Inviting students to Engage with Mathematics (part 1) | Donna Gabai, Princeton University | IAS/PCMI

Welcome. Full disclosure, I am not a mathematician. I am married to a mathematician. Not the same. Um but I have taught math. I have a masters in math education. And um show of hands, have you ever after revealing what you do to a new acquaintance? You're a math major. You're a mathematician. Had the reaction, "Oh, I can't do math. I've never been good at math." Or it's silence. They move away. Show of hands. Those of you that don't have your hands up, you need to get out more. Okay. So, there's kind of an attitude towards math that it's something foreign, that it's something tough. And I always I always say that my my superpower as a teacher is that I struggled as a student. And so, I remember that things are hard. I showed up to my high school algebra teacher's office after school so often, she started bringing me a snack. Oh, speaking of which, there are trays of lollipops around. Just please don't leave the wrappers and sticks on the table. There's trash cans on the inside wall. So, I am very grateful to that algebra teacher, Miss McCarti. She was kind of the dragon lady of the math department. Never cracked a joke. I'm not sure I ever saw her smile, but when I didn't understand something, she'd kind of go like, she'd ask me some questions to figure out what I did know, what I did understand, and then she'd explain it to me in a way that was completely different. And so, amazingly to both of us, I actually earned an A in algebra that year. And and I was hooked. It was worth the pain. It was not something I did easily, but it was something that was exciting to be able to do. So, I'm hoping to convince you of the importance of trying to sell your students on the idea of math to make them more comfortable. And so, let's uh just text some technology. So, I hope everybody has either a phone or a tablet or a laptop and please go to menty.com and use code 9308-3271. I normally don't teach in a large lecture hall and I'm used to having some feedback and so we're going to use um meny.com for you to be able to answer questions as a group. After 20 years of teaching, I went back to school to earn a master's in math education. And there was one course, methods of instruction, that was such a revelation to me because suddenly I realized it wasn't that okay, knowing my material and being able to explain it clearly was necessary, but it wasn't sufficient. [snorts] That there was more I could be doing to guide my students through this world of mathematics. And so the um this was an entire course on methods of instruction and I'm going to try to just hit the greatest hits, you know, the distill it down into a 50-minute lecture. And some of the techniques I'm going to talk about, you're going to say, "Oh, that's easy. I could do that." And some of them you're going to say, "I would never do that." All right? And that's fine because you need to find your own teaching voice. Because bottom line, if you want your students to be comfortable, you need to feel comfortable. Okay? So everybody on menty just finish the sentence. I teach um it can be a word or a phrase but you've got a 25 character limit. as the ones that get larger are the ones that more people are putting in. So you'll notice math is kind of taking center stage there. All right. And notice we're mostly getting the names of the course. Okay. But there are a few people who put math to college students. Okay, undergraduate math. If asked, I say I teach undergraduates. And by putting my students first, it changes my emphasis a little bit. All right? It's not enough for me to cover the material. I need them to cover it with me. And so I'm going to be demonstrating some techniques to hopefully help you help your students and whoops. We're going to start with the rule of three. So the rule of three is first step, tell them what's coming. Tell your students what you're going to tell them. Okay? It's kind of like you can't tell the players without a scorecard, without a program. Let them know what you're going to be doing and then tell them, but don't just tell them, invite them to participate with you. And at the end, remind them what you've done. to make people talk to each other. The people they're sitting with, they get to know. They become more comfortable. When you are more relaxed and more comfortable, you are more open and more receptive to new ideas and new techniques. So, we're going to after the icebreaker get into the meat and potatoes, mechanics of teaching. You should all know that. It'll go fast. And then the three types of student teacher interactions, lively lectures, comfortable classrooms, effective office hours, and then how to get feedback about your teaching. And then at the end, tell them you've told them. We'll do a wrap-up and summarize. So the agenda is going to stay on the blackboard. We're going to move on. So we're back to the mentimeter. So I just want to I kind of want to feel from the room sort of where people are. So we've got three statements. And is everybody able to see this on mentter? Yes. Okay. Agree, strongly agree, strongly disagree. So it's on a scale of one to five. Just click along. There's no right or wrong answers here. These are oversimplified questions. The point is I want you to start thinking about teaching or thinking about your classroom experiences in general. I have to say I'm kind of gratified to see that number two that I find math really satisfying and I wish I could transmit that enthusiasm to my students is generally being agreed with. I know that we have some heavy duty researchers in here who um who may not agree with that statement, but if you need to teach, it's part of your job to do it with goodwill. the high have too much material to cover. It depends on what you're teaching. If you're in a large lecture hall and you have a lot of material that needs to be transmitted in a fixed amount of time, yeah, it might be true, but I'll still try to make the argument that there are things you can do to help your students stay awake and on task. And teaching is math is teaching tougher than teaching other subjects. We're right in the middle there. Okay. Um, the only thing I'll say about that is the one thing that I find does make it a little tough is the attitude that students come in with. I can't do this. And that's what we want to change. So, we want to do something called lowering the effective filter. And so, this is going to seem like a nonsequiter, but which do you prefer, the nightingale or the lark? Nightingale is a nighttime song bird. The lark is a daytime song bird. Oh no, [laughter] it looks like the night and gales have it. All right, you are in your groups. Whoever got to bed the latest last night, you are the leader of your group. And so I want the leaders to get a worksheet. There's only one worksheet per group. So, talk for a second. Figure out who's the leader. >> H who's the leader? >> I guess you're the leader. Okay. >> Who's my leader? >> You are Who's the leader? >> Okay. Who got who didn't get sleep last night? [laughter] >> Okay. >> Who's the leader here? >> Oops. Can't separate it. We have >> If your group does not have a worksheet, let me know. Here we go. >> Does every group have a worksheet? Not yet. Oops. Is that one or two? Is that just one? Okay, >> I think all the leaders have worked. >> Okay, great. >> Okay, so I love the buzz. Give me just a couple just give me a half a minute to talk about what we're doing. Motivation to make your students more comfortable. It's called lowering the effective only doing to the dotted line. So, only the top section. I'm going to set a timer for seven minutes. Go for it. Is it like us as a teacher or like our teachers? >> So either way, it's your favorite memory either as a teacher or as a student. I realize that not everybody here is a teacher. >> Okay.