16 Dec 2022


Mathematical Experiences: A Collection of Problems and Activities

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Academic level: College

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Every person faces a certain type of challenge when going through his or her learning phase. Some people have trouble with sciences and others have a problem understanding literature. Just because one area is problematic in the subject does not necessarily mean that you are poor at the subject. In fact, the problem may end when you reach a certain age. Teachers and parents have observed that most students struggle with math. There is always a challenging concept that a student’s faces at some point in their life as a student. It does not matter how good the student is in math since this problem area becomes a real problem in their progress. I am no different from most people. While I had no problem with math in general, there are certain principles whose concepts I never seemed to grasp. My greatest challenge in math was in division. I never seemed to grasp the concept of long method division as well as word problems. Research indicates that understanding division is not only something that students find challenging but also one that poses a challenge to the teachers as well. 

According to Ball (1990), some teachers have a problem explaining the concepts of division not to mention the explanations and meaning behind these concepts. Some teachers cannot derive representations that are appropriate to some division problems. It is therefore not surprising when a student fails to understand the basic concepts of division when the teacher cannot relay it properly. The major problem in division is failing to understand the units in division problems. While solving the problems may not be difficult, failure to knowing what units to match each part. Most students and teachers misunderstand the remainder unit or fractional quotient part in the division problem. Unfortunately, failure to understand these units can hinder the general grasping of the entire division concept. This is something I came to appreciate through my learning. While I could get some of the answers right, I did not understand how they came to be which was a problem. 

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Children generally develop math skills and utilize these skills outside a class setting. More often than not children have demonstrated the ability to apply algorithms before learning them in class. The basics of division and fractions come easy to children as they make use of them in everyday life though not in a formal way. Most children show the ability to solve problems involving fractions at an early age (Parmar, 2003). Children use self-invented procedures to tackle these problems. The challenge comes in a school or classroom setup when children fail to relate with the real life situation. I believe this was probably what was happening to me. I could not relate the concept being taught in class with what I knew to be true from outside. It is recommended that teachers encourage the use of such techniques that most children can identify with. This distorts the notion that math is difficult and impossible. Research has shown that when math is made to simulate real life situations it becomes easy to understand. 

Division is a concept that builds from additional and subtraction. This means that there needs to be a strong foundation of the basics. Building this understanding is crucial for future knowledge (Parmar, 2003). For early stages of earning, division should be viewed as a primitive model of repeated subtraction. The same way a primitive model of repeated addition is multiplication. Understanding these two concepts from this angle helps make it easier to master the complex aspects. These primitive concepts are built to create a better understanding of the real concepts in future. It is easy therefore, to understand why children have misconceptions about division .Most of them believe that division makes smaller which is something that plays a major role in the misconception of how division works. The misinterpretations for children and other students are easily seen in their inability to explain or make an interpretation of what their responses are. Not many students are able to give an accurate interpretation of their response. This same thing used to happen to me. In the few instances that I would be lucky to get the answer right it would be impossible to explain how I derived it. Writing a word problem to accompany a certain expression was impossible for me. While I could comfortably compute a problem sometimes, it was always impossible to make sense of it. This meant that I could not explain the solution effectively. The other problematic area for me when it came to division was the aspect of remainders. I had no idea what to do with the remainder. Knowing what to do with the remainder is a crucial part of understanding the word problem. The aspect of units comes in because the way to express a remainder depends on the unit and wording of the problem. There are different instances when a remainder is expressed as a fraction or decimal, a whole number or at certain times, it may be rounded off to the nearest whole number (Parmar, 2003). This challenge could be stemming from the fact that most students are not sure of the method that they are using to solve the problem. This means that they are inadequately prepared to use the remainder. I believe that one of the issues I faced was because I misinterpreted the signs almost all the time especially when dealing with fractions. Most students have the understanding of what fractions are but cannot relate the same concepts to symbolic representations. 

Word problems have always been a challenge ever since I started learning division. The fact is that such problems pose a unique test. A student is required to figure out how the problem is best set up. This is a different scenario than one where the problem is already set up for you. In addition, word problems come with numerous complexities that affect the outcome of the problem. It is even more challenging if remainders and fractions are involved. The challenge stems from the fact that a slight change in wording makes a dramatic change in how problems are solved. Any slight variation in the wording causes a significant difference in how the problem should be computed. 

The number of variables in division problems is also important when solving them. The type of variable determines if the problem will have a remainder. Discrete and continuous variables determine the remainder factor. Discrete variables cannot be divided onto pieces hence in case of a remainder it remains as a whole and not fraction as is the case with continuous variables. There are different methods of solving division problems including the long division method, multiplication method and repeated addition and subtraction method. Long division is applicable n most basic problems when dealing with numbers with two or more digits. This method requires one to understand the skills of addition and subtraction. When using this technique to solve word problems there is, need to ensure that you identify the variables. For the multiplication method, some people reverse the division process and use multiplication. I sought to understand the challenge by talking to a teacher who deal with students on a daily basis. I interviewed one of the junior school math teachers as a way of tracing some of the issues that I faced while going through school. My focus was on division since his was the area that challenged me the most during my time in school. 


Me: Are students interested in learning math 

Teacher: Yes. Most students are willing to learn math concepts. However, the attitude towards this subject is not always the best since students believe that it is a difficult subject. 

Me: My concern is division. I always find it difficult solving division problems especially the worded problems. Are students today experiencing the same challenges? 

Teacher: Yes. Most of the challenges students face in a math class involves division. There is the issue of interpreting the question especially when dealing with word problems. Some students are able to resolve problems but they cannot interpret the solution. 

Me: Are there any remedies that can be applied to resolve the problem? 

Teacher: Improvements can happen if teachers and students have a change of attitude. Math is easy when approached with the right attitude. Teachers should be willing to explore practical teaching methods whereas students should be open minded. 


Horton, L. ( 2007). Understanding the Concept of Division . Retrieved April 30, 2016 From: http://faculty.etsu.edu/gardnerr/math-honors/theses/horton-thesis.pdf 

Spector, L. (2016). The Meaning of Division, Lesson 11 . Retrieved April 30, 2016 From: http://www.themathpage.com/arith/division.htm 

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StudyBounty. (2023, September 15). Mathematical Experiences: A Collection of Problems and Activities.


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