If you’re in my class, every day starts out with a tip of the day. I first got the idea from my Dinosaurs Writing class (yes, it was a class dedicated to writing about dinosaurs, and yes, it was awesome) where the instructor would give us a tip of the day that had to do with writing, such as “Do NOT say ‘very unique,’ if it’s unique, it’s unique. It can’t be very unique.” These tips stuck with me and I thought it was a great attention-getter and it made the class more structured. Additionally, the classes I am teaching are supposed to be math content courses, but I thought that it would be a disservice to my students if I do not talk about pedagogy at all, so this would be the perfect way to sneak some pedagogy in there.
Here are some of my favorite tips of the day:
Math is the study of patterns
A lot of people confuse math with arithmetic. This is one of my first tips of the day that I give my students because we need to know what this subject really is about. Where do formulas come from? Well, we found patterns with specific numbers, and we were able to generalize. One student at the end wrote: Overall, I no longer fear or dread math. I’ve always liked patterns and trying to figure out what comes next so referring to math as the study of patterns has really helped me…I am now able to understand why math works and how to create a formula rather than trying to memorize formulas and when to use them.
“You learn 1,000 times more from your mistakes than your successes.” – Alice Keeler
Alice stated this about 4-5 years ago when I was taking her class and it stuck with me. It showed that we need to embrace our mistakes in order to learn. We are all going to make mistakes. It is not shameful at all.
When you teach, pretend that students can hear you but can’t see you.
I forgot where I heard this from, but I wanted to point out to students that we need to be precise in our language. When we are explaining how to do problems, we should replace “this” and “that” with specific words. For example, saying “subtract 2x from both sides to get 3x=6, then divide both sides by 3 to get x=2” is much more precise than “subtract this from both sides, then divide to get the answer.”
To be a good math teacher, you must know three things: 1. The content. 2. How to effectively teach the content. 3. The standards that you need to hit.
This was inspired by Tony Cotton, author of “Understanding and Teaching Primary Mathematics.” These three things aren’t the only things you need to know to become a good math teacher, but it forces students to know that it’s not just about the content. You could have the smartest person up in front but if they don’t know how to effectively teach the content, it’s pointless.
If you don’t believe in rounding an 89.9%, you are saying that you can accurately grade to the nearest 0.1%.
I had a chemistry teacher that would boast about this all the time and it was annoying. We are human. Do we completely understand the difference between a 94 and a 95 on a term paper? If we don’t, how would we know the difference between an 89.9% and a 90%?
You are going to have roughly 40 college instructors. What are you going to take from each of them?
I am huge on reflections. When students have the opportunity to see roughly 40 different styles of teaching, they should take note of that and start to develop who they want to be as a teacher.
Math should not be about speed.
A lot of my students have a fear of timed tests. It’s important to state this really early on to show them that they can be good at math, and speed is definitely not a factor. I care way more about conceptual understanding than speed.
Show, not tell.
I tell this to students so they can practice with their justification skills. Sure, they can tell me the Pythagorean Theorem or the product of two negative numbers is a positive number, but I want them to SHOW why these are true.
Design the class so you (the teacher) are learning too.
Having a student-centered classroom is still a relatively new concept for a lot of my students, but I want to show them the beauty of opening up the lesson so I am learning too. For example, 3 semesters ago, I wrote down the arithmetic sequence 3, 7, 11, 15, 19,… and told them to find the 100th term. I didn’t tell them the arithmetic sequence formula yet, so they relied on their problem solving skills. One student went up to the board and said that each number is one less than a multiple of 4, (4, 8, 12, 16, 20,…) so the answer is 4×100 – 1 = 399. I cannot believe it. I NEVER saw it that way before, and it really empowered the student. Another example was to find the area of a specific trapezoid. One student said that he saw the trapezoid as the bottom part of a triangle, but with the top part of the triangle cut off. I was in awe. Having student voice in the class was one of the best things I’ve done in the class because it really empowers students, showing them that they are completely capable.
Do not give formulas/procedures you do not completely understand
Math is not just about formulas/procedures. You can completely be successful in math without relying heavily on them. When I was student-teaching, my master teacher would say “don’t ask why, just flip the second and multiply” when dividing two fractions. Then a student asked why. The teacher said “don’t ask.” That stuck with me and I learned that I need to completely understand why these procedures work because I do not want to shoot down student curiosity. I want them to ask me why so I can have them explore the justification with me.
Your GPA does not determine how great of a teacher you can be.
When I was a student, I was super competitive. I took pride in my GPA. But now that I’m not a student anymore, I look back and notice that I cared way too much. Sure, you need a minimum GPA to get into a master’s program, but other than that, a 3.9 student isn’t automatically going to be a better teacher than a 2.9 student. When I told this to my students, they seemed relieved. By no means does it mean that they should just do the bare minimum to get a C in the course, it’s just that they need to focus on the learning, not the GPA.
These are just a few tips that I give my students and oftentimes I theme the entire day around that tip. I know that for a grade school teacher, that would mean around 180 tips, so maybe a tip of the week would be better suited if you want to do this. We all have a little bit of extra knowledge that students are missing out on, so maybe this would be the avenue to share that information with them.
Thank you for reading.