I also am not talking about them as tools for formally teaching about angle quantification. I’m saying that, even as a way to play around with and become familiar with angular properties, they’re not a tool I’d use: telling time on an analog clock does not focus the brain on angles. It’s the tips of the hands, not the angle they make, that’s important. The angle of the hands is barely more relevant than the circular shape of the clock itself.
It’s true that, to some degree, elapsed time involves angles; but analog clocks aren’t great tools for that, since the angle involved in elapsed time problems involves two sets of imaginary clock hands, and ignores the existing angle between the existing clock hands.
I may be misunderstanding what you’re meaning here. It sounds like you’re saying something about how, say, the right angle formed at 3:00 is somehow conducive to building some sort of understanding of angle orientation and quantity, as is the 30-degree angle formed at 1:00.
Is that right? If so, can you explain how it’d build understanding of orientation and/or quantity? If not, can you explain what you mean?
I mean, yes–but so are toy bulldozers and kitchens. That doesn’t translate to kids knowing how to cook or operate heavy machinery. Clocks make good toys because they’re a familiar object with moveable parts, and as preschoolers learn to count they can point at the numbers and say them, and the occasional precocious kid can learn some basic time-telling on them. I’ve worked with a few kids that come to kindergarten knowing their times tables and triple-digit addition and subtraction, and one kid who could glance at a pile of 28 blocks and know instantly how many there were; but I’ve never worked with a kid who entered kindergarten able to read an analog clock.
Nope, I’m talking about something much more basic than that. Not that children consciously use the specific angles formed by analog clock hands to articulate particular quantitative properties of angles. But that constantly seeing the rotational sweep of the clock hands through growing angles correlated with measured passing time gives them a much more embodied and built-in awareness of the basic physical geometry of angle, rotation and orientation. As @puzzlegal put it, “visceral”.
(I also think that part of the confusion may stem from the fact that you seem really focused on the concept of the angle between the clock hands at some given time, whereas what I’m thinking about is more the angular rotation of a clock hand with respect to the axis. “Starting from the top of the clock, how far round the circle have we got?” That sort of thing, not “what is the angle between the hour hand and the minute hand?” And again, to forestall objections that that’s not how you’d teach children to explicitly articulate the related concepts, I’m talking instead about reinforcing physical intuition.)
I acknowledge, though, that the adverb “constantly” is an important part of that sentence. If children’s cognition about angles, rotation, orientation etc. is all being derived just from the artificial and limited environment of school instruction, then yeah, playing with polygons may well be a more effective use of their time than trying to decipher an analog clock.
I think the key thing is the understanding that as time passes, the hand (either one, the useful one depends on the amount of time) moves a distance, and makes a larger angle with where it used to be. And that yes, you need to understand how the clock hands represent time for this to be effective.
(And fwiw, i entered kindergarten knowing how to read an amazing clock, but not knowing my times tables, nor how to add more than one digit numbers.)
I don’t think the angle between the clock hands is of any special interest, unless you want to know what time it is. It’s how they move and mapping time to space, and mapping distance to angles that are interesting and generally useful concepts. I think that builds the foundation for reading and creating graphs, for instance.
I think the ability to actually decode the visual impressions of position, number, rotation that the clock face shows is helpful for learning, yes. Again, though, the extent to which it reinforces learning depends a whole lot on how much a child is actually doing it.
If a child’s hardly ever seeing a clock face, and never needs to try to figure out any information from a clock face, then it’s not clear to me that being taught the clock decoding techniques will contribute anything to developing this visceral understanding that I’m bemoaning the possible loss of.
Is there anything these days that kids do routinely look at that gives them that sort of embodied sense of rotation orientation and position?
Yes, that was supposed to say “analog”. But i did have a wooden jigsaw puzzle of a clock, with a piece for each hour, showing things a child might be doing or seeing at that hour (some of the bedtime hours were things like a moon) and clock hands i could move. That was pretty cool, if not actually amazing. It might have been instrumental in my learning to tell time early.
As a surveyor and genealogist, the vast majority of source documents I need to refer to are written in cursive. While many of them have been digitized as images, it is unlikely in the extreme that more than a fraction will ever be transcribed into searchable meaningful text.
But do I trust them? Beside, I enjoy the challenge of puzzling out Swedish parish records written with nearly frozen ink by candlelight in 1750. On the other hand, some of the local deeds here in Providence, RI were written in a fine clerkly copperplate hand, even though the books have been roof-leaked on in the archives since. On the gripping hand, many of those clerks and clergy apparently had their handwriting enhanced by a wee dram or two of a Friday afternoon.
Hey, if the big hand is the hour, and the little hand is for minutes, is the sweep second the gripping hand?
I had one of those reversed clocks for a while. I hung it in the bathroom, across from the mirror, so that when I was getting ready in the morning I would know the time.
Minor nitpick: In the old days, when asked what time it was with analog hands showing, e.g. 2:56,
the reply would be “about three” or even just “three o’clock.” Nowadays, with digital clock, a youngster’s reply is often “two something” or just “two.”
When I was a wee lad in the early 1970s, my uncle and aunt had a jewellery store. One Christmas they gave me a Fisher-Price clock face toy, so I could learn to read the time. A few months later, on my birthday, they gave me an actual watch, a Cardinal, dark red dial with while hands, really nice. I started crying because I hadn’t yet learned how to read the time from the toy.
Maybe so, but I think they should. Both metric and English measurements are used daily, all around the world. If you don’t at least have a passing knowledge of both, you are severely restricted in how you can treat the world. Reducing that severity should be the goal of all educational systems.
It’s how they move and mapping time to space, and mapping distance to angles that are interesting and generally useful concepts. I think that builds the foundation for reading and creating graphs, for instance.