Its very common to encounter a few roadblocks when it comes to math or
science coursework. As these are the subjects that most students struggle with. Unless mathematically inclined, or working with a strong foundation, you may find it extremely difficult to make it through even the most basic of math courses. And often times your first sign of trouble will manifest itself when asked to complete a set of calculations for a project or assignment.
What exactly are calculations?
By definition, a calculation is simply a process that changes "one or more inputs" to produce a result. In other words, it is a computation, mathematical determination, forecast, or an "estimate based on the known facts." So from this its pretty clear that a firm grounding in the process of calculation is essential to success in any math or science related course.
And what are some of the common difficulties that people face with them?
Though there are certainly many things that can be listed here, the foremost of them is difficulty understanding or comprehending presented problems. Often times people will fail before they even begin by misunderstanding the problem that is in front of them. So first we will explore this major issue; the mathematical process of problem solving.
#1 Understanding the problem and applying different techniques or strategies to solve it
The first step, understanding the problem, is one that many people have trouble getting through. It often leads to incorrect answers, misunderstandings, and overall confusion surrounding the
coursework that is being presented.
So what's the best way to go about understanding a problem? Well initially you would first;
- recall any previous knowledge that you may have regarding the problem (such as a problem that resembles it)
- select the best problem solving strategy to utilize (or test a few out if you are unsure)
Problem solving strategies and techniques
Rest assure that even top performing students rely on good strategies to help them get through tough questions. Various problem solving strategies and techniques have been developed throughout the ages to provide students with clear systematic steps to follow to obtain the answers they need.
So if an answer doesn't come to you right away, or you're unsure of which method to take on, you may want to keep some of the following strategies in mind.
Some basic problem solving strategies - find one that works for you
- look for a pattern
- model draw
- work backwards
- guess and check
- make a systematic list
- logical reasoning
Though many of these are common sense techniques, some may not come to mind as readily as others. And model drawing may be one of them. This strategy in particular is a popular method that works well with visual or kinesthetic learners. Though it is pretty limited to word problems, its a safe and reliable method that only requires the student to draw a picture to accompany the problem they are attempting to solve (a basic strategy that can be done at home, in the classroom, or even on exam day).
Systematic listing
Another technique is systematic listing. It may sound a bit drawn out, but systematic listing is great when your possibilities for a particular problem are slim. It involves listing the possible results that can be derived from the question be asked. For instance, if you need to determine how many different possibilities or number combinations can come about from rolling dice; you would make a list of all the possible combinations that may be obtained based on the number options given on each die.
Logical reasoning
And finally, logical reasoning is just as it sounds. It involves using rational procedures or steps to perform mathematical calculations. This process in itself may be less useful for certain kinds of math; so as with the other strategies, you would have to determine if it is appropriate for your particular problem. Logical reasoning for instance is heavily embedded in geometric proofs and would be good for work in this area (as several if-then statements or conditional statements are found in geometry).
In addition to issues connected to problem solving, another difficulty that some people may face is with mathematical reasoning.
#2 Poor reasoning skills
In order to understand many mathematical concepts and equations a level of reasoning needs to be in place. And some skills may come naturally while others may require more focus and training.
Some examples of reasoning skills that can improve the process of calculation;
- recognizing relationships and patterns
- hypothesizing and making conjectures
- identifying qualities of a good/bad argument or proof
- making use of counter-examples
- utilizing inductive reasoning
As can be seen from the above list there are several reasoning skills that can help you get through a difficult situation. Counterexamples, for instance, are common to calculus and used to falsify conjectures. Likewise, reasoning skills in general also allow you to make inferences and come to sound conclusions by way of educated guessing or hypothesizing; whether it be in assuming a solution or the best method to obtaining one. All crucial and relevant skills for mathematics as well as many other fields.
So how do you sharpen up on your reasoning? Well there are a few things you can do, some of them include...
- Ask What if? questions while working
- Take risk, go with a hypothesis even if you're worried about it being wrong
- Think about the reason behind your answer once you've arrived at one
- Consider why a statement is true and why a statement is false
#3 Struggling with a poor foundation
Lastly, many instructors note that students struggle with mathematics simply due to a weak elementary foundation. Seeing as though math is a cumulative subject, it builds on the knowledge that you already have; so it would be almost impossible to succeed in it with a shaky or faulty foundation. This foundation may refer to basic mathematical concepts and principles or other crucial steps and points covered in the course of learning. For instance, its very common for individuals who never obtained a thorough understanding of arithmetic, pre-algebra, or algebra, to struggle significantly in higher levels of mathematics.
But thankfully the solution is simple. To rebuild a shaky foundation all one needs to do is go back to the basics. A quick review of arithmetic and other elementary, middle, or high school concepts is all that is needed to establish a firm mathematical foundation.