because kids do so many other things in everyday life that parents are interested in. Maybe it's sports or it's music or it's art or it's some other thing and it's not grade-based and it's based more on feedback. You hear what the coach says and you watch what your child's doing out there. And yet it's almost like parents, because they've been through the system as well, but also it's like they're trained that this is how it happens, it's almost like just tell me the mark so I don't have to worry about it. That will allow me to not have to worry about it.
I totally see where parents are coming from there, but I want to just do a little hat tip to you for sticking to your guns there and really trying to help them see that actually this feedback actually goes a lot further for students. Because the reality is it kind of doesn't matter what that mark is, whether it be really high like you were experiencing or really low like I was describing, what matters is what's the next step. We all need to be working on a next step. I fear when a parent sees a 90, the next step is good job and that's it, right? Versus a student who has a 50, then it's like, "Get the tutor." It's like an emergency.
But in reality, either of those options isn't that helpful. What's really helpful is exactly what the next step should be. It sounds like you're working towards that in your practice. Congrats to you.

Guillaume Paré: You're comparing that with training. I'm also a coach. I coach air rifle and air pistol shooting. We get the same problems there. Because at the end of the day, they shoot a score over 600 and their parents are always saying, "Well, you shot 580. You should have done better," but 580 is really, really good. Doing something better, just saying that, it's not something that we can do. You have to work on your technique. You have to work in your mental state. You have to work on specific thing, and then the score is going to change.
It is the same thing in school. Saying that you should have got 80%, it's not the same thing as make sure that when you're calculating equation, you make sure to respect the order in which the calculation has to be done. That's something the kids can work on. Just trying to get the grade to go up, that's not something you can work on.

Jon Orr: Guillaume, I'm curious what you're seeing from the students when you are using this style of assessment with them. You're holding back those marks. You're giving the feedback. What have you seen in terms of improvement? I'm sure you didn't start your career like this, is that correct? Right. You've got this comparison that you can kind of refer back to. Hey, I used to do it this way. Now I do it this way. I'm curious what you're noticing as a benefit from doing this with the students. You're telling us how you do it, but I'm curious what improvement have you seen. Can you give us some details on that improvement? I know there's lots of teachers listening going like, "I'm very curious about this part."

Guillaume Paré: I would not say that I've seen improvement in every student, that's for sure. But for the students that are engaged and that wants to do better, that's a way for them to know what to work on instead of just saying, "I have to work on everything." Like what you said, we need a tutor. What is the tutor going to work on? We don't know. We need a tutor. That way now at the grading part of the work, they know what to work on. If I have a kid that is doing let's say less well than everyone else, the comments on his paper are going to be different than everyone else. I'm not trying to get him to go to 100%.
Like you said earlier, I'm trying to get him to go to the next step. Everyone get comments on their sheets, everyone knows what to work on, but they have what to work on according on where they are right now. The kids that were only shooting for the marks and they just take their paper and say, "Oh, I don't know how much I got," some of them they don't look at the comments, but they would not have looked at the comments anyway.
At least now I'm trying to focus them on the important thing and say, "Well, you want to improve your marks that you don't know what it is? Work on that. Come back and see me. I'm going to reevaluate you. And if you change what I wrote on the paper on your exam, that way you're going to be able to raise your marks, even if you don't know what it is."

Kyle Pearce: I love it. I love it. You're highlighting this idea as well that with assessment and evaluation, if the assessment and evaluation is I'm going to call it valid, if it's actually real, it's true, it's actually done well, it's very difficult for a student to go from whatever that number was anyway to 20% higher. That's a really hard thing to do if it's true and real assessment and evaluation. Because as you mentioned in your air rifle example, it's unlikely that you're going to go from missing the target completely to suddenly you're just like a laser, you're hitting the target every time. It's going to be gradual and you have to make those steps and those shifts.
Bravo to you that you're on this journey. It is a hard journey as well, as you've articulated, that it's not an overnight thing where all of a sudden every student wants to get better and they all want to take advantage of this feedback and they're all going to use it, but it definitely points us in the right direction. Just like for our students, we can as educators expect things to go 180 immediately. Sometimes we're going to overshoot or overalign and we're going to have to try to find that balance. My wonder for you is, what would you say is a current struggle, what's a current pebble in your shoe right now?
I know that this is where your head is at in terms of trying to improve in your own teaching practice. Where is the pebble appearing right now in your assessment and evaluation practices?

Guillaume Paré: I'm wondering, when I evaluate my students, and let's say I'm teaching about calculating means and kids are doing mistakes that are not aligned with what I'm trying to evaluate, they have some concept from previous years that they are not good with them and they do mistakes on those years, but I'm trying to evaluate what they're doing this year. What part of our evaluation should be on those things?
Should I say, "Well, that was a mistake from grade six and you already passed grade six, so I'm not taking care of it," or I would not do that, but just to see what would be able, or I would say, "Well, you don't get the answer. If you don't get the answer, that means that you are not able to do math right now, so I'm going to penalize you a lot for that mistake." Those are the two extremes, but where should we be between those two?

Jon Orr: Got it. What I'm hearing is you got a piece of evidence from a student. You're looking at it and you notice that they're making a continued mistake on a skill that you're not necessarily talking about, you're not necessarily looking at to give feedback on, and it's preventing them from getting the right answer. Is that correct?

Guillaume Paré: Exactly.

Jon Orr: Got it.

Guillaume Paré: Not only once, but I can see that that mistake is coming back and back and back. But when I'm looking at my evaluation grade, it's not something that it isn't it because it's not a grade 10 skill that I should evaluate. It's something that should have been mastered already by the kids.

Jon Orr: Right. Guillaume, what would you like to do in this situation?

Guillaume Paré: Good question. When I'm trying to get the kids to learn stuff, that's something I want them to learn. In a perfect world, I would like the kids say, "Well, that's the third time that Guillaume is telling me that mistake. That it's not something that we are working currently on, but something that we did work on let's say three years ago, and I really need that to become efficient so I can prove that I do know what we are talking about right now." That's what I would like the kids to figure out by themselves.
Say, "Well, I need to work on that. I'm going to go and talk with Guillaume to ask him, well, what can I do, even if it's outside of the class I'm teaching right now, but what can I do to make sure that I don't repeat those mistakes again and again and again."

Jon Orr: When you're looking at that piece of evidence and you're about to write the comment on what they're going to do next, what have you set up? What are your look fors? I know that it's specific to different topics, different concepts, different skills, but generally, what are you looking for on say that piece of evidence before you write that comment? Now, what I mean by that is... I'll classify a little bit more. We all teachers know when we see a piece of evidence to go, "Yeah, they got it, or no, they don't." This is our professional judgment that comes into play after our experience. We can see solutions. We can know where some mistakes happen.
We know when they clearly demonstrated their understanding of this particular concept. You know what to look for. But when you're going to write a piece of feedback to them, we want to think about what are we looking for so that I can give them the right feedback. I guess my question here is, when you're about to write that feedback, what are you looking for to write that piece of feedback?

Guillaume Paré: When I'm writing that feedback, sometimes I write it, I will tell the kids, I will say, "I can see that what I'm teaching you right now, you understand. But because you don't know how to add fractions, you are not able to get the right answers." That's where my pebble is. What is asked of me is, is that kid good in grade 10? For the grade 10 skills, this kid is perfect, but he gets no right answers. That's what I'm trying to get the kids to figure out. If you would like to go back on those skills and make sure that you get them and you are able to work with them, it's going to show up with getting the right answers every time, even if it is not something that I'm teaching you right now.

Kyle Pearce: Right, right. I'm sort of trying to think of an analogy, and I'm thinking almost as thinking about like an advanced biking course or something like that where you're trying to become more efficient and you're trying to get faster as a biker, or maybe it's in a sport and you're taking power skating classes and you're getting better in those power skating moves, but your stick handling hasn't caught up to your speed. You're looking at it going, "But wait a second, it's a power skating course and all of those things are going well."

Guillaume Paré: Exactly.

Kyle Pearce: But ultimately, at the end of the day, you're not a complete hockey player yet. And in math in particular... Yeah, go ahead, Jon.

Jon Orr: I was just going to interject on this analogy here on some level that the student thinks about themselves as well. It's kind of like you're saying they've done these things over here, but they're not the complete hockey player yet. I'm wondering, does the hockey player also not feel that confidence that they know that they're not a complete hockey player yet because they're experiencing this lack of skill or lack of deficiency somewhere along this line? We translate that to a student. It's when you are thinking about assessing or writing this piece of feedback.
Are you looking for confidence in a sense that says, look, am I seeing consistent evidence in the products and the observations and the conversations that this student is confident and consistent, can demonstrate the skill I'm looking for? I think we have to be clear on what skill you're looking for. You can say, "Look, I've got my grade book. I've got my comments ready to go. I'm looking on this particular skill. How are they doing on that?" This is something I remember battling a long time ago with communication marks. How well are kids communicating ideas?
It's like, well, some questions I'm looking for how well they explain and communicate their thinking and some questions over here, I might be looking at how well they demonstrate the understanding of mathematics on this skill. That's why I asked that question about when we're looking at the feedback, we have to I think focus and pick what's the thing I'm looking for here, and then I can write my piece of feedback, and then I can also say how well this student is doing. And that translates back to the student also feeling like they might themselves know they're not confident in this area because they're getting this feedback consistently.
It's like, I'm not the complete hockey player yet. I have to move forward there. They're also feeling like that because they have this deficiency in these areas that they need to spruce up. We're giving them the right comments over here, but we know we got to push them to pull this all together.

Kyle Pearce: I'm wondering too, and this is something interesting that I'm picturing that hockey example or analogy and thinking about a math class, and I wonder if there's almost like two buckets that we have to think of as well. Jon, you're talking about what is it we're looking for. And in this what we're looking for thought or reflection, I feel like you almost have to look at, okay, is this concept or skill, I want to see if the students what they know understanding can do with it. Is there something happening here that actually is hindering them from being successful with this new concept or skill?
And if the answer is yes, then in this current moment, and maybe I'll change my mind by the time I speak about this again next week or next month, I almost feel as though that is connected, it's like those are together. Without that other piece, this piece isn't going to work well. You're never going to be successful with that piece. For example, let's say Pythagorean theorem. It's like you seem to understand the sides and you seem to understand the two shorter legs and you see that third side, you understand all of these things. You even understand where to substitute values into the formula for Pythagorean theorem.
But it just seems like every time you try to square a number, you're doubling the number instead. It's like even though that concept itself isn't Pythagorean theorem, but it's essential for it, I feel like there's something that keeps it glued at the hip. It's like that's got to have some connection there. However, on the other hand, if there's this other concept that's going on and let's say they make an error, maybe it's a careless error, I think careless errors are very common where maybe they just make a silly computational error or something, the understanding of the concept isn't hinged on it, then that might be maybe a separate scenario.
You might still provide some feedback. Overall you're like, "They've got this. They've got this." I wonder if that's maybe something that when you're looking at these problems, if you almost put it through this first filter of is this error actually directly connected to this idea, in that without this understanding, your success with this new idea is going to forever be hindered. If that's the case, it's almost like we need to ensure that this is addressed sooner than later.
If it's something maybe unrelated or maybe it's a certain scenario or problem where you're integrating two ideas together and it's like this idea is separate from this other idea, you can see understanding here, but you can see maybe they're not understanding this particular idea. Maybe that's something that's a little more fragmented or separate. What are your thoughts on that? Does that help you with any clarity, or how do you feel there?

Guillaume Paré: I like the two different cases, because using the Pythagorean theorem as an example, the kid that is able to use that theorem to calculate everything as long as it is whole numbers and...

Jon Orr: And pretty numbers.

Guillaume Paré: They're good. But as soon as I get one-half or one-third for one of the sides, they're not able to do anything, because they know the theorem, they know what to do with it, but their knowledge of fraction is keeping them from showing what they know.

Kyle Pearce: That's an excellent example that you just shared of those two ideas for sure.

Jon Orr: And it definitely is. Now, this example brings up an idea that I usually consider in these types of situations. If you think about a rubric on the Pythagorean theorem, so you're thinking about the stages of where are the students understanding lies on this, you're thinking about can they do it with easy numbers? Can they do this with these skills, and can you witness that? You might get almost all the way there with the rubric, but then also your specific example seems to be like that could be a completely separate thing going, look, I can witness them doing this Pythagorean theorem.
But over here I'm seeing every time I substitute into this particular problem or in this student that they're lacking some of the skill with fractions, or maybe that's what Kyle's example with, exponents in multiplying, that part seems like if it's fractions, it's like over here on this other skill I have down here, that's a fraction skill and I now have evidence that says we need work on fractions. All of a sudden, now I have to consider that say standard to be captured over in this area versus this area. Whereas this area I'm seeing, hey, they've got the Pythagorean theorem, but it's very clear that it's over here we need to have that working recorded over here instead.

Kyle Pearce: And you know what, Jon? What pops into my mind as well, which is kind of a philosophical debate or discussion to have, is oftentimes, I'm not sure in Quebec what this looks like in terms of your curriculum or your standards, but at some point, some standards fade away, which is almost like the curriculum writer is suggesting, "We've introduced it during these grades. We've come back to it and gone deeper. We've gone deeper. We've gone deepest," and now it's almost like assumed that it's good. In grade 10, for example, you might not have an explicit expectation or standard that says students will be able to multiply fractions.
When you have Pythagorean theorem with fractional side lengths and now they have to square three-fourths of a meter or whatever it might be, now you run into this other challenge where you go, "Well, this isn't even a part of this course." But at least in my personal belief, I go, actually it is. Because I believe that if you're in this course, the thought is, is that we're strong with all of these ideas behind this course. I totally understand that most students come in not strong in all of the previous prerequisite concepts.
But to me, I look at that and go, all right, I might actually create another bucket, another standard that isn't formally connected to my course, but it is something that I want these students, I want them to have feedback and I want them to get better in that area. And then you'd have to decide later on how does that impact or influence that final grade at the end.
But my gut would suggest is that by offering that feedback and by students seeing that like, "Hey, all these new concepts you're doing really well with, but you're almost hitting this ceiling," like Jon said, as soon as those numbers turn from good looking numbers to not so great looking numbers, all of a sudden things start to crumble away, and again, it's highlighting some challenges or some areas that we can work on, which again is really what this is all about.
It's by highlighting that, hey, it's not Pythagorean theorem that you're struggling with. Hey, now when we get to that tutor we were talking about, we have something real we can work on here instead of just trying all these random problems and hoping more practice of random things is going to help fix the problem.

Guillaume Paré: Like you said too, I have my grade 10 curriculum and now I just figured out that I need to add something, because for that kid, that part, which is not part of the curriculum, is now something that they need to work on. I really, really like that part.

Jon Orr: Think about the power that you and your students are going to have right now because you're working in a standards-based grading environment, the way you've outlined it at the beginning of this call, to say that you're giving feedback on specific skills. I'm sure you're tracking those skills and think about if you set that up. Now it's like we were working on Pythagorean theorem, but we hit the wall here on Pythagorean theorem because of this deficiency over here. If we work on fixing that deficiency and because you're using standards-based grading, it's like, hey, let's give a shot at another Pythagorean theorem and let's see if that wall's broken.

Kyle Pearce: I love it.

Guillaume Paré: Yeah, that's pretty good.

Kyle Pearce: How are you feeling right now, Guillaume? First of all, again, some great successes, some great ideas. Really I like the forward thinking in terms of your assessment and evaluation and your goals for your students. It's very clear that that is first and foremost, which I think is so important as educators, that you're actually trying to help students grow. You're not just teaching curriculum, you're actually looking at helping them grow. You've come with this pebble. How are you feeling now? You came in with this pebble. Where's your mind at now? Are there maybe takeaways that you're going to be thinking on and maybe trying to put into place as you move forward?

Guillaume Paré: Right now, I'm going to have to think about it later on, but now what I'm thinking is in my grade book to really add for something else for that kid. Let's use the example with the fractions with the Pythagorean theorem. When they do succeed in understanding that part, I can just erase that part of the curriculum, because now they're able to show me that everything else is good.

Jon Orr: I love it. You're tracking this area just so that you can provide growth, which is the whole point of what you're trying to do anyway.

Guillaume Paré: Yeah, exactly. I really, really love that idea.

Kyle Pearce: I love it. I love it. I think you're latching onto it in exactly how we're perceiving it, where it's like ensuring students understand that. I think sometimes students look at grading as punishment. You had mentioned this in your math moment even, just about this idea of a mistake and why did that influence my grades so much on these report cards? I think students kind of look at grading in that way. As long as that story for students is that this is for growth and this is to help, not to hurt, I think it helps you navigate maybe some of the trickiness.
Because if someone wants to go, "Well, wait a second, there isn't a standard that says you have to do this, this, or this," I mean, you could probably argue it that, well, guess what? We're dealing with rational numbers in this course and they come up in Pythagorean theorem. That would be your way around it. But I don't even think you'd have to go down that route to argue with someone as to why you're doing it, because I think your intention is very clear. You make that very clear with students that, hey, this is a growth piece. Again, you look at it as a win, that you're like, hey, the new concepts you've got. It's the old concepts.
You probably had this maybe a couple years ago and maybe we're just a little rusty on it, so let's focus on this. I could see it in your eyes that you've got some plans, you've got some thoughts on what that might look like. We're wondering, would it be okay if maybe we check in with you nine, 12 months from now and see where your mind's at then. Maybe that pebble has been removed. But as we always say, new pebbles. As you fix one or take one out, another one seems to pop in or something related to what you've just solved introduces another down the road. Would that be okay if we check in with you and see how things are going?

Guillaume Paré: Of course.

Jon Orr: Awesome stuff. Thanks so much, Guillaume, for taking the time to chat with us, and we look forward to catching up later.

Guillaume Paré: Thank you.

Kyle Pearce: All right, my friend. We'll chat real soon. Hey friends, as always, Jon and I learned so much from these episodes. As Jon mentioned before the episode, we've got a pretty awesome course that's all about assessment for growth. In that course, we help to set you up, get on that path from the beginning, doing some of what Guillaume's doing in his classroom right now in terms of really trying to shift the focus away from grades. We understand there's report cards and there's things that you have to do, your district mandates or maybe even your jurisdiction. Your province or your state might mandate certain things that have to be done, but there's a lot we can control in our classrooms.
It really starts with shifting our thinking around assessment and evaluation. And while this conversation was a great one, there might be some of you wondering, "How do we get going? How do I actually start on this journey? It seems overwhelming. It seems different. It seems hard." We have the perfect solution for you. It is the Assessment For Growth course. The first module is actually wide open so you can go and check it out right now. No logins needed. Nothing like that. You can dive right into the first lesson and dig in over at makemathmoments.com/afg. That's Assessment For growth, so AFG is the short form. Makemathmoments.com/afg and you can dive into it right now.

Jon Orr: Awesome stuff there. Thanks for sharing that, Kyle.0 If this is the first time, this is your first episode listening to our podcast, then welcome, welcome. We hope you enjoyed it and we would ask you, hey, we're going to ask you to hit subscribe. Hit subscribe so that you can get all of the episodes as we publish them every Monday morning each week. New episode comes out early Eastern Standard Time so that you can listen to it on the way to work. If this is more than your first time, you've listened a few times, maybe you've listened to many, many of our over 200 right now episodes at the time of this recording, Kyle, that sounds crazy when I say that, but 200 episodes, welcome back.
Welcome back and maybe consider leaving a review over on Apple Podcasts. Hit that review button. Tell us a little bit about what the podcast has done to influence your classroom. If you've listened to many already, you know that it must have influenced you somewhere. Otherwise, why did you come back? Why did you come back and listen a little bit longer? Please consider leaving us a review over on Apple Podcasts. We would greatly appreciate it. The teacher who has not yet listened to a podcast will greatly appreciate it. Because when you leave that review, it triggers the algorithm to put it in front of that other teacher who's waiting for that next action so that they can change their classroom as well.

Kyle Pearce: I love it. In order for Jon and I to engage in these, our favorite type of episode, the Math Mentoring Moment episode, we need friends like you to share those struggles, which means becoming a little vulnerable, opening up to us and the Math Moment Maker community. But knowing in your heart of hearts that first of all, you'll get some different perspectives, maybe just a different glimpse into your context, your situation, and you'll be helping other Math Moment Makers just like you who are struggling with similar problems. Head on over to makemathmoments.com/mentor.
That's makemathmoments.com/mentor where you can dig in and just give us a short description of that pebble that's currently kicking around in your shoes. Friends, don't forget, show notes, resources, transcripts, all of the goodies, including links to our Assessment For Growth course can be found over on our show notes page on the makemathmoments.com website, makemathmoments.com/episode217. That is makemathmoments.com/episode217. Friends, until next time, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us.

Jon Orr: And a high five for you.

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1 Comment

  1. Carmen Sinatra

    Great episode! I feel like I do similar things to Guillaume. I strongly believe that standards based grading (grading by expectations), really is the way to go. It gives more information to students and teachers of their strengths and areas of need. I am not sure how he enters results in his gradebook, but perhaps the achievement of an expectation can be on a sliding scale. So, for example, if a student can do Pythagorean theorem, but only with “pretty” numbers, then they are at a “refining” level. If they can do Pythagorean theorem with fractions, then they would be at mastery level. Both levels would translate to achievement, but mastery would equate to a higher “mark”.


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