The Base Twelve-System

I found binary much easier when adding the place value at the top of each column.

Trying to forget what everything you have previously understood about maths is extremely challenging. This was the case when we attempted to understand the dozenal-base system. When 12 means 10 and 13 means 11 we were overwhelmed. Our understanding of maths has been built using the base ten system, which actually restricted our learning of the base 12 system. Although to us the dozenal-base system seems extremely confusing, it actually has some advantages over the base-10 decimal method of counting. 12 is a highly composite number — the smallest number with exactly four divisors: 2, 3, 4, and 6 (six if you count 1 and 12). This means that using fractions is much easier, diving into halves, thirds and quarters is much easier using twelve. (½ = 6, 1/3= 4, ¼ = 3) where as diving 10 into fractions is much more complex ( ½ =5, 1/3 = 3.33, ¼ =2.5). The dozenal system is exceptionally friendly to computer science, in fact the dozenal system is all around us. George Dvorsky explores this and says:

“a carpenter’s ruler has 12 subdivisions, grocers deal in dozens and grosses (12 dozen equals a gross), pharmacists and jewelers use the 12 ounce pound, and minters divide shillings into 12 pence. Even our timing and dating system depends on it; there are 12 months in the year, and our day is measured in 2 sets of 12.”

12 equals 10?!

This course has taught me that there is so much more to maths that meets the eye. Before this, I had never explored different number systems. One benefit of the base 10 system is that it is extremely easy to count due to humans having 10 fingers and 10 toes. Zero serves as the placeholder in the base-ten system.

Binary

Another number system we have explored recently was described as the most simple number system, Binary. Although it had been described as simple, understanding the concept of base-2 system proved more than difficult to us as again our knowledge of the base 10 system restricted our learning. It wasn’t until we started writing down the system on a piece of paper that it actually began to click. This also reminded me that teacher’s should explore a topic in several ways as what works for one child won’t work for others. I think the reason that I personally struggled with this was because we were using the numerals 1 and zero which have different values in the binary and base 10 system. Perhaps if I was to ever explore this with children I would use letters to begin with. Richard spoke to us about the English schooling system and how primary aged pupils learn binary and are tested on this. The teaching of binary is important as it is the system used in computing and technologies. I found binary much easier to understand when writing it out myself with the place value written above each column.

I think it is important to explore different base systems as it can deepen our understanding of the world. Binary helps us to understand codings in computing systems, the base 60 system is used in time and the base 12 system is used in bakeries and calendar months.

When it finally clicked