How to Avoid Common Math Mistakes – A Guide for Online Students

Interactive online learning systems are powerful tools for practising mathematics, but they demand a high degree of precision. 

Most LMSs like MyMathLab often come with instant feedback. However, this feature is a double-edged sword; it flags when an answer is wrong, but does not explain where you went wrong.

While some systems offer unlimited remediation sub-parts that waste time on a single question, some LMS allow only limited attempts, which, if reached, eventually affect the overall grades.

However, there’s a solution- understand the mistakes first and not repeat them in the future. In this article, we will dive deep into the five common mistakes online math students make and offer actionable tips with examples to fix them. Let’s begin:

Mistake 1: Avoiding Parentheses in the Order of Operations

While it is often taught in introductory algebra, students keep repeating this mistake. Forgetting parentheses is a failure to recognize when an implicit grouping exists within complex functions and expressions.

For example, in a calculus question, a student needs to find the derivative of f(x) = (2x+1) / (x-3) using the quotient rule: (g(x)f’ (x) – f(x)g’ (x)) / [g(x)]^2.

In the numerator, they correctly find the derivatives but mishandle the subtraction.

They write (x-3)(2) – 2x+1(1) in the numerator. The minus sign is only applied to the 2x term, not the +1.

The resulting numerator is 2x – 6 – 2x + 1 = -5. And, the whole equation becomes wrong.

Correct Calculation: The entire second term must be subtracted, requiring parentheses: (x-3)(2) – (2x+1)(1).

This correctly distributes to 2x – 6 – 2x – 1 = -7. Therefore, a seemingly tiny error drastically changes the result.

Actionable Tips

1. Treat every multi-term expression as a single, packaged unit.
2. When substituting, replacing, or, most importantly, subtracting an expression, always enclose it in parentheses.
3. For formulas like the quotient rule, write the template with parentheses first—[ ( ) ( )’ – ( ) ( )’] / ( )^2—and then fill in the functions.

Mistake 2: Focusing Only on the Final Answer

When you do math homework online, it’s easy to fall into the trap of only caring about the final answer you type in the box. This is a bad habit because getting good at math is about understanding the steps, not just getting the right result.

If you don’t write down your work clearly, it’s almost impossible to find where you went wrong.

Suppose you have to find the inverse of a 3×3 matrix in Linear Algebra on MyMathLab. This is a long problem with many steps: calculating the determinant, finding cofactors, and so on.

You try to do some of it in your head or on messy scrap paper. You get the final answer wrong and have no idea why. You have to start the whole problem over because the mistake could be one tiny sign error from the very first step.

How to Do it Right?

1. Get a notebook just for your math class. For every problem, write down each step of your work, neatly and in order. You are basically creating a roadmap that you can check later.
2. If your answer is marked incorrect, your first move should be to review your written steps. You’ll often find your own mistake.
3. If you can’t, show your organized notes to a tutor or professor to get the right MyMathLab Answers.
4. Also, compare your wrong steps with the right solution to understand your conceptual mistake.

Mistake 3: The Chain Rule Catastrophe

In calculus, the chain rule is a frequent point of failure. Students often forget to apply it or misidentify the “inner” and “outer” functions, especially when multiple rules are combined in one problem.

The Scenario: A student needs to differentiate g(x) = e^(sin(x^2)). This requires applying the chain rule three times.

Incorrect Application: The student might differentiate the outer e^x function and the inner sin(x) function, but forget the innermost x^2. Or they might add the derivatives instead of multiplying them. A common mistake is e^(sin(x^2)) * cos(x^2).

Correct Application: You must work from the outside in, multiplying by the derivative of each subsequent inner layer: 

d/dx[e^(sin(x^2))] = e^(sin(x^2)) * d/dx[sin(x^2)] = e^(sin(x^2)) * cos(x^2) * d/dx[x^2] = e^(sin(x^2)) * cos(x^2) * 2x.

Actionable Tips

1. Use the “onion” analogy. The function is like an onion with multiple layers. To get to the center, you must peel each layer one at a time.
2. Write down each layer as a separate function: f(u) = e^u, u(v) = sin(v), v(x) = x^2.
3. Find the derivative of each piece separately, then chain them together with multiplication.

This systematic approach breaks a complex problem into manageable parts and ensures no layer is missed.

Mistake 4: Misreading the Formatting Instructions

Online answer systems can be very strict about how your answer is written. A common way to lose points, even if your math is right, is by not following the system’s formatting rules.

Let’s say a Statistics problem asks you to round your answer to four decimal places. Your calculator shows the answer is 0.047619. You correctly round this to 0.048 and type it in, but the LMS marks it as wrong. The right format would have been 0.0476.

Another common mistake is typing an exact fraction like sqrt(3)/2 when the problem asks for a decimal number, or the other way around.

How to Avoid This Mistake:

1. Before you start doing any math, figure out how the problem wants the answer formatted.
2. Read the instructions carefully, even twice. It helps to say the rule out loud, like, “Okay, the answer must be an exact integer or a simplified fraction.”
3. You should also write a quick note in your workbook, like “ROUND TO 3 DECIMALS,” right next to the problem. This small step makes sure you remember the rule before you get lost in the calculations.

If you are suffering from formatting errors in MyMathLab, you can request a custom MyMathLab Answer Key from experts to use as a learning guide.

Mistake 5: The Logarithm Law Tangle

The properties of logarithms are essential for solving exponential equations and are foundational in many STEM fields. However, they are often misremembered and misapplied, leading to unsolvable equations.

For example, a student is asked to condense the expression 2log(x) – log(y).

They might incorrectly mix up the rules, resulting in log(x^2 / y) (correct!) but then try to “simplify” further with false properties like log(x^2) / log(y).

Another devastatingly common error is misapplying the sum rule to the terms inside a log, for instance, treating log(x-y) as log(x) – log(y).

Correct Application

1. First, apply the power rule: log(x^2) – log(y).
2. Then, apply the quotient rule: log(x^2 / y).
3. The expression is now fully condensed. There is no rule for splitting up log(x-y).

Tips on Correct Approach

Create a reference sheet with the three core logarithm laws written clearly

1. log(a) + log(b) = log(ab)
2. log(a) – log(b) = log(a/b)
3. c*log(a) = log(a^c)

More importantly, write down the non-rules next to them: 

log(a+b) ≠ log(a) + log(b) and log(a) * log(b) ≠ log(ab)

Consider using the “Help Me Solve This” or “View an Example” tools provided by the LMS. These resources are designed to walk you through the correct application of logarithm laws step-by-step for a similar problem.

Conclusion

Getting through college-level math is its own kind of skill. The mistakes mentioned here are a normal part of your learning journey. When you start focusing on how to solve the problem instead of just on the final answer, you’ll start to feel more comfortable with math. Treat every wrong answer as an opportunity to figure out exactly what you don’t understand. By using these tips, you’ll build strong math skills that will help you throughout your time in the academy and in your future career.