Clocking On

A few years ago I was in the school office when a Grade 12 student (whom I knew as being bright) came in and asked what time her exam began. I told her 12:30 and she replied "What time is it now?" I pointed to the analogue clock behind me (it was 11:45). She paused, then confessed, "I don't know how to tell the time".
I have heard the argument that kids these days don't need to tell the time using analogue clocks as everything is now digital but I would wholeheartedly disagree with this. In fact, I believe that if students don't learn how to read an analogue clock, then they are at a disadvantage mathematically. Being able to read analogue clocks allows students to use, develop and practice so many math skills:

Estimating ("It's about two o'clock", "It's about ten to two.")

Skip Counting ("It's (5, 10, 15) 20 to three.")

Non-standard skip-counting ("It's (5, 10, 15, 20, 21, 22) 23 minutes past four.")

Fractions ("I can see two quarter hours are the same as a half hour.")

Decomposition ("15 minutes to is the same as 45 minutes past.")

Angles (Since angles measure turn, we can see the hands of the clock continually forming angles. When is the time an acute angle? An obtuse angle?)

All of this is fantastic for developing number sense and my view is that you cannot get anywhere close to this only by reading the digits off a digital clock.

I also feel though that analogue clocks (with their built in spatial nature) are far superior than digital clocks in getting students to understand what time is. They help students see the cyclical nature of time more clearly (something which will be important when they are working with elapsed time.)

The best sort of clocks for students to learn with are geared such that the hour hand moves with the minute hand. They might cost more than cardboard versions but the learning is much better. I also look for clocks that have clear numerals on the face: I often tell parents that they should buy analogue watches for their kids that have all the numbers 1 to 12 and not Roman numerals. I also recommend the Feel Clock app (available at itunes) because it has a very clear display and animates the background to emphasise the difference between a.m. and p.m.  

If students have access to these then they can also attempt problems like this one:

I can see a clock. The two hands are nearly touching but not on top of each other. What could the time be?

I tried this in a Grade 4 class recently. Initially it was interesting seeing how many kids tried to draw their solutions. This does beg the question: why do we get students to draw clocks? It is a tricky thing to do accurately (especially for times other than the o'clocks and half-pasts) and it is not a skill needed in real life. In the time it takes for a child to draw a given time on a piece of paper, I reckon another child could show at least four different times on Feel Clock. Anyway, one student realised that they could use the analogue clocks and before long, all groups were doing so: it allowed them to tackle the problem far more effectively.

Notice how the students have recorded their times digitally: they do need to know how digital times work as this is how time is often shown. In fact, this group saw a pattern in their first three solutions which they used to predict their next six.

Extensions of his question could be:

What times are the hands at right angles?

How many times a day do the hands form a straight line?