Episode #32 The Formative Five: An Interview with Skip Fennell
In this episode we speak with Skip Fennell, math teacher, principal, A Maryland Council of Teachers of Mathematics’ Educator of the Year , Past NCTM President, He’s also the author of dozens of articles and books and is a coauthor of the book The Formative Five.
We chat with Skip about all things formative assessment. He shares with you 5 formative assessment strategies that will ensure you’re making math moments that matter! Join us as we dive into a great discussion with a contagiously passionate math educator at heart, Skip Fennell.
- Ways teachers are missing the mark with formative assessment;
- How to embed assessment in your daily routines;
- 5 formative assessment strategies and how to start using them now.
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Skip Fennell: I mentioned earlier the fact that we use this artist metaphor, the artist pallet for the five techniques. By implication that means that while I’m going to talk about observation first, that doesn’t necessarily mean you do it first. You do it whenever. We observed in our work in terms of determining these techniques and deciding how and when to use them, we observed a number of classroom across all kinds of levels, elementary, middle, and high school, and found that teachers observe all the time. They don’t pay any attention to it. And so what we’re saying is, you observe your students all day long. Pay attention to it. Do something with it. So, in our chapter on observation, and for each of these five techniques, we created a number of tools that teachers can use to help them get started with it. A planning tool for using observation. A tool that you might use with individual students. A tool that you might use for the whole class and so forth and so on to keep records of doing-
Kyle Pierce: You are listening to Skip Fennel, math teacher, principal, and Maryland Council of Teachers Mathematics Educator of the Year, past NCTM President. He’s also the author of dozens of articles and books and is a co-author of the book The Formative Five.
John Orr: We chat with Skip about all things formative assessment in this episode. He shares with you five formative assessment strategies that will ensure you’re making mass moments that matter every day. Stay with us as we dive into a great discussion with a contagiously passionate math educator at the heart. Skip Fennel. Hit that wonderful music.
Kyle Pierce: Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pierce.
John Orr: And I’m John Ore. We’re two math teachers who together-
Kyle Pierce: With you, the community of educators worldwide who want to build and deliver math lessons that spark engagement-
John Orr: Fuel learning-
Kyle Pierce: And ignite teacher action. Are you ready, John, for episode number 32?
John Orr: Oh, yeah. For sure. For sure. In this interview, Skip not only shares with you five formative assessment strategies you can implement in your classroom but gives you the background on why we should be using these strategies too.
Kyle Pierce: Before we begin the Making Math Moments That Matter podcast is excited to bring you the Math Moments with Corwin Mathematics book give away. That’s right. We’ll be giving away 10 books from Corwin Mathematics. Including Skip’s book, The Formative Five. Plus you’ll receive special Corwin discounts and digital downloads just for entering the draw. You can get in on this giveaway by visiting, MakeMathMoments.com/giveaway by Wednesday, July 31st, 2019.
John Orr: Listening after July 31st, 2019? No sweat.
Kyle Pierce: We are always actively running giveaways so check out MakeMathMoments.com/giveaway by Wednesday, July 31st, 2019 to get on the Math Moments with Corwin Mathematics book give away. Or if you’ve already missed this one, check out that same link to learn about the current giveaway we have running. Don’t miss out. Dive in at MakeMathMoments.com/giveaway.
John Orr: That’s MakeMathMoments.com/giveaway. Without further ado, here’s our chat with Skip Fennel.
Kyle Pierce: All right. Hey there, Skip. Welcome to the Making Math Moments That Matter podcast. We are so excited to have you on the show today. How are things over on your end?
Skip Fennell: Well, first of all, I’m just as excited to be here. On my end, in West Minister, Maryland, which is about 45 minutes outside of Baltimore, it’s, for us, a pretty nice day. Probably 70 degrees. Lots of sun. I guess rain’s coming next couple days but it’s been a pretty productive day for me, both getting ready for this opportunity and I do consider it an opportunity, and also dealing with a few other things on my end. Glad to be here. This is the best part of my day.
Kyle Pierce: Skip, now you bring up the weather and this time of year. The time when we’re recording this. It’s early June, and you know what always makes me wonder, the different school areas in states and when they end for summer. Here in Ontario, almost all of Ontario ends right at the end of June and then we have two months off and we come back after Labor Day. That’s always been our thing and only just the last couple years I’ve started to realize that there’s lots of states and lots of districts that end very early compared to us. What’s going on in your area for that? I’m always curious about that.
Skip Fennell: Yeah. It’s interesting that you say that because over the years I’ve found the same thing very curious and interesting to me as well. We’re the first state below the Mason Dixon Line and so we adhere to a school calendar very similar to all of the Mid Atlantic states. That is we start school around Labor Day, in Maryland, this year we started a few days before Labor Day, end of August. And kids are graduating from high school, they began graduation ceremonies this week. But other children, including virtually all of my grandchildren, except one, will be in school for another couple of weeks. Another one of my grandchildren who lives in Atlanta, Georgia, they finished school a week or so ago. And they start Mid August. But it’s probably 90 degrees down there and I think heat and humidity has a lot to do with, particularly in the south, it has a schedule way ahead of us in terms of when they go and also when they finish. You’re a little bit behind us in terms of that.
Kyle Pierce: Skip, could you help our listeners, we know a little bit about you but our listeners, maybe they do, maybe they don’t but could you help our listeners understand a little bit about yourself? Maybe give a little background on you and maybe what inspired you to become a math educator and get into the math field?
Skip Fennell: First of all, I’m one of these people who, and friends know this, I don’t like to talk about myself a lot. I’m a pretty private person, but I’ll give you a little bit. I’ll give you a little bit. I’m a first generation college graduate. My father was a self made engineer. He was the kind of guy who, if you will, pushed me into what we now call STEM stuff and like most first sons, I rebelled at that. And so dad wanted me to go to the United States Air Force Academy and to be an engineer. And so I decided, I’ll tell you what I’m going to do. I’m going to go to college and I’m going to be an elementary classroom teacher. Which is what I did. So I began teaching upper level elementary aged children, but I also taught primary grade children and God love him, his interest in the sciences and mathematics came to me. I found math pretty easy for me although I was never a full math major. I took a bunch of courses and I found myself helping friends with the subject. Frankly, because it came easy for me. By the way, that doesn’t mean I necessarily understood it, it was just one of those things where I could do it. By the way, there are a lot of people like that and I’ve heard some of your shows. One of you are like that. I forget which one.
Kyle Pierce: Oh, yeah.
John Orr: Definitely me.
Skip Fennell: Okay. So I’ve had this interest in math that came at me sort of indirectly and then I just pursued it. When I was teaching, they wanted me to teach all the math. So I did that. And I was good at it and then what happened was, I feel partially into this trap, people wanted me to do other things and so I was at one point in Central Pennsylvania in the town of Williamsport, Pennsylvania. The home of little league baseball. I was a head teacher. What that meant was that I was a principal for half of the day and then for the other half of the day, I taught fourth grade children.
Kyle Pierce: That seems like a busy schedule.
Skip Fennell: Yeah. It was. It was interesting. Then along the way I finished a masters degree and then I left that position and my wife and I took what we had left in the name of savings and our newly born son and we went to the Pennsylvania State University and I did a PhD at Penn State in mathematics education and really got hooked there with some good advisors and people who cared about me and I took a job at one of the state institutions in Pennsylvania. It’s now Mansfield University of Pennsylvania. Very rural, in fairness. And she’s not in the room, so I can say this, my wife hated the place and so I figured we’re going to have to end the relationship and I’m going to stay. And decided to leave because I love my wife. I went back into the public schools and I took a job as a principal. I advanced to being supervisor of instruction and then knew, frankly, that I was on a fast track to be a school superintendent and I would have been a lousy one because I didn’t care about a bunch of the stuff that they have to care about.
Skip Fennell: I care about curriculum, I care about kids and so forth but somebody else ought to figure out buses and somebody else ought to figure out who’s going to use what. It’s just not in my skillset. That doesn’t mean I’m trying to be arrogant with that statement at all, it’s just there’s certain things you can do and there’s certain things you can’t and I didn’t want to do all of that and so I went back into higher education, what was then called Western Maryland College in the town of West Minister where I now live. And I was faculty member there for 39 years. And during that time, I taught a bunch of courses in mathematics and mathematics education as well as education. I advanced to the rank of full professor. I got fully involved in math education to the point where I served on some committees for the National Council of Teachers of Mathematics. I wrote textbooks for children. I did research. I wrote manuscripts. I was at one point elected to the NCTM board of directors. Later on I left McDaniel and took a leave, Western Maryland College then was renamed McDaniel College a number of years ago.
Skip Fennell: I took a leave and I worked at the National Science Foundation in Washington as program officer. Was elected to be the president of the National Council of Teachers of Mathematics and served in that role from 2006 to 2008. I was also elected to be the president of the Association of Math Teacher Educators, the people who help prepare teachers and are directly involved in teacher education. I was president there from I think 2002 to 2004. Those dates are probably incorrect. Along the way I was president of the Research Council for Mathematics learning. Which is a smaller group of math educators very much interested in research, specific research, plans, and initiatives for children. I’ve had a number of leadership positions in the field and then continued to be involved. I spent a lot of time working on research grants and initiatives in the area of number sense which is why I was so interested in your most recent interview, at least the interview that was most recently posted on the 180 materials. I have spent the latter part of close to 20 years involved with initiatives around elementary math specialists and written in that area and continued to direct a project called the elementary math specialists and teacher leaders project.
Skip Fennell: That still comes out of McDaniel College where I retired in 2015. In 2012 I received the National Council of Teachers of Mathematics lifetime achievement award. In 2015, I retired. Last year I was honored to receive the Maryland Council Teachers of Mathematics Initial Inaugural, I guess the word is, Lifetime Achievement Award. And also received an honorary degree from McDaniel College and was the commencement speaker last year.
Kyle Pierce: Skip, I’m telling you right now, I had a list of credentials, usually when we record the intro, which is after the interview, I had a list and I’m realizing now that I’m like, “Oh, my gosh. I’m going to have to redo that whole list.” Because you, my friend, I don’t think I’ve ever had the pleasure of speaking with someone who has such a, not just the quantity of opportunities and experiences but just the diversity in all of those experiences. From teaching primary and upper elementary through all the way into post secondary and it seems like everything in between. I know I’m shocked. I was excited to be able to announce five things at the beginning of the show but now I’m going to have to just randomly select here.
John Orr: We’ll just recut this and put it right at the beginning of the episode.
Skip Fennell: I mean, I have a brother-in-law who always told me, he said, “You know, you always blow me away.” I said, “What are you talking about, Jerry?” He says, “You’re one of the only guys I know who loves to go to work.” I said, “Yeah, because there’s stuff that I don’t know. And there’s stuff that we can fix.” And I’ve tried to stay as grounded as I possibly can, which is, as I said earlier, I don’t talk personally about … I mean, those are accomplishments. I’m okay with that but the other stuff that got me to where I am, and the stuff that continues to drive me to this day, is stuff I generally don’t talk about because frankly, it’s nobody else’s business. But I do compete and I compete in pretty much everything I do. I’ve finished nine marathons. Probably 30 half marathons. And continue to run, horribly, I might add. And I’m positive that anybody who walks fast can beat me running but that’s okay.
John Orr: You’re still doing it.
Kyle Pierce: That’s amazing.
John Orr: You’re still doing it.
Kyle Pierce: I’m tipping my cap over here.
John Orr: If you don’t mind sharing, Skip, how long, I guess if you consider all of the schooling you’ve got and your educational experience, how long has your career in math spread out in span?
Skip Fennell: Well, I taught at McDaniel College for 39 years. We can add about eight years of public school experience on top of that. So that’s going to take us to what? 47. I continue to direct a project for the elementary math specialists and teacher leaders. So that’s a few more. So, 50 couple.
John Orr: Amazing.
Kyle Pierce: Wow. Again, had tipped to you for not only taking and diving into the math education space, but like you said, I loved how you said you compete and you’re out there and you are doing the work and clearly there’s a passion there in order to keep you wanting to continue doing that work. That’s just fantastic. Now, if you’ve listened to some episodes and it sounds like you have, you know this question is coming and because it is the Making Math Moments That Matter podcast, we have to ask you, and you have a span here to work with, what would be your most memorable moment from math class? Some people choose to do something from their experience in the math classroom. Maybe something that may have inspired them to become a math educator. Or it could be something from your experience actually on the other end of the coin, or the other side of the coin, where you were involved as the math educator. Do you mind sharing that with us?
Skip Fennell: I can share a couple of them because I did have the heads up. One of the things that I learned without knowing it and that is when I was a college student and I went for my bachelor’s degree, I went to what was then called Lock Haven State College, which was a primarily grown up, normal school which is predominant in all the states in this country. And was a teachers college and now is a university. As I indicated, I was working in the field of elementary education but I was noticing that the math courses that they had us do were pretty easy for me. And so I found myself helping others. At the time I was also in a fraternity and fraternity brothers that I was around were having a lot of trouble dealing with a logic course. I’d never had a logic course, but I figured it out and I ended up having little sessions with them and they kept giving me all this stuff about how bright I am. I said, “No, I’m not. Whatever this is, this comes easy to me. There’s stuff that you can do by the way, that will come easy to you that I can’t do.” And that’s by the way, pretty much the way it is for everything as we learn and find skillsets and so forth and so on. So I remember that sort of vividly.
Skip Fennell: And frankly, I remember the joy of my early years of teaching where I was teaching all the math in this elementary school for 5th grade kids and so I had them all. Hundreds of kids. And we had fun. I could see some things light up and I could recognize where I needed to spend time and so forth and X years later, as I was teaching college students who were preparing to become teachers, I saw the same thing. I saw kids who were lighting up and learning mathematics, in some cases for the first time, at least conceptually and then I saw kids who were really struggling and it was my challenge, again, I compete. It was my challenge to help them see the light of day with that stuff. I have to say that you walk across the stage and somebody gives you that plaque and says those very nice things about you, but the smile a kid gives or a learner gives when they finally get something is probably a lot better. By the way, I’m sitting in an office where those plaques are up and these guys are teachers. You see the same thing. Kids have that aha moment, man it makes your day. Week. Month.
Kyle Pierce: Absolutely. You remind me of that turning point in my career where I was teaching and I don’t think I was getting those moments very often because I wasn’t reaching such a large percentage of my class and I carried that weight but once I started trying to dig deeper and I started trying to change things, that’s when those moments started to happen more often and that’s what fuels you to keep going and I can only imagine for someone like yourself who’s had all of that experience and to be able to receive that award, how many of those looks you received from students over the years? What a blessing to have.
Skip Fennell: You just hit on what allows that to happen and they’re related. And that is, first of all, experience is really important. I think back and I’m thinking, my god, I was a first year teacher, by the way, so were you, we were probably awful. You know? If we were MDs, we were probably killing people. And yet, they let us come back the next day. You know? Or whatever. But experience is a wonderful teacher and so you tried stuff that didn’t work and this is the other connection to that and that’s a willingness. A willingness to look at it differently. A willingness to realize, that kid is different than the kid who is sitting next to him or her. And so forth and so you know what? It’s not going to work the same way for that person and so with your experience and your willingness and that competitiveness, find a way to work for him. It’s sort of like, I love sports. And so to some extent, we’re all coaches.
Kyle Pierce: That reminds me of exactly what we hope that we do in the classroom. When you think about coaching and you go in with a plan and with intentionality but you have to pivot that plan based on the player that you’re working with, right? And depending on what they need at that time and coaches are really good at picking up on those things, right?
John Orr: Yeah. You said something very interesting I think and it goes to what kind of teachers are going to be the ones that have those aha moments and you said it’s the teachers that are the willing ones. It’s the ones that are going, “I am going to take that information, that lesson was a huge flop.” And then it’s like, “Do I come back in tomorrow and do it again or do I go, you know what? I have to do better.” Those are the moments that are going to be make or break for becoming a better teacher. It’s like that willingness has to be there. And the drive to take that information and realize, “Hey, I may have not done something great, but I’m going to do something great next time.”
Skip Fennell: I’ve been a teacher, educator pretty much my whole career and I don’t think teacher educator programs have ever prepared the teacher candidate for that. You know what? It’s your school. It’s your class. And guess what? They’re coming back tomorrow. So, you know, get over it. Take that game plan, rip it up, because you’re going to have to have another one tomorrow and I think you learn planning and you learn, if you will, the importance of assessment as you, if you will, muddle through it. To the point where you get good at it. And then you have to deal with the danger of not flat lining. In other words, yeah, okay, you’re good. Are you going to be good tomorrow? Are you going to be good with a different class of kids? Are you going to be good when you move from that algebra class to say geometry which you haven’t taught in a number of years?
Kyle Pierce: It’s like you can never actually sit back and stop thinking. You’re always thinking and you’re always going, that experience is only helpful if you’re going to use it in your planning and your reflection and obviously all of the during piece as well, right?
Skip Fennell: Well, that’s like where people who say, “Well, the kids aren’t like they used to be.” I said, “You know what? You’re right. And they shouldn’t be because they’re new ones. They’re the ones today.” Don’t expect them to be like children 20 years ago because that didn’t work then so don’t expect it to work now. You know? Deal with what’s in front of you.
Kyle Pierce: I think we could talk about so many different areas of math with you but we wanted to specifically chat with you about your book and about assessment. That book you co-wrote with Beth Cobet and Jonathan Ray. Yeah. Called The Formative Five. And specifically talk about assessment and maybe we can just chat about this first question here about that. What experiences in your career do you think had the most influence on you to drive this passion to talk about assessment? And think deeply about assessment? What sparked you to kind of pursue this particular path of teaching?
Skip Fennell: Well, it’s something I’ve been thinking about for a long time. When I did my doctorate in math education at Penn State, I had a minor that was pretty much in educational statistics and educational measurement. So I had, if you will, the background in all of that stuff and that’s where I first got to sort of understand from an academic level, the issues around assessment. And then as it turned out in my early, well, actually for a number of years, while teaching at Western Maryland College, which more recently was renamed McDaniel College, I taught assessment courses. Assessment courses at the graduate level for grad students in all fields of education or certainly a variety of fields of education. And also at the undergraduate level. And I was struck by the fact that people didn’t get assessment. I saw that in lots of context and I harken back to frankly when I was teaching. And I remember vividly when it was time for me to, I guess you ought to give a test here. I wonder how I do that?
Skip Fennell: I remember, this is such a bad story in some ways, because I remember going to my next door teaching neighbor, Rodin. I said, “Hey, Rodin, I have to give a test tomorrow. Can I look at your test or whatever?” And I’m just about going to use her test with my kids. Finally it dawned on me, they’re different than your students. Why would you do that? My point is, and the issue around assessment literacy as being a real important issue as we prepare teachers, people need to know about assessment and the role of assessment. In particular, I think there’s a lot of mystery around formative assessment. It’s not well understood even though it’s talked about a lot. When I was NCTM president, I had this opportunity, sometimes it was a problem just getting motivated to do it but every month I had to write a column that went out to the full membership and I title one, I actually sent it to you earlier today. It was something along the lines of, “Go ahead and teach to the test.” And I used that headline because I knew that people weren’t going to like the headline.
Skip Fennell: What do you mean teach to the test? But typically if you’re teaching and you’re connecting, your planning, to your instruction, then you’re right in the cross hairs of doing classroom based formative assessment. And that’s what the formative five is all about. So the notion about formative assessment has been in my head for a while. And then as I indicated, for close to 10 years, John and Beth and I have been involved in, and I directed and John is the program manager and Beth is our lead consultant and it’s the Elementary Math Specialists and Teacher Leaders Project. There’s a link there that’s out there and people use it and we work with I’ve different county based school districts in Maryland and we meet with these math specialists to provide professional development for them and also to help us understand what their issues were and we were hearing far too frequently, “Well, my teachers really need help with assessment. They really don’t understand formative assessment. Blah. Blah. Blah.” And so fine, we’re doing this.
Skip Fennell: We decided to go after formative assessment and very specifically, classroom based formative assessment. Partly because it was horribly understand and, if you will, misunderstood around the country. By the way, a good check for that, and I always do this when I present, Google formative assessment. I did today and I got around 33 million hits. That means there a lot of interest about this topic. Doesn’t necessarily mean that what’s there is necessarily what you want. John and Beth and I spent, actually, several years thinking about ways that you could, at the classroom level, really manage your planning and your instruction and connect it very directly with formative assessment techniques. And we tried lots of things and we ended with five. And hence, The Formative Five. We titled them as observation and interviews and something we created called show me and the hinge point, hinge question. Which I’ll talk about a little bit later. And also exit tasks. Not exit tickets. Because we found that exit tickets, are used often very trivial. We call it a test for a reason.
Skip Fennell: Because we want it to be meatier and I can say a little bit more about that as we move forward. So we spent a couple years piloting all these techniques and kind of latched on to those five. And then you know, went into classrooms and worked with our math specialists and they worked with their teachers to both define and sort of see how this is. Essentially that got started and the metaphor we like to use with The Formative Five is the artists pallet that the artist has his pallet of multiple colors and we view that the classroom teacher every single day, or at least five days of the week, is an artist. And as you sort of paint that picture that is your classroom lesson in mathematics, and as you think about the mathematics you’re teaching. Think about those assessment techniques and how and when you’re going to use them as they integrate with the instruction that you’re providing across however much time you have to teach. That’s how it got started. I can talk about each of the five techniques if you want or we can-
Kyle Pierce: Yeah. Skip we definitely want to dive into those five. We’ll try to go as deeply as we possibly can. I know it’s so difficult in a short period here. Over the podcast. However, I wanted to back up to your article about teaching to the test. Now, I thought, first of all, a genius title. But also the whole point being that when we are assessing, we’re trying to assess best the things we’re teaching? So I know it seems a little bit cart before the horse, if you think of it that way with teaching to the test, but at the end of the day, we’re supposed to be assessing what we were teaching to see were students were in understanding. And I know here in Ontario, we still struggle, even though we have a document called Growing Success, which was released, I believe it was 2010. In there they talk about observations, conversations, and product. Really just trying to push away from this idea that everything has to be student product that’s submitted. They really want us to be thinking about these things.
Kyle Pierce: They didn’t go as deeply into five ideas like you’re going to share with us today but I find it interesting that in the US as well as here in Ontario, where we try to be very progressive with our assessment and eval, we still have some struggles and I wanted to, before we move on, just to make sure for all the listeners, that we’re clear, I’m wondering, do you see a different in between assessment and evaluation? Because I feel like sometimes teachers lump them together. So they tend to look at assessment and evaluation as the same thing. Whereas I tend to see assessment is the process of learning and it’s very dynamic, it’s very fluid. Whereas evaluation is sort of more at the end. I’m wondering if you can give us a little perspective on your thoughts between those two ideas and then we can start diving into those formative five.
Skip Fennell: Sure. I really like what you just said because one of the things we tried to do with the formative five is to get away from this notion about, “Okay, here’s planning and teaching and assessment is somewhere else.” What we’re trying to say is, it’s new. It’s right there. It’s right connected with it. And so to your point earlier, we use these classroom based formative assessment techniques very directly as you plan that lesson, which of these techniques is going to go where within that lesson. In other words, you’re right there, it’s part of the planning process and so ti’s not something else. Whereas an evaluation, I would think of as something more summative. Something like you have to give a grade at the end of X weeks. And so that’s an evaluation moment that is summative.
Skip Fennell: It takes a look at all the stuff we just referred to plus some quizzes and tests and so forth and so on. And you make an evaluative decision. I think that classroom based formative assessments are more dynamic and they lead to the point where if you’re doing this regularly and if you’re doing it right, you can make that evaluation because you have all of this data. Some of it’s informative. Some of it is paper, pencil, or on the computer. Whatever. Tangible on something you can look at. But I think all of them get you to the point of evaluation as opposed to evaluation first. You can only evaluate once you have enough information about the person or the class or what have you. So the classroom based techniques really drive it day to day to get you to the point where you can make an evaluation would be how I would summarize it.
Kyle Pierce: Right. It’s been a learning journey for me especially on this because I was the high school teacher for a long time that viewed formative assessment as the quiz partway through the unit and I would take that, mark it, and put that in my mark book, and in my grade book, so I had a grade for the students and then back then it never occurred to me that, and I don’t know why, years later I’ve evolved from that but I would take that and put it in the grade book and I never really thought, you’d look at the results and go, “The kids got killed on this quiz.” And you still wouldn’t go back and change anything. You’re like, “Well, I don’t have any time.” You know? I don’t have time to go back and fix all that. Or it’s not fair if I remove that from my grade book, even though they now understand it. It’s like, it was a quiz so it has to go in there. Right?
Skip Fennell: And generally speaking, for the Formative Five, you can probably talk me into grading exit tests.
John Orr: I think so. I was just going to say that I think that right now in Ontario, this is a very common question. When you’re looking at your observations in your interviews and your show me techniques that you’re going to dive into in a little bit, like Kyle said, we have observations and conversations as kind of like, even though they’ve been around since 2010, it seems to be new in some people’s minds and people are saying, “Well, how do I grade that?” And I think you’ve hit it there, Skip. I don’t think you have to. That’s not the point of what those are all about. You know?
Skip Fennell: And the fact is, one of the things we say to teachers all the time, and I could say more about this later but this whole thing has blown up in a sense that there’s a lot of interest in this and we talk about it in a variety of context all over this country and beyond and we get this issue all the time and so yes, you can certainly make record … By the way, what you’re doing in Ontario sounds very similar as I noted earlier when I read your comments, to what we’re talking about for at least the first two, maybe the first three of the Formative Five. Kudos to you guys in terms of valuing classroom based formative assessment. You can take notes. I mean you’re in the classroom, you know this. You know what that kid is doing. Because you have a mental record of those observations. As well as maybe you’re taking some notes and so forth because frankly, if we don’t do that, we’re going to lose certain things the kids did and so forth that you might want to have around. But I don’t know that a letter grade necessarily does anything for anybody. I’d rather have running record of what kids are able to do and the progress they’ve made from time to time and be able to recount that come evaluation time.
Kyle Pierce: Absolutely. And I found when I actually started doing these things and I convinced myself not to get too wrapped up with the, “How will I grade it?” Because that was a struggle I had as well. For those who are listening, it’s very common for people to kind of, we’ve kind of grown up in this grade, mark frenzy sort of scenario where it’s all about marks and what I realized when I started to do more formative, or at least, really all it was was opening my eyes and using more rich tasks, me doing less of the talking and letting kids do more of the talking, it was like I actually knew what they understood before any formal assessment, that summative piece that you had mentioned earlier. Down the road, instead of me going home and I’ve said it on another podcast, I don’t know which episode it was, but I’d go home and I would be marking watching the hockey game or something and I would be sad because the hockey team would lose and my students were doing poorly on the assessment. How is it possible that I taught an entire unit and I didn’t realize that was going to happen? And really what, over time, I realized was because I wasn’t actually listening. I wasn’t actually observing and interviewing and asking some of these pieces.
Kyle Pierce: I think this is an amazing segue. And the other thing I wanted to mention too is, that question teachers say they receive all the time and especially when you get into older grades, you get into the middle years and then you move into secondary or into high school as you call it in the US, students are always asking, “Is this for marks?” When you’re in an environment where assessment, where it’s a formative assessment rich environment, students don’t ask those questions because they know that you are, whether it is, you actually anecdotally writing down those running records, whether you’re taking photos or video or however you choose, kids know that you’re recognizing their progress. Right? It comes out through the feedback you provide them. I’m really excited to be diving into these. I’m wondering, can you start us off with first the observations? What does this look like, sound like, and in particular if I’m a teacher who’s saying, “How do I get started with some of these?” If you can give them some little tips to get them started and then obviously at the end we’re going to be sharing some details about the actual book which would be a no brainer for people to pick up after this if they’re liking it.
Skip Fennell: I mentioned earlier the fact that we use this artist metaphor of the artist pallet for the five techniques. By implication that means that while I’m going to talk about observation first, that doesn’t necessarily mean you do it first. You do it whenever. We observed in our work, in terms of determining these techniques and deciding how and when to use them, we observed a number of classrooms across all kinds of levels, elementary, middle, and high school and found that teachers observe all the time. They don’t pay any attention to it and so what we’re saying is, you observe your students all day long. Pay attention to it. Do something with it. In our chapter on observation and for each of these five techniques, we’ve created a number of tools that teachers can use to help them get started with it. A planning tool for using observation.
Skip Fennell: A tool that you might use with individual students. A tool that you might use for the whole class. And so forth and so on. To keep records of doing what. And so let’s say you’re doing this lesson on equivalent fractions and you ask yourself, as you’re planning, what do you expect the kids to be doing in this lesson? That’s important and that ties back to your objective of the day. And then frankly, and here’s the kicker, how would you know it if you saw it? What would they have to do to sort of demonstrate your expectation? And then frankly look for it. And so then to what extent are you seeing this? Do you want to just walk around and use check lists to see where people are? And again, the tools I alluded to earlier would help you do that. But in large measure, when we did this and interviewed teachers like, “Well, yeah, I always observe my students. I didn’t necessarily think about it in the process of planning my lesson and then frankly watch for things as I taught the lesson.” And so we said, “Well, then you ought to.” So that was easy. And then the interview kind of flows from the observation.
Skip Fennell: You’re observing students and Kyle, I want you to come over here and I want you to tell me what you’re doing with that problem? And the key thing for the teacher there is to just shut up and just let the child talk and then the second question might be, “Well, tell me why you did it that way.” And then maybe a question about, “Is there another way you might do it?” Or whatever. But we have a very simplistic sort of plan for a short, five minute or so interview that you might want to use just to see where particular kids are. We don’t view these as necessarily clinical interviews that might occur in children receiving some level of special education or what have you. These are instructional interviews that are not deficit based. So it’s important that they are made available and that you have an opportunity to see what kids are doing with that. As we piloted this, and to this day, we find that certain teachers will just have a corner in the classroom and they’ll say, “Meet me back in the corner.” Where they can have a little bit of privacy with the interview.
Skip Fennell: Some teachers like to do the interview with a small group of kids who might be working on the same topic but it basically allows you to dig a little deeper into what you observed. And it’s also, I mean, again, you’re planning this lesson. Here’s the lesson on equivalent fractions, where do you think the bumps in the road in this lesson might be? That’s maybe where that interview process will occur. The other thing that is non-negotiable in one sense, that is, and you’ve been there. You’re observing your class, you’re walking around seeing what they’re doing, seeing how they’re doing things, and somebody is doing something and you have no idea what they’re doing. Kids do quirky things. And frankly over my years of experience, I love to say, “Well, tell me about that. What are you doing there?” Again, it’s important to let them talk and you sort of try and decode what’s going on. But quirky responses, responses that the teacher doesn’t understand, responses that are just out there to the point where you might want to challenge somebody because you know that this child can do a little bit more. These are five minute or so episodes where you’re managing your observation by including the opportunity to have an interview.
Kyle Pierce: I love that. You know, the question I always say when I’m walking around and I run into one of those, I like your coining it as kind of a quirky sort of way of going about it. A way that probably you or I have never, ever taught of doing it, right? And early in my career, it would be easy enough for me to be like, “I wouldn’t do it that way.” And for years, I would say those things and looking back I’d say, “Oh my gosh, what a way to shut down a student who maybe isn’t feeling super confident and yet they picked it up, they tried, they did their best and the sad part is, they probably were way more clever than I ever was.
Kyle Pierce: And that’s how they came out with that particular strategy. So I was around and I always say, “Wow. That’s really interesting. Tell me more about that.” And what I do is, when I get in the habit of saying that all the time, I say it when it’s a quirky solution or I say it when it’s one I anticipated. Right? The most common one. And then it’s almost like students have no idea which zone they’re in and whereas if I go … If I act really surprised, then a student goes, “Uh oh, he doesn’t know what I did here and maybe I should erase this.” So really trying to be neutral took a long time for me when asking those students in formal or informal interviews.
Skip Fennell: There are all kinds of reasons for interviewing kids. I mean, including personal social. I mean, there’s some kids who just are very introverted and you frankly don’t know what to think and so it’s an opportunity for them to talk and for you to listen and maybe pull them over to the interview corner if they’re self conscious about anything and so forth. The important thing for us is that we don’t want anybody to think that you’re having this chat because it’s deficit based. That there’s a problem. I have a friend who’s a principal who actually coined a term, it was after we published the book so I couldn’t use it. But I liked it. She calls it a check in. Rather than an interview. “Hey, Kyle, I want to have a check in. Come over here.” So it doesn’t give you the sense that it’s in some sort of court of law or whatever.
Skip Fennell: And so I liked her take on it but the notion of it essentially expanding the observation is how we got to that and then if you don’t mind, I’m just going to move right into the show me. Because we created that. In other words, there’s history around interviews. Clinical interviews and so forth. And there’s history around using observations. But we coined show me because it’s the spontaneity that the teacher has with his or her lesson that allows that teacher to say, “Hey, right now, I want you all to show me using fraction block or what have you, three equivalent fractions.” Or you can do that individually. Show me how you did that. Show me with the number line, how you might add those two fractions or what have you. Often we find that this technique is very useful in terms of representations that kids might have. Whether those are representations involving manipulative materials, or a graphic material, whether it’s a number line or coordinates or what have you, but it just gives that opportunity to sort of see what’s going on. On the spot.
Skip Fennell: So it connects very nicely to observation and interview. We think actually that observation, interview, and show me, to some extent, run together and then again, there’s no sequence here. You might have somebody show you right off the top of a lesson based on something that you did yesterday to sort of get them up to speed in where you might be going today. We see all kinds of ways that those three are twisted around.
John Orr: You know, this reminds me because I was thinking when you were talking about observations in interviews, that it’s almost like those can’t really happen without this idea of show me. Think about our lesson structure, and I don’t know if your math classes Skip, when you were learning math, when I was learning math, the teacher just did example, example, example. Now do a whole bunch of homework questions. Those observations in interviews are hard to come by when you’re listening to kids reason through problems when you didn’t give them that opportunity. So it’s almost like that, am I right to think this show me has to happen almost like, you have to think about how can I get kids to show me stuff so that I can then observe them and interview them at the same time.
Skip Fennell: Well, see that’s in my view, the byproduct of the Formative Five. If you plan this lesson and you ask yourself, what do you expect kids to do and then how do you know what it looks like when they do it? It’s forcing a different kind of lesson. You’re not now talking to kids. They’re getting involved. And so you want to observe them doing something and as you move around, my implication, you’re not staying in the front of the room, you’re moving around observing, watching them do whatever the tasks happen to be, and then you’ll decide, “Well, Kyle, I’d like to talk to you about what you just did there.” And so it pushes you deeper into that lesson yourself and then the show me is that spontaneity driven kind of activity that says, “Hey, that’s interesting. Show me how you did that.” Or, “What if we doubled the numbers? Show me how you would do it then.” Or something like that. It forces a different look at the lesson and frankly, a more engaged implementation.
Kyle Pierce: Yeah. For sure. And I know that I mentioned it earlier just trying to shift and I love how you said it, it’s like if you’re actually trying to do these things, it forces you to shift. So if you’re struggling or you find yourself that habit keeps you stuck at the front, and you’re in your mind saying, “I really want to switch this up.” Well, I wonder if maybe the focus now becomes more about these five ideas around formative assessment whereas, “Well, if I’m going to do that, it’s going to force me to set up the conditions to make sure that these things happen and not feel like it was almost foreshadowing towards hinge questions where you had mentioned saying, “Hey, how about … ” and almost sounded like we didn’t have an exact question, but it’s almost like this idea of stretching the students thinking a little bit and really trying to get to the root of how much do they understand here? I can see that maybe they have a correct solution and a helpful solution strategy, but how well do they understand this concept in general? So I’m wondering, can you help us understand what that might look like or sound like for hinge questions?
Skip Fennell: Yeah. Well, the first three as they indicate, are very close together. I mean, as teachers plan and they think about their lesson and what they’re going to observe, and where they interview might play out and would there be opportunities for show me and how might that play out, could be whole class, small group, a couple kids, what have you. In our work with teachers is, yeah, I’ve been doing all those things. I haven’t called them that but that’s easy for them. The latter two are more challenging. The hinge question comes from Dillon William. Dillon William in my personal view is the guru of the formative assessment in this country and perhaps the world.
Skip Fennell: I’m a fan of Dillon William and what we did basically was take his notion of a hinge question, a hinge point question, and kind of blow it up. By that I mean, John Ray gives me a hard time every time I talk about that. But to me, the hinge question is the deal breaker of the lesson. It’s the question you ask at the end of the lesson or towards the end of the lesson that sort of captures the major focus of that lesson. And there’s certain things to consider here as you do it. The hinge question. Those are whether or not it’s going to be multiple choice or not. And then also what we refer to as the two minute rule. In other words, you ask the question and you give kids time to process and then you, on your feet, sort of assess where people are because right there, that’s what you’re going to do tonight as you plan the next step and that next step might be, guess what? Based on that response, we’re not moving forward.
Skip Fennell: I’ve got to come at this a little bit differently tomorrow, based on what I’m hearing. Or, man, they’re doing great. We can move on. We also talk in the book, as does William, about a hinge point question because we’re conscious that not every lesson is the same concept throughout the whole lesson. Many lessons are multi concept lessons. In other words, you’re finishing one topic and you’re moving on to the next. Or you’re starting it with one concept and then you’re going a little bit deeper in the same period. And so a hinge point would be that question to be the capstone of the point of that lesson where you say perhaps move from equivalence into addition, subtraction, fractions, or what have you. But the same notions apply and that is, here’s a carefully throughout question. Be it multiple choice or not. That you’re going to phrase and that you’re going to give kids time to process a little bit and then you’re going to figure out in your head where you’re going to go next. So it’s a really important element of the lesson.
Skip Fennell: As we work with teachers, we have found that of the five, this by far is the most difficult for teachers to pull off. Partly because, I want you to think about this, I don’t think any of us when we began in this field were particularly good at asking questions and we still see that and so here we have a curriculum and here we have standards where you have to think about questions that are really appropriate to that lesson and so in our work with teachers, we have found they do all kinds of cool things that we frankly, initially didn’t think about but we wrote about in the book and that is, they come together and they bounce questions off each other and then create files of questions that they can fix and use differently the next year or what have you. They create resources for these things but the hinge point question is really important. I know I’m talking fast here. So, come back to me. Help me explain this a little bit better if you need me to do so.
Kyle Pierce: Yeah. Well, the part that I really appreciate is the importance of us learning how to ask good questions but then I almost want to back up as well and I know that this isn’t mine for you of course, but we have to have a really intentional lesson planned right? So really having that learning goal clearly in our minds to know, “Okay, so we’re delivering this lesson and it’s going to be almost near impossible to come up with a good hinge question if I don’t even have that intentionality articulated in my own mind. Because how am I going to ask an effective question, right?” So really focusing on that big idea. What is it I want students to walk away with at the end of this lesson and then I love what you had mentioned about then you’re going home and saying, “Did they walk away with that?” This is a great way to know and if they didn’t, now what, right? What am I going to do differently? So that, I think, is excellent.
Skip Fennell: I think that the whole notion of the importance of asking good questions and this particular type of question is a challenge for teachers. Again, I’m guessing that none of us were good when we started out. And once again, your comment gets right back to the point that we’re trying to make and that is planning and implementation and assessment are the same conversation. As you plan that lesson, as you think about teaching that lesson, how do these techniques float through that lesson so that you’re grabbing indicators of student progress and the hinge being one of them.
John Orr: Take us onto exit tasks. You mentioned that they’re different than exit tickets. Let us know on the difference.
Skip Fennell: Sure. As indicated, we did a lot of work prior to coming up with these five, and found books that said, Here Are 50 Assessment Quickies, or stuff like that. Which kind of drove us crazy but we also found that, if you will, almost a culture relative to exit tickets, exit slips and so forth. I got to the point where I one time said to Beth, I said, where are they going with these exit things? And so we very intentionally said, we’re not going to call these tickets because there’s a ticket to nowhere. We’re now going to call them slips. This is a task. This is a legitimate math task that the class is going to do towards the end of the period typically, that gives an indication of a capstone for that lesson.
Skip Fennell: And as I indicated earlier, I could almost be talked into grading these but here’s a product. In the case of what you observe, in the case of an interview, you could have a product for that. You could have a product for show me, if it’s something tangible. You may have a product for the hinge, often not. But you’re definitely going to have a product for the exit task and it’s the one of the I’ve techniques where we’ve said, “You know what? Maybe you don’t do the exit task five days a week. Maybe you do it three days a week.” Because at some point your eyes are going to have to be on these to see to what extent, where are they? And so forth. But again, it gives you, if you will, more evidence in terms of the student path towards proficiency for particular lessons or within the unit or what have you.
Skip Fennell: Unlike the hinge, we have found that teachers are particularly creative because you know what? At 9:30 at night, my brain is dead. I’m not going to be able to create a good exit task. So they found different resources, be that online or whatever. Illustrative Math Website is one example that people like and they’ll just take some of those tasks and if you will, fix them or tweak them to meet their needs or they’ll find tasks in text books that they don’t particularly like in the context within the textbook but they provide them with a germ of the idea that they can use for the exit task. And frankly, teachers create resource folders of all this stuff. And so they can repurpose them for the future years.
John Orr: I like how you’ve elaborated that. You know? This is a task and not just a ticket where an exit ticket can be helpful at times, but it is very limiting in what you can actually find out when it’s something that’s done in five minutes or in a math class, I might almost want to call the exit ticket more of a reflective journal right? It’s like a reflection. Those are really, really helpful as well for us to get a good idea as to what students heard in the lesson but I like the idea of this actual task and I like that you’ve elaborated that there will be some product of some sort that comes from this and the fact that you recognized with how jam packed a math block could be, that it might not happen five days a week. Other parts of the lesson are going to have tasks. So what might that concluding task me to sort of take it to the next step and maybe it might even be more direct too.
John Orr: Because on the show, we always talk about sparking curiosity and really trying to get kids to lean in and that’s great when we’re learning a new concept but when you’re trying to actually fuel sense making and try to push students a little bit further, you can ride that context and I see that as a great opportunity, as a way to slide in your exit ticket, right? Stick with maybe the same context, but let’s change the scenario or let’s change the values or maybe a new person or thing comes into the scenario where now you can stretch it just a little bit further to see where is everyone on the continuum here and what are we going to do about it tomorrow?
Skip Fennell: I just looked at one of your shows on the kind of iteration of the three arch task and so forth, and maybe that’s where the three arch test could go as well. I mean, it’s sort of a culminating experience of the lesson. It’s definitely a product that the teacher has in terms of looking at student performance and again, throughout all of this we say to teachers, and teachers recognize it, don’t hesitate to make some notes as you observe. Don’t hesitate to keep those interview comment sheets that you might have with kids. Or a show me response or an exit task. Or even a hinge, because at certain points in the year, you are going to have a conference with parents and it provides you with lots of, if you will, data. To give you a real story about how a child has been doing in mathematics. In a variety of ways. Not just one technique.
Kyle Pierce: Yeah. These five are great. Like we’ve said before, and here in Ontario, we’ve been really thinking about two of these and you’ve elaborated to give us some more tips and advice here to help with our students. I’m just thinking about the folks listening. If teachers are starting this process, what is a one tip or one low hanging fruit for them to get started and what would you recommend and say if you’re going to do anything, let’s focus here first.
Skip Fennell: First of all, it’s a great question. Because one of the things we always say is, you’re not going to start doing all five techniques all at once. Let’s learn about the process. Let’s understand the importance of connecting your planning to formative assessment and to the instruction that you’re going to provide and so maybe you want to start with observation and really paying attention because you have been observing. You observe your students all day long and you do that every day. Maybe you do observation and show me and then move into the interview. I would be somewhat comfortable with the first three of those before I would move into the hinge and I wouldn’t move from the hinge into the exit task until you felt pretty comfortable with the hinge. Again, our experience and one of the nice things about trying all this stuff out for two years before we wrote about any of it, is that we knew. We knew that the hinge was harder because teachers told us.
Skip Fennell: And you know, they got better with it but again, and I think, I know I shared with you Corwin very recently got this idea, they’re referred to as on your feet guides and it’s basically the Formative Five on a fold out folder and something like that just in your hand to sort of help you as you walk around implementing these things is useful as well. We’re finding that schools and school districts are finding very creative ways to on their own have webinars to walk people through these techniques one at a time. To come together, whether it’s online chats or through webinars or what have you, to say, “Hey, you know what? I tried this and it’s just like anything else when we try it instructionally, it didn’t work.” Why didn’t it work? And talk people through those. I would start gradually.
Kyle Pierce: We’ll definitely include a link to the Formative Five. The foldable, we checked it out as well. Definitely great resource. I thought it’s less handy for carrying around in class, but it is something that you could have in either near your teacher desk, or in your prep area. Inside the book, there’s actually a poster with the Formative Five in it. I think it gives a really good summary of each one and sort of gives you kind of just so that you get familiar with it and it does a great job of talking about the what, the when, the how long, and then there’s also some other handy quotes about the importance of assessment.
Skip Fennell: Well, there’s a bunch of quotes from classroom teachers that we’ve worked with over the years about this whole process that helps bring this to life as well. It’s one of the things that we wanted to do is, we knew that these five techniques were believable and doable and I think that’s what we want. We want a plan that teachers can count on which teachers can understand themselves and are going to use on a regular basis. We’re just blow away at the number of requests we have to talk about the Formative Five at the number of different ways that NCTM, which because the book is co-published by NCTM and Corwin have found ways to create professional development opportunities with the program, provide online courses about the Formative Five, you name it and people are doing it.
Kyle Pierce: Nice. Well, you know, this has been such a powerful conversation. I know that folks are going to be raving about this conversation because of the learning that they’re going to get out of this. But keeping in mind for those listening at home. This is just a quick summary of what is a great read. So definitely make sure that you check out the Formative Five. We’re going to have everything linked up in the show notes including that foldable that Skip just referenced. At this point in the conversation, we can’t keep you all night, although we would love to, what we would love to know is, what are you currently working on? I know it sounds like you have one project on the go, and do you mind sharing a little bit about what’s keeping your math ed brain busy these days before we wrap it up?
Skip Fennell: Sure. First of all, I’m busy with lots of things. The Formative Five, as I indicated, it was like, we knew that there was a need here but I guess it was a greater need than we thought. So that continues to keep us busy but Beth Cobet and I are working on a, actually she’s the lead on this and I’m helping her out, is a good friend and colleague. Best plan is to look hard at the issue of what really is a math task? And what should a math task look like? And how is that connected in a very direct way to your planning to teach mathematics? Where does that test go and how are you going to use that implantation wise? So, because … and I’m speaking for Beth now, I think there’s a lot of myth out there about what is a legitimate math task? And by that I mean a mathematics opportunity that engages students at an appropriate higher level to both challenge and provide access for them to the mathematics.
Skip Fennell: And so we’re going to do two or three books for K-2, I guess three books. K-1, 2-3, and 4-5 for the elementary level focusing on what is a good math task and then thinking about how to connect those tasks to planning and helping Beth with that. Again, she’s the lead on that. I’m involved with National Teacher Accreditation Group in this country entitled CAPE, I’m on the board for that organization and working with teacher education in that context, in national standards there. I was one of the writers of the common core state standards and so one wonders about next steps relative to that. I know that doesn’t influence your Canadian audience, but I also know in both countries, we pay attention to what others are doing. So that’s a little bit of my time. Other than that, trying to keep track of my own personal life and following around nine grandchildren.
John Orr: Oh, wow. That must keep you busy. Those books sound super interesting. Just because I know we throw around tasks, activity, lesson. People use them interchangeably. I think it would be pretty nice to read those other books. One last one here, Skip, where can our listeners find more from you? Can they follow you on some sort of social media or is there a link they can go to to learn more about you?
Skip Fennell: I’m on both Facebook and Twitter. I’m at @SkipFennel on Twitter. You can find me pretty easily on Facebook as well. I’m very active in the National Council Teachers of Mathematics Community as well as the Association of Math Teacher Educators Community. I think if you Google me, you’ll find me pretty quickly. I have my own website. The Math Specialist project that I mentioned earlier, we have our own website there too if you just Google elementary math specialist. I think that will come up. I’m the project director of that and we have lots of stuff on our website that anybody can take down. So we encourage you to use it.
John Orr: Awesome. Thank you for that. We’ll put all that in the show notes. For sure. Skip, we want to thank you for coming on and sharing your great wisdom and all those tips that you gave us on the Formative Five. I think, like Kyle said, we’re getting a lot out of that ourselves. I’m sure the listeners are too. So again, thank you so much. We appreciate you and the time that you’re spending with us.
Skip Fennell: My pleasure. I enjoyed it immensely.
John Orr: Thank you so much. Have a great night and we will talk to you soon.
Skip Fennell: Sounds great. Thanks again.
John Orr: We want to thank Skip again for spending time with us to share his insights with us and you, the Math Moment Maker community. Skip gave us some amazing ways to build formative assessment into our daily teaching practice.
Kyle Pierce: As always, how will you reflect on what you’ve heard from this episode? Have you written ideas down? Drawn a sketch note? Sent out a tweet? Called a colleague? Be sure to engage in some form of reflection to ensure that the learning sticks.
John Orr: And don’t forget about the Math Moments with Corwin Math Book giveaway. That’s right. We’ll be giving away 10 books from Corwin Mathematics including Skip’s book, The Formative Five. Plus you’ll receive special Corwin discounts and digital downloads just for entering the draw. You can get in on the giveaway by visiting MakeMathMoments.com/giveaway by Wednesday, July 31st, 2019.
Kyle Pierce: Listening after July 31st, 2019? No sweat. We’re always actively running giveaways so check out MakeMathMoments.com/giveaway by Wednesday July 31, 2019 to get in on the Math Moments with Corwin Mathematics book give away. Or if you’ve already missed that one, check out the same link to learn about the current give away we have running.
John Orr: Don’t miss out. Dive in now at MakeMathMoments.com/giveaway.
Kyle Pierce: That’s MakeMathMoments.com/giveaway.
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John Orr: We release a new episode every Monday morning. Keep an eye out for our next episode.
Kyle Pierce: Well, until next time, I’m Kyle Pierce.
John Orr: And I’m John Ore.
Kyle Pierce: High fives for us.
John Orr: And high fives for you.
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