Mathematics 24x7

There is no escape...believe it or not. Mathematics is everywhere.

I have realized that though many students struggle w/ remembering simple concepts in mathematics, simple mnemonic devices often prove to be helpful. Here's a poem which I recently discovered which makes distinguishing between formulas for the area and circumference of a circle much easier:


Tweedle-dee-dum and Tweedle-dee-dee,
Around the circle is pi times 3,
But if the area is declared,
Think of the formula pi "r" squared.

"Around the circle" means circumference.

Aside from some of the classics such as "All Students Take Calculus", "PEMDAS", and Chief"Soh-Cah-Toa" I wonder what other mnemonic devices you use in your classes.

Incidentally, years ago, when teaching order of operations to seventh grade students, I had them create posters using their own mnemonic devices using GPMDAS (Groups ...parentheses, brackets, braces, vinculum...Powers (or exponents)...Multiply OR Divide (whichever comes first in order from left to right)...Add OR Subtract (whichever comes first in order from left to right. To this day, I recall some of these:
General Patton Made Direct Air Strikes
Girls Prefer Magnificent Diamonds and Sapphires
Geepers, Pretend My Dog Ate Snausages

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What about songs?!

......have you heard the circle song?!

This makes me laugh every time I hear it! I once met some students singing it the day I first played it to them in a lesson.

....and at my school everybody knows about the area of a trapezium thanks to a little song!
I found this strategy very useful . Some of mnemonics which are used by my students are ...

1)Pi mnemonics are memory aids for remembering the first few decimal digits of Pi:
3.1415926535897932384626433....
The most common type of mnemonic is the word-length mnemonic in which the number of letters in each word corresponds to a digit. This simple one gives pi to seven decimal places:
How I wish I could calculate pi.
May I have a large container of coffee?
Counting the letters of each word gives you the value of pi to 7 places.
2)Please Excuse My Dear Aunt Sally
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
3) Lucky Cows Drink Milk
The ascending order of Roman numerals: LCDM ...
This is such an old corny one but The Quadratic Formula Song is still around.
http://www.youtube.com/watch?v=TBBBHel5Kdk

There are lots of new tunes and versions of it on You Tube.

Sandra
www.realmathinaminute.com
One of the teachers in my department wrote a much better one! :)
'Somewhere over the 2a'
....sung to the tune of 'Somewhere over the rainbow'

sandra said:
This is such an old corny one but The Quadratic Formula Song is still around.
http://www.youtube.com/watch?v=TBBBHel5Kdk

There are lots of new tunes and versions of it on You Tube.

Sandra
www.realmathinaminute.com
It's silly, but the kids always have trouble with absolute value inequalities - what's "and" and what's "or"? I always tell them to think of "great-OR" to help them remember.

And we do the quadratic formula to the Pop Goes The Weasel tune. :)

Kristen
I would not use a mnemonic for circumference/area, because it's important to understand about lengths of things being proportional to first powers, areas to second, volumes to third and so on. It's cute, though :-)

I use mnemonics for things that do not have any internal math relations to names. One cute mnemonic for a "hard" multiplication fact:
5, 6, 7, 8
56=7*8
(Though it's not very easy to remember, either).

There is a "semi-mnemonic" explanation about order of operations: they go from the strongest to the weakest, mathematically. So powers go before multiplication/division and that before addition/subtraction. It kinda makes conceptual sense.
I feel mnemonics are useful for teaching factual information, but when it comes to the conceptual knowledge it may not be sufficient. A concept have to be developed in the mind of a child.
Instead of PEMDAS we use GEMS - Groupings, Exponents, Mult/Div, Add/Subt.

For integer addition, we sing to the tune of Row, Row, Row Your Boat:

Same Signs add and keep.
Different Signs subtract and
keep the sign of the higher number.
Then it will be exact.

I created a Glog (online interactive poster) for integer addition that you can see here: http://willkimbley.glogster.com/Integer-Addition/

For integer subtraction, we use Keep, Change, Change then follow the rules for addition.

So, for (-5) - (-7) = we perform the following steps

Keep Change Change
-5 - -7
| | |
-5 + 7
then follow the rules for addition, (different signs subtract) so rewrite and solve the problem:
7 - 5 = 2
the sign of the higher number (7) is positive, so the answer is positive 2
In all of this I think we have to remember that we are all different - us and the children we teach.

No doubt that the understanding is the most important but then for some those mnemonics can help them remember things for exams which can be stressful. If a mnemonic helps them then so be it!

I find it is actually useful to discuss how we are going to remember key points with a class when we have completed something. If I ever tell them about some mnemonic I know about we then find out who it helps!
In my experience for any given mnemonic, some will find it helpful whilst it does nothing for others in the same class.
I'm unfamiliar with the circle song (you'll have to share that one), though I do know a song for quadratic formula sung to the tune of "Pop Goes the Weasel." For years...and after my students had learned completing the square method for solving quadratics...we would derive the Quadratic Formula, which my students already knew by heart thanks to their 7th grade teachers having taught them the song version! ...took the wind right out of my sail...every time! *L*

Colleen Young said:
What about songs?!

......have you heard the circle song?!

This makes me laugh every time I hear it! I once met some students singing it the day I first played it to them in a lesson.

....and at my school everybody knows about the area of a trapezium thanks to a little song!
..so very true! I would guess that all of us who teach share your experiences, Colleen.

Colleen Young said:
In all of this I think we have to remember that we are all different - us and the children we teach.

No doubt that the understanding is the most important but then for some those mnemonics can help them remember things for exams which can be stressful. If a mnemonic helps them then so be it!

I find it is actually useful to discuss how we are going to remember key points with a class when we have completed something. If I ever tell them about some mnemonic I know about we then find out who it helps!
In my experience for any given mnemonic, some will find it helpful whilst it does nothing for others in the same class.
I'll share these w/ some of my colleagues at the 6th grade level. I can think of a few who would absolutely LOVE these!...thanks for sharing!

Will Kimbley said:
Instead of PEMDAS we use GEMS - Groupings, Exponents, Mult/Div, Add/Subt.

For integer addition, we sing to the tune of Row, Row, Row Your Boat:

Same Signs add and keep.
Different Signs subtract and
keep the sign of the higher number.
Then it will be exact.

I created a Glog (online interactive poster) for integer addition that you can see here: http://willkimbley.glogster.com/Integer-Addition/

For integer subtraction, we use Keep, Change, Change then follow the rules for addition.

So, for (-5) - (-7) = we perform the following steps

Keep Change Change
-5 - -7
| | |
-5 + 7
then follow the rules for addition, (different signs subtract) so rewrite and solve the problem:
7 - 5 = 2
the sign of the higher number (7) is positive, so the answer is positive 2

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