In this episode, Sharona and Bosley interview one of their former students. Dr. Mary Reeves took the MAA OPEN Math intensive training on "Redesigning Your Course for Mastery Grading" in the summer of 2023. Subsequently, she redesigned two of the math content courses for future Elementary and Middle School Math teachers. Join us to hear about Mary's experiences working with, and impacting, future teachers.

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• Random Thoughts on Teaching Future Elementary Teachers, by Dr. Mary Reeves
• 60 – The Role of Depth of Knowledge (DOK) in Aligning Assessments to Learning Outcomes: An Interview with Erik Francis

[00:00:00] Mary Reeves: I was like, in 35 years I've never seen a student knock it completely out of the park on the very first try the way Isabella just did. And I'm not saying the rest of you didn't do a good job, you did, but this is amazing. And I want you to appreciate how incredible I think this is after doing this for years and years. Afterwards I told her, I'm like, this is going to be an assignment. I'm going to go ahead and put Mastery in your guidebook. You do not have to do it. Because you did it so beautifully the first time. Focus on something else. You've already accomplished everything that I wanted you to accomplish. After class she stayed for a few minutes and told me that was the first time she'd ever been singled out in a math class for something positive. And I'm not going to say that we both cried, but that's entirely possible.

[00:00:57] Boz: Welcome to the Grading Podcast, where we'll take a critical lens to the methods of assessing students learning, from traditional grading to alternative methods of grading. We'll look at how grades impact our classrooms and our students success. I'm Robert Bosley, a high school math teacher, instructional coach, intervention specialist, and instructional designer in the Los Angeles Unified School District and with Cal State LA.

[00:01:23] Sharona: And I'm Sharona Krinsky, a math instructor at Cal State Los Angeles, faculty coach and instructional designer. Whether you work in Higher ed or K 12, whatever your discipline is, whether you are a teacher, a coach or an administrator, this podcast is for you. Each week you will get the practical detailed information you need to be able to actually implement effective grading practices in your class and at your institution.

[00:01:51] Boz: Hello and welcome back to the podcast. I'm Robert Bosley, one of your two co hosts and with me as always Sharona Krinsky. How are you doing today, Sharona?

[00:02:00] Sharona: I am doing well. I have a theme for this semester for myself. This is the theme of Exam generation semester, because with the new job I have, I'm writing a lot of exams and it's really making me aware of how much I've enjoyed my alternative grading over the last number of years. Because I haven't had to write exams in probably six years. And now that I have to do it as part of my new job, it's proving to be a little challenging.

[00:02:32] Boz: Well, but give a little bit more detail about that. Cause you're not just writing exams to give. What's going on with your new role that you're having to do that?

[00:02:43] Sharona: So in my new role, I have nine different courses that I coordinate of those nine, seven of them are in a traditional grading format, which means that five of the seven are not standards aligned. So they have learning outcomes, but the work to align the teaching with those learning outcomes hasn't happened. And in those I also have numerous, numerous sections. So I'm having to create exams that have a lot of problems on them. They're all mathematics So they're all having formatting issues. I need many many versions. So it's challenging, because you're working with me on this and you're asking me, so why am I asking this problem? And I'm looking at you going, I have no idea other than it's a section in the book.

[00:03:35] Boz: Well, but you're and the kind of the point I was hoping you would go to is these are all coordinated courses. So you're not writing test for a class. You're writing test for like common assessments. So that is kind of the first step that you've taken with all of these new courses that you're coordinating is you're at least getting common assessments in there as you know, you, and rightfully so, probably couldn't have jumped straight to alternative grading with all of these different math courses that you're now coordinating with six days in advance before the semester started getting the job right.

[00:04:13] Sharona: Exactly. Although I will say that yes, I'd say that the entry points that I have had with this sudden adjustment back into more traditional grading, I'm still me. I can't let things go unchallenged. So I'm very, very pleased to report that a couple of the fundamental features of alternative grading are creeping in right away. So I'd say the first thing is the idea of retakes. Almost all of my classes are offering some form of retake, even if it's not to the degree I would like. And the instructors very much want that, especially because they don't have to generate the exams for the retakes. So that's helpful. And everyone is cooperating to allow these common assessments. So those have both been really helpful very positive steps. We're also using some form of proficiency scaling because we're trying to do common grading. And so we're starting down the baby step paths to all that.

[00:05:09] Boz: So, and that's a key component, and one that I'm actually kind of surprised you're pulling off as well as you are, is anytime you have common assessments, the point of common assessments, you know, is to have kind of a equal measurement through the different instructors. That doesn't happen if you're not also calibrating your grading, which, like I said with as little time as you had and as big as teams as you have and as many that you have, the fact that you're pulling that off is also an incredible feat.

[00:05:43] Sharona: Well, and I have to give a big shout out to my instructors because they're the ones that are open and allowing this. And we have some people more skeptical and some people less skeptical, but everyone's at least willing to listen. And think about what we're asking. So that's been really good. But I am spending a lot of time head down in LaTex code and the things that make mathematics formatting happen.

[00:06:08] Boz: And we're not alone today, are we? So you want to introduce our guest today?

[00:06:14] Sharona: We are very happy to have with us in the virtual studio today, dr. Mary Reeves. Mary is a professor in the Department of Mathematics at Northwestern State University of Louisiana. She specializes, her little niche, is elementary and middle school math for teachers, so working with a lot of future teachers on the fundamentals of teaching math at those levels. She has her PhD in education from Louisiana State University. Welcome Mary to the pod.

[00:06:47] Mary Reeves: Thank you so much. It's great to be here.

[00:06:49] Boz: One of the things, Mary, that we always like to ask our new guests when they first come on is just how did you get involved in this crazy world of alternative grading?

[00:07:01] Mary Reeves: Well, it was 100 percent a coincidence. I was flipping through my email and I saw a message from MAA about the courses that they were offering for the following summer. This would have been fairly early in the spring. of 2023 so about February, and I just, I don't have anything to do right now, I thought, and I'm just going to take a look and see what the titles are. So I was expecting, and found, a lot of things that were clearly aimed at mathematicians who do different work than I do. Some very content focused workshops that were going on, but the very last one was enticing and intriguing and I don't remember exactly what the description said, but it really spoke to me about some things that I'd been dissatisfied with about my course.

[00:08:00] I taught elementary methods for decades, then I switched into mathematics, still teaching the same population, but at a different point in their studies. But I had been experiencing dissatisfaction with the amount of time I spent talking with students about their grade versus the amount of time I spent talking with them about what they had or had not learned in the course. So they would take exams, they would do not as well as they would have liked and then they would come to me and they were concerned about how they could score more points and get a better grade because they're required to attain at least a C or better. So they have to pass the course or they have to retake it. So I had those conversations that I think anyone who teaches mathematics has had. What do I do? How do I improve my grade? How do I accumulate more points? In a system where once they'd taken the test and we'd moved on, that was sort of finalized and their period for learning was over.

[00:09:04] So in reading, the description of the summer workshop. I just felt like this was something that I'd been kind of searching for. How can I shift my focus away from grades to learning? While still maintaining standards. So it was just a series of I clicked here, I clicked there, and saw it and I immediately went and told my husband, I'm going to be doing this workshop in July. I'm signing up for it right now.

[00:09:36] Sharona: And so that name of that course, I believe, was Redesigning Your Course for Mastery Grading through the MAA Open Math program and that was in 2023. That was the one that Bosley and Kate Owens and I facilitated, I believe.

[00:09:54] Boz: I don't think I realized when you were there that you hadn't had some introduction to it already, because most of the people that come to that workshop, the two years that we ran it, they had at least done some reading or they'd had some experience. So I don't know if I realized that course was your first kind of experience with it. That's kind of cool.

[00:10:18] Mary Reeves: Yeah, it was very interesting. And engaging with pedagogical topics, how to construct a lesson, how to design assessments, that's all part of my background as an educational professor, but it was very refreshing to work with content area people who were so interested in teaching and learning. So that was really exciting.

[00:10:43] Boz: Yeah. I remember working with you during that workshop and in that workshop, we do a lot of small group stuff, even though it's virtual, and everyone is planning their learning targets and they're dealing with calc issues and they're dealing with linear algebra and we're working with you and you're working with, how to teach how to simplify fractions.

[00:11:06] Mary Reeves: The basics of place value and the difference between tens and tenths. Yeah, that's where I spend my days.

[00:11:13] Boz: But it was very fun and interesting because yeah, the math that we were doing at that course, most of it was at least calculus and then we'd work with you and we're doing third, fourth grade math and I had a daughter at the time that was, and still is, in elementary school. She would have been in, I think, second grade, going into third grade, over that summer, and looking at your stuff, and just knowing what I'd worked with her over the past year, I was like, I wish her teachers had some of this.

[00:11:51] Mary Reeves: Well, that's really what led me to it. I started off as a high school teacher. And found that my students did not know things like basic arithmetic and multiplication facts that were a clear impediment to them learning the algebra that I was prepared to teach them. So as a new teacher, when I realized that some of my kids didn't, for example, know what 6 plus 5 was, it's hard to figure out what 6x plus 5x is if you don't know what 6 plus 5 is.

[00:12:19] And they didn't know that and I didn't know how to teach that to them. I had no idea how they'd ever learned that. So that's what really drove me in graduate school to focus on what I was focusing on. Because the foundation for the work that all of us do is what happens in those lower elementary grades, in those upper elementary grades, and that transition from middle school to algebra. That sets the stage for calculus. When we lose kids there, we're never going to lose them in calculus because they're never going to show up. So my question was, well, my assumption was elementary school teachers don't want to teach math badly. They don't want to inflict math trauma, but they do, because they don't know any other way than how they learned. So it seemed to me that rather than looking for who to blame, which is a game we often play to our students detriment in education, high school blames, middle school blames, elementary school blames parents. So that doesn't help. So, I looked at what I was doing and thought, how can I be part of the solution? Where would I step in? What would I want to do to help elementary school teachers know more math, understand it better, and then help children to learn math in a more efficient and less traumatic way?

[00:13:42] Boz: Yeah, and that's such an important idea and concept, cause I know when I was in school, when I was getting my undergrad, I basically paid for my last two semesters tutoring two groups of people, the sociology majors that had to take this action research class that was nothing more than advanced statistics. And then all the Multisubject candidates that had to pass the math part of the Oklahoma qualifying test called the, OGET, Oklahoma general educators test, I think. And I know how many just absolutely despise the math part of it. And I've also read several different researches and studies that, basically say it takes three to five great teachers to make up for one bad math teacher. If you have that experience as a student with a math instructor at a primary grade, like it really does. It, takes so long to try to make up for that and get caught back up. It's ridiculous.

[00:14:56] Sharona: And Mary, I just wanted to say that you're going to make me cry right now because what you are saying is what I spent my formative years listening to my mother say. So my mother had a master's in pure math, a PhD in education with a cognate in math and worked primarily with K through eight teachers. And she was the content specialist. Yet, she was very pedagogically minded because she had herself been a junior high school math teacher. So she was saying the same things. And she talked about that blame game, and you said high school blames middle school, middle school blames elementary, elementary blames pre K, and then they all go back and say then they blame the teachers, and the teachers blame their graduate advisors, then who blames the undergraduate, who blames the calculus, so it becomes this cycle, this circle. And my mom used to say the only way to make change in math education is you have to break the circle at every single one of those points.

[00:15:57] So for me to have found alternative grading as one of the linchpins, it doesn't do the work for you, but it removes this huge impediment. So it's amazing to hear you say the same things and be addressing it. My mom spent her life's work really working with things like cooperative learning, which we now call active learning, which has started to really embed itself. And so the fact that we're doing this work in alt grading is just exciting. So I'm so happy that you found the course. So I guess my question is when you, when you showed up, what happened when you showed up to the course?

[00:16:36] Mary Reeves: Well, we began to dive into the literature and get some definitions for some basic ideas, like the four pillars.

[00:16:46] Sharona: I was thinking more about what was your reaction to like, what happened? You showed up the course. What happened for you?

[00:16:52] Mary Reeves: Well, I was, I thought the course itself was great. It was, like I said, it was so exciting to engage with content people who were so devoted to and interested in improving their practice in the classroom and their experience with students and what students were, were We're walking away from the course with, so that was really interesting. It was not surprising to me that so many people were looking at math at such a different level. I expected most people were going to be mathematicians teaching upper level math courses.

[00:17:29] Looking back on it, I found the conversations around student buy in to be very interesting. But I wasn't really expecting them to be particularly relevant. And as it turned out, they weren't. So that's one of the things that I've learned is how easy it is to get students to buy into an alternative grading structure depends very much on how much the current system has rewarded those students. So people who end up in math major courses are people who've been rewarded for being good at the way the math education game is played. So they have always gotten good grades. They've always responded well to traditional instruction and traditional assessments. They are unlikely to have high levels of math test anxiety which contrasts significantly with the bulk of my population.

[00:18:30] I won't say that all of my students are math phobic or highly anxious. Every semester I have a few who tell me math is my favorite subject, I can't wait to teach that. I don't tell them this, but I actually worry about them for my course more than the students who tell me that they're afraid and concerned and weak and they hate math and math has always been their worst thing. But, in the three semesters now that I've introduced alternative grading to my students, I first ask them what they've heard about the course. This semester, the overwhelming consensus was we've heard that the course is really, really hard, but that you're easy to work with.

[00:19:12] And it's like, okay, well, that's that's probably fair. Because I think we have to take the content very seriously. I certainly do. There's a lot they need to learn. Some of them know procedures very well, but they can't really tell me much more than a fraction is part of a whole which is a problematic definition that we don't have to go into, because seven fourths, for example, is not part of a whole. Or it's not, you can't have seven out of four.

[00:19:41] So, they may know some of the surface level skills, but the deeper understandings, what is the structure of our place value system? And how can you help a child to build a complex and nuanced understanding of place value as they're going into working with the operations in place value? That's those are not questions that anyone has ever asked them. So I've always focused on those kinds of things and I've tried to ramp up...

Mary Reeves: I was like, in 35 years I've never seen a student knock it completely out of the park on the very first try the way Isabella just did. And I'm not saying the rest of you didn't do a good job, you did, but this is amazing. And I want you to appreciate how incredible I think this is after doing this for years and years. Afterwards I told her, I'm like, this is going to be an assignment. I'm going to go ahead and put Mastery in your guidebook. You do not have to do it. Because you did it so beautifully the first time. Focus on something else. You've already accomplished everything that I wanted you to accomplish. After class she stayed for a few minutes and told me that was the first time she'd ever been singled out in a math class for something positive. And I'm not going to say that we both cried, but that's entirely possible.

Boz: Welcome to the Grading Podcast, where we'll take a critical lens to the methods of assessing students learning, from traditional grading to alternative methods of grading. We'll look at how grades impact our classrooms and our students success. I'm Robert Bosley, a high school math teacher, instructional coach, intervention specialist, and instructional designer in the Los Angeles Unified School District and with Cal State LA.

Sharona: And I'm Sharona Krinsky, a math instructor at Cal State Los Angeles, faculty coach and instructional designer. Whether you work in Higher ed or K 12, whatever your discipline is, whether you are a teacher, a coach or an administrator, this podcast is for you. Each week you will get the practical detailed information you need to be able to actually implement effective grading practices in your class and at your institution.

Boz: Hello and welcome back to the podcast. I'm Robert Bosley, one of your two co hosts and with me as always Sharona Krinsky. How are you doing today, Sharona?

Sharona: I am doing well. I have a theme for this semester for myself. This is the theme of Exam generation semester, because with the new job I have, I'm writing a lot of exams and it's really making me aware of how much I've enjoyed my alternative grading over the last number of years. Because I haven't had to write exams in probably six years. And now that I have to do it as part of my new job, it's proving to be a little challenging.

Boz: Well, but give a little bit more detail about that. Cause you're not just writing exams to give. What's going on with your new role that you're having to do that?

Sharona: So in my new role, I have nine different courses that I coordinate of those nine, seven of them are in a traditional grading format, which means that five of the seven are not standards aligned. So they have learning outcomes, but the work to align the teaching with those learning outcomes hasn't happened. And in those I also have numerous, numerous sections. So I'm having to create exams that have a lot of problems on them. They're all mathematics So they're all having formatting issues. I need many many versions. So it's challenging, because you're working with me on this and you're asking me, so why am I asking this problem? And I'm looking at you going, I have no idea other than it's a section in the book.

Boz: Well, but you're and the kind of the point I was hoping you would go to is these are all coordinated courses. So you're not writing test for a class. You're writing test for like common assessments. So that is kind of the first step that you've taken with all of these new courses that you're coordinating is you're at least getting common assessments in there as you know, you, and rightfully so, probably couldn't have jumped straight to alternative grading with all of these different math courses that you're now coordinating with six days in advance before the semester started getting the job right.

Sharona: Exactly. Although I will say that yes, I'd say that the entry points that I have had with this sudden adjustment back into more traditional grading, I'm still me. I can't let things go unchallenged. So I'm very, very pleased to report that a couple of the fundamental features of alternative grading are creeping in right away. So I'd say the first thing is the idea of retakes. Almost all of my classes are offering some form of retake, even if it's not to the degree I would like. And the instructors very much want that, especially because they don't have to generate the exams for the retakes. So that's helpful. And everyone is cooperating to allow these common assessments. So those have both been really helpful very positive steps. We're also using some form of proficiency scaling because we're trying to do common grading. And so we're starting down the baby step paths to all that.

Boz: So, and that's a key component, and one that I'm actually kind of surprised you're pulling off as well as you are, is anytime you have common assessments, the point of common assessments, you know, is to have kind of a equal measurement through the different instructors. That doesn't happen if you're not also calibrating your grading, which, like I said with as little time as you had and as big as teams as you have and as many that you have, the fact that you're pulling that off is also an incredible feat.

Sharona: Well, and I have to give a big shout out to my instructors because they're the ones that are open and allowing this. And we have some people more skeptical and some people less skeptical, but everyone's at least willing to listen. And think about what we're asking. So that's been really good. But I am spending a lot of time head down in LaTex code and the things that make mathematics formatting happen.

Boz: And we're not alone today, are we? So you want to introduce our guest today?

Sharona: We are very happy to have with us in the virtual studio today, dr. Mary Reeves. Mary is a professor in the Department of Mathematics at Northwestern State University of Louisiana. She specializes, her little niche, is elementary and middle school math for teachers, so working with a lot of future teachers on the fundamentals of teaching math at those levels. She has her PhD in education from Louisiana State University. Welcome Mary to the pod.

Mary Reeves: Thank you so much. It's great to be here.

Boz: One of the things, Mary, that we always like to ask our new guests when they first come on is just how did you get involved in this crazy world of alternative grading?

I taught elementary methods for decades, then I switched into mathematics, still teaching the same population, but at a different point in their studies. But I had been experiencing dissatisfaction with the amount of time I spent talking with students about their grade versus the amount of time I spent talking with them about what they had or had not learned in the course. So they would take exams, they would do not as well as they would have liked and then they would come to me and they were concerned about how they could score more points and get a better grade because they're required to attain at least a C or better. So they have to pass the course or they have to retake it. So I had those conversations that I think anyone who teaches mathematics has had. What do I do? How do I improve my grade? How do I accumulate more points? In a system where once they'd taken the test and we'd moved on, that was sort of finalized and their period for learning was over.

So in reading, the description of the summer workshop. I just felt like this was something that I'd been kind of searching for. How can I shift my focus away from grades to learning? While still maintaining standards. So it was just a series of I clicked here, I clicked there, and saw it and I immediately went and told my husband, I'm going to be doing this workshop in July. I'm signing up for it right now.

Boz: I don't think I realized when you were there that you hadn't had some introduction to it already, because most of the people that come to that workshop, the two years that we ran it, they had at least done some reading or they'd had some experience. So I don't know if I realized that course was your first kind of experience with it. That's kind of cool.

Mary Reeves: Yeah, it was very interesting. And engaging with pedagogical topics, how to construct a lesson, how to design assessments, that's all part of my background as an educational professor, but it was very refreshing to work with content area people who were so interested in teaching and learning. So that was really exciting.

Boz: Yeah. I remember working with you during that workshop and in that workshop, we do a lot of small group stuff, even though it's virtual, and everyone is planning their learning targets and they're dealing with calc issues and they're dealing with linear algebra and we're working with you and you're working with, how to teach how to simplify fractions.

Mary Reeves: The basics of place value and the difference between tens and tenths. Yeah, that's where I spend my days.

Boz: But it was very fun and interesting because yeah, the math that we were doing at that course, most of it was at least calculus and then we'd work with you and we're doing third, fourth grade math and I had a daughter at the time that was, and still is, in elementary school. She would have been in, I think, second grade, going into third grade, over that summer, and looking at your stuff, and just knowing what I'd worked with her over the past year, I was like, I wish her teachers had some of this.

Mary Reeves: Well, that's really what led me to it. I started off as a high school teacher. And found that my students did not know things like basic arithmetic and multiplication facts that were a clear impediment to them learning the algebra that I was prepared to teach them. So as a new teacher, when I realized that some of my kids didn't, for example, know what 6 plus 5 was, it's hard to figure out what 6x plus 5x is if you don't know what 6 plus 5 is.

And they didn't know that and I didn't know how to teach that to them. I had no idea how they'd ever learned that. So that's what really drove me in graduate school to focus on what I was focusing on. Because the foundation for the work that all of us do is what happens in those lower elementary grades, in those upper elementary grades, and that transition from middle school to algebra. That sets the stage for calculus. When we lose kids there, we're never going to lose them in calculus because they're never going to show up. So my question was, well, my assumption was elementary school teachers don't want to teach math badly. They don't want to inflict math trauma, but they do, because they don't know any other way than how they learned. So it seemed to me that rather than looking for who to blame, which is a game we often play to our students detriment in education, high school blames, middle school blames, elementary school blames parents. So that doesn't help. So, I looked at what I was doing and thought, how can I be part of the solution? Where would I step in? What would I want to do to help elementary school teachers know more math, understand it better, and then help children to learn math in a more efficient and less traumatic way?

Boz: Yeah, and that's such an important idea and concept, cause I know when I was in school, when I was getting my undergrad, I basically paid for my last two semesters tutoring two groups of people, the sociology majors that had to take this action research class that was nothing more than advanced statistics. And then all the Multisubject candidates that had to pass the math part of the Oklahoma qualifying test called the, OGET, Oklahoma general educators test, I think. And I know how many just absolutely despise the math part of it. And I've also read several different researches and studies that, basically say it takes three to five great teachers to make up for one bad math teacher. If you have that experience as a student with a math instructor at a primary grade, like it really does. It, takes so long to try to make up for that and get caught back up. It's ridiculous.

Sharona: And Mary, I just wanted to say that you're going to make me cry right now because what you are saying is what I spent my formative years listening to my mother say. So my mother had a master's in pure math, a PhD in education with a cognate in math and worked primarily with K through eight teachers. And she was the content specialist. Yet, she was very pedagogically minded because she had herself been a junior high school math teacher. So she was saying the same things. And she talked about that blame game, and you said high school blames middle school, middle school blames elementary, elementary blames pre K, and then they all go back and say then they blame the teachers, and the teachers blame their graduate advisors, then who blames the undergraduate, who blames the calculus, so it becomes this cycle, this circle. And my mom used to say the only way to make change in math education is you have to break the circle at every single one of those points.

So for me to have found alternative grading as one of the linchpins, it doesn't do the work for you, but it removes this huge impediment. So it's amazing to hear you say the same things and be addressing it. My mom spent her life's work really working with things like cooperative learning, which we now call active learning, which has started to really embed itself. And so the fact that we're doing this work in alt grading is just exciting. So I'm so happy that you found the course. So I guess my question is when you, when you showed up, what happened when you showed up to the course?

Mary Reeves: Well, we began to dive into the literature and get some definitions for some basic ideas, like the four pillars.

Sharona: I was thinking more about what was your reaction to like, what happened? You showed up the course. What happened for you?

Mary Reeves: Well, I was, I thought the course itself was great. It was, like I said, it was so exciting to engage with content people who were so devoted to and interested in improving their practice in the classroom and their experience with students and what students were, were We're walking away from the course with, so that was really interesting. It was not surprising to me that so many people were looking at math at such a different level. I expected most people were going to be mathematicians teaching upper level math courses.

Looking back on it, I found the conversations around student buy in to be very interesting. But I wasn't really expecting them to be particularly relevant. And as it turned out, they weren't. So that's one of the things that I've learned is how easy it is to get students to buy into an alternative grading structure depends very much on how much the current system has rewarded those students. So people who end up in math major courses are people who've been rewarded for being good at the way the math education game is played. So they have always gotten good grades. They've always responded well to traditional instruction and traditional assessments. They are unlikely to have high levels of math test anxiety which contrasts significantly with the bulk of my population.

I won't say that all of my students are math phobic or highly anxious. Every semester I have a few who tell me math is my favorite subject, I can't wait to teach that. I don't tell them this, but I actually worry about them for my course more than the students who tell me that they're afraid and concerned and weak and they hate math and math has always been their worst thing. But, in the three semesters now that I've introduced alternative grading to my students, I first ask them what they've heard about the course. This semester, the overwhelming consensus was we've heard that the course is really, really hard, but that you're easy to work with.

And it's like, okay, well, that's that's probably fair. Because I think we have to take the content very seriously. I certainly do. There's a lot they need to learn. Some of them know procedures very well, but they can't really tell me much more than a fraction is part of a whole which is a problematic definition that we don't have to go into, because seven fourths, for example, is not part of a whole. Or it's not, you can't have seven out of four.

So, they may know some of the surface level skills, but the deeper understandings, what is the structure of our place value system? And how can you help a child to build a complex and nuanced understanding of place value as they're going into working with the operations in place value? That's those are not questions that anyone has ever asked them. So I've always focused on those kinds of things and I've tried to ramp up their ability to think more deeply and to express their thinking in a way that makes sense. But they were afraid. They were, oh, I'm going to have to take these tests and they're going to be timed and it's going to be terrible.

And so they have these fears. As soon as I tell them that they're going to be doing assignments and we're not going to have exams other than the final that I'm obligated to give, they're in. 100 percent all the way, okay, I don't have to take a math test. I will do almost anything in place of that. So when I say you may have to submit multiple, sure, sure. I'll redo the work. I'll keep doing it. As long as I don't have to come in, in that highly anxious, stressful environment and take that test. So my thinking is that may give us some insights into other audiences for which this would be very attractive and sort of draw them in, which would be those non major general ed courses that every math department teaches.

There's another group of students, another audience that I think would buy into this approach. Managing it is more difficult because certainly there are more students in those courses. But I think that's a place where this sort of logically fits because they're willing and able to show what they've learned. But at least I know my theater and dance majors also have very high anxiety about taking tests that can inhibit their ability to perform.

Boz: That's interesting that you brought up that specific audience because that's exactly who I teach at Cal State LA and the course that Sharona redesigned and was the coordinator of for several years before getting her new position, which now she's still coordinates that course, but

Sharona: I was going to say, that's my, that's my safe space, is that course.

Boz: But that's exactly our audience, we do this math class that is not a prereq for calc. So most of our students in there are non STEM majors. And yeah, one of the things that we do early on is as part of our building community and stuff is this math autobiography. And I don't know about you, Sharona, but I'd say at least, you know, 70 to 80 percent of my students over the years have talked about how much they dislike math or how much they liked math until a certain point and then have disliked it since. Which is usually upper elementary to middle school, going back to exactly what you were talking about, Mary, but, I think it takes a little bit.

I don't know if it's based on trust and not believing us when we talk about how our grading system values mistakes and how that's okay, but once our students trust us and believe it and start to see it, yeah, they absolutely, not just buy in, but definitely I think value, the grading system. And you're right. The few that students over the years that I've gotten that have really pushed back on my grading system have been those students that typically were high achieving in math, and they're the ones that are always like trying to get every single little triple P point or trying to not just get the mastery on my proficiency scale, but the exceeds and they drive themselves nuts. And I'm like, dude, quit. This is all unnecessary. You're doing what you need to do. I

Sharona: I would say there's actually two groups. One group is the just general high achievers. They've learned to play the system, and they've learned to play the system to success. There's actually a second group that we get pushback from, which is they've learned to play the system and they're really good at playing the system to get the bare minimum grade to get through without having to actually learn. We have a group of those. Those ones are actually my worst ones. Those are the ones that are going to give me grade disputes and things because the mastery grading system or alternative grading system exposes that they're not learning anything.

And so those are those are actually the most challenging group for me to get to buy in. The ones who have essentially lost their trust in themselves to be able to learn and do well, but they've learned the game really well.

Mary Reeves: I see that in my students as well. I said that sometimes the students who start this semester saying I love math. I was always good at math. I always made straight A's in math. Those are the ones that I'm initially can be concerned about because they're accustomed to that traditional approach where the teacher, you're gonna show me how to set up and complete a problem, and then we're gonna practice some of those together, and then you're gonna give me some to do on my own, and since I'm good at remembering the rules and following them to completion, I'm gonna get a good grade.

Well, that's not what I asked them to do, because sometimes we'll start a problem and I go, okay, the answer to this question is 15. So now we don't have to worry about that. We know the answer. I've already, here are the steps. Here's what it looks like algorithmically. Why? We had to find a common, to go back to basic fractions, we had to find a common denominator. Why do we have to do that for addition and subtraction and not for multiplication or division? Why? What did it do for us? Why do we add the numerators and not the denominators? Why does that make sense?

And so those students sometimes struggle because they want to just be affirmed for getting the answer and that's not sufficient if you're going to teach this to other people. You need to know, because they need to know why. They're going to ask you why. And I want you to have a better answer than my teachers did. Which was, that's just the way it's done.

Boz: That's just the way you do it.

Mary Reeves: You just do. Which is a way of saying without saying, I don't know why, please stop asking. I tell them that, you know, on some level I'm a five year old, because everything you do I'm going to come back with why. Why? Because in math, there's a reason. There's always a reason. And usually it's fairly, you know, once we dig into it as adults, it's fairly obvious. But if I don't know what the numerator and denominator of a fraction mean in relation to one another, if I don't know what that information is telling me, then I can't answer that question. So I have a lot well not a lot, but Some of my students who say they're good at math they know lots of procedures, they can get right answers but they're no more adept at really digging into the why than anyone else in my course. And sometimes they're less interested in trying to do so because again, they want to be affirmed in the same way that they have in the past. Now, when they have a breakthrough? It's amazing because once they push through that wall between answers and explanations I can see the fire really light up in them because they can see that this is so much more interesting than just getting the answers.

Boz: Exactly. And that understanding how all the underlines lay and once you start seeing those, can actually see the connections in mathematics from things that don't look like they're connected, and yet everything in math is. So. But yeah, I don't know if you've listened to the podcast very often, but we had an episode, a couple episodes back with Erik Francis about DOK level, which is exactly what you were just talking about going from that low level of understanding of just being able to do. To be able to answer the question, why? And then explain that. So if you get a chance, you might want to go back and listen to that episode. You might find that DOK discussion very interesting.

Mary Reeves: Yes, that I started at the beginning, so I haven't gotten to anything recent. I'm kind of working my way from the beginning. So.

Sharona: So I have a couple of questions. So you took the course, at what point was it during the course or after the course or that you said, this is it. I mean. I know you said from the description, you were really excited, but you could have come to the thing and been like, yeah, no, this isn't what I thought it was going to be. At what point did you say, this is the right thing for me? And then tell us a little bit about what happened. What was the timeline for your adoption and stuff like that?

Mary Reeves: Well, I, I was ready to be all in from the beginning, like I said, I read the description and I'm like, this sounds like what I've been looking for. So I came into it with the idea that this is going to be something I'm going to do unless there's something here that convinces me otherwise. So I was pretty much in all the way from the beginning. It was challenging for me to try to do the analysis that was asked for in the course by establishing the standards. I either came up with a list that was way too long and detailed or way too short and vague. And finding a place in between was a challenge.

So I decided, look, the semester is about to start. I'm still not quite there yet. That's okay. We're going to figure this out as we go. So again, I kind of struggled with that to get that in a happy medium. I think now having done it for several semesters, I'm in a better place. I can more closely articulate to students but I still bounce back and forth between that very vague, these very large sorts of goals, and a very specific list of exactly how you're going to use the number line for this kind of numbers and this kind of numbers, this kind of numbers. All under the umbrella of using number lines to relate numbers to one another. I'm generally not an do things in small baby steps kind of person.

Sharona: My kind of person.

Mary Reeves: You know, it's like, if this is great, then it's great for everybody. So, in the fall of 23, I had two sections of my intro course for elementary education majors. I describe that as the lower elementary course. So basically stuff from K through 3rd or 4th grade. We get through place value operations and fraction operations up through division. Then I teach a second course that's actually the third course in the sequence for my students. So they take a number course with me, a geometry course with someone else, and then they come back for upper elementary and middle school number stuff. Ratios and proportions, number theory and pre algebraic reasoning are the main components of that course.

So I had two sections of the early course and one section of the final course and I said I'm doing it on all three of them. We're just, we're doing this. And it was going pretty well and then my life kind of got shifted sideways by, my husband had a medical emergency right about just after midterm, that kind of derailed the end of the semester because my personal life just loomed up in a way that is not typical.

So I learned a lot that semester. I think my students learned pretty well. And then in the spring I had just one section of the early course. Which was nice. I had more gen ed classes that I had to work with. But they kind of, I've done them so much, they kind of managed themselves. So I could really focus in on the ten or so students who were taking that one section. And really dig into their work really look carefully at what they were submitting and really see the fruits of that summer workshop in a way that I had not completely in that first semester. I don't know if I answered your question or not. At this point, I'm not, I talked so long, I'm not sure what your question was.

Sharona: Well, I was trying to sort of see what happened. Then you answered some of that, which is you went all in on two courses. And you think it went pretty well. What have you seen showing up then. Like what is happening in your courses now, because now you've been doing it, a year and a half. Right?

Mary Reeves: Right.

Sharona: A little over a year. What are you seeing? What are you noticing?

Mary Reeves: Well, the first, biggest change is the affect of my students. Their fear, their anxiety. anticipation of the negative things about the courses, about grades and exams, that evaporates pretty early. And when that happens, it seems like that makes room, more room for them to really engage. So since they can let go of that fear and anxiety about grades, they can focus more fully on the course, on the material, on trying to dig in, in the way that I'm asking them to do.

The other thing that should not have been surprising to me, but was, was what giving them this freedom to have the time that they need to think more deeply on their assessed activities, how much that was going to reveal to me. Not just about them, that I expected, but about maybe some gaps or some things that I hadn't noticed in my teaching. I've been teaching this material either as part of the School of Education or the Department of Mathematics now for over three decades. And just last spring realized that I've been doing something that I had no idea that I was doing that was leading at least some of my students to misinterpret what I was trying to show them.

This is from a student. We were doing the compensation or sharing addition. Compensation is you take a math problem. And we're going to make it easier, but wrong. So we're going to make it easy enough to do in our heads, but we're going to then fix it so that the answer's right. So, for example, if I'm adding 368 plus 196, instead of adding 196 and doing all the regrouping the way we would traditionally teach it to be done on paper, I can add 200. All right. and subtract 4. So, take your first number add your second number, and this is how I've taught it. It's, what I didn't realize was, in addition, well, I realized it, but I didn't realize I was giving this sort of false sense. In addition, you can compensate with either number. So, I could do 398 plus 156, and I could make that first number 400. Add 400 and then subtract 2 to compensate for the 398.

But in my examples, the number I compensated with was always the second number. So this student wrote in compensation addition, you add to the smaller number to make it become the next hundredths place. So 196 becomes 200, It becomes 200 by adding 4. And when I read that, it was like, wait, you don't have to do it with the smaller number. You can just, now in subtraction, it works much better if it's the second number. It's easier to subtract 200 than it is to subtract a number from 200. So we do talk about that. But this was not a lesson that I intended to teach. It was something that I was teaching and had no idea I was teaching until my student had the time to reflect that back to me.

Because in a testing situation, she might not have written that because she was trying to conserve her time. So that she could answer all of the questions in the time allowed. But with a mastery approach or an alternative grading approach she had the time to tell me all of her thoughts and as soon as I read that I went, wow I only showed examples where this was true. I'm going to have to change and adapt as a result. I need to make sure that going forward that where we do that. where the first number is easier to alter than the second number, or, where it makes more sense. And after 35 years, that was really exciting.

Sharona: I had a similar experience recently. I wrote a question that I didn't think was that much harder. Everyone else is telling me it's much harder than usual, but I was writing a practice test and this is for precalculus. So instead of giving them a polynomial and saying, tell me this coefficient, that coefficient, this linear term, that term, whatever, whatever, I said, create a polynomial that has these conditions. And then answer the same questions I would have asked if I had given you the polynomial. To me, that didn't seem that much harder because these are pre calculus students. They've been working with polynomials since pre algebra. Okay?

And yeah, we said, okay, it has to be at least a degree three term. It has to have these coefficients, whatever. What was fascinating, and this was on the practice test. Now we give it on the real test too, but we gave it on the practice test first. And the types of mistakes that I saw, because I had to go in and sub for one of my instructors in the workshop, the types of mistakes that I saw made me realize that we are assuming too much when we say here's a polynomial. Because when they started to create these things, they would drop the x's from some of the terms. They didn't realize that usually in a polynomial there's only one constant term, not two. There can be two, but normally we don't write it that way.

Boz: And you simplify it.

Sharona: Usually you do. But we didn't say simplify. But when we said there needs to be at least five terms, I again in my head was thinking terms with non zero coefficients because this is pre calculus, we haven't gotten into zero coefficients. So we saw all kinds of fascinating mistakes in the creation of these polynomials. Literally you could create x to the fourth plus minus x to the third plus x to the squared minus x plus one and that would be a good enough one pretty much. So I realized that sometimes when we give these problems, even the giving of the problem scaffolds too much and hides misconceptions. And I've been teaching for 35 years, this content.

Mary Reeves: Right. And that's one of the things that I tell my education students. That's why teaching is such a wonderful occupation because it's never the same. It may be exactly the same. My fall schedule is exactly the same every semester, but it's also never the same, because the students are different. I'm different. So that's what to me keeps, even after decades of doing more or less the same thing, keeps it fresh and invigorating. Another example of sort of what this opened the door for we do all kinds of different strategies. So subtraction of place value numbers is one where we talk about five or six different strategies. Different approaches to subtraction.

And I have a catch all category that I call student invented subtraction. Well, and I usually bring in base 10 blocks. So, I'm looking at an example that I collected from student work. The original problem was 431 minus 157.. We're going to take out some base 10 blocks, which, if people are not familiar are physical materials that represents the different place values. So I have centimeter cubes to represent the ones place, 10 centimeter rods to represent the tens place, and 100 centimeter flats to represent the hundreds place. So we take these materials and initially in class we just do it with the materials. So we take out four flats, three rods, and one cube. We look to see if we can take away one flat for a hundred. But we can't take five rods for fifty because we only have three. So we have to trade those in get more rods. So we trade in a flat, get 10 more rods. Now we can subtract.

And then, we finished the problem and we pushed the blocks off to the side and all of our thinking, all of our talking, all of our work is gone. We can't come back and look at it tomorrow. I can't share it with a student. He was absent because it was all in the physical manipulation and oral discussion that we just did. So what do we do when we're in that sort of situation? Well, we record it. We write it down in some particular way. So I just, here's a piece of paper. You've got boxes with colored pencils and markers and highlighters and things like that. Figure out how you're going to write down what you just did. Go through the problem again, step by step, just like we did, and write it down in a way that makes sense to you.

What they've typically done in the past is look to me to show them how to write it down. What do you want to see on the paper? Because, again, that's the way the math class game is played. You show me what you want to write, I practice that and I satisfy you by parroting back to you what you would do. Well, in the spring, I didn't do that. I just said, write it out. Draw whatever makes sense to you, it should make sense to someone else who is in this class. So it doesn't have to make sense to a random stranger on the street, but to you, to me, to your classmates, it should absolutely make sense.

And what some of them came up with was just amazing. I have one example of a student on her very first try her picture was so well crafted if you look at it you can, she drew like a little stack of flats, so you can actually see her flats, her 400 representation drawn like in a little stack she used color, to, you know, to indicate this was my top number and this was my bottom number. And here are my trades. She put in some arrows and just, I mean, she did it so beautifully. I ended up taking a picture of it and displaying that with her permission to all of the other students.

Cause I was like, in 35 years, I've never seen a student knock it completely out of the park on the very first try the way Isabella just did and I'm not saying the rest of you didn't do a good job, you did, but this is amazing and I want you to appreciate how incredible I think this is after doing this for years and years. I, afterwards I told her, I'm like, this is going to be an assignment. I'm going to go ahead and put mastery in your gradebook. You do not have to do this because you did it so beautifully the first time. Focus on something else. You've already accomplished everything that I wanted you to accomplish. After class, she stayed for a few minutes and told me that was the first time she'd ever been singled out in a math class for something positive. And I'm not going to say that we both cried, but that's entirely possible.

But she was just, she was so inflated. She was so, it meant so much to her to see her work valued and appreciated in a way that she'd never seen before. And that both made me really happy and very, very sad.

Boz: I was about to say that inflation of value is usually the opposite of what we unfortunately see in math classes a lot. It's much more common to see our students feeling deflated.

Mary Reeves: Yes.

Boz: But you're right. Had you done the typical, I do, we do, you do kind of method with that, all that creativity. Yeah, you would have seen the mimic of what you had done. And not seeing that creativity and that just different way of looking at it. And that student would have never felt that kind of value, even though they might've mimicked what you did absolutely beautifully and perfectly. But it wouldn't have stood out. It wouldn't have given that personal, okay, this is my take. And wow, my take is really good.

Mary Reeves: Yeah. And that was not the only one. Like I said, small class. I only had one section, nine or 10 students in there. But with the same topic, student invented subtraction, one of the other students took a little bit from two different things that I did show them and combined them in a way that she created something that was uniquely hers. So she took a little bit of the idea of compensation, she took a little bit of the idea of partial differences and decomposing. So she drew from several different strands and put them together into something that, again, I've never seen before from anyone.

And this was another student who came in feeling that she was weak. She was very uncertain. Her confidence level was fairly low. She didn't speak up much in class, but over time as she could feel that what she was doing was working for her, she became more engaged and was another opportunity for me to provide some feedback. Some praise for a job exceptionally well done to another student who'd never had that experience in a math class. And that just reinforced by, I want more of this. I want to see this happening in every class I teach.

Boz: See, and those are going to end up being, likely, some of the best math teachers ever. Because the students that struggle and get through it then become a teacher that can sympathize with that. For years, and this is long before I started doing alternative grading, of course, but when I first started teaching. California had a high school exit exam that students had to pass to graduate called the CAHSEE. I teach at a inner city, lower socioeconomic, lower performing school. We always had students that struggled with the CAHSEE. So we had CAHSEE bootcamps and CAHSEE intervention classes. The most successful teacher that we had year after year after year, wasn't a math teacher. It was our econ teacher who said that he struggled, like that was the hardest thing that he had to do getting through his pre service and bachelor's and master's degree with some of the math things.

So the fact that he could sympathize with the students that were struggling in math, cause he had struggled as well and made it through, he became our best CAHSEE prep teacher. So, those elementary teachers that have struggled and now have started to find value in that, they're going to be your best, most successful math teacher. So that is so great that you were able to give that moment to those teachers.

Mary Reeves: And, it seems to me that having experienced that themselves, that sudden wonderful feeling of going, I get that, this is exciting. That they would want that then .For their students. So especially if they're teaching like fourth or fifth grade, where they're going to get some students who've already had those bad school math experiences. They're going to bring their trauma with them, much like these students did to my class. That they're going to seek opportunities, I hope, to have that sort of transformative experience for those children in their classes because they know what it did for them and what a big difference it made for them. So their engagement was just through the roof after that, they were willing to do anything. Sure, we'll give it a try. Whereas before they might've been there's no way I can do that.

Boz: So I know we're getting close on time and Sharona, it looks like you've been trying to jump in for a little bit, but there's one question that I've got to ask you, Mary at the very top of this. You said you kind of found the description of our MAA course and it drew it to you because you were so dissatisfied with the students conversations that you would have. That it was always about the grade, the points, how do I get extra credit, and not about the learning. I know you're still new at this, you're only in your third semester of doing alternative grading, but have you seen a change in those conversations with your students?

Mary Reeves: Yes. I set up a grading scale for them in Moodle, which is our learning management system, where I can actually give them mastery, revise, redo and not submitted. Now because it's a computer program, Moodle turns that into numbers. But you know, I tell them, these are your grades and once it says mastery, you're great. We don't talk about their grade. We talk about their work.

So they submit their work electronically and I give them feedback much like I would have done traditionally. So most of what they're submitting electronically is pictures of work they've done on paper that I can then make notes on, make comments on. Sometimes I ask questions. Sometimes I ask them to tell me more about this, this is a little vague, can you be a little more specific here? And we spend a lot more time focusing on what that feedback means so that they can go back and respond to it. Then we do about the difference, how do I get from redo to revise?

How many points do I need to, because that's not an aspect of it. So, they don't stop at their grade. They might look at their grade first, but then their question is, what's the feedback and how do I move the needle on this particular work? How do I move this from revise to mastery? So, we're not having conversations about grades. Now they are interested in how all of these scores, all of these evaluations are going to turn into a grade. So I do provide that information about you and these are what my expectations are. But we're more focused on reaching those expectations rather than trying to fill that bucket with enough points to get that C that I so desperately need to pass this course.

Those super anxious sometimes actually mathematically weak students are not aiming for Cs, but they can see themselves potentially getting a B or an A. One of the things that I saw in my notes that I was reviewing from the spring, after classes were over, I had a student who had done enough to get a B. She wasn't satisfied. She wanted an A. She was still turning in assignments. She was still doing revisions. We had a couple of meetings online so that she could do some responses orally because she now felt that an A was within her grasp and that's how she wanted to finish her semester.

Boz: I asked that question because I've said it, but my first attempt at alternative grading was a disaster. And the reason I never went back is because those conversations were the first thing that changed. It went from, Mr. How do I get more points? How do I get extra credit? How many more points do I need to get a B? To okay, what am I not showing you about my understanding of, inferential statistics or what am I not showing you about my understanding of graphical analysis? So it instantly, like I said, it was a disaster. My first attempt was really bad, but still, those conversations instantly changed, and that's the single reason I have never even thought about looking back.

Mary Reeves: Absolutely. In general, grading is not any teacher's favorite aspect of the work that we do. When you ask, Teachers complain about all kinds of stuff but grading is always up there as it's something that's necessary. And like we talked about in the workshop, causes anxiety on both sides of it. I've never really thought about my anxiety about grading. And how much time I spent, is this a two point mistake or a three point mistake or a four point mistake? Did I give Chrissy a seven for a similar answer and now I have to give this student a seven? Keeping all of that straight, that I didn't realize how much emotional labor was really going into that on my part. So what I have now is a constant stream of a small number of things to grade rather than occasional piles of things to grade.

So I don't think I'm doing any less grading but it feels I don't know if joyful is the right word to use. I'm not sure I actually go, Oh, yay, I get to go grade student papers. But I don't feel the stress and anxiety about their grades because if they didn't do well, they and I get another chance. I can give them the feedback that I want to give them and tell them, Here's how you can improve. Give me a little bit more. Take another look at this. Explain to me what was going on in your head a little bit more. And then we can move you into the mastery column. So it feels both weightier in the sense that the work we're doing is more meaningful, but also less weighty in the sense that everything doesn't hang on your one opportunity. And so it feels both very intense and very freeing at the same time.

Sharona: So we do have to wrap this up. So my question to sort of end this whole thing is what's next for you? What are you planning? Where are you going in your journey?

Mary Reeves: Like I said earlier, I think the audience in a general education course at least the ones that I teach on my campus. The students I see in there are a lot like my elementary ed majors. Some of them are my elementary ed majors. I teach the two courses. in the core for us that they take. So I have some of them early on. But for my dance majors, for my sociology majors, for my, all my non STEM majors, I think this would fit their needs. So that's not something I want to do immediately. I still feel like I need to get my feet up under me a little bit more with my education courses. We also just redesigned one of those core courses. So we have a new book, we have new assignments, we have new assessments.

But that's sort of what I'm thinking in the next year or two. Is that I would really like to take one of those core courses. And build in some mastery, or take it to a mastery approach. That's going to be a little more complicated because I'm not the only person who teaches that. My courses for elementary ed majors, it's me guys. That's all you get. So you might as well grin and bear it because it's just going to be me. But it also means that I don't have a team where we're all trying to do more or less the same thing. So that would be a challenge in that core course because there are several other people who teach it who are of a more traditional mindset when it comes to how assessment should be done. But I can see where that would really have a lot of potential for that particular audience. So that's kind of where I see this going in the next maybe a couple of years. I'd also like to, and plan to, turn some of this into actual publications in particular for people in because I'm not sure people in the schools of education are aware that this is happening in their content departments.

Boz: Oh, so if you do get anything published, definitely reach out to us after it's published. We'd love to have you back on to talk about that publication.

Mary Reeves: Okay.

Boz: I also want to thank you for coming on. This has been a unique experience to have someone that's got as much experience teaching as you do, especially in a single course. You said you've been doing basically the, your math for elementary teachers for like three decades and yet is so new to alternative grading. So that's, I think that's a really unique perspective. I know Sharona, we talked about, I've got a brand new teacher that is only two years in that we want to try to get on next as kind of a mirror, but yet opposite a viewpoint as still new to alternative grading, but also new to the profession of education itself. So I want to thank you. Sharona, is there anything that you want to close on?

Sharona: Yeah, I just wanted to say, Mary, you provided some written materials of the examples you were talking about. So we're going to put in the show notes some of those images and some of the discussion from your students. And I wanted people listening to the pod, if they've made it this far to understand that, please go to the show notes and take a look at this piece of it. It's fascinating to to see the visuals.

Boz: All right. And with that, then thank you for joining us and we'll see you next week.

Sharona: Please share your thoughts and comments about this episode by commenting on this episode's page on our website. www. thegradingpod. com, or you can share with us publicly on Twitter, Facebook, or Instagram. If you would like to suggest a future topic for the show, or would like to be considered as a potential guest for the show, please use the contact us form on our website. The Grading Podcast is created and produced by Robert Bosley and Sharona Krinsky. The full transcript of this episode is available on our

website.

Boz: The views expressed here are those of the host and our guest. These views are not necessarily endorsed by the Cal State system or by the Los Angeles Unified School District.