Signs your teen is falling behind in CEGEP Calculus I

Why a slow start costs more in Calculus I

Calculus I covers one competency of the ministry's Science program, “Analyze problems by applying differential calculus,” taught in 75 periods of instruction. The program breaks it into four elements, and each one is built on the one before:

1. determine the limit of a function;
2. determine the derivative function, which is defined using a limit;
3. use the methods of differential calculus, which run on the derivative rules;
4. analyze problems from the natural sciences, which use all of the above at once.

So a topic that did not land in the third week is still missing in the eighth, now buried under two newer ones that are built out of it.

The signs you can actually see

You do not need to know any calculus to notice these, and none of them requires seeing a mark.

• Homework done by copying examples. If you see the homework, the exercises follow the worked examples from class line for line, with the numbers changed. The exercises that mix two ideas, usually the last ones in a set, are left blank. The simplest check is to ask, in passing, how they would start one with the notes closed.
• A first test mark that gets explained away. “Everyone did badly.” “I ran out of time.” “Just careless mistakes.” Any of these can be true once. Running out of time usually means steps that should be automatic are still being worked out. And “careless” mistakes that are always in the algebra (a sign, a fraction, a factor) are a gap from high school, not carelessness.
• Avoiding the subject. Every course comes up at dinner except this one. Calculus homework is always the last thing of the evening, then tomorrow's thing. A missed class gets mentioned as if it did not matter.
• Hours in, nothing on paper. Long evenings of rereading notes or watching solutions, with very little worked out by hand. Following a solution feels like understanding it; producing one is what a test asks for.
• Everything happens the night before. A week of exercises done in one sitting just before a test.

Which signs need help now, and which can wait a week

Act this week

• Your teen cannot start an exercise without a worked example open beside it, and it has been that way for two weeks or more.
• The first test came back low and they cannot say where the marks went, or the answer is “everywhere.”
• The mistakes are in the algebra rather than the calculus. That gap does not close by itself, because every new topic leans on it harder.
• They have stopped doing the assigned exercises, or stopped going to class.

Watch, and ask again in a week

• One bad week with a clear cause: an illness, or three deadlines in other courses at once.
• A lower mark than they were used to in high school, but they can point to each lost mark and redo the question correctly. A lower mark is not, on its own, a sign of trouble.
• They find it hard, say so, and keep doing the exercises on time. That is what learning calculus usually feels like.

How to raise it without monitoring

Your teen is close to adulthood or already there, and college treats them that way: they receive the course outline, they deal with the teacher, and the regulations leave the decision to drop a course with them. Checking up works less well than it did in Secondary 5. Asking works better.

1. Pick a quiet moment, not the evening a test comes back.
2. Ask about the work, not the mark. Questions that tend to open it up:
   • “What are you doing in calculus right now?” If they cannot name the topic, that tells you something.
   • “When you start a homework problem, how do you decide what to do first?”
   • “On the first test, where did the marks go?”
   • “Is there a kind of question you would skip if you could?”
   • “Is there anything you want from me?”
3. Say what you noticed once, without a verdict. “Calculus seems to be the thing left for last most nights.” Then let it sit.
4. Read the course outline together, if they are willing. Every student receives one at the start of term, and it sets out how the course is evaluated, which shows what is still ahead.
5. Offer, do not arrange. Suggest taking one specific question to the teacher, offer to cover the cost of help if it comes to that, and let your teen choose.

When outside help makes sense

• When a sign from the “act this week” list has lasted two weeks.
• When the trouble is high-school algebra, functions or trigonometry showing through the calculus. The program lists those as previously acquired concepts, so the course treats them as already learned from the first day.
• When your teen asks. That is the best case: help someone has chosen is help they use.

Earlier is easier. In a course where each topic is the tool for the next, a gap found early is one topic to repair; found at the end, it sits under everything that came after it. A useful first session finds which earlier topic the trouble actually lives in, rather than redoing this week's homework. If your teen wants work between sessions, I write it for that exact topic and mark it before we meet again. Whoever books receives the recaps, so it is worth agreeing between you who that is.

Whatever you decide, the free CEGEP Calculus I worksheets follow the course topic by topic. If your teen can do the current topic's sheet with the notes closed, the method is theirs.

Free worksheets for the first Calculus I topics

• CEGEP Calculus I: Limits and Continuity worksheet
• CEGEP Calculus I: The Derivative worksheet
• CEGEP Calculus I: Differentiation Rules worksheet