Tom Schimmer: My first advice to people thinking about grading is don't make a meal out of it. Be focused on what you want the grade to communicate and be more obsessed with the assessment practices that produce the grades than the symbols we use to report. Think about how I assess, make sure my assessments are at the right cognitive complexity. Make sure that my assessments are designed well so that the evidence... Your grades are only as accurate as the assessments they're based on. Right? How many times have we seen a math test, for example, where there's some-

Jon Orr: Today, we speak with an independent education author, speaker and consultant from Vancouver, British Columbia here in Canada over the course of his career. Tom Schimmer, that's who we're talking with here, folks, has been a classroom teacher, school administrator and district level leader. Tom is an internationally recognized leader and an expert in the areas of assessment, grading, RTI, and educational leadership.

Kyle Pearce: In our discussion, we're going to be talking about which assessment practices are timeless and which are transformative and why knowing this matters in the classroom, why assessment must drive every decision we're making in the classroom from planning our lessons to designing our classroom rules. And finally, we get into a discussion about standard space grading. And if you're not doing your grades based on standards, Tom's wondering what are your grades based on then.

Jon Orr: Let's hit it.
(singing)

Kyle Pearce: Welcome to the making math moments that matter podcast. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr, and we're from makingmathmoments.com. And together...

Kyle Pearce: With you, the community of math moment makers worldwide who want to build and deliver math lessons that spark curiosity...

Jon Orr: Fuel sense-making.

Kyle Pearce: And ignite those teacher moves. My math moment maker, friends, we are back on with Tom Schimmer. Tom hasn't been on the podcast yet, but he was a presenter, a speaker at last year's virtual summit back in 2021. And we are eager to dive into a conversation two on one, I suppose. Not a one-on-one conversation, but a two-on-one conversation with Tom here where we dig into everything, assessment and evaluation.

Jon Orr: Let's do this.

Kyle Pearce: Here we go. Hey, hey there, Tom, thanks for joining us here on the Making Math Moments That Matter podcast. It's a little earlier where you are right now, but we were just chatting. Sounds like just like Jon and I, you are an early riser. You look wide awake, ready to go, sporting your A's cap. I'm a little disappointed in that decision because I'm sure there's got to be a Jays cap somewhere back there. How's things in your world right now?

Tom Schimmer: Things are great. Thanks for having me on. Yeah, the A's cap was just the one that was up in the rotation. I have an unhealthy relationship with ball caps. And I do have a Jays hat. I probably being from the West Coast in Vancouver, my allegiances are split. I do cheer for the Jays, but I also cheer for the Mariners. My favorite baseball team is actually the San Francisco Giants, so I'm wearing their rival hat today. But all is good in the world, from my perspective. Glad to be with you this morning.

Jon Orr: Awesome stuff. I also welcome you to the podcast. And you said you're on the West Coast. I know you're in BC, here in Canada. But Tom, tell us a little bit about yourself. We've chatted. We had you on the Make Math Moments That Matter virtual summit back in November. You gave a great session there. I've been to some of your live workshops on assessment, but our listeners, this might be new to them. So give us a little snapshot. What's your role in education and how did you get there? Give us a little backstory as well.

Tom Schimmer: All right. So yeah, I started teaching in 1991. I was a high school history teacher when I started. I taught for seven years full time in the classroom, then got into administration. And during my time as assistant principal, I taught 50% of the day. And it was in that capacity when I began to branch out in my teaching. It's funny because my fork in the road, when I was in university was math or history. I was almost poised to become a math teacher. And then I had an assessment experience, which maybe I'll get into later. I had an assessment experience in my college days that sent me to the history department.
So maybe I'll bring that story back as a bit of a teaser. Seven years as a classroom teacher, 11 years as a school-based administrator, and in seven of those 11 years, I was a part-time teacher as well. So I taught three out of six periods each day at the middle school level. And that's when I began to teach middle school math. I taught middle school social studies and English. After 11 years as a school administrator, I moved into central office two years as a kind of a coordinator district leader around curriculum and assessment and instruction.
It was in 2011 when I resigned from my job. My first book was being published around assessment in May of 2011. Prior to that, I had sort of been contemplating this other side of my career that I wanted to explore. So in February of 2011 I walked into my superintendent's office, which was right next door to mine and said, "I'm resigning." She looked at me and said, "Oh, that's terrible timing." She said, "I just got off the phone with the board chair who said they've agreed to promote you."
So I'm like, "Oh, well, I've spent a long time thinking about this. So here's my letter. I've already written the letter. I'm leaving." So it moved me into the world, so my title now would be educational consultant, author, speaker, et cetera. And I've been doing that for 11 years. I just finished my 31st year in education and things going strong, eight books later and more to come. It's one of those things that's got me working with schools and school districts across Canada, across the United States and around the world. So I'm very grateful for the way my risk, my venture turned out. It's been a great run for a long time, so I appreciate it. Yeah.

Kyle Pearce: I love it. And congratulations on all of that work. What a fantastic story. I don't know if this is going to be your math moment, if that was the foreshadowing event, but everybody knows when they're listening to the podcast, we ask every guest to share a math moment from their own educational experience. Could be K to 12, could be K to 16 or 18 or whatever, how far you went in schooling. Tell us a little bit about yours. I'm super curious.

Tom Schimmer: Okay. So I loved math in school. I did well in math. I mean, I was a good student. I wasn't a great student. And part of it was just, I didn't have the time. I was an athlete. I played a lot of sports and even my parents understood that I could not dedicate all of my time to school. So I did well. I started tutoring math when I was in grade 11. So math was something I was really drawn to. So when I went to university, so I went to Boise State University in Idaho. When I was at the school in my freshman year I wasn't really sure what I was going to do, but I had an epiphany in the second semester and I thought... Or heading toward the second semester, I thought, "Maybe I want to become math teacher."
Now, I became a teacher because I was trying to think about what I wanted to do as a career. And it was more around coaching than it was around teaching. I wanted to become a coach because I had a great basketball coach when I was in high school who was just an inspiration to me, a father figure that kind of thing. So I wanted to be that for kids. Right? So I went to the math department and I said, "Okay, so how do I get into math?" And they said, "Well, you first have to take an entrance exam."
This is actually December of 1985. So I go to the math department, they schedule me for the entrance exam. It's 25 multiple choice questions, really progressive assessment practices back then. 25 multiple choice questions. And guess who scores perfect on the entrance exam? This guy right here. I score perfect on the entrance exam. And so they say to me, "That is fantastic. Second semester you can skip first year sort of 101. We're going to put you into sophomore calculus. You can get into that class."
So I'm feeling at that in that moment like the smartest person on the planet. Mere mortals do not know who you're dealing with here. I got in. So I buy the textbook. It was a $40 textbook. Again, back in 1986, early '86, I buy the textbook. I get into the class. It is the single hardest class I've ever taken my entire life. I must have thrown my textbook across my dorm room every other night, trying to do the homework. So the first test comes along and this is the moment leading... The build up to the moment.
The first test comes along. And you have to remember, I just turned 18 years old. I'm a November baby. So when I got to school, I was 17. I turned 18 that fall. I'm an 18-year-old kid and I'm in this class and here comes the test and the test isn't even stapled. The test is one question on the front page, one question on the back page, right? It was just layers of questions.
When I look back, what I love about that moment, just as a tangent, was it wasn't just a series of equations or formulas. It was a really intricate question that had everything kind of enter... All the things we'd been learning kind of spiraled into the question. So we get the test back the next class period. So the test, I think, was on a Monday. We come back to class on Wednesday and I get my test back and I'm looking at the two sides of my paper.
And as an 18-year-old kid who doesn't really know a lot about assessment, I can't make sense of the two sides, because on the left hand side, my grade is a B plus. On the right hand side, my grade is a 38%. And I cannot figure... Now, I look back now and I realize that, well, my professor did is he curved the grades. But to an 18-year-old kid, this didn't make any sense to me. I'm like, "I'm no math genius clearly based on my 38%."

Kyle Pearce: You used to be.

Tom Schimmer: I used to be. inaudible That's right. So long story short, I got really frustrated in that class and I didn't have a lot of support. So I just thought, "Maybe math is not cut out for me. Because calculus, I'd never really taken it before. So off I went and I changed my major to history. I found out after in talking to some of my classmates, and colleagues, and teammates that he was hands down, the hardest professor on campus. Everybody cringed when I told them who I had and everybody kind of, "Oh yeah, Bill, he's tough." So that's the math story. Unfortunately, it shattered my confidence. I didn't understand how a 38% could be a B plus and all of that. That's my math story. That's why became a history teacher.

Kyle Pearce: I got to say my experience was similar. It was second year university and it was the same idea and I actually had a professor tell me, look me in the eyes and say, "You don't know anything about math." I guess fortunately for me I had no other plan. So I stuck it through. But you sort of had like plan B, and you took plan B. And for me, I was like, "Oh," and I maybe just thought the professor was bad and I moved on from there. When I think of your story and I also connect it to mine, I also wonder too, just the implication of like, I know that I never felt a challenge through my K to 12. And I wonder too, the implication of that.
Of course, I'm not advocating for that assessment practice or the evaluation practice that the professor used, but I think it does also articulate sometimes this idea of looking at math is either you get it or you don't, and there's sort of this no in between. There's this no opportunity for growth. I wonder if that experience had been taking place over time and you worked through them and you had the support there, like what that would change about your own mindset. I'm curious, does that impact or how does that influence who you are now as an educator and how that impacts your work around assessment and evaluation?

Tom Schimmer: Totally. It totally would have, because what I was good at in my K12 experience was doing math. I was not good at the thinking. I was never taught the thinking. I didn't understand math. And that was the difference. Right? I was good at following the formulas, the algorithms. I was good at procedures. I could remember and memorize and do all of those things, so I was never in my K-12 experience.
Now, again, early 1980s, we know a lot more about teaching and learning now than we did back then, but I was never put in a position to really do too much thinking because all that we had here in BC was algebra. My grade 12 course was algebra 12. And so there was no calculus. I never took calculus or anything like that. For sure, that affected me. I think had I been kind of brought along in a situation where I was asked to do more thinking, asked to do more investigating, asked to do more problem solving in a way where I had to make decisions, because it's an interesting thing in math is that... And it's like a lot of subjects. You can look like you're doing thinking, but you're actually following procedures. Solving an equation is a procedure.
And if you know your rules and understand math facts, you can solve an equation without understanding the thinking behind the solution. Right? So I definitely think that affected me in how I approached that. I don't know. Maybe, Kyle, you're just tougher than me.

Kyle Pearce: I had just no plan B, my friend. No plan B, that's all.

Tom Schimmer: That's a kind of way of putting that. But it really was a fork in the road, but I really wanted to be a math teacher. But how it affected me now is that... I realized how... And a lot of these lessons I learned not in the moment, but I learned them in retrospect. I look back and then things kind of make sense, right? I think we do that a lot in life where we kind of look back and then we make meaning out of that. Okay. Now, I understand why that happened. Not why it happened from some divine kind of intervention, but why it shaped who I am today and what it was for me is just, I think the confidence piece, right?
My confidence was shattered. My confidence maybe was a little too high after that interest exam and maybe was a little too shattered. It was fragile, right? Because I was of the mindset like a lot of people that you either have the math gene or you don't. You either can do math or you can't. There's a certain group of people in this world that can do math. And that gets perpetuated in society. Nowadays, you hear people, and it frustrates me nowadays, when I always hear people saying, "Look, I'm no math guy or I know it's math."
We just dismiss it as if we would never say that about literacy. We'd never say, "Well, I can't read." We would never celebrate that. But it's almost a badge of honor when people talk about their inability to do simple math. It's not even math. It's like arithmetic. Right? So I think for me, it was a shattering of my confidence, which has led me in the work I do now and has for a lot of a number of years, had me focused on the emotional side of assessment. And it isn't the only reason, but it's one of the reasons why I focus on not just the clinical side of assessment, but the emotional side, the impact it has on students, the impact it has on human beings when we face the prospect of being assessed. So it definitely is a part of me that will always be there because it was a pretty pivotal moment at a very impressionable time in my life.

Jon Orr: Yeah. And that emotional side of assessment, I do want to dive into a little later in this chat, but I also want to go back to that part where you were saying like you were this procedurally driven student. And it brings up like a lot of the work that Kyle and I do because we often think like we were also exactly that way as students and became math teachers who viewed math as that was math is if you were good at math is because you were good at following procedures. It wasn't until later that we realized that mathematics and teaching mathematics and learning mathematics isn't actually about the procedures in understanding the procedures, it's about problem solving. It's about how these things work more than the actual procedures, because we were the same way. It's like, "Hey, I was great because I could just follow steps in the right order."
But if you mix that order up, I was out of luck. I had a tough time because like you, I think there was very little back then in my classrooms on teaching how to think. And I started teaching that way too is that math was a very procedural thing. And it makes us think about... And this is the work that we're doing now is because I think so many students still are taught that math is this procedural thing. If you can follow these steps, hey, you're going to be fine. You're going to move on, and you can go off in complete mathematics courses because you're just doing that.
When teachers are still, I think, pushing that agenda of what math is, and this podcast is actually about how to change that and how to help teachers realize, and the tools needed to change that mindset of what mathematics and problem solving really is in classes.

Kyle Pearce: Well, and the big piece too, Jon, the word that I use so often now is reasoning, right? I never reasoned in math class. I never thought about an answer. When teachers say, is that reasonable? They would ask me that and I'd be like, "Is it?" I didn't understand what the problem was. Most of the problems were what we call naked problems, right, where it's just like, "Do these operations, do these series of steps, and come out with this answer." It was like, "How could I understand if that's reasonable or not if I don't have a context to connect it to." I don't have any of those things. And now we see that as like, wow, as educators, we have so much work to do. We say it on the podcast all the time, it is so hard to teach.
And not only shift the mindset that you just mentioned, Jon, from this procedural mindset, but we also have to relearn what math is, how math works, because the reality is, is that if we didn't experience it ourself, it's really hard for us to help students experience something that we've never done ourself. Right? And that's where I think there's so much work to be done not only in assessment and evaluation for math, but then also thinking about, "Wow, when I'm dividing fractions, what does that even mean?"
If you ask teachers in general, you say, "Give me a scenario that involves dividing fractions, like a context, like a real scenario that involves dividing fractions."

Jon Orr: They start sweating.

Kyle Pearce: Oftentimes... Yeah. You start to sweat because you're like, "I actually don't know of a scenario in the real world where I'm dividing fractions. I've never really thought about it." Or maybe they remember that word problem in the textbook that they've taught before, but there's so much work to be done here and I'm wondering, maybe we're jumping ahead here, but I'm wondering when you're working with math educators and you're talking about an assessment and evaluation, I feel like that has to be such a hard place to be because not only are... I would say math teachers, we tend to be very traditional. And I say, we because we were there. We're sort of born again math teachers, we'll say, and we've kind of made this shift. But I remember things being exactly that. The procedure and then like assessment was also very procedural. It was like, it was this or it was that. And there's no in between.
Where's your head at when you're working with math teachers? Does that make you excited because you loved math and you want to affect change or do you look at that as like, "Wow, this is a hard place to be trying to help shift the mindset of math educators around assessment when we have so much shifting to do in even just our own mindsets and instructional practice."

Tom Schimmer: It's interesting because when I work with math teams, they are usually fairly polarized in this sense. They are either the group in the school that is leading the charge. They are the ones that are ahead of the curve. They are looking at problem solving and they've got clear criteria and they're using rubrics and all of that. They're either that group.
Now, I wouldn't say this is split. That is sometimes. But the majority of the time, they are often the toughest crowd to bring along because they are so locked into. And I know I'm casting everybody with the same sort of like treating them as a monolith and they're not. But if I had to, if I'm forced to sort of say, "What is it like working with math teams?" A lot of times they are that traditional kind of locked in ratios around seven to 10, 15 out of 20 and just right wrong focused. And that's why we did that session back in November is trying to get past right wrong and get to the thinking, right?
Like we said earlier, you can do the math, but not do a lot of thinking. So it is exciting. I do like working with math teams because a lot of times math teams, again, to characterize them as a sort of singular entity, when math teams get it, they almost leapfrog a lot of other departments. It's like somebody who is most resistant to some idea suddenly has a breakthrough. And now they're leading the charge and looking at everybody else saying, "What's the matter with you, people? We have to do this."
It's like, "Wait a minute. Weren't you six months ago the one that was completely against this idea?" But it's one of those things where you get them to understand some of the nuances. For example, not every 15 out of 20 is the same, right? You can have a student can score a 15 out of 20 and leave five questions blank and have no idea how to answer them.
A student can get 15 out of 20 and make five simple mistakes, but conceptually understand how to answer the problem. Those two learners are in different places, but the percentage score, the 75% will never account for the type of error that the student made. And when they can get that breakthrough and realize that those ratios aren't as sacred as we make them out to be, this percentage symbol, then I know I'm talking to math teachers. But this percentage symbol is not as accurate as you might think it is when it comes to assessment because of that one simple fact is that you have to account for the type of error, the type of thinking the student presented to you.
So it can be both daunting when you get... I mean, at this point, I'm a little over that part of it, because I can pretty much speak to every group. And that's just because of practice. It's not a statement of arrogance or that I'm smarter than anybody, it just I've been doing this... Assessment has been a part of my life for 18 years. I've been doing this 11 years full time and talking to groups on a weekly basis. So talking about assessment to any group is not that challenging in the sense of concepts. What's challenging is the personal part is trying to reach people and trying to figure out what makes them tick and how can I help them see some of the misunderstandings that they might believe or hold to be true that isn't really that true.
So the percentage example I just gave is an example of that where you try to help people have those breakthroughs. And when they have those breakthroughs, it is exhilarating work. That's for sure.

Jon Orr: Yeah. If I go back to your example there about 15 out of 20 and they mean different things. And I think it's so important when we think about like, "What are we measuring when we provide these assessments?" And you said that when you get a teacher to realize that, they have almost like the permission to not think of this ratio or this mark as like the be all, end all. It's when they make that realization that they actually have control over how that actually affects a student's assessment.
What do you do when you're working with those teachers to help them come to that realization? Because I think there's listeners out there right now who heard you use that example and are like, "Wait. I'm in that position right now with my teachers." Because we have a lot of coaches and administrators who listen and they're like, "I want to help them with understanding that piece."

Tom Schimmer: One of the hardest hurdles to get over for many is using your professional judgment and judging more holistically, right instead of marking and coming up with a score. It would be the idea that you look at the totality of the evidence and you judge the degree to which the student has met the learning goals. I had a recent experience a few months ago. It's not that recent, but a few months ago, a recent experience with a math team in Utah. I'll tell the story very quickly. They said, "Tom, can you look at our summative assessment, our unit assessment?" I said, "Sure."
Okay. So always my first question when they asked me to look at an assessment is, "What standards are you assessing? What is the focus? What are the outcomes like? What are you trying to accomplish?" Because I want to make sure that the test is actually... So it was a traditional test and it was a standard about writing functions. So we said, "Okay, this is functions." And then we went through the test. What I noticed right away was I said, "You only have four questions on this test." And so I said, "Is that enough?" Now, I wasn't challenging them saying, "You have to have more questions." I was legitimately asking them a question, "Do you feel like this is an adequate sample?"
And the math department chair who was leading the conversation with me said something that... She said it in a way that I've picked up on that phrasing and I've started to use it in a lot of my workshops. She said, "Tom," she said, "We do think it's enough because we interact with our students constantly and we see their demonstrations already. So going into this test, we kind of have a sense. We already know where they are in their learning. This test just confirms what we already know." And I said, "That is one of the most brilliant things I've heard in a long time around assessment."
So when you look at your unit test, let's not try to ask every iteration or every possible combination and make this test long and spiral bound and all of that, let's just ask enough questions to confirm... And I changed the wording slightly. I said, "You make your summative assessment a test or whatever. It's something that is going to confirm what you already suspect about the learner. You already have interacted with them."
So what that leads me to back to the idea of holistic grading is that if I walked into any teacher's classroom and I said, "Okay, turn off your computer. I don't want you to look at any artifacts. And when I ask you to..." We would never do this in actuality, because it would embarrass students. We wouldn't want to do this publicly, but hypothetically if we did this, I walked into your classroom and I said, "Okay..." So let's just say, Jon, I come into your classroom, I say, "Here's what I want you to do. We've been working on writing functions. In that corner to my left, in that corner, I want you to put all of the students that you feel have a deep, thorough, sophisticated understanding of writing functions."
So I'm holding up four fingers just for listeners, right? So we think about judging on four levels. I say, "In the opposite corner, the other side of that wall, I want you to put the students..." Now holding up three fingers, "I want you to put the students that have a good, solid, proficient understanding." It's not deep and thorough. You could throw them a curve ball and they might not, but they definitely have a solid understanding of functions. Okay?
Now, I turn around and I face two other corners. I say, "Jon, in one corner," I'm holding up two fingers, "I want you to put the students that you feel have kind of a partial understanding. They have some understanding. There's some strengths there, but there are definitely some aspects of running functions that they struggle with, that they still need to improve." And then in the other corner, the fourth corner, holding up one finger, I say, "Jon, in that corner, I want you to put the students that have shown you a minimally acceptable level of understanding, but almost every aspect of writing functions needs some addressing, needs some improvement."
My guess is that if I walked into your classroom toward the end of that functions unit or whatever you were working on, my guess is you could do that in about two and a half to three minutes without looking at an artifact and without opening up your computer. If I asked you to put your 100s, your 99s, your 98s, then now you need your machine. But to judge it more holistically and think about what is the depth of understanding or what is the degree to which the student understands, the learning goals, that is where we get into more thoughtful decisions using our professional judgment.
And that is an important... The word to emphasize is professional. My friend and Solution Tree colleague, Luis Cruz always says to audiences, and I've picked up on this because I love the way he phrases this, he'll often look at a room full of teachers and he'll say, "Listen, just as a reminder, you are professional educators. You're not amateurs. Right? People pay you for your experience and your judgment and all of that. It's our job to make those decisions."
When people say, "Well, how am I supposed to know what this learning outcome means?" Well, it's your job to know what it means. You're a professional educator. You're not an amateur. People pay you for this work." Right? So he has a bit of fun with that and I try to have a bit of fun with that as well, but it's a good reminder that it's our judgment that really does matter. And that's how you'll distinguish between the one student who left five questions, blank, and the other student who made five simple mistakes. Your judgment will tell you that one learner is in different place than the other.

Kyle Pearce: I love it. You said so much that I want to comment on. I was jotting a few things down. You might have heard me typing away over here. I don't know if I can get to all of them, but one thing I want to go all the way back and the part I really love about that experience you had a couple months ago on that assessment and trying to confirm or reaffirm, or just to ensure that students are where maybe you perceive them to be. Something else to add in there too, that I think can be helpful, as long as we're doing this from an assessment lens and not as a evaluation lens where it's sort of in stone is maybe putting a question on there that you want to know more about.
Meaning like, I actually don't know if Jon can do this. And if I can build that classroom culture where my students aren't afraid of that scenario, because they know that I'm going to do those things, not as a punishment, but to learn more about you, Tom, as a learner, I go, "Listen, one of these questions, I'm putting it on here. I want to see what you do with it." And then when I'm looking and I'm kind of sorting in that room, this is the other piece I loved was kind of this visual. I feel like you had said, all teachers could do this exercise. And then from there, if we're using assessment for what assessment really should be, we should be able to then go, "Okay. So for my friends over in this room, what's my next steps for them. What am I going to do? What am I going to change in my practice in order to help nudge that group to the next place?"
It would be great to get them all moving around the room to that first corner that you had described. And that journey might look a little bit different depending on the students and where they are. So all of those things you said there, I think are awesome. I'm wondering, we talk about standards-based grading a lot here, the math moment maker community. I'm wondering what are your thoughts on standards-based grading? And what would you say are maybe some tips for someone who wants to go there and maybe they're a little bit nervous, or they're a little apprehensive?
I remember making this shift and I remember feeling very vulnerable, right? It's like, "I know this, I know this world, it happened to me as a student, I did this for many years, and now I'm like venturing out. And that can be kind of a scary thing. Do you have any, maybe your thoughts on standards-based grading in general or whatever your version or however you see that everyone defines it different and then where might someone go to start? Where would you suggest they start on that journey?

Tom Schimmer: Well, it's interesting because there are a lot of different definitions floating around and I think that's unfortunate because I think the definition of standards-based grading is just to say it backwards. It's grading based on the standards and that's it. You write it on the back of a napkin. And I think that sometimes we make a meal out of things and we overthink it, and it would be a fair question to ask. So I'm old enough to remember a time where there weren't outcomes. When I started teaching, I didn't have learning outcomes when I started in 1991. What I had was a curriculum guide and that told me as the teacher what to cover, that the outcomes or what they call the standards movement in the United States happened in the '90s. That was a '90s phenomenon, right?
And what's significant about that is that moved us into an era of criterion referencing, right? So when I was in college doing my teacher training in the late '80s, I didn't even know what a rubric was, unless you're talking about those really sort of kind of pedestrian type rubrics, where it was like title page 1, 2, 3, 4, 5. Neatness 1, 2, 3, 5. I didn't know what a rubric was.
So when we moved to outcomes in the '90s, we switched to criterion referencing and we essentially moved to standards-based teaching, outcome-based teaching. It's somewhat astonishing that we did not move to outcome-based or standards-based grading at the same time. So we fractured the relationship and that is perpetuated a long time. So from a standard based grading perspective, just remind yourself what it is. It's grading based on the learning outcomes. And it would be a fair question to ask of any teacher up until this moment, if your grades have not been based on the evidence that students have produced against the standards you've been teaching, then it would be fair to ask what exactly have they been based on.
You've been teaching to outcomes and teaching to standards. Another question that I would have for teachers to contemplate as they're thinking, if they feel like they're going solo and no one else in their school is doing it and things like that, ask yourself this question. What do you want a grade to communicate? What is it that you want it to say? Even if you're producing a singular grade for an entire subject, which it's still a little bit kind of hodgepodge. I often remind people that imagine if I took your height, your weight, your shoe size and your inseam and I combined it into a singular number?
That's what we do with a single grade for a subject. And somebody said, "But Tom, it's all about math." And I said, "But those numbers are all about your body, your height, weight, shoe size and inseam."
They're just a combination. So height, weight, shoe size inseam, you're a 12. That doesn't mean anything to you, right? But what do you want that single grade to communicate? Do you want the grade to be a reflection of the degree to which the student has met the learning goals overall, holistically, some strengths, some aspects that need strengthening, but where are they overall or do you want that grade to be a byproduct of the points they have harvested throughout the course of a semester or the year.
So remind yourself of what you want the grade to communicate and then do what you can to protect that purpose in your mind. I want a grade to communicate the degree to which a student has met the learning goals. So do that. That means anything that is not related to the learning goals has to be handled elsewhere.
It has to be handled outside the grade book. It needs to be handled. For example, late work is not okay. And I'll say this to audiences until I'm blue in the face. Especially with high school kids. It is not okay that students turn work in late. It's not. I mean, kids need to be accountable and they need to be responsible. But here's the rub. It is equally not okay for any teacher to distort the student's achievement level as a result of the lateness, right?
And the irony, math teachers... Now I'm speaking to you all right now. The irony of any math teacher in the history of grading ever using a zero when using a zero to a hundred percentage scale that is some kind of irony. When math teachers teach their students that the one vulnerability to the mean is extreme scores. That is the one mathematical vulnerability, and you know this. I'm preaching to the choir here, but when you talk about the idea. So when a teacher uses... The irony of a math teacher using a zero when a student hasn't handed in their mean median and mode work, that is about as ironic as it gets.
You just violated the mathematical principle, nevermind the philosophical position, right? So for me, for what it is, my first advice to people thinking about grading is don't make a meal out of it. Be focused on what you want the grade to communicate and be more obsessed with the assessment practices that produce the grades than the symbols we use to report. Think about how I assess, make sure my assessments are at the right cognitive complexity. Make sure that my assessments are designed well so that the evidence... Your grades are only as accurate as the assessments they're based on. Right? How many times have we seen a math test, for example, where there's some redundancy or repetition that produces a grade that does not really fit the picture of where that student is? Quick example. Let's say the outcome we're working on is solving the third side of a right triangle using Pythagoras. And I'm going to keep this simple. I mean, I wouldn't have a test like this, but just to simplify to make the point. Let's imagine section A of my unit test is asking students to calculate squares and square roots.
What's the square root of 49? What's eight squared? That type of work. Right? 25 times. Now that's a lot, I know, but I'm just going to keep the math simple here. 25 times, the student gets 24 out of 25 on the squares and square roots. Section B of my test ask the students to find the third side of a right triangle using the Pythagorean relationship 25 times. The student scores, 11 out of 25 on that second section.
So I'll often ask audiences, does anyone in this room think this student has any level of proficiency when it comes to solving the third side of a right triangle? And everyone shakes their head and says, "No." I said, "But how often is this combination turned into 35 out of 50 and that student gets a 70% on that test?" Because we've asked questions that represent the underpinnings. 24 out of 25, the squares and square roots is redundant because it's built into the questions in section B,.
If you can solve the third side of a right triangle, you know how to calculate squares and square roots. I don't need to ask you that separately. It's baked into the question. Just because you can calculate squares and square roots does not mean you can find the third side of a right triangle, but if you can find the third side of a right triangle, you can definitely calculate squares and square roots. So those questions become redundant.
So that's where a teacher really needs to be focused on what the outcomes are and what the underpinnings are. And making sure that those underpinnings are used, the evidence is used informatively to lead to the idea of meeting the outcomes. That's just an example. Keep everything that is non-achievement or non-learning, so the late work is handled as a behavioral misstep, not as an academic reduction.

Jon Orr: Yeah. And those are some great examples to help explain standards-based grading to folks who are still trying to wrap their minds around it. I really like how you started that off with saying that we've been teaching towards standards and curriculum documents, but that grading practice didn't follow through. And then here in Ontario, I think we have been taking the steps in the right directions for the last 10 years. We have an assessment document that it outlines all of these things whether it's being followed here in Ontario is still-

Kyle Pearce: Up for debate.

Jon Orr: Yeah, still up for debate is that how long it's going to take for everyone to realize this policy that we do have here on assessing in these ways that you've been talking about. I think still a lot of teachers might still be assessing based off the standards, but just are lacking a way of recording it. Right? It's like, "I want my grade book to also mimic-"

Kyle Pearce: Or interpreting. What does it tell me? What is it telling me? And that's what I heard from what Tom just said. Right?

Jon Orr: Yeah. I know how a student might be able to do on these skills, and I think that still is like maybe if that traditional teacher has got a unit test, they've got all that and they can say, "Hey, on functions we're doing this much so far." But then they're like, "How do I record that?" And I think there's a shift that has to happen for those teachers to go, "Look, it's okay. You have permission. You have your professional judgment to change the way your grade book looks so that you can actually give off this information that says what a kid can and can't do on those standards."

Tom Schimmer: You bring up a good point, Jon, about grade books because since the onset of outcomes, our outcomes have never been organized by task type. There is no justification or rationale as to why anyone continues to organize their grade book by tests, quizzes, assignments, projects, labs. Your math outcomes, your math standards are organized by strands, categories and domains. And the name of the event... And this is where for some people when it comes to grading is when you explain the traditional grading system out loud, it sounds almost incompetent. It really does. If I were to say to a parent out loud, "We're going to assess your children on their ability to meet these math standards. But the name of the event is going to dictate the degree to what weight it carries towards your grade."
If I ask your child to find the third side of a right triangle, but I call it a quiz, it'll count for 25% of their grade. But if I ask them to find the third side of a right triangle, but I call that event a test, now it's worth 40% of their grade. It's illogical. The obsession with the name of the event. Now, if we put you in a gym and we line up all the desks and it's warm outside and we call it an exam, now it's worth a lot more.
That to me, is it... I hate to use this term and I'm not saying this about teachers, but I am saying that rationale sounds moronic. It sounds like you can't... How do you even defend that? I often say to people, "You want to know what standards-based grading is? Flip over the back of a hockey card. Just flip a hockey card over. You're going to see a bunch of different categories and you're going to see a separation of those categories, and you're going to get the complete picture. You're going to get games played. You're going to get penalty minutes. You're going to get goals, assists. You're going to get the complete picture of the player."
And none of it is really combined into a singular entity. But the grade book is a big culprit of that. And unfortunately the electronic grade book has contributed to this. So the timing of that was unfortunate because we had this outcomes or standards-based movement of the nineties, but we also had the tech explosion in the late '90s and early 2000s, and the electronic grade book companies tricked us and fooled us into thinking that we could calculate that we know... Not that they brought it, but not only could we distinguish between 101 levels of performance, which is absurd. They let us calculate grades to two decimal places.
And that assertion alone says there are 10,000 distinct levels of performance and 5,000 of which in Canada are passing. If you're in the United States, 400 of which are passing. It's kind of an absurd assertion that we can do that. So the electronic grade book has been both the greatest and the worst invention in education from my perspective because it has never made us more clinically efficient, but we've lost the art of grading.
We've lost the art of our judgment and now we've deferred to the machine to make decisions for us when it's just a glorified day book that we used to do this by hand and now it's done on a computer. So we've given up too much of our professional control to that computer.

Jon Orr: And when you brought back that idea about call... The naming. We're so obsessed with the naming of quizzes and tests. It just made me think about this also dynamic that when early 2000s was when all of a sudden we started to talk about formative and summative assessments, and that became terminology that teachers didn't know how to handle. When I first started teaching, Tom, I was told that a quiz is a formative assessment.

Tom Schimmer: Yeah, that's formative.

Jon Orr: And a summative assessment is a test. So when you were talking about like naming, we just changed the names when I first started teaching. I was like, "Okay. Oh, that's what a formative assessment is, not understanding what really and coming to realize what-

Tom Schimmer: Yeah, I really get this.

Jon Orr: ... a formative assessment is. And I know you chatted about this also specifically in that session that you did with us about the differences there. I know that most teachers who are listening to this right now know the difference, but maybe want to chat about like formative or summative and how teachers can actually use those effectively?

Tom Schimmer: Every assessment has the potential to be used both formatively or summatively. Right? It's because the distinction between the two is how you use the information. So formative is not just a summative that doesn't count. I think that is a good start, but it's not the definition, how you use the evidence. So formative ins summative comes down to one of the most important assessment tenants, which is purpose. Whenever a teacher assesses, and I would say this to all of your listeners is whenever you assess your students, ask yourself internally the question why? Why do you want this information?
In other words, what do you intend to do with it? Once you answer that question, then you'll know what your intention is and then stick with it. Right? So a lot of times we will speak out of both sides of our mouth. So math teacher, end of the class. Here's your homework for tonight? 900 questions. Odds only. Go. Right? And we say, "Here's some questions for practice." We'll say it out loud. Here's some questions for practice. But then the next day we treat it like a game. We score it, we record it.
So we're saying two things, right? So ask yourself the question why. If you say to yourself, I want this evidence to take inventory on where my students currently are, so I can help provide guidance and feedback and next steps for them so they can grow toward meeting the outcome. Then you've just described the formative purpose. So do that. If you say to yourself, this moment is designed to verify the degree to which the students have met the learning outcome or met the learning goal, then you've described the summative purpose.
So when you start with the question, I know it's a little cliche to say start with your why, but from an assessment perspective, it is important to understand why you want the evidence. So the distinction between the two is how you use it. So labeling something formative doesn't make it so. An assessment is only formative when it's used informatively, right?
So when people say, "Oh, Tom, we do formative assessment." I say, "That's great. How do you use formative assessment?" Because if it's not at least having you contemplate an instructional adjustment, it may not always result in an instructional adjustment because sometimes your formative evidence tells you that what you had planned for the next 15 minutes is exactly what you should do. But did you contemplate an adjustment?
What Cassandra, Nicole and I call being instructionally agile. Are you thinking about what's next for my learners? If you're gathering it and recording it and zero waiting it, that's a good first step, but it's the use of that evidence instructionally that really takes formative evidence to a new level.
And that's where the promise came from as you mentioned. I think Jon you mentioned the late '90s and early 2000s this Renaissance and assessment practices was around using assessment evidence instructionally. So we think of formative assessment. I try to help people understand that formative assessment is more a verb than a noun. It's not a summative. That doesn't count. It's an action. So when we say you should be assessing your students every day, you should be assessing them every single day, because you should know whether or not they've learned what you taught them today.
Now, people look at me and say, "Well, Tom, if I'm always assessing, when am I teaching?" And that right there is a clue that that person sees assessment as a noun, as a thing that I have to stop teaching and conduct versus here's a math problem on the board. What I want each of you to do in your groups of four. I want you to talk about the strategy you would use to solve this problem. And as a teacher, I'm going to walk around the room and I'm just going to listen to their conversations.
As an aside, engineering conversations in a classroom amongst your students is one of the most underutilized and yet one of the most effective formative assessment strategies you can use because you'll hear the understandings and the misunderstandings as they are talking to each other. They don't even know they're being assessed. So when I say assess every day, informally exit tickets, conversations, you are just purposefully gathering evidence to know whether or not the students are picking up what you're putting down that day.
So for me, that is the way assessment works and that's using it formatively. You're not going to quantify it. You're not going to record it. You're going to use it instructionally. That's what we should be doing every day. Now, periodically, you might sprinkle in a a more formal formative moment. You know what a pivotal moment during the unit where you say, "Okay, if I can get them all here, that's the breakthrough."
So we have maybe a common formative assessment amongst our colleagues, or we do something a little bit more formal. So I think of it as like a triangle where it divided into thirds. So the bottom third of the triangle is the widest part sort of indicating that's what we do the most. Informal formative moments. Then you go to the middle. That's what we do a little less often. That is formal formative moments at those pivot points and then the top third of the triangle, that's the evidence we use to grade. That's the evidence we use for summative assessment.
So bottom of the triangle, we assess because we have to. You can't teach without assessment. Top of the triangle we grade when we need to. Assess, because you have to, grade when you need to. And that to me creates a nice balanced assessment system in your classroom.

Kyle Pearce: I love that. So many things pop into my mind about that. I think about my, I'm going to say my old self, my more... I call it traditional. My version of traditional was I did a lot of talking. I did a lot of writing things down on the board. I did a lot of doing, and when I was doing those things, it made it really difficult for me to spend that time at the bottom of the triangle as you've mentioned. Right? So it's like when we think about our teaching practice in a math context, if I'm there at the front delivering, and when that teacher asked you about, "If I have to assess, when will I teach?" Immediately my head... And I'm making an assumption here, but immediately my head sort of shifts to this, "Okay, what is teaching in that classroom? What does it mean to teach?"
And if it's me doing all the talking and the students are there, I am not able to get any information about where students are. Jon and I call it pivoting or proceeding. How do I know whether to pivot or whether to proceed? Well, what do I do? I just keep proceeding. And then I find out on my quiz, which I now call a formative assessment in four or five days that, "Oh my gosh, I didn't know anything." I look back to how many times that would happen to me and I think, "How is it possible that I went through five days of instruction and I was not expecting what I'm looking at right now." Right?
Like you had said, it's like, you should be looking at this and it should confirm what you're suspecting. And there was so many times where I would be so saddened by how shocked and surprised I was. And now when we look at more of a problem-based approach and more giving students the opportunity to investigate problems and then consolidate the learning based on what you're hearing, that I think aligns with exactly what you're saying here. And that's a huge takeaway for me and I'm sure for the math moment makers.
I'm wondering, Tom, we can't take up your entire morning, although we would love to. So I want to know from you, if there was one thing that listeners, they've listened to this episode, they've probably got all kinds of ideas here. If there was one thing that they could take away from this conversation or that you hope they take away, what would that be before we sign off for the day?

Tom Schimmer: Oh, there's many. But if I were to say one thing, for sure, I would say if I were to phrase it in a way, I would say, assess their thinking, not their answers. Now, look, asterisk on that one, I know it's important to get it right. And so people say, "Well, in math, it's not about the answers, it's about the problem." Well, at some point it is about the answer. At some point I can't keep saying, "Well, I think two plus two is five."
I really in my heart believe that. I'm wrong. Okay, so I get that. We do have to look at their answers. But dig deeper, go past the answer and say, "How did they get there?" Because they could have got the right answer. You know the expression. What is it? Three left turns make a right. Right? And it happens. I don't know if you've seen this, but I mean I've seen that when I taught middle school math. It's like, "Wait a minute. That's an error." Now, that error corrected the previous error and they got to the right answers.
So if I just marked answers then they would've got the question right. But if I dig into their thinking, I realized they were way off. They used the wrong strategy. But if you make enough mistakes, you may come full circle and get the right answer. So assess their thinking. And that'll help you distinguish the types of errors that they're making. So that even if you're using a percentage system, you can come at those percentage systems with a little more substance for that.
I think one of the advantages of being old, I'm not that old, but I always say I'm almost 55. I'm not 85, but I'm not 25 either, is a little bit of this historical kind of view. These things didn't just fall out of the sky. The assertion of assessing students on fewer more clearly distinguishable levels came out of the research that said, we are just not that consistent as teachers when we either... So the one scenario, the best case scenario, it's the best case scenario with the percentage system is the type of error is not there.
You get an incomplete view of the learner. Or when you make an indirect scoring inference using a rubric, there's usually a margin of error between plus or minus five to six points. So that research led us to a place in education where we said fewer, more clearly distinguishable levels will be more reliable, more accurate than a zero to 100 scale. So I think sometimes people who say started teaching in 2012 or started teaching in 2005, think that someone was just bored and decided to say, "Hey, let's do this thing called standards-based grading. Let's do that."
But this stuff has a lineage. There is a sort of historical progression that has led us to that point. So part of where we are at with coming back to the original answer, part of where we're at with assessment is we've got to get behind the answer and we've got to look at their thinking. We've got to see what their thinking is where the errors are, where they're correct, and really capitalize on that because a more granular examination of the evidence will allow you more specific instructions as to how they can move forward.
And then ultimately turning that over to them and helping them. I mean, we didn't even talk about self-assessment, but that idea of getting them involved. It's not helping them become part of that process and judging where they are. So in that corner's example I gave earlier, the iteration of that, again, hypothetically would be put yourself in the corner where you believe your understanding is and then we would interact with them to say, "What lead you to think this?" And then we would either correct them, say, "You've underrated yourself, or you've overrated yourself." Things like that. But focus on their thinking, not just their answers.

Jon Orr: I think that's a good kind of one liner to summarize a lot of the things we chatted about here today, Tom. I want to thank you for joining us and, hey, if you're open to it, we could bring you back and we could chat all about self-assessment and feedback. We didn't even get into that too. So we'd love to have you back. But Tom, before we let you go, where can our listeners learn more about you and your work? And I think you also have a podcast.

Tom Schimmer: I do. I always say to people, I probably have, at this point too many social media accounts to account for. So Twitter is a good place to connect with me @tomschimmer. Also my podcast, which is cleverly named The Tom Schimmer Podcast, because I got bored of trying to think of a name and I didn't want to copy anybody else. And I thought, "Well, I'll just name it after myself. Why not?" Nothing like a little ego centricity when it comes to naming.

Kyle Pearce: Hey, I tried to name this one, the Kyle Pearce show, but Jon wasn't on it.

Tom Schimmer: The Kyle Pearce show. The podcast @TomSchimmerPod on Twitter. On Instagram and TikTok, it's at @tomschimmerpodcast. I'm on LinkedIn, Facebook, Schimmer Education. You can reach me anywhere. If people have assessment questions or want to just engage, my email is tschimmer@live.ca. That's public. It's on my website, which is tomschimmer.com. So there's lots of different ways to reach out if folks want to just engage in a conversation or want to connect. And of course I do have the podcast, The Tom Schimmer Podcast, which is focused on primarily interviewing different leaders in education.
There is always an assessment segment at the end of the podcast, which I call assessment corner, where I'll either take a question from a listener or a question that's come up in one of my workshops I've been doing during the week and I'll just kind of share how I answer the question or some concepts where I'll talk about rubrics or feedback or things like that.
It usually is once a week over the summer. I'm going every other week just to slow the pace for myself and for listeners because I know people want to kind of disconnect a little bit from work, which is always important. And then we'll kind of get back to our weekly schedule in the fall. It's pretty hard not to find me online. I still have Snapchat. I don't even know why I have Snapchat, but I have Snapchat.

Kyle Pearce: It sounds like a funny idea.

Tom Schimmer: I saw the icon on my phone. I open it up. It's like I have an account? So anyway, I don't know. So don't engage me on Snapchat. I don't use it.

Kyle Pearce: That's funny. There you go. That is awesome. Well, thank you so much for spending some time with us. Again, we are going to post this to YouTube even though you've got an A's hat on. So we're really, really-

Tom Schimmer: It's all good.

Kyle Pearce: ... excited to share this with the community. Thank you for the work you're doing in education and in particular assessment and evaluation, and really just shifting that thinking and that philosophy. You would think we would be there by now, but it does take time and I feel like educators are eager to make the shift. So I think the timing is great and yeah, we're looking forward to connecting with you again real soon.

Tom Schimmer: Yeah. Thanks to you both. I really appreciate the opportunity to be here.

Jon Orr: Thanks, Tom.

Kyle Pearce: Have a good one, my friend.

Tom Schimmer: Thanks.

Kyle Pearce: As always math moment maker friends, Jon and I learned so much. We are big fans of Tom's work. We've learned a lot from his books and also from some of the sessions we've seen both live and also online, including the virtual summit back in 2021. So what was your big takeaway? I know for me, something that I never really thought about was this discussion we have about standards-based grading. We talk about it all the time. And Tom sort of generalizes the idea and says like, "Isn't everyone using standards-based grading. What are you grading then?"
And I think it sort of made me reflect on the fact that I think when we talk about it, we're usually talking about how we record it, how we sort of formalize it, how we do it. But what Tom is saying is really true, right? We are using the standard. So I wonder for me is like, "Should our language be more about like how do we most effectively ensure that we're grading on all of the standards in a holistic way as he had referenced?" So that was my big takeaway. What's your big takeaway from this episode here, Jon?

Jon Orr: Yeah. I think that is his way of saying standards-based grading was great too. He's like, "Just say it in reverse." I thought that was so elegant, but also just short too. It's like just say grading based on the standards. It was just so like, "You're right. Why is that?" And I think you're right, Kyle, that he was saying like, "What have you been doing?" I think that was also, I think my big takeaway from this conversation and I think he had lots of nuggets for folks to take away. I think he used a lot of great examples to make it very clear of what practices we should be employing in our classroom.
So I wanted to... Like you said, he's influenced our work. We have a full course on assessment called assessment for growth inside our academy. So all academy members have access to that course. It's based off many people's different works and the work that we are doing in our classrooms, Kyle, but his work we reference, we also reference Dylan William's work. So there's lots of works referenced in there where we dive into setting up that grade book.
How does that look? We talked about that's the big shift. It's like, "We are assessing by standards. However, how do I record that in my grade book? What should my grade book look like?" That's a module in our course of how to actually do this kind of stuff in your classroom. So if you are looking for a deeper dive into assessment, you can check out that course over at makemathmoments.com/assessment or makemathmoments.com/afg, which is the course for Assessment for Growth.

Kyle Pearce: I love it. So hey, friends, whatever your big takeaway, make sure you're sharing it with a colleague, with a partner, with a friend online. You can do that on social media @MakeMathMoments. We have a Facebook group, Math Moment Makers K through 12. And remember on podcast platforms, it's great, leave a takeaway as a review in the podcast. A rating and review goes a long way to help us reach an even wider audience.

Jon Orr: Show notes and links to resources from this episode can be found at makemathmoments.com/189. Transcripts are there as well. Again, that's makemathmoments.com/189.

Kyle Pearce: Well, my math moment maker friends, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us...

Jon Orr: And a big high five for you.