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# 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

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.This resource was uploaded by: Mutayyab