Quickie: Making the Most of Extra Time on an Exam

One question I get a lot goes something like this:

I finish an exam with 5 or 10 minutes left. I’m really tired and don’t have the energy or time to check the entire thing over, so what could I do in these few minutes?

Before you get to this stage, on your first run through the questions, annotate your exam. Put these symbols besides each question.

: for questions you have no idea how to do.
+: for questions you aren’t sure about or that are tricky.
nothing: for questions you are fairly confident about.

When you only have a few minutes left, go back and try the “-” questions first. Always try to write something, even it’s just the questions rewritten as an equation, a equation that has something to do with that question, or a relevant key word, time period, or person. You might luck out and get some partial marks.

While you might get a few extra marks, “-” questions are pretty much hopeless at this point because you don’t actually know the answer (and there may not be enough time to come up with one). Spending a lot more time on these questions won’t raise your grades a whole lot. On the other hand, the questions you left unlabeled are thing’s you’re pretty comfortable with already and there isn’t a whole lot you can gain from revisiting these questions. Thus the “+” questions are the most important questions you can revisit. Really dissect these questions, try to figure out why they’re hard or tricky, and get as many marks as you can. The reason this might work well is because you might be very close to the right answer. Giving it some more thought may allow you to get the full (or most) marks.

If you still have time or energy left over, look through the unlabeled questions and see if you can get a few more points here or there.

Of course, this technique works better with certain question types and marking schemes. It works best with things like multiple choice (where taking those few extra minutes to really dissect a question may get you to the right answer) and tests with benevolent markers (who’ll gladly give you the few marks). It might not work so well for results-centric and nit-picky markers, but nonetheless, if you’ve only got a few minutes, give this technique a try.

Happy Easter!


Reader Question: How do I choose electives?

… I’m not sure what electives to take. There are lots of different requirements, I don’t know what I like, and I don’t know what to take…

Every degree requires taking certain electives. Be they credits from a different faculty, English or other language requirements, or breadth requirements in your faculty, electives are an important part of your undergraduate degree. However, if you’re overwhelmed by the choices, don’t know what you’re interested in, and/or can’t decide what to take, this guide might help you.

First, figure out what the elective requirements are. Otherwise, you’ll be bumbling along in the dark and may end up taking courses that you don’t like and that don’t fulfill any requirements. If you’re in first year, have a general idea because just about everything you take will probably count for something. However, as you get up to the higher years, it’s important to know the details. It would be a pain in the rear end to realize at the end of fourth year that you’re 1 course away from graduating (and having to do the course in summer school or next year).

So, now that you know what’s going on, how do you decide on what electives to take?

Try these strategies: 

1. Path of least resistance

This is both the easiest and hardest method. It’s hard because you have to go through all of your degree and specialization requirements (basically everything about what you need to do to graduate) and figuring out exactly what electives you need. Then you simply take the easiest courses to fulfill those requirements. How do you know what the easiest courses are? Ask around! Perhaps your friends or classmates have taken courses they found easy. As well, certain courses are reputedly easier (a.k.a. bird courses). However, reputations are not always deserved, so use your better judgement. If you find yourself struggling within the first week, the course is probably not as easy as you expected and switching courses might be easier.


  • Easier course load
  • Don’t have to take more courses than absolutely necessary


  • Not always possible to tell what courses are easy
  • The easiest courses may not be the most interesting courses


2. Whatever fits

The involves having a rough idea of the requirements you need to graduate, then taking courses that fulfill those requirements and fit nicely in your time table.


  • Class fits nicely in time table – no need to take 8 am electives if you don’t want to
  • Courses may not be easy or interesting


3. à la carte

This involves having a rough idea of the requirements, then taking any course that would fulfill those requirements and seem interesting. There needn’t be any overarching theme here, just take whatever strikes your fancy.


  • All the courses will be interesting
  • Can gain understanding of a broad range of topics


  • Courses may be more challenging than expected
  • May only obtain surface understanding of each discipline with no real depth


4. Second love

If your major is your first love, then your minor (or second major) may be a second love. This is probably the hardest strategy to use because it involves some more planning. If you find yourself taking a few courses in a discipline and really loving it, it might be tempting to do a minor or second major in that topic. If that’s the case, figure out what you need to do to get that minor or second major and see if there are any overlapping requirements with your first major. Then figure out what courses would fulfill those requirements (and that are easy, fit nicely in your timetable, or that seem the most interesting). This is the situation I found myself in when I discovered that I love economics. I got a late start (I realized how much I liked econ in second year) and am now playing catch-up with my courses. So if possible, plan it as best as you can. If you got a late start and still really want to do it, give it a shot anyway and see if you make it.


  • Studying something you love
  • Obtaining true understanding of a specific discipline
  • It looks better on a transcript to have a minor or a second major


  • May be taking courses that are more challenging than any of the other strategies above. e.g. for a minor, a certain number of courses must be third or fourth year courses (whereas the elective requirements may be satisfied with lower level courses)
  • May still have to take some other courses (on top of the courses for your minor) to fulfill all elective requirements
  • Obtaining a narrow knowledge-base because you’re not taking a wide range of courses

Which strategy you choose is up to you. In general, if you have a second love, go for the minor or second major. Otherwise, use one of the other strategies to ensure you fulfill all of the requirements with the least number of courses.

Material from Science One Presentation

Hello Sci-Oners,

Here are the slides from the guest lecture I did last Tuesday. It’s contents are very similar to that of A Research Approach to Learning (but is more Science One-specific).

Academic Success in Science One (PowerPoint Slides in PDF)

Research Approach to Learning Handout (Handout at the end)

Good luck with your finals (you might want to check the exam prep series on how to start)!

Feel free to e-mail me with any questions that you may have.


Reader Questions: What do I do if I failed an exam?

… I thought I was ready for this exam but I blanked out. I failed! I’ve never failed an exam before! What do I do? What if I get an F for the course? None of my friends seem to have as much trouble with this class. I feel so stupid!

You’re not stupid. Most students fail an exam at some point in academic careers, and that first below 50% grade is always hard to take. You’re not even unique in your failure. Your gut reaction may be “oh god, I’m such a failure”, or “f*** you professor! I’ve studied so hard for this exam, how dare you fail me”, or “the universe is out to get me”, or “what? what? I FAILED? How could I fail? I was the smartest person at my high school!”. Whether it’s listless acceptance, indignation, or a feeling of incompetence, get over them. Yes, it’s harder said than done. Take that failed midterm, bury it in the bottom of your binder or filing folder, and don’t look at it for a week. If you’ve calmed down by then, look at it. If not, wait another week.

You know that Robert Frost poem? The Road not Taken?

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could

You are the traveler, except you’re not looking the roads often taken and not taken. Instead, one road is success and the other failure. What road you end up on – how successful you are from this point onward – depends solely on you. So how can you ensure that you are on the path to success?

1. Recognize that YOU and you alone was responsible for that failed midterm. It’s no one else’s fault. Take responsibility for your own actions (or perhaps inactions).

2. Also recognize that this exam is a reflection of how you’re doing in the course. It is NOT a judgement of your worth or competence as a person. .

3. Resist falling into the “I’m such a failure” hole. You failed an exam, but you are not a failure as a person.

4. Promise yourself that you will do better. Promise yourself to take action and responsibility for your own learning. Promise yourself that you will find better study strategies and overcome any reservations or issues you have with this class.

Aside from taking on new attitudes, what are some concrete actions you could take now? 

1. Perform an exam post-mortem. Cal Newport, one of my favourite study bloggers, has an excellent article on it already. Figure out what was working, what wasn’t, and find solutions for things that weren’t working. Come up with a plan of attack. List how you will study, what might hold you back, what outcomes you expect (e.g. final grade, amount of content learned), and how you can gauge the efficacy of your own studying (in fact, this is very close to the Research Approach to Learning).

2. Visit your professor or TA. No, you are not to mark grub. In fact, unless you still don’t understand a question on the exam, you are not to talk about any specific question with your prof or TA. You are not to whine about your mark, how the exam was marked, and why you think someone else’s test was marked so much easier than yours. What you will do is show them the results of your post-mortem and your study plan. Ask them for advice. For example, do they know of any more study techniques you could try? When they were a student, what were some things that worked well for them?

3. If your issue is related to text anxiety, I can definitely sympathize. Unfortunately, this isn’t a problem that can be solved overnight. The best cure to test anxiety is confidence in your own abilities. And that confidence takes time to build. There are some good tips on the internet, but it really comes down to believing in yourself. This is extraordinarily hard after a failed exam, but fake it ’til you make it, and it gets better.

4. If your issue is related to not internalizing enough content or not being able to apply what you learned during the exam, try some new study strategies! Force yourself to re-organize data (e.g. tables and charts), summarize it (cheat sheets), or teach it to someone (real or imaginary). Pretend you’re the professor and come up with questions that you think would really challenge a student’s understanding of the topic. If possible, apply what you’re learning to real world situations.

Fall down seven times, stand up eight. – Chinese Proverb

Yes, you failed an exam. But climb back up. It is not the end of the world. If your’e failing an exam in first year, take it as a wake-up call and use it as motivation to never fail an exam again. If this is a midterm (especially THE first midterm), all the better. The exam is probably worth so little you could still do really well in the course despite failing it.

You’ve made it to university and you have what it takes to excel. It takes time to adjust and a failed midterm is simply a sign of that. Don’t let it hold you back. Learn for your mistakes, move on to bigger and better things, and your grades on your future exams will reflect your abilities as a better learner and student.

Reader Questions: Should I Pre-read?

Meeting the Three Little Pig on Main Street

Image "Meeting the Three Little Pig on Main Street" courtesy of flickr user Loren Javier, licensed under CC BY-ND 2.0.

“My professor tells me I should read the textbook before each lecture, but I’m so busy and don’t have time to do it. Should I pre-read?”

This is a question I get very, very, very often. The answer is simple (though somewhat unfulfilling): it depends.

But first, what is the point of pre-reading? Pre-reading is used so students get a basic understanding of a topic before it is covered in class. After pre-reading, a students should recognize (if not understand) key terms, be able to follow most of the images and diagrams, and know enough background information to learn the new topic. Unless the professor is terrible, it is NOT necessary to understand everything. Pre-readings should NOT be used by students to learn everything by themselves. You know you’ve done enough preparation work (including pre-reading) if you can follow the prof in lectures and not feel completely overwhelmed.

But what determines whether one should pre-read? Let’s say Moe, Larry, and Curly are in a first year differential calculus class. Moe has taken calculus Advanced Placement in high school and did well on his AP exam, but elected to take the first year differential calculus class anyway. He has a very good grasp of calculus. Larry, on the other hand, did a little bit of calculus in high school. His teacher taught him what calculus is, how limits work, and basic differentiation. He’s not very comfortable with the calculus, but he understands the basics. Curly, by contrast, has never taken a calculus class before and doesn’t quite know what it is. He also did not do very well in math in high school and is only taking calculus because it’s part of his program.

In the above example, Moe doesn’t really need to pre-read. He already has a good grasp of calculus and just needs to listen to the lecture to remember everything again. Larry could benefit from some pre-reading, but he’s got the basics and thus just needs to quickly skim the book to ensure there isn’t anything too out there. Curly, on the other hand, really needs to pre-read or he won’t be able to follow the lecture at all. He’ll probably have to spend some time going over the key terms, interpreting the graphs, and filling in any gaps in his background knowledge (for example, if he’s learning how to differentiate trig functions, he’ll need to brush up on his trigonometry).

In first year, students’ arrive at university with different levels of skills in each topic and subject. Pre-reading should put everyone on a more similar level and allows the prof to focus on what is new without reviewing everything.

The bottom line is to pre-read if you can’t follow the lecture or if you think you can understand things more thoroughly. Pre-read less if the topic feels repetitive or boring because you’ve seen it 200 times before.  

Get a question about first year or studying? Let us know what they are and we’ll try to answer them the best we can. 

School and the Academy – Some Thoughts on Math Education

Last Friday, I had the pleasure of sitting on the student panel at the “School and the Academy” conference on math education. In the 40-minute panel discussion, high school teachers, TAs, and professors posed some great questions about the transition from high school to university mathematics to us students. I really enjoyed the session and thought I would expand upon my answers a little more in this blog post. I don’t remember all of the questions, so if you would like another question answered, post it in the comments or e-mail me (this is not restricted to the people at the conference!). Unfortunately, I don’t have inputs from the other 3 members of the panel. Nonetheless, I hope my comments will provoke some interesting thoughts.


Q: Did high school math prepare you for university math? Why or why not?

A: Yes and no. There are really two types of preparedness – academic and mental. Being prepared academically entails having a good enough grasp on the fundamentals to handle the contents of university courses. Being prepared mentally involves adjusting to the university learning environment, orienting oneself on campus, redefining the role of teacher and student, and figuring out how to study. I was academically if not mentally prepared (though that was my own fault as I really dragged my feet). I think that a high school teacher can realistically prepare students academically, but not necessarily mentally. Mental preparation is really up to the students to do (though see below for some suggestions).

Q: What is the biggest difference between high school and university math? What’s the most challenging part of university math?

A: High school math is cookie cutter math. One learns a concept, follows the steps, and arrives at the answer. Everything is black and white. University math is a lot more conceptual and a lot less plug and chug. Someone in the room during the conference used an elephants analogy that I really liked, so here is my car analogy. In high school, students are presented with a blue Toyota, a purple Toyota, and a red Toyota. On an exam, they would be asked about one of the three, or if the teacher is daring, about a yellow or a green Toyota. In university, students are presented with Toyotas, Hondas, Volvos, and Fords. On an exam, they would be given a Mazda. Students would have to realize it’s a Japanese car, figure out which car they learned in class is most similar to it, and then solve the problem using the steps to learned (if they exist). As one gets into more difficult math, things either become a lot more specific (the different types of tires on one brand of a car) or a lot more abstract (throw in buses, trains, and boats).

In high school, it’s easy to recognize where one should start – it’s the how, the steps – that are truly challenging. In university, the steps are the easy part. It’s the starting – realizing that a Mazda is the most similar to one of the Japanese cars – that is most difficult.

Aside from seeing the connections to what is learned in class, students are also introduced to more concepts they haven’t seen before (Fermat’s Last Theorem, differential equations, matrices, graph theory, etc.) and that can be overwhelming. If possible, I would encourage grade 12 teachers to even just name some higher level math concepts in their classes along with some of the most famous questions in mathematics. Sure students would have no idea what they are, but when they are exposed to it in the future, they are better off than than their classmates (who would be going “huh??? What the heck is that? I’ve never even heard of it before”). That extra boost of confidence may encourage them and make math seem less daunting.

Q: What were some things that your high school teachers told you about university that were true, but that you didn’t believe?

A: So many things, here are some that I remember: (italics are my notes)

  • Getting into university is easier than staying there
  • No hand-holding:
    • No one cares if you show up to class and no one will chase after you for your homework
    • No spoon-feeding information and exams that require straight regurgitation
    • Mark grubbing won’t get you anywhere
  • Grades will drop 10 to 15% across the board, providing you don’t fail
  • Not all professors are created equal and not all are understandable. Professors are not paid to teach and some are absolutely terrible at it though there are some great professors. Professors probably won’t know your name.
  • Some courses are taught by TAs and not all TAs can teach. I’ve found that TAs are consistently better across the board than profs – I’ve yet to have a terrible TA but I’ve had some abysmal profs
  • Classes can be really large and it’s easy to feel like a number

Q: What more can high school teachers do to prepare their students? What about professors/TAs in university?

A: High school teachers could prepare students academically and maybe mentally. Teach the topics as thoroughly as possible and really hammer home the fundamentals (I believe the professor panel had some suggestions of what they would like incoming students to know). On the mental side, say some of the things from the answer to the question above. Students won’t believe you when you tell them that they have to take charge of their own education, but they will be able to orient themselves faster than other students once they do get to university. If possible, bring in a few recent graduates and have them tell the students these things. Students may take what their peers say more seriously. As for TAs and professors, I’m not sure. Aside from teaching to the best of your abilities, the rest is really up to the students. Perhaps you could stress that you’re always there to support them and that there are other resources available, such as academic coaching and tutoring, if they are not comfortable going to their profs.


I hope this post is somewhat helpful to the teachers and students reading it! If you have any more questions, please write them in the comments! Happy Canada Day!

What if you miss an exam?

Puppy Dog Look

Image "Puppy Dog Look" courtesy of Flickr User Rhiannon McCluskey, Attribution-NonCommercial 2.0 Generic (CC BY-NC 2.0).

WordPress generates a fairly extensive set of site stats for this blog. One useful thing it tells me is what people type in Google (or other search engines) to find this site. Ever since the exam season started, there have been an upsurge of people looking for advice about what to do if they missed an exam. Thus this post is for everyone who find themselves in that unfortunate situation.

I suppose some disclaimers are in order before I start. One, I do not condone missing exams unless you have legitimate excuses, and two, I have never actually missed an exam, so I cannot vouch for effectiveness of these strategies. Use them at your own risk!

If you miss an exam, especially a final, get in touch with your professor right away. Go see them in person or call them. Use e-mail as a last resort as face-to-face or voice-to-voice will help you gauge your prof’s feelings (i.e. how mad are they?). However, do not stalk, leave 10 voice messages, or send 20 e-mails to them! You want your professor to be tolerant or sympathetic, not annoyed. As well, follow your school’s official procedure for missing exams if they have one.

When discussing (or e-mailing) your professor about the missed exam, be polite and courteous. Do not attempt to nag, guilt, or trick your prof into giving you a second chance. As well, avoid sounding defensive as though they are attacking you (even if they are!). Apologize and own up to your mistakes fully. Take full responsibility for your mistake. Unless you had a legitimate excuse, it was your fault you missed that exam. Don’t ever imply it was anyone else’s – or God forbid – the prof’s fault. Explain why you missed the exam. If you overslept, say so. If the bus broke down, let them know. Tell you the truth. An lie will bite you in the ass later. If you told your professor your grandmother died when you simply overslept and that professor finds out, you’ll have one very pissed off prof. Depending on school policy, your professor could even void your makeup exam and report you for academic dishonesty.

If you are e-mailing your prof, remember to still follow the rules of good email etiquette.

Luckily, there are often already scheduled makeup exam times for people with conflicts and legitimate excuses at most universities. Your goal is to convince your professor to let you in on one of them. This could be fairly easy (I had a friend who’s prof didn’t even bother asking him why) or extremely difficult (no means no). However, you might find yourself writing that exam next exam season or even next year!

If it is not possible to make up the exam for whatever reason, ask if you could complete an extra credit assignment to obtain a passing mark on the exam or course. Think creatively. Use your resources and create an honest “deal” that your professor cannot refuse.

Sometimes, there are other people you could turn to for help. If for example, you are an arts student who missed a science exam (or insert any other two non-identical faculties/departments), head to your faculty advising and explain the situation. They might be able to send a note to your prof encouraging him or her to give you a makeup. It’s not a guarantee that your prof will, but it is an extra endorsement.

If all else fails and there is just no way to make up that exam, take a deep breath. Yes, you screwed up, maybe big time. It might feel like it’s the end of the world for a while, especially if you end up failing the course. However, don’t let this affect your mindset for the rest of the exam season. Hit the books for your upcoming exams and use this as extra motivation to do better. Be extra vigilant about exam times and locations, and learn from the experience and ensure that you never make the same mistake again.

Good luck on your exams, and Happy Belated Earth Day!

Have a story idea or a question? Contact me!