UPDATE: Amy’s Age: The Big Debate Between Maths and English Teachers

(UPDATE on Aug. 5 with MOE’s confirmation in the last section of the article.)

Never had I been so eager in trying to find out a woman’s age. 

A few days ago, I was posed a question. Tom is 10 years old. Amy is three times older than Tom. How old is Amy?

It seems to be a very simple question but there’s a lot of disagreement in Amy’s age.

There are two camps of thoughts.  The first team thinks Amy must be 30 years old.  Another group says Amy should be 40.  To be absolutely sure, we approached a reporter, a news editor, a scientist, a trader, an English teacher, a Maths tutor and four Maths school teachers.

The six non-Maths teachers unanimously understood that the answer is 30 and the four Maths teachers said the answer is 40.  

It is interesting to see the difference between how the English teacher and news editors think from a linguistic point of view and how the Mathematicians view this from their perspective.

Camp 1: Why 30

The first school of thought thinks “three times older than” is equivalent to “three times as old as” so the way to derive Amy’s age is 10×3.

Many Maths questions on international websites are also in this camp (see examples below).

Camp 2: Why 40

If the question is “Mary is 30 years older than Tom,” the solution is: 10+30=40.

Going by this logic, Mary is “three times older than Tom,” so it is 10+(10×3)=40

Where the Confusion Arises

A professor from Ausberg College says this:

“If B is three times as much as A, then B is two times more than A – not three times more than A. The essential feature is the difference is between ‘as much as’ and ‘more than’. ‘As much as’ indicates a ratio; ‘more than’ indicates a difference. ‘More than ’means ‘added onto the base’.”

For other comparative adjectives, like “times older than”, “times faster than”, “times bigger than”, “times longer than”, the interpretation is less clear cut.

What to do if this happens during the examinations

If it does appear in your examinations, one teacher suggests showing both answers to show your thought process, creativity and critical thinking.

We decided to seek the authority’s view on the matter and wrote an e-mail to the Ministry of Education. Fortunately, MOE confirmed that this is no longer in the current syllabus.

“We do not use such language in our current syllabus,” Ruth Teng, the curriculum planning officer for Maths said in an e-mail reply to our queries on Aug. 5.

It’s great the MOE has acknowledged the amiguity of our question and spared our children such questions. Kudos to them for the wise move and good luck to all of you for future Maths exams. 

This article was written jointly by Wallace and Wei. Wallace is a trader, while Wei is a reporter. We have recently started a Facebook site to help PSLE queries. Like us here http://facebook.com/studyroomjr

 


References:

“more than”

http://web.augsburg.edu/~schield/MiloPapers/984OfSigCompare3.pdf

http://english.stackexchange.com/questions/7894/x-times-as-many-as-or-x-times-more-than

http://english.stackexchange.com/questions/30060/is-four-times-more-grammatically-correct-and-if-so-what-precisely-does-it-m

 “faster than”

http://math.stackexchange.com/questions/12768/what-does-1-13-times-faster-mean

http://www.mathscore.com/math/practice/Work%20Word%20Problems/

http://www.mathisfunforum.com/viewtopic.php?id=18899

http://www.purplemath.com/modules/workprob.htm

“older than”

http://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.104504.html

http://www.hawaii.edu/suremath/k4_12dir/jayMary1.html

https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/old-school-equations/v/age-word-problems-1

http://www.assignmentexpert.com/free-questions/question-on-math-algebra-16970.html

“bigger /greater than”

http://www.astronomynotes.com/mathrev/s1.htm

http://www.mathsisfun.com/place-value.html

http://www.mathsisfun.com/decimals.html

 “longer than”

http://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.231283.html

http://www.chacha.com/question/if-a-rectangular-field-is-5-times-longer-than-it-is-wide-and-the-fields-perimeter-is-540-ft,-what-are-the-dimensions-%28length-and-width%29-of-the-field

http://www.softmath.com/algebra-word-problems/show.php?id=282

http://math.stackexchange.com/questions/311378/algebra-2-completing-the-square-find-the-dimensions

A math test should be a

A math test should be a proper math test, what is the point having a twist or trick of English in math test question. Math questions should PRECISE and straight forward. Student who is poor in Language usually strong in other field such as Math. they should be cultivated instead of penalized in this way. 天生我才必有用。

confirmed

Yes we’ve received confirmation that it’s out of syllabus. However there may be a chance that it may get overlooked so since you’ve read about it here, be prepared for it :).

Indeed PSLE maths sometimes seem more like English comprehension questions. It helps to break down the problem into smaller workable steps. Yes it’s not easy and I’m also feeling the pain of these young kids (and parents!).

confirm its out?

i really hope so…. cos i hate psle math questions which requires students to have a good grasp of english.  My p3 neighbour had come to me once with his math worksheet and is very amused that I could not do a single of his problem sums.  so embarrassed.  by the time i finished reading teh sentence, i forgot what was in the first part of the sentence.  so cheem.  so worried for my kid who is entering p1 next year :-p

huh?

i don’t get camp 2 logic. so glad it is not in syllabus.

Yes!

I’m trained as an engineer and I still think camp 1 should be the correct interpretation!  Camp 1!  Camp 1!

PSLEguru,You have summarized

PSLEguru,

You have summarized our pain. I disagree that camp 2 should prevail! Camp 1! Camp 1! After all maths is for using!  If camp 2 wins, that means all the financial reports and economic outlook reviews need to be rewritten! 

When our children move on to JC economics, what do they write?? 

Kkkekeke... great post.  Now

Kkkekeke… great post.  Now I know why Primary school math is so difficult.  The way the question was framed simply sucked.

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