In this essay I will be looking at the definition of place value and what does it mean, I will then explore the importance of the base-ten system in relation to place value and why knowing the base-ten system is important for understanding place value. I will then discuss the reason for why learners struggle with understanding the concept of place value, also I will discuss the importance of using concrete material. Finally I will look at the progression of levels from grade 2 into grade 3 learners according to the CAPS document. Definition
Price (2001), state that place value refers to our base-ten system, where each digit in a number represents a partial amount, this amount is determined by the structure of the number and the position of the digit in the number. In the base-ten system the position of a digit represents its value, therefore each digit has its own value in relation to another written symbol. This concept can be very easy to understand or it can be very complex, it can also be extended to many extends such as moving to the left to or to the right where numbers become decimals or fraction.
The importance of the base ten system .
According to Klimam (2000), in order for a learner to understand place value, they need to understand the structure and sequence of the base ten number system. As learners count, they interpret the values of written and spoken numbers, they are able to distinguish which number is larger or smaller, and explore relationships among numbers, through doing this they are developing a picture of our denary number system.
The importance of understanding place value is that the learners are able to use the base-ten system to form accurate, flexible, conceptual structures for quantities represented by written symbols. The learners need to be able to manipulate numerical values in a meaningful manner to solve mathematical problems(Price, 2001).
Through teaching the learners the base-ten system they develop schemes in their head, when the learners understand the base-ten system it is easy for them to apply it, to the new knowledge, in this case place value. This concept of place value becomes the new knowledge and can be link to prior knowledge. This process is known as assimilation. The understand of the new knowledge can happen through using a variety of different materials either concrete or these materials can be the thoughts of the learners and their ideas( Lombard, 2013:2)
Why do learners struggle with the place value concept
Learners tend to struggle with the concept of place value, as there is a lack of fundamental understanding and experience with positional systems. Therefore, learners tend to struggle with trading groups for collections of groups, such as regrouping 10 tens for 1 hundred. As there is a lack of understanding of the place value structure, that is, multiplying each place value position to the left of a number by the base 10 and dividing each place to the right of the decimal point by the base. If the learners mistakes are conceptual, the teacher will intervenes and she will begin to use manipulative materials to help develop an understanding of the concept. These materials used could be place value blocks, counters of any type, and place value charts. If the learners mistakes are more procedural, then the learner has forgotten the rules and algorithmic steps but they understand how the system works. Interventions do not necessarily have to involve manipulative materials in those cases. Lessons are focused on drawing and representing objects and then connecting numerals to those figures or making notations as reminders. For example, when subtracting, students can draw an arrow over the “2” if that helps them remember where to start. Or, pupils could circle the ones column in each example, prior to computing, in order to remember to regroup that place and not the tens place (Sherman, Richardson and Yard, 2009).
References: Kliman, M. TERC. 2000. HOW DO STUDENTS BUILD AN UNDERSTANDING OF PLACE VALUE IN INVESTIGATIONS? http://investigations.terc.edu/library/curric-math/qa-1ed/place_value.cfm [ 6 May 2013].
Kwenda, C. 2012. Education: Vgotsky 's socio-cultural theory of development. Cape Town: Cape Peninsula University of Technology.
Lombard, A.P. 2013. Numeracy: What does it mean to learn Mathematics? Cape Town: Cape Peninsula University of Technology.
Moodley, T. 2011. Education: Cognitive Development Theory. Cape Town: Cape Peninsula University of Technology.
Price, P.S. 2001 The development of Year 3 students ' place-value understanding representation and concepts. Queensland University of Technology, Australia. [online]
http://eprints.qut.edu.au/15783/1/Peter_Price_Thesis.pdf [8 May2013]
Sherman, H.J Richardson, L.I & Yard, G.J. 2009. The Impact of Place Value on Mathematic. Pearson Education Inc. http://www.education.com/reference/article/impact-place-value-mathematics [ 6 May 2013]
South Africa. Department of Education. 2011. Curriculum and assessment policy statement grades 1-3. Pretoria: Government Printing Works.
Thompson, P.W. 1994. Concrete materials and teaching for mathematical
understanding. Arithmetic Teacher, 41(9). http://www.pat-thompson.net/PDFversions/1994Concrete.pdf [ 8 May 2013]
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