5. Instead of re-reading, test yourself on the material by solving additional problems and
by explaining it to someone else
6. Use examples as a road map: rather than focusing on the individual steps, think about
how they are connected to the overall goal of the problem
7. ‘Interleave’ your practice: mix up the types of problems, solutions, and approaches as
you review rather than only reviewing one section at a time.
8. Do not ‘cram’: complete reading and homework when they are assigned
9. Think in class: don’t be a passive listener
10. Use the free resources available to you as a student of University of Toronto (see the
Resources section of this syllabus)
How to improve your problem-solving skills
The key to improving your problem solving skills is to work through many problems. When
faced with a new problem, resist the temptation to immediately search the textbook or the
web for a similar problem. Instead, start by asking yourself what you know and identifying
what the goal of solving the problem is. Problem-solving is all about ﬁnding a path between
what you know and what you want to know, and developing strategies to build this path
is a key to success. You will be discussing speciﬁc problem solving strategies during many
Working with your classmates can be very valuable in getting past roadblocks and im-
proving your problem-solving skills. Simply discussing a problem with someone else can help
you better understand the problem and a solution. Remember that the process of solving the
problem is more important than the answer.
How to get the most from lectures
During classes, you may be asked to participate in tasks like thinking about problems, talking
to other students, writing a solution, or explaining a concept to the class. By approaching
these activities with enthusiasm and doing your best, you will not only help your own learning
but also the learning of those around you. In a large class, it is easy to feel as though you
are just one in a crowd and that what you do is not noticed by anyone else. However, if you
change perspectives and think about how you have been inﬂuenced by others in large groups
you’ll see this isn’t true: you notice your neighbour browsing the internet on their laptops,
are distracted by loud coughing ﬁt or cellphone reminder, wonder what a whispering group
of people across the room is talking about, or look over when you hear someone packing their
bags up. You’ve probably also experienced the eﬀect of small behaviours spreading in a crowd.
When you return to thinking about your own behaviour, you should be able to see why what
you do matters to others.
Creating a positive learning environment requires the participation of everyone involved.
Your instructor will set a structure and activities to help you learn calculus well. By actively
engaging in course activities and working with your classmates, you will not only help your
own learning but theirs’ as well.