Time is something that I hadn’t really thought about as it just something that we have come to learn and know. It is probably one of the most important aspects of mathematics that directs our lives. Everything we do is according to a time and schedule.
It was a bit of a surprise to me that some aspects of time are man-made, such as second, minute, hour and week. However, days, months and years are not. The latter are natural aspects of time are shown from the Earth turning to turn light to dark (day), the moon and its shape (month) and changing of seasons and migration leading to recognition of division of seasons and therefore a year.
All aspects of time coincide with the sun and the moon. To me, I know that it is a new month because another day has passed and my calendar tells me so. But without a calendar of a digital clock telling the day how did people before this invention tell the time. The oldest artefact found and thought to be 35,000 years old, called the “Lebomba bone,” had 29 lines scratched in to which could represent the recording of a lunar cycle (Bellos, 2010).
There are various theories about how the 24-hour day developed. The fact that the day was divided into 12 hours might be because 12 is a factor of 60. There is also reason to believe finger-counting with base 12 was a possibility – the fingers each have 3 joints, and so counting on the joints gives one ‘full hand’ of 12. Another theory based on Egyptian time was that the 24-hour day was broken down to 10 hours of sunlight, 10 hours of darkness, 2 hours of dusk and 2 hours of dawn. However, how did they account for time at night as one of the oldest ways of telling time was a sundial. We looked at the history of water clock which again seem so simple yet the sophistication of this invention is amazing considering the period of time.
Time is not something I had put much thought in to before and this occurred to me that it is because the foundations of it were taught at elementary stage (Ma, 2007, pg. 124). We are so used to telling the time in 60, but that really is quite a hard concept to understand as a student. During my placement I was teaching hand of clocks and just the language such as “quarter past, 
half past and quarter to” are quite difficult concepts to understand. Not only do you need knowledge of how to divide something by two and four, it becomes more difficult where using fraction on the number 60, which is easy enough for you and I because we know it so well. However, when breaking this down to teach and trying to reframe my methods was something I found difficult as it is just something that I’ve come to know so well and use every single day.
Profound Understanding of Fundamental Mathematics (PUFM)
I think many of Ma’s principles of PUFM can be applied to the concept of time. However, defining “telling time” is very difficult as there are so many stages and blocks to build on.
Basic ideas – recognising numbers in a sequence that is different to the base 10 system we use for everything else. Children may not be able to tell the time but they can recognise the numbers on a clock.
Connectedness – Following simple routines for break and lunch times e.g. knowing that it is nearly lunchtime due to positioning on the clock. To moving on to connecting language from other topics such as fractions e.g. “quarter past”, “half past”.
Multiple perspectives – time becomes very confusing switching between 12 and 24 hour clocks so knowing when to it is necessary for children to be able to differ between the two is also important. Children are exposed, even more so nowadays in our digital world, to digital clocks telling 24-hour time so it is important the difference is taught as soon as possible without causing confusion.
Longitudinal coherence – I think this principle plays a vital part when learning, understanding and teaching “time”. Being able to tell the time is not the only part children need to understand. The ability to understand a routine or a timetable are difficult concepts to grasp along with “telling the time”. The level of intellect used in problem solving for structuring and deciphering timetables is optimum at elementary level. Teachers who keep in mind why they are laying foundations of basic ideas of time exhibit longitudinal coherence and showing responsibility out with their horizontal teaching.
What have I learned?
As I’ve said, the mathematical concept of “time” does direct the world around us in all that we have ever done. I have taken from granted my own ability to tell the time and use it to direct my own day. My new knowledge of how some aspects of time were developed has given me a deeper understanding and confidence for teaching this topic in schools in the future. Connecting the language between topics e.g. quarter past for time, which I taught on placement would have been greatly beneficial to appreciate and understand at the time. Children often think they are learning isolated topics and I’d have said, before delving in to this module, I would agree slightly. Based on, that a lot of mathematics I think I learned is no longer of any use to me. Deciphering and making up my own timetables in school may have been a boring subject but I did not realise the learning and “time” it would have taken me to get to that stage now helps me organise my own day.
What do I want to find out?
Day lights saving is a fairly new concept that was introduced in the last 100 years or so what that’s all I know of the why. It is something that will affect all of us – in the winter we get an extra hour in bed – win! However, understanding why and what happened before this was introduced would be something further to research.
References
Bellos, A. (2010). Alex’s Adventures in Numberland. London. Bloomsbury Publishing Plc.
Ma, L. (2010) ‘Knowing and teaching elementary mathematics’. London: Routledge.
Rogers, L. (2011). A Brief History of Time Measurement. https://nrich.maths.org/6070 (Accessed: 14th November 2016).
