 and page paper on eating disorder. So tasks might be like, okay, number one, maybe come up with a thesis statement and then come up with an outline of the evidence that you might want to build in order to argue for your thesis and then maybe look for sources, right? So these might be steps. And then as criteria, you might actually give annotated examples of papers from the past. And not just ones that have like check minus, check minus plus, you know, like not like that, but actually maybe marginal comments have said things like, oh, this is a really great example of where you use the evidence in a really distinctive way and blah, blah, blah, and I like that a lot. So those are things that you can do. Now taking it back to math example, so I find this work about transparency is really most helpful whenever you do things like projects in the class, like making a poster, giving a presentation. Those larger tasks are often places where those explications become unclear to students and what you know in your mind of what you want as a final product is not quite exactly what students give you at the end. And so those are places where you might want to be careful about separating the lists of tasks to perform and then criteria for what good work like looks like for that particular assignment. Thank you, Melissa. Did you have a thought, question, comment? All right, okay. In the remaining time, let me tell you a bit about active learning. Okay, so active learning. Active learning is a term that somehow is specific to the higher ed world. I don't know why we use the term active learning. All of my teacher friends are just like, oh, that's just teaching. I don't know why you're making a distinction. They call it active learning. But just so you know, for the higher ed folks in the room, the conference board of mathematical sciences, which is like the Uber professional society. It's like the society for all the societies put out the statement in 2016. We call on institutions of higher ed, mathematics departments and mathematics faculty, public policy makers and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classroom. Okay, so what might be included in the term active learning? So if you read papers, there's a lot of different definitions. Let me give you what I might consider a definition for active learning. I think active learning is basically using teaching strategies that reduce classroom time in which students are passively receiving information and increasing the time in which they do think, predict, discuss, practice, apply or otherwise engage with course content so as to provide students with opportunities to reflect on their learning and or receive feedback from other students or an instructor. And so that's, I know a word, a mouthful. But basically, getting students to do group work, getting them to work on a task in class, going to the board, writing something down, having a discussion with a neighbor. These are all examples of being more active in a classroom as opposed to just, as you are now, I'm sorry, sort of passively receiving information from the instructor, okay? So just so you know, this is a common mode of instruction still in higher ed. So most math classes are still taught in a pretty direct lecture style. And I'm not, I don't wanna get into a huge discussion about that, but there is a lot of evidence these days that it's not very effective. The more students have a chance to engage and to think for themselves in the middle of class, the better they actually seem to learn. Okay, but in addition to this active learning being a good thing, there's also this very interesting line of research these days that shows that active learning actually has a secondary wonderful effect. Not only does it help students learn more, it seems, not more and more, that it helps all students learn more and it helps students of color, first generation students, women in particularly underrepresented situations to learn even more than their majority peers. So what it does is it helps to decrease any particular gaps they may exist between students before going into the class. It helps to reduce those gaps, helps them have everyone learn more, but for particular groups of students to learn even more. So that's an interesting thing. I can tell you more about that line of research if you want, but so I guess what I'm trying to say here is it's amazing and that's great. We should all be doing more active learning, but let's apply those questions that I raised to you earlier critically so as to ask ourselves whenever you get students on the board to work, for example, who might feel included, who might feel excluded, who is likely to benefit, who might not benefit, who is likely to have access, who might not have access and how would you know if you had to intervene? So all of those things that we do that are either those unique things that we do or if you get students to go to the board or any of these active things in your classroom, I hope that you will continue to ask yourself these questions. So let me give you an example. Okay, so here is, okay, here's an example. So a common active learning strategy is think, pair, share, right? So like, oh everyone, what are the things that make you most unique as an instructor? Talk to your neighbor now and blah, blah, blah, blah, so that's a very common kind of classroom strategy where I pose a question, I ask you to turn to your neighbor and you talk and then somehow maybe I might get some responses back from you, right? That's a classic think, pair, share kind of situation, right? Do folks use this strategy in your class? Yeah, thumbs up, thumbs sideways sometimes, thumbs down not so much. Okay, yeah, great. So let's just think about that particular teaching strategy and the questions that I posed to you earlier, all right? So in my experience as a teacher and visiting other people's classrooms, I am often the worst at the think part and a lot of people are too. So a lot of times it's not think, pair, share, it's just pair, share, it's just turn to your neighbor and blah, blah, blah, blah, blah, blah, blah, okay? What does that do if you just do the pair, share? What typically happens is the more outspoken person will speak first. Who tends to be the outspoken people in the classroom? They tend to be the men. They tend to be the people who have more social capital for whatever reason, the more popular or the jock kids or the whatever, right? We all know the social standing and the pecking order in our classrooms. Students who have learning disabilities may not be the first to speak because they need a little time to process their thoughts. Students for whom English is not their first language also will need some time to process and so they'll probably not be the first one person to talk. And usually the person who talks first will sort of like get the ideas out and maybe they'll steal the thunder and then the other person will be like, uh-huh, yeah, cool. Or they might not say anything at all, right? So in that situation, let's just think about who might feel included, who might not feel included. So people for whom English is not the first language might not feel included. People who are just shy and introverted might not feel included. They might not feel like they belong. And I am a person who's rather introverted and I really hate that situation. Especially when I'm in a room with people I don't know and then there's this awkward moment where you're like, oh crap, like are they gonna talk to me or are they gonna talk to that person and then I'm gonna have to find somebody else to talk to. It's like this awkward dance where you don't know exactly who you're supposed to talk to. You know, I hate that. I hate that so much. So that often puts people at a really weird situation. Let's also think about who else. People who might just be willing to talk while they're thinking. I don't know how to say this well. I guess, not being born in this country, I notice that there's this thing that my husband does, my American husband, where whenever you ask a question, he will just start talking to you even before he's already finished his answer. And in a way it's great because you get to hear the thought process as it's happening. But in another way, it just steals all of the thinking power out of the process whenever you're posing a question that people are thinking about. And so all I'm saying in the situation is one way to make the pair share better is just to do the think pair share, to really do the think pair share. So if you give people time to think in advance to form their thoughts, you'll allow a more equitable exchange between those two people. Another tip that you might have is you might say, okay, think about this question and then you might say, okay everyone, the person closest to that fire alarm light will go first. It just takes out the question of who's gonna speak first. And then maybe the next time you'll say it again, the person on the other side will speak first. It just makes that interaction go a little bit smoother. So you're not having to guess that interaction where it's like, are you gonna go first? That weird interaction at the beginning. Okay. So that's an example of what I mean when I say to go through these questions. So the last part here, I'm gonna turn it over to you. So here is a common thing that happens in my class. I give students a task. And then I say, okay, go to the ward and work on this problem. And all the teachers in the room, like vertical non-permanent surfaces are like suddenly very hot. For a lot of us, it's just going to the board. It's not anything more fancy than that. But whatever you call it, going to the board or vertical non-permanent surfaces, okay. You do this thing, I bet a lot of you do, okay. And so in the context of your classroom, let's say you do this particular thing. Who do you think might feel included or excluded? Who's likely to benefit? Who might not? Who is likely to have access? Who might not? And how would you need to know to intervene? The fourth one is actually the most important to me that I'm hoping to focus on right now. Okay, so I'm gonna do the good thing. I'm gonna give you 45 seconds to think about this. And then I'm gonna ask you to talk with people around you. But first, silent think time. Okay, so what I'm gonna do is I'm gonna turn you loose. I might ask for a few people to share out the whole group in a minute or two. And then we'll do that thing where the person who's closest to where I'm standing right now in your pair or your three or whatever we'll start speaking for. So hopefully you have someone near you and it's not super awkward, so please start. Okay. If the other person hasn't talked yet, let them talk too. Oh, whoops, okay, I messed up. So sometimes this weird thing happens in a group where you give an instruction and then sound level dies. I don't know why that happens. It's a group think thing. Anyway, okay, so I'm sorry, cutting off your discussion, maybe prematurely, but maybe you all have some thoughts already to share. So maybe could I get five different people to give their thoughts to who you think might feel included to benefit or to have access and who might not. So any thoughts about that? Okay, I have one, two in the back, is that Melvin? Okay, three, Betty, four, thank you. One more person, maybe from this side? Okay, fine, okay, great, let's start with you. Go ahead. You guys speak pretty loud. Thank you, yeah, thank you for, I didn't think of that, awesome. Go ahead, Melvin. Okay, mm-hmm, mm-hmm, yeah. What if you're a group with all lefties? I don't know, then everyone's equally, I don't know. Okay, there was a, I'm thinking Betty was next. Mm-hmm, mm-hmm, okay, go ahead, next. Yeah. Yeah, okay, great. So I think one of the issues that you can have these kind of writing things and kind of anything that involves putting up language before is if it's not your first language, or like you've been introduced to a language later on that you're expecting to perform at, it's difficult to have the initiative to go up and take the marker and actually write things down if you're not comfortable with that. Right, so just in case you couldn't hear it, just to summarize briefly, it's if English was not your first language, you feel less likely to be the first person to go up and start writing on the board, okay? Yeah, these are all great answers. I love the comment that you made. It almost is getting at the fourth question. How might you know if you had to intervene if you see one student doing all the writing, one person doing all the talking and the other people just sitting there like this? That might be a way to know based on body language. That's a very easy way to know. I thought about that a lot. When I was looking at, for pictures, I didn't know whether this particular picture would give it in a way, but one thing that I noticed from this picture is I only see one person's handwriting on the board. And that might be something that you could include in just the natural process of things. You might say, oh, I wanna see at least three different people's handwriting on the board. Like if there are three people in your group, I wanna see everybody's handwriting or it could be everyone has a different marker. I wanna see all the different color of markers on the wall when you're done. That could be just the simple way to rotate around and describe. Another thing I do in my class is I say, the person who's got the pen has to be silent. They can't say a word. So it sort of encourages the thing you were saying, like the person who's scribing is getting the most of the benefit. They're the ones who are listening and synthesizing and then they rotate that role so everyone gets a chance to do that thing. I think I saw a hand back there. The different colors, uh-huh, yeah. Yeah, yeah, great question, right? Sorry, great point, yeah. Those who've been taught to fail, that failing is a natural part of learning, are gonna feel more willing to go up on the board and just put their ideas out there in front of everyone else. Yeah, and just recognizing that the stakes are higher for people, for different people. For some people who feel in the numerical minority in a group, they're gonna have a harder time feeling that bravery necessary to go up on the board and put their ideas out there, right? Cool, any other thoughts? Okay, what about ways, how you would know if you had to intervene? Other things that you would think about about how you would know if something's not going quite right? Okay, Andy says body language, go ahead. If you go up to the ground. Yes, going up to a group and if several people can't explain what's going on, yeah, that's often a sign of trouble. Yes, that's right. If a couple of people are interacting with the group, yeah, go ahead, right. So just even the amount of noise that you hear can tell you a lot. Yeah, these are all great answers. Thank you. So I hope you can see that this is not a super complicated question. You were able to think of the answers very readily, but what I'm trying to ask us all to do is to go through this process of asking ourselves these questions every time we do something in our classrooms because when you do that, you develop the practice of being able to identify when there might be issues that you were unaware of and then in the process of thinking this way over time your classroom becomes more and more equitable. So I think I'll leave it at that and then if you have any questions or comments, I think we are out of time so maybe we can just have a discussion afterwards. Thank you.