Building Students’ Confidence in Intro College Classes
“My teaching strengths really shine in these introductory mathematics classes.”
The video above is a talk that I was invited to give at the Mathematical Association of America Southeastern Sectional Conference after winning the Distinguished Teaching by a Beginner College Faculty Member Award in 2022.
Below is a transcript of the talk. I’ve included headers and timestamps to allow for easy navigation and consumption.
The Demographics of My Classes
I am a lecturer at the University of Georgia and I was hired as part of the small class size initiative on my campus where the introductory level math classes, like Pre-calculus and Calculus 1 have 19 students or less. This allows us to have a lot of FaceTime with our students so that we can get to know them and provide more individualized support.
Having such small classes allows me to use the strategies that I will share here really well.
However, the strategies that I'll share aren't just for small classes and they can work in larger classes. Personally, I do believe that my teaching strengths. Really work well with these introductory mathematics classes.
So I'm excited to share how I approach teaching my classes and how that builds my students confidence, how it makes my students feel really included in my classes, how they're not afraid to. [00:01:00] Speak up, ask questions, and actually learn math in my classes. I will say that while a lot of my strategies are research backed, everything I'll say will be like anecdotal.
These are just things that I've noticed from my students and noticed in my classes, and these are the things that I really like to talk about most. So I'm often teaching pre-calculus. Or a calculus one, mostly pre-calculus. This is the course that I worked on the redesign for, and I noticed something with my students in this class.
These are students who traditionally have struggled in math. Perhaps they just need the class. For credit for their major. For some reason, pre-calculus is the last math class some students have, which is strange because it's a pre, like, it actually leads to another class, which is the last class they have to take.
I typically will poll my students every semester and out of 19, maybe four of my students will need to take calculus one. after pre-calculus. And so a lot of the students in my class are really used to [00:02:00] feeling like deflated or feeling lost in a math class. So that's kinda like the demographic of the students that are in my classes.
And so a huge priority for me when I'm teaching my classes is to really get all of my students involved and help to build their confidence in the math class. Everyone can learn math. Everyone can be good at math. I take it as a personal challenge to show my students that they can be good at math, they can understand and they may enjoy it.
Comments from my students about my class:
[00:02:40] So here are a few comments from my students through our thank a teacher program as well as an email. The first student said,
I've never been one to be confident in my math skills, but since I took your class, I feel so much better about math and am no longer scared of it. You taught in a way that was so organized and thorough, I had time to understand every section. Your kindness hasn't gone unnoticed, and I'm eternally grateful for your class.
The second student said,
Despite pre-calculus being notoriously hard intro course at uga, you've made the course much more enjoyable, and understandable. , I'm not the fastest at understanding concepts, but you are always open for questions and just so good at breaking down the contents into understandable chunks.
And the final student I wrote a letter of recommendation for, but they said,
I would like to thank you as a professor for making our academic endeavors feel much more attainable. Your class is truly enjoyable. Even when I don't immediately understand all of the concepts, you still make me feel capable of growing as a math student.
5 Strategies to Improve Students Confidence in Intro Math Classes
So in this talk, I'm gonna share five strategies that I use to improve my students confidence in my introductory level math classes, as well as improve their experience in a math class.
So, spoiler alert, I will say many of these strategies actually have nothing to do with the actual teaching of math.
It's more about the approach to the classroom.
#1 Organization and Structure
All right, so the first strategy that I use, Being very organized and structured in my classes. My students appreciate this so, so [00:04:00] much. So on the first day of class, I give my students a, who am I worksheet. So it's something I hand out as they're coming into class.
While we're waiting for class to begin, students are typically pretty early on the first day. So this gives them something to do cuz we're gonna use it as an activity. And so they share a little bit about who they are. They even draw a self-portrait. They always try to avoid the self-portrait and. Say, don't avoid the self portrait.
And I show them mine is horrible. I'm not great at drawing at all. , and one of the questions is, what are the qualities of a good math teacher? And so I've done this who in my activity for about seven years now, and students say the same three things.
Number one, they say the quality that they value, the.
In a math instructor is organization. They love it when their math professors are organized. They hate it when their math professors are not organized. They also really value clarity, so being able to clearly articulate the expectations to the students, being able [00:05:00] to clearly explain math concepts.
They value that a lot. And then occasionally I'll see they're knowledgeable about the subject . That's usually last on the list. They really value structure, organization clarity.
3 Simple Ways I Add Organization and Structure to My Classes
So here are three very simple ways that I add structure and organization into my classes. So every day when I come in, the first thing that I write on the board is a to-do list for the day.
So I write out exactly what we're gonna do every single day in a bulleted list so the students can look up and know where we are, know what we're doing, and know what we're doing next. They like to have like a gauge of like what's going on and what's expected of them in the class. And then I also will write up the announcements.
Now the announcements are online in our learning management system, but I. Also put the most relevant announcements on the board every single day, and that is the first thing that we start with the to-do list for the day and the announcements for the day. So [00:06:00] this has organizational structure because I use the exact same workflow every single day.
Every single class is almost exactly the same. We go through the same workflow. There can be some variations. So on test review days or days where we'll have a quiz or a. Then the schedule changes up a little bit, but I have like organization and structure within that as well. So I always use consistent due dates and deadlines.
So I'm not having, you know, this week the homework assignment is due on Monday next week. The homework assignment is due on Thursday, the next week we don't have an assignment due. Right. This can be very challenging for students who are navigating d. homework frequencies for like four different classes, so, I use consistent due dates and deadlines.
So for example, our quizzes will always be on Wednesdays. They can expect a quiz every single Wednesday. Homework will be due on Tuesdays and Thursdays. If it's not a Tuesday [00:07:00] or a Thursday, then their homework is not going to be due. tests are typically gonna be on this type of day. Maybe on a Tuesday, we'll have our tests in classes where I don't do group work every single day.
So for example, this is not an introductory level class, but for my applied linear algebra class, I'm mostly lecturing. But then we'll have these special group work days every other week. So I would have. Group work Wednesdays where the whole day is all group work. And so this is something that they can expect and this will only happen on this type of day.
So I find this really helps my students even beyond my class because it gives them a consistent schedule to figure out like when do I need to be dedicating time outside of class to math? And so they can study on the same day every single week, and it helps them build out their schedule. For the rest of their classes and they really appreciate this.
And then finally, my third way to add more organization and structure into my class is having a very like organized and well thought out learning management system. Like for our [00:08:00] course online, everything is labeled. I use modules with like sub folders. So everything is easily found. The really important things.
Add it to my navigation bar so they can get to it with just a click. So I use the weekly announcement feature where everything they need to do is linked in the weekly announcement. I also use consistent language throughout. So this semester I'm calling my quizzes gateways. So I'm always gonna use the word gateway on my learning management system and not sometimes gateway, sometimes quizzes, sometimes this sometimes.
Consistent language throughout. If I'm labeling my, um, sections of the class A one, A two B one bk , I'm not gonna then also use section 2.1, 3.1, things like that. All right, so let's talk about the structure of my class. So I use a flipped classroom. So for me, I have created video lectures for my students.
They have a workbook, they can. Write [00:09:00] in the notes from the video lectures, they can bring the workbook to class and work on the in-class problems all within that same workbook. Okay, so how does it work? So the students are responsible for watching video lectures before class. The each video is about 10 minutes, and they'll typically watch three or four videos per night before.
And then before they come to class, they will submit a pre-class assignment. So this pre-class assignment is in their workbook. So they'll use their phone, they'll take a picture, scan it and upload it into the assignments folder into our learning management system. And so they will do that before class.
And I do this because I want them to actually try to learn something from the video. I actually do grade these pre-class assignments for accuracy in not just participation and completion. And I do this because I want them to actually read my feedback. If they're getting a hundred percent on everything, they will like likely not go back [00:10:00] and look at any words that I wrote on their document.
I take off minimal points. Typically, half a point for a mistake and the lowest students can make is like a seven out of 10, or even a six out of 10 students are typically making nine point. , 8.5 out of 10, typically really high scores on these pre-class assignments. So they watch the videos, complete the pre-class assignment.
And then when we come to class, I'll do a brief recap of the lesson, 10 minutes or so, mostly just to get the definitions or formulas or graphs on the board so that they're there for the students. So after my recap, I'll ask them if there are any questions that they have on the pre-class assign. , and if they do, we'll go over that.
And then after. We get into our in-class work. So inside of their workbook there are worksheets for the students to work on together in groups. I actually use group work every single day in class. So the students are working in groups [00:11:00] and they were working on their in-class worksheet related to the videos they watched.
And the problems can be a bit challenging for the students, but I get the, I give them tools to help them work through, um, more challenging problems. What I'll, which I'll talk about. So as they're working, I'm walking around seeing if they're having any questions, and then after class they have online homework just to continue practicing those, um, foundational mathematics skills because I'm gonna ask them much deeper questions in class and on quizzes and tests.
So the, on the purpose of the online homework is just to make sure that they have the foundation, they know their properties, they can apply math properties and rules. Solve equations. So after the students do their group work in class, we'll wrap up maybe going over a more challenging problem, or I'll have a student go over something.
We'll talk about what students need to watch out for in the section, and then we're done for the day, and then they have their homework. And my [00:12:00] students expect this process every single day. Every single day we do this exact thing, so they know exactly what they're responsible for every single day in class.
#2 Providing Regular Opportunities for Quick Wins
All right, so my second strategy for building students confidence and improving their experience in introductory level math classes is providing regular opportunities for quick wins. So I am rarely speaking for a full five minutes without getting feedback from my students, without asking them a question or without having them ask me questions.
I am not just like giving a 30 minute monologue in class. So what are some examples of quick wins that I use in my classes? So when I'm doing my little recap, it's kind of like a mini lecture. So I would do the same thing if I were lecturing instead of having a flipped class. So I would have them recall formula.
So I'll ask, okay, so how do we find the distance between these two points? And I was like, let's build it together. So they'll yell out the components. I'll ask them if there's anything missing, and then we'll come [00:13:00] up with the formula that I've asked for on the board. Often I'll draw something on the board or write something and ask them what we call it.
So like, what is the name of this? So I've just drawn a line. between these two points. What do we call this type of line? And so I'm looking for second line as their answer just to make sure that we're connecting everything that we've learned and to help the students remember that the things we learned in the previous section still apply in this new section.
I'm very often asking what's the next step? All right, so we have this, this is our. What is the next step that will help us reach the goal? I often ask questions like, especially if it's particularly silent in the classroom. I'll ask, can I do this? So particularly, can I distribute or can I cancel things out?
This is a huge struggle for my students, and so I'm always like quizzing them on the math principles and foundations that I notice that they struggle with often. So also for quick wins, I try to get them quick win. when they're first [00:14:00] starting their in-class work as well. So the in-class work is a bit more challenging than what they're required to do for the pre-class work.
And so what I like to do is let the first question for the in-class work be very similar to something I have on the board. This helps 'em get started. They're not immediately stuck as soon as I let them start working. I also let participation be part of the grade. So just coming to class and working in your.
we'll give you 5% of your overall, um, score in the class. So in a flip class, being in class is really important to actually work through the problems and ask your questions. And I think often students, especially in introductory level math class, is kind of underestimate how important being in class is.
And so I do make that part of their. Just showing up. I've noticed the students that show up, they do so well in my classes and the ones that don't show up, they do horribly in my [00:15:00] classes. So I tell my students this, and this is why it's important. And I almost have perfect attendance every single day in my classes, student, even when I teach 8:00 AM students are there and they are learning because they know that being in class is valuable for learning and also they get a grade for it.
And then finally, another quick win for them is sometimes I'll. Reflection assignments, and so I'll talk more about those in a moment. But having students reflect on how they learn, how they prepared for a quiz or a test, how they studied, what they might need to do different, what was uh, particularly helpful, what was not helpful, and getting 'em to think about this so that they can use these tools going forward.
And then actually collecting the reflections for a grade. This is a quick win, but it's helpful for the. All right. My third strategy for building my students confidence, creating a more inclusive classroom, is having more lower stakes assignments. So it's not just the tests and the quizzes that determine my [00:16:00] students grades.
That feels like a lot of pressure for my students, so I like to give them lower stakes assignment to help. Build their confidence so that they're ready for the big test. So in pre-calculus, I give a quiz every single week. And so this is strategic on my part because it forces my students to study every week because they should be actively engaging with the content every single week.
But often our students don't, and they'll wait until test time to try to learn everything. So what I like to do is have my students. and study every single week through giving weekly quizzes. And so I frame the quizzes as this is prep for the test, right? You wanna see how you're doing on the quiz so you can verify whether you really understand a topic or if you need to do a little more work, come to office hours, ask more questions about a specific topic.
That way you can figure out what you need to know so that you can be ready for the test. Also, having homework every single week, right? This is [00:17:00] framed. Prep for the quizzes and then pre-class assignment every single day before we come to class. Some, some sections may take more than one day, so there may be a few days within the semester where they don't have a pre-class assignment, but this is framed as prep for the in-class work, right?
And so I'm grading all of these things and. The reason they are there is to help them prepare for the next thing that we're going to do. And so the theme here in this section is everything has a purpose that is explicitly stated to the students. So the students know exactly why they're doing things and they know exactly why they are helpful, even if they don't realize that it's gonna be helpful immediately.
Halfway through the semester they're like, This is what I need to do to be successful in the class. Right?
#4 Opportunities for Redemption
Number four, opportunities for redemption. Every one semester Doesn't start out strong , but I do like to give my students opportunities to redeem themselves, right? There are many times when I go into the.
[00:18:00] First couple days of the semester, and I'll identify a student that's really struggling and I'll think, oh, wow. I don't know if they're gonna make it through this class, but inevitably they will turn it around and be one of the strongest students in the class. So I never want the beginning of the semester, like if it's rough for them, I don't want it to hold them back from doing well in the class.
So here's how I provide opportunities for redemption in my. So I do exam reflections after each test. So my exam reflections, they're designed to help students study. So there is a pre-exam reflection where it kind of walks students through, like how they're preparing for the test. I'm asking them what they're nervous about, asking them what things they need to study more, what notation is tripping them up, and then.
I give them a checklist of things to check off on how they're studying. Like are they practicing the practice test? Are they working back through their in-class work? Are they doing homework so they can check off the [00:19:00] things? And this is like giving them a list of things to do to study, because often students don't know how to study for math.
So that is the pre-exam part of the reflection. And then after the exam, after I've given their grades back, I ask them questions like, well, how did you do was, did you get the grades you expected? Were there any questions that surprised you on the exam? What did you do that when you were studying that you found to be really helpful that you'll do again?
How will you prepare differently next time? How long did you study? Right. So this is getting students to think about what they're doing that is making them successful and what they're doing or not doing that is leading them to not have success in the class. And then finally, the third part of the exam reflections is correcting.
Any mistakes that they made on the test. So any problem that they missed, they get to correct the problem and then explain what happened. Like, why did you miss this problem? What concept were you missing? Was it just a simple mistake or was there a [00:20:00] big conceptual thing that you didn't understand, that you understand now?
And so they turn this in for a grade. They do not get points back on the test, however, , it is for a quiz grade, and so I give a quiz every week. So not every quiz is gonna be stellar for the students. So this gives them a nice little boost to their quiz average, but also gives them a second chance to show that they've learned the content that they missed on the test.
Often students will say, okay, the test is over. I'll forget about this material. Move on with my life. Also, since I do give a quiz every single week, not every quiz will be stellar, so I will. The two lowest quiz scores at the end of the semester, particularly their first couple quizzes aren't the best. Um, and so we can pretend that they never happened at the end of the semester.
#5 Teach Them How to Study
And then my final strategy is teaching them how to study math. Often students have never learned what it takes to study math. They don't realize that practice and practicing from scratch [00:21:00] is the way to do it. They often kind of fall back on their study strategies for other classes where they read over their.
Try to memorize things and just like glance like, oh yeah, I remember that. I remember when we did that. Makes sense. Makes sense. I was like, that is the quickest way to not do well on the test. You wanna pretend like you don't have any solutions, right? You shouldn't be practicing with the solutions in front of you.
You should be working from scratch. And so that's like the foundation of how I teach my students to study for math. The exam reflections that I mentioned before helps them prepare. And I also teach them how to problem solve. So I kind of model this in class through their group work. So I've created a group work process for my students that I put on the board very early on to teach them how they should be working together in groups.
And it also, keeps them from asking me questions at every little hurdle. Okay, so here's the group work process that I get [00:22:00] from my students. So number one, they need to read the question with their group. And so once they've read the question, they will just. Discuss with their group what the question is asking for and see if they can determine the format of the answer.
Often this is a clue to tell you how to approach the problem. So should the format of the answer be a point like a coordinate (x,y) , should it just be a number? Is the format of the answer and equation, or do you need to draw a graph? Do you need to write a sentence? So having the students determine what the answer should be.
It's a great first step. Number two, I have them circle or underline any important information in the problem, and then have them write down anything they know about the information. So for example, if the question says something about an X intercept, they would write down the point x zero, or we know that Y equals zero.
If it mentions a function, they'll kind of sketch a graph of what that [00:23:00] function looks like. So this gives them somewhere to get. . And so that's the final step is discuss with your group a starting point. Like how do you think we should start this problem? And I tell my students they should be going through this process, especially for the more challenging problems together.
And this is the type of thought process that they should use with themselves when they're taking their quizzes or their tests. So I actually don't answer my students' questions until they go through this process. And so if they raise their hand, I will go over and say, all right, so what have you discussed?
And I ask them, all right, number one, what is, what did you all decide the format of the answer would be? Number two, what equations or formulas did you come up with into number three? What was your first strategy to try to get started? And then if they're still stuck, then I will kind of nudge them in the right direction.
This kind of gives them a little more independence in the class, and they don't depend on me always to answer every single question. So I'm building up those [00:24:00] problem solving skills so that when they do see a question they may not have ever seen before, they have strategies to approach it. All right, so these are my strategies for building my.
Self-confidence in my classes as well as making the class more inclusive. Thank you so much for inviting me to share. I am so honored to have won the teaching award last year, so honored. Thank you so much. Um, that is the end of my presentation. If you have any questions, feel free to reach out to me.