What's the best way to prepare for first-year math?

 Students studying in a group

Clare Written by Clare (she/her), student

Every math student at the University of Waterloo has one thing in common.

Well, they probably have many things in common, but what I’m referring to is that every first-year math student takes Algebra and Calculus in their first term. Most students take MATH 135: Algebra for Honours Mathematics and MATH 137: Calculus 1 for Honour Mathematics, although you could also take MATH 145 and MATH 147 (advanced versions of the courses) if you’re up for a challenge.

Since you’ll definitely take both of these courses as a first-year math student at Waterloo, it doesn't hurt to come prepared. As someone who took both of the courses (and later was a Teaching Assistant for MATH 135), I have a few tips for you.

I also interviewed two top professors at Waterloo, Judith Koeller and Marek Stastna, who have a few additional tips when it comes to preparing for these classes.

Tip #1: Residence tutoring

I made this tip #1 because it’s the single most helpful thing available to you in first year, in my opinion.

The absolute best thing I did for myself academically in first year was take advantage of the tutoring in residence. (If you’re not planning to live in residence, don’t fret! This tutoring is open to all Waterloo students!)

Residence tutoring is completely free and is available almost every day, so you really have no excuse not to go! You walk into the room, sign in, and meet with a tutor.

I’m not going to lie, I went to residence tutoring at least once a week to get my MATH 135 assignments done. Not only are the tutors there to help you, but your peers in the same class will also be there with the same questions as you, so now you have the opportunity to collaborate with them.

Another top tip — if you walk into a study space and see that tutoring is going on in that room, don't walk out!

Anyone is welcome to attend a tutoring session, even if you’re not taking the class. I found the environment to be so conducive to studying that I sometimes sought out tutoring sessions for other classes just because I knew I could get my own work done in the room.

Residence tutoring has a schedule each term so you’ll get an idea of how frequently it runs and the wide variety of classes tutoring is available for — it’s not just math!

Tip #2: Study groups

Form a study group! Discuss problems! Your peers are smart, so leverage their knowledge. One of the biggest mistakes I made in first year was thinking that I was the only one struggling in my class. This is never true. If you’re having a hard time grasping a concept, chances are other people in your class are struggling with it too. So why not get together to work it out as a team?

Meeting with a few classmates to discuss what you learned in class will help you understand concepts that you weren't fully absorbing and will solidify your knowledge of what you already understand. (Psst… if you don’t know how to put a study group together, start with residence tutoring! You know that the students who will be there are willing to put in the extra effort, and they’ll likely enjoy collaborating with you. I promise that’s the last time I’ll plug residence tutoring. The hard sell is in my nature.)

Teacher giving a lecture

Count some more ways you can prepare yourself by adding in these additional resources.


Tip #3: Talk to your professors!

Don't be afraid to talk to your professors.

True, they are very smart. True, they are very accomplished. This can be intimidating — but don’t be scared to talk your professor! They want you to do well, too. Professors will often have scheduled office hours where you can go and ask questions.

If you have a very quick question, you can usually just ask your professor after class. If you have a question during class, raise your hand and ask it! Someone else in the lecture hall likely has the same question you do.

Most importantly, participate in class. I was once told by a taxi driver to raise my hand at least once per class — whether it’s to ask a question or answer one. I didn’t take his advice 100% — sometimes I don’t know the answer and I don’t have a question, and I don’t believe in saying something just for the sake of saying something — but his advice was very good.

While we’re all guilty of this sometimes, try not to sit in the classroom and zone out. Try to actively listen in class. Think about what the professor is saying, and take good notes. Of course, this is easier said than done — and I’m still working on it myself — but it’s a good thing to be aware of when you’re starting school.

Now, enough from me! Let’s hear from the true experts… the people who teach the courses! Here’s what they had to say.

Students completing a math equation.

How would you describe your course?

Judith Koeller: Math 135 ties together mathematics that goes back hundreds, even thousands of years with techniques used to secure communications on the internet today. It helps students develop skills that they’ll use in almost every math course they take in university.

Marek Stastna: Math 137 (I teach the physics-based section) is a more complete look at differential calculus compared to what students see in high school. We see both what calculus is for and some of the basic mathematical tools that form the foundation of the subject.

What would you say to a student who's nervous for Math 135 and Math 137?

Judith: It’s a really common experience to feel like you understand the concepts, but to struggle with combining them into a proof. Many students will write a proof that has a lot of the necessary ingredients, but is missing a few important details or doesn’t link the ideas into a smooth flow.

Don’t be discouraged! These skills take years to develop, and no one expects you to be perfect at the start. Learning to write mathematical proofs is similar to learning a new language — you refine your skills by reading and listening to mathematics and by getting feedback on your work. Just practise as much as you can.

Marek: Come ready to learn and commit the time. The number one problem students have in this class is thinking they know it all already.

What is one thing you wish students knew before starting your class?

Judith: Your marks in university do not need to be as high as your marks in high school were. You’re adjusting to so much when you start in first-year mathematics. Take good care of your mental health.

Try to develop good work habits and work in a way that suits your learning style. Do your best and give yourself some time to adjust to everything that’s new.

Marek: That mathematics is used for other things than making more math.

Students completing a math equation together.

What is your #1 tip for students taking Math 135? Math 137?

Judith: Ask questions in class. Ask questions after class.

If you have a question, others almost certainly have the same question. Talking about mathematics with others is a great way to get better at mathematics. Most instructors are constantly scanning the room, assessing whether students are following the material or are confused. When students ask questions and give non-verbal feedback, instructors are much better able to pace the material appropriately.

Sometimes when a student asks a question, there can be a back-and-forth as the student tries to articulate the question and the instructor tries to understand what the student is asking. Don’t shy away from these moments, as everyone in the class can learn from them.

Marek: Read the notes before class.

What do you like to see students doing to succeed in your class?

Judith: Students can learn a lot by working with other students.

You must try every assigned problem on your own, and come back to it a few times before collaborating with others. And whatever work you submit needs to be in your own words. If you’ve discussed problems with others, write the work up independently at least a few hours later, without referring back to your notes from the discussion.

But in between those moments, have conversations about mathematics. I encourage students to talk with each other about math problems. In doing so, you’ll have fun, you’ll improve your skills in reading and writing and listening, and you’ll expand your ability to think creatively.

Marek: Asking questions.

So, there you have it, advice from two professors to kick start your first-year math courses. You never know, maybe you’ll have Judith Koeller or Marek Stastna teaching you a class — lucky you!

A huge thank you goes out to Judith and Marek for the interview and wonderful advice.


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