The concept of place value is premised on wider ideas about the number system. These ideas are quite difficult and complex for students to learn. In particular, many children do not realize the purpose and essence of place value system and, therefore, they need active assistance in developing full comprehension of the number system structure.
Hence, it has been found that junior students do not understand that 1 in 14, for example, defines the first ten (Associated of Independent Schools of South Australia, 2004). Many students under 3 and 4 years do not understand the concept of value place either. The problem is that students can write 14 for fourteen objects in the right order, though they fail to understand its place value as a number made up of one ten and four ones.
It has also been reported that children can conceive up to four digits by the third year. Children, however, are seen little progress after the third year. At year 6, about 42 % of students are not able to single out ten thousands place (Associated of Independent Schools of South Australia, 2004).
Within 2-6 years period, some students are unable to analyze the number system structure (Associated of Independent Schools of South Australia). In particular, children count figures only in ones, even though the figures are presented on a 100 chart. They fail to notice tens and hundreds, which is also the basic problem to be corrected. Such a difficulty can lead to serious confusions and prevent children from understanding the main principles of place values.
Aside from difficulties with understanding, there are many other sources of misconception among children. Hence, such issues as boredom and distraction can come to the forth when children are not interested in the subject, or they are not enough motivating to studying mathematics (Bottle, 2005).
In addition, lack of practice is also among the main causes of misconception. Some students are not able to apply the theory and rules in practice because application has been presented in an irrelevant context (Bottle, 2005). Finally, lack of understanding can occur as the result of vocabulary misunderstanding. For instance, children may fail to understand the meaning of ‘subtraction’ or ‘multiplying’.
These confusions, therefore, can distort students’ understanding of place value due to their false perception of numbers. The corresponding solutions should be presented to correct the existing misconceptions. The best way to address students who miscount object is to introduce person-centered approaches to introduce the basis of place value theory (Department of Education and Early Childhood Development, 2006).
Teacher’s task is to define the weaknesses and strengths that each student possesses and analyze which techniques can be used to eliminate the problems. Specific emphasis should be placed on establishing the source of the problem, which is often confined to one person.
Second, the introduction of comprehensive games and educational courses will contribute to problem elimination and provide a solid basis for further improvements. Finally, the introduction of ICT and enhanced teaching will also be among the most effective means of solving the problem with place value misconception.
In conclusion, teachers should pay close attention to the role of place value in understanding numeracy, as well as the importance of numeracy in further study of mathematics. They should also realize that numeracy is the foundation for further studies because numeracy and place value set base for learning more complicated learning. In this respect, it is imperative for teachers to understand the main constraints that children might face while mastering the concept of place value.
References
Associated of Independent Schools of South Australia. (2004). Understanding Place Value: A case Study of the Base Ten Game. Australia: Commonwealth of Australia.
Bottle, G. (2005). Teaching Mathematics in the Primary School. US: Continuum International Publishing Group.
Department of Education and Early Childhood Development. (2006). A Note on Common Misunderstandings. State Government Victoria. Web.