What Makes Mathematical Reasoning Difficult Under Exam Conditions?

The ways of mathematical reasoning can be entirely different within an examination hall. Questions that may be clear during revision may suddenly become murky when the clock is ticking, and the teacher is not present to clarify the words. This is because mathematical success is more than knowing formulas. Students should be familiar with information, be able to find relationships among information, select a strategy, compute correctly, and verify whether the answer is reasonable or not. 

When under stress, these steps can be more difficult to regulate.  Anxiety can cause someone to become so focused that they don’t see the big picture; time constraints may lead to hasty decision-making, and an error early in the process can have repercussions throughout. It helps to have an understanding of why this occurs, as it will change how students prepare. 

Why do you need to know the formula?

Numerous students think that after they memorise the appropriate formulas, mathematics becomes easy. Unfortunately, tests don’t always specify the particular formula to use.

Information in a question can be extraneous to the information that is necessary. Pupils must first be able to identify what the problem is asking before starting to work out.

This is where it is very difficult to see mathematical reasoning challenges. A learner can grasp the idea behind a question, but have difficulty converting a written question into a mathematical procedure.

A student might be able to get the right answer when computing a percentage, but become confused when the idea of a percentage is used in a word problem that involves a discount, growth, or comparison.

Students’ Strategies for Solving Problems Involving Pressure Change

The added mental challenge in an examination is that of knowing that you have a time constraint before you.

Students may rush or skip over critical words and instructions, or quit a sensible approach if they hit one tricky step when they’re feeling anxious. There are others who spend too much time trying to solve one problem because they don’t want to go ahead.

To pass rigorous tests, students may sometimes try to find a way to get a shortcut, and in some cases they may resort to Take My Algebra Exam For Me services, but this cannot teach them the reasoning skills that are required for future studies or careers. It’s much better to get used to the various types of questions and develop practice in realistic time constraints.

Unfamiliar Questions Can Create a Mental Block

The same exercises are frequently repeated. Students are continually asked to answer questions that are a repetition of the examples in their textbook.

Then, the exam poses a question in a new way, or in a way that is a combination of two concepts. The student “feels like he/she has never studied the topic.

This is very relevant with respect to exam problem-solving. Well-prepared questions should be answered in such a way that the student needs to choose a method and not just make use of the last formula he/she remembers.

In revision, use some easy, moderate and unfamiliar problems. Solving each one, explain your choice of a method. More often than not, it’s better to explain the reasoning than to just check if the last digit matches the answer.

Working Memory is Limited!

Sometimes students will have to maintain multiple pieces of information in their head when solving mathematical problems.

A student might have to recall a formula, keep several calculations in mind, understand a diagram, and be aware of units as well. Especially when stressed, this can be even more difficult to bear.

Intermediate steps can be written down to decrease the information that needs to be retained. This is also a benefit in terms of working out where an error has been made.

The same issues are present with students who are studying for professional exams. Take My PMP searchers, for instance, might be uncertain about handling the complex scenario-based questions rather than a lack of factual knowledge.

The consequences of errors can be serious!

In maths, there are sometimes ‘steps’ in learning. If a sign, a number, decimal or unit is incorrectly copied, it can impact several subsequent steps.

This can lead to frustration as students may be able to grasp the concept but still end up with a wrong answer.

Establish a speedy checking method. Before proceeding, check to see if the answer makes sense, if the units are correct, and if the answer is similar to what the question is asking.

But screening should be calculated. It can create time pressure on other problems if you spend some time trying to figure out the same simple problem over and over again.

How to do Mathematical Reasoning better

Preparing well is a process which goes beyond the completion of hundreds of questions. First, try doing the exercises without reference to any solutions. Take time to read through the problem and find a strategy.

Secondly, have an error log. Do not just write the right answer and not explain why the error occurred, but write an explanation of why the error occurred. Did the question get the wrong interpretation? Was the incorrect formula used? Has an error been made?

Third, incorporate timed practice periodically. This allows students to get some practice in choosing a decision to make in a limited amount of time.

Last, provide verbal and/or written solutions. Being able to state clearly why a method works means you will be more likely to identify when this method is applicable.

The National Council of Teachers of Mathematics is not interested in viewing mathematical learning as mere memorisation, but in promoting mathematical reasoning, problem solving and connection in learning mathematics. (nctm.org)

Conclusion

When students have to meet several demands under test conditions, mathematical reasoning is difficult. They need to guess at the meanings of words they don’t know, choose suitable strategies, recall facts or information, and perform calculations correctly as time pressures increase. All these activities can seem more challenging when under pressure. Teaching itself is not the answer; it is studying for longer. Improved preparation will include: working through unfamiliar problems, analysing errors, clear working, and timed tasks. If students are able to view challenging questions as a series of manageable choices, then maths is not such a daunting subject.