Why Do So Many Students Struggle With First-Year University Math?

First-year university math isn’t just “harder high school.” It’s built on a different set of assumptions:

• In high school, you were often trained to follow a procedure that matched a question type. In calculus and linear algebra, you’re expected to recognize which idea applies and justify steps.
• The pace is faster. A topic that took two weeks in high school can be covered in one lecture, and the homework assumes you can fill in gaps on your own.
• Your grade depends heavily on a few timed assessments. One midterm can reveal weaknesses that have been building quietly for a month.

On top of that, first-year courses frequently mix skills. In first-year calculus (differential/integral calculus) you might need algebra, trigonometry, and function intuition just to start a derivative question. In Math 110/180, you can understand the concept but still lose marks if you can’t compute cleanly under time pressure.

The result is that students who were used to “doing what the teacher showed” suddenly need to plan their learning, diagnose mistakes, and practice independently.

Most struggling students aren’t doing nothing”they’re doing things that feel like studying but don’t build exam-ready skill.

Mistake 1: Treating math like reading. Watching a solution, nodding along, and thinking “that makes sense” is not the same as being able to do it alone with a blank page. This is why students can follow lecture examples but freeze on WeBWorK or a midterm.

Mistake 2: Doing homework as a deadline task, not a learning tool. If WeBWorK is done the night before, you never have time to notice patterns, fix mistakes, and re-try problems. You also miss the best use of office hours: showing up with specific questions.

Mistake 3: Memorizing without meaning. Students try to “store” formulas like the product rule, chain rule, or standard integral patterns, but they can’t recognize when to use them. In linear algebra, they memorize steps for row reduction but can’t explain what a pivot means.

Mistake 4: Ignoring the prerequisites. Many first-year math problems fail because of algebra: factoring, rearranging, handling exponents, trig identities, or simplifying expressions. Calculus amplifies small algebra errors.

Mistake 5: Practicing only easy, familiar questions. It’s natural to repeat the ones you can already do. But exam questions are designed to test whether you can adapt. If your practice never includes “slightly different,” your midterm will feel unfair.

The students who turn things around aren’t necessarily “smarter.” They do a few key things consistently.

They practice actively. They attempt a question before looking at notes, even if they get stuck. They treat stuckness as useful information: “Which step is unclear? Is it algebra, concept, or strategy?”

They build a personal error list. After each assignment or quiz, they write down:

• what type of mistake happened (setup, algebra, concept, interpretation)
• what to do next time (a rule, a check, a reminder)

Over a semester, that list becomes more valuable than any formula sheet.

They separate concept learning from speed training. Early in the week they work slowly, explaining steps. Closer to the midterm they do timed sets, because exams reward both understanding and execution.

They ask questions early. Not “I don’t get derivatives,” but “When I use the chain rule here, why does the inner derivative appear?” or “How do I choose u in substitution when there are multiple options?” Those are questions you can actually fix.

Here’s a weekly approach that works well in first-year calculus (differential/integral calculus), and it also translates to Math 110/180.

1) After lecture: do a 15-minute ‘rebuild’

• Close your notes.
• Write the main idea in your own words (one or two sentences).
• Do one representative problem from memory.

This is short, but it forces retrieval”the skill exams demand.

2) For WeBWorK: turn each set into a mini skill list

• Before starting, skim the whole set and group questions by type (limits, derivative rules, optimization, integrals).
• When you miss one, don’t just “fix it.” Write the reason in a single line.
• Re-do that question (or a similar one) the next day without looking.

3) Build a “midterm set” Pick 8–12 questions that represent the core skills. Recycle them each week until they feel routine. Then add 2–3 “twist” questions (the kind that changes one detail and forces you to think).

Concrete example (first-year calculus (differential/integral calculus) style): You’re asked to find the derivative of f(x) = (3x^2 - 1)^5.

A common approach is to memorize “chain rule” and still get stuck. A better approach is to name the layers:

• Outer: (\textsomething)^5
• Inner: 3x^2 - 1

Then you do two clean steps:

• Differentiate outer: 5(3x^2 - 1)^4
• Multiply by derivative of inner: (d)/(dx)(3x^2 - 1) = 6x

So f'(x) = 30x(3x^2 - 1)^4.

Now here’s the exam habit: check quickly. If x=0, the original function is (-1)^5 = -1. The slope at x=0 should be 0 because the inner derivative gives a factor of x. Your answer has a factor of x, so that passes a sanity check.

Those tiny checks prevent a lot of midterm heartbreak.

• First-year math feels hard because the expectations change: faster pace, deeper thinking, fewer “guided” steps.
• The biggest traps are passive studying, last-minute WeBWorK, and ignoring prerequisite algebra.
• Strong students practice actively, track mistakes, and separate understanding from timed performance.
• A simple weekly system beats occasional long “study marathons.”

If you want structured, concept-focused help, Learn4Less offers tutoring sessions designed specifically for first-year university math.