Base 8

Looking at Base 8 to understand how to teach mastery of Base 10 to children. Place value is a key foundation in children`s mathematical learning.

Date : 02/12/2017

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Subject : Maths

The importance of place value is emphasised by the number of times it appears throughout the key stages in the National Curriculum, starting in key stage 1 where children in years 1 and 2 should achieve mental fluency with place value (DfES, 2013). It is a substantial notion in the development of a child s understanding of mathematics and the meaning of a number. Children may require imparted knowledge to develop their understanding of how numbers are written (NCTM, 2000, p. 81). If a child has a good understanding of place value that child is considered ready to move onto using basic algorithms when adding, subtracting, multiplying or dividing. However, if children do not grasp the concept of place value they may struggle applying algorithms to their learning, understanding and fluency are related . . . and there is some evidence that understanding is the basis for developing procedural fluency (Kilpatrick, Swafford, & Findell, 2001).

Our place value system is Hindu-Arabic where all numbers can be represented using a finite set of digits, namely, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (Haylock, 2005), where 0 is used as a place holder. The Romans didn t have a place holder and that s why using Roman Numerals makes it difficult to calculate. Place value is where the value of a number is determined by where it is positioned. To teach children the number system we use base 10 which uses the Hindu-Arabic system which Haylock mentions. We see that one digit numbers which are numbers up to 9 all belong in the one s column, sometimes referred to as the unit s column, of a place value chart, however, after 9 we move to the ten s column and after 99, which is 9 ten s and 9 one s we move to the 100 s column and so on. For a number with a 0 in it such as 10, 0 will be the place holder and there is 1 ten and no one s and for 100, there will be 1 hundred and no ten s or one s. Therefore, from this we see that in base 10 to move to the left of the place value chart from the one s column each value is multiplied by 10 and thus we are working in powers with the base 10, as each power would increase with a base number of 10. The reason why base 10 is the most widest used notation is because we have two hands which make up 10 fingers, because when we count using our fingers and we get up to 10 we start on another set of 10 fingers.

For children to grasp the base 10 concept they go through many hurdles and challenges. However, if we are going to teach the base 10 concept which is a base for the development of children s numeracy we need to understand the hurdles and challenges and why children encounter them and how they can be overcome. To understand the process children go through, I challenged myself to understand and use the concept of base 8.

The base 8 number system uses the symbols: 0, 1, 2, 3, 4, 5, 6, 7, where just like base 10, 0 is used as a place holder. After 7 we move from the one s column to the 8 s column. We can see from this that in base 8 to move to the next column you have to multiply the column to the right by 8, in other words we also go to the left of the place value chart in powers of 8. When tackling the base 8 task, I found it really difficult that I had no visual aids to help me. For children who prefer visual aids there are two effective concrete embodiments of the place-value principle that help us to explain the way the system works and these are the 1) base-ten blocks and 2) 1p, 10p and £1 coins (Haylock, 2005). When I was STUCK! (Mason, Burton and Stacey, 2010) with the initial understand of the base 8 system, I decided to create my own base 8 blocks to help me to reach AHA! (Mason, Burton and Stacey, 2010). However, if we have stimulus for children to use we need to remember that merely having manipulatives available does not insure that students will think about how to group the quantities and express them symbolically (NCTM, 2000, p. 80). However, when using equipment, it doesn t always have to be introduced in the beginning, Children can CHECK! (Mason, Burton and Stacey, 2010) to see if they ve understood the concept using the equipment.

Number lines are also a very significant tool because they can demonstrate place value quantities for less than 1. Children tend to use their prior knowledge of base 10 to count using number lines. For example, if a child wanted to count to 347, the child would count in 100 s till the child reaches 300 then count on in 10 s until 340 then count on in one s reaching to 347.

As teachers we have to be careful of teaching children rules rather than aiding them to understand a concept. If children are taught to add a zero they will be learning a rule that they will have to unlearn later (Thompson, 2003). This is because when children are tackled with solving problems using place value and they haven t really understood the concept, they will struggle.

References

Department for Education (2013) The National Curriculum in England: Key Stages 1 and 2 framework document. Available at: https://www.gov.uk/government/publications/national-curriculum-in-england-primary-curriculum (Accessed: 23 November 2017).

Haylock, D. (2005). Mathematics explained for primary teachers. 3rd ed. London: P. Chapman Pub.

Kilpatrick, J., Swafford, J. and Findell, B. (2001). Adding it up. Washington, DC: National Academy Press.

Mason, J., Burton, L. and Stacey, K. (2010). Thinking mathematically. Harlow: Pearson.

NCTM. (2000). Principles and Standards.

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