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I'm teaching my 6 year old how to tell the time. She can read analogue clocks comfortably.

We want her to be able to tell the time so when she wakes, if the time is past 6:15 then she is allowed to get up. So I'm trying to help her understand what time is in relation to this time (is it before or after). If I ask her the following questions

  1. Is ten past five before or after quarter past six
  2. Is seven thirty before or after quarter past six

Then she gets them right because (I think) she works the answer out by the hour (in the first example it's 5 which is before 6, in the second example the hour is 7 which is after 6).

The issue I have is if I ask her the following

  1. Is five minutes to six before or after quarter past six

This type of question, where the hour remains at 6, tricks her and she guesses the answer.

A clock with moveable hands does not help as she'll happily spin the clock round a dozen times to show it was after as she's moved the clock hands forward!!

Is there a common way (ideally visual) to teach children this concept?

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Don't use the constructions of "five minutes to six" and "quarter past six", which are tricky and somewhat slang-y. Use the proper terminology of "five fifty-five" and "six fifteen", etc., and the problem should resolve itself. Perhaps later she can add the slang comparisons to her vocabulary.

Historically, there's a reason we got away from naming numbers as in Latin like "one from twenty" (undeviginti, 19) and "two from twenty" (duodeviginti, 18). The comparisons are indeed easier with proper and consistent use of place values; and this also explains decimalization in our own age.

And likewise: The simple linguistic difference in naming numbers in Chinese (standard places: "ten-one, ten-two, ten-three...") versus English (nonstandard places: "eleven, twelve, thirteen...") has been demonstrated to delay counting skills for English-speakers, on average, at young ages.

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Miller, Kevin F., et al. "Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems." Psychological Science 6.1 (1995): 56-60. (Link)

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    $\begingroup$ I was skeptical about this at first, until I read the graphs and information associated with it. I didn't realize "quarter past" was slang either :S Thank you, as soon as I switched to this, it worked fine. Meaning I explained it in the way you suggested yesterday morning and again early afternoon (she loved it, there was lots of sweets for the right answers) and today she is using it! $\endgroup$ – Dave Mar 31 '16 at 7:34
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If she knows how to compare numbers, as you said, then your task is easy. If the hour is the same, then tell her to compare the minutes and if those are also the same then compare the seconds.

With this strategy she will better understand

-how do we compare ?

-Which is the largest amount ?

-Which two numbers are equal ?

and this will also help her for the next standard.

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Since she was getting confused about what was before (quater past 6 or quater to 6) I felt she may not have understood what time is or why we show it on a clock. The approach I took (which definatley helped) was to draw time out on a piece of paper. Something like

5, 5 past 5, 10 past 5, quarter past 5, 20 past 5 etc

This went on for as long as I could (until I ran out of paper). I then explained to my daughter that we couldn't fit any more time on the page so that was a bit rubbish and that since time doesn't stop we would need more paper. It didn't take long for her to realize that that no piece of paper would ever be big enough.

We tried a few other things but came to the same conclusion.

Finally we tried with a piece of string. We put 12 colors on the string, evenly spaced, and numbered them 1 - 12, but we ran out of string so couldn't repeat. I could then show her we could bend (loop) the string to a circle to show it can be represented in a different way.

I then stuck the string on her clock face to show how it matched up with the hours and she then realized why the clock was a circle (this meant preparing the string etc).

This helped to reduce her errors and I'm sure with practice she would have understood but the accepted answer was obviously the best solution.

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