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Arithmetical Problem-Solving Difficulties of Students

One of the most common complaints among students at all levels has to be one that involves difficulty comprehending the concepts and constructs of mathematics. Each day students are struggling when attempting to arrive at solutions for mathematical problems. Educators and laypersons alike attribute these difficulties to several causes. Among those are organic problems which interfere with an individual’s ability to process mathematical constructs in a logical manner. Other reasons include an inherent fear of the perceived difficulty, which leads to mathematical blocks, the inability to think logically, and the nature of mathematics.

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First and foremost, a person’s inability to grasp mathematical concepts may be related to a developmental problem which translates to a mathematics disability called dyscalculia. Dyscalculia is very similar to dyslexia in that there is a problem in which the individual’s ability to process certain constructs is hampered. In the case of dyslexia, there is a problem processing letters which is evident when an individual with dyslexia writes his/her letters backward or may misread a word.

This problem can be corrected by learning the way in which a dyslexic mind works and processes information and adapting teaching methods to counteract the effects of the disorder. Dyscalculia, on the other hand, is not as readily detected as dyslexia. Detecting dyscalculia involves working with an individual over time and realizing that there is a mathematical problem whereby it appears that there is a tendency to forget concepts previously taught, and there is a problem applying those concepts to different situations. An example of this in a school-age child can be seen when the child is taught addition. The child is able to master addition problems, but when the child progresses to subtraction and returns to addition, the prior knowledge with regards to the methods of solving addition problems seems to have disappeared.

The presence of such behavior in the absence of a memory problem is one indication of the possibility of dyscalculia. In teaching an individual with dyscalculia, one needs to adopt strategies that will take the disability into consideration and teach the individual to function in light of the disability. One strategy may be to teach a child who is struggling with multiplication the concepts involved in multiplication through the use of addition. For example, in teaching the child to multiply 3*2, one may teach the child that 3*2 is the same as a 3 + 3. The addition is something the child already knows and can readily relate to.

In addition to a learning disability being responsible for the inability to grasp mathematical concepts and constructs, it may just be the presence of an aversion to mathematics. This is one that develops over time, and it can relate to the student not being taught the correct concepts when they should have been taught. Essentially, if, as a child, a student was not taught addition correctly and was ridiculed when trying to solve math problems, he/she will develop an intense dislike for mathematics. In addition to a dislike, he/she may not even try to solve mathematics problems because he/she feels that he/she is not capable of solving problems in such an area.

In such cases, it is prudent that someone works with that individual in order to develop the necessary confidence to succeed in mathematics. In so doing, they may begin with concepts the student has already mastered and slowly build on those. It is simply a matter of assuring that student that he/she is able to achieve and is able to excel.

Finally, as one progresses in the level of mathematics being taught, he/she can have difficulty in the subject based on an inherent ability to grasp complex subjects which are not as concrete as they used to be. An example of this can be seen when a student progresses from arithmetic to algebra. The student had become accustomed to dealing with numbers and quantities he/she can count, and now for the first time, he/she has to deal with using letters to represent those tangible numbers. This is complicated for some students because the combination of numbers and letters is no longer concrete. It involves some imagination, and the student becomes baffled.

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In dealing with such problems, it is prudent that the student understands that despite the fact that numbers are represented by letters, the underlying concepts are the same. In adding, subtracting, multiplying, and dividing algebraic constructs, one uses the same tools as in the equivalent arithmetic constructs.

Essentially, the reasons why students do poorly in mathematics vary. Some students may do poorly because of a disability, while others will do poorly as a result of a lack of self-esteem. Yet others will do poorly as a direct result of the inability to readily comprehend non-concrete concepts. Whatever the reason, this can be combated by first learning the cause(s) of the difficulty and then impacting the appropriate corrective measure. One thing to be garnered from this discussion is that mathematical difficulties can be combated with knowledge and persistent exposure to mathematical problems of all kinds.

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