Teaching in Harmony wrote on Mathematics24x7
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
Replies...
Collen 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!
Some mnemonics shared by me...
I find 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 ...
Sandra (www.realmathinaminute.com ) said...
This is such an old corny one but The Quadratic Formula Song is still around.
There are lots of new tunes and versions of it on You Tube.
Kristen Fouss said...
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. :)
Maria D said...
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.
Sharad sure said...
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.
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
Collen 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.
Teaching in Harmony said...
I don't think a mnemonic is particularly useful for teaching conceptual knowledge. It is, as its name implies, a memory device only. Keeping Bloom's taxonomy in mind, I always tell my students, "Memorization is the easiest form of learning." Given the choice between memorizing Quadratic Formula, or recognizing and applying its applications, I believe the latter has greater significance.
Sandra said...
I like the mnemonics as an additional teaching/learning tool. Sometimes when a student says, "Move this up and this down" and they have no idea what they are doing, I groan inside....however it does allow a weak student to continue and perhaps reach a point that does make sense conceptually to him. When I teach a student who strugges greatly with math, I appreciate anything that helps him move forward....even if it causes me to groan silently!
A student once told me that you couldn't divide by zero because if you put the eggs in the bottom of the grocery bag they would break. It was okay to have the eggs on top. He would always get this correct but thought it was all about eggs......groan....
Anirban said...
While I was a stuudent in class-3,I remember the mnemonic BODMAS (Big Old Dot Made A Shot ) while approaching Simplification sums to remember the seuence of function from left to right.
BODMAS -----> Bracket, Open, Division, Multplication,Addition, Subtraction.
Girishkumar said...
There is one to remember the conversion
King (Km)
Hitler (Hecto metre)
Died in (Deca metre)
Mumbai ( Metre)
Due to ( Decimetre)
Cholera and ( Centimetre)
Malaria (Milimetre)
Teaching in Harmony said...
I know EXACTLY what you mean, Sandra! *L* ...it's just another tool, though for me, teaching so that students truly understand the concept is most important! I have a friend who teaches students that the "sun shines ABOVE the horizon" and not "below the horizon" to show that division by zero is undefined! *shaking my head* In my geometry classes, I have reserted to pointing out the "SOS" in the word "iSOSceles" to show that help (SOS) is here to show that two Sides are congruent, the two l's in the word parallel to show 'two sides parallel," etc. ....so many others come to mind now that I am facing the beginning of another school year...and am once again in teaching mode!
Lim Ee Hai said...
I believe this form of teaching using songs, poem or otherwise is to trigger the left and right brain similar to mind mapping concept. We can always use or try whatever methods that the students can accept as long as they like them and enjoy them. It is indiectly reducing the anxiety for those facing problem in math. Triggering all senses is the objective, if possible.
But I like this method of poem to excite the students.
Teaching in Harmony said...
I have always told my students that the more they inolve their senses in learning, the easier it becomes....definitely thinking VAKT (visual, auditory, kinesthetic, and tactile) on this one!
Jerry said...
For the trig formulas sin(x+y) and cos(x+y) we had a cheer:
SINE COSINE, COSINE SINE
COSINE COSINE, SIGN SINE SINE
What do you think about mnemonic devices?
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
Replies...
Collen 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!
Some mnemonics shared by me...
I find 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 ...
Sandra (www.realmathinaminute.com ) said...
This is such an old corny one but The Quadratic Formula Song is still around.
There are lots of new tunes and versions of it on You Tube.
Kristen Fouss said...
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. :)
Maria D said...
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.
Sharad sure said...
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.
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
Collen 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.
Teaching in Harmony said...
I don't think a mnemonic is particularly useful for teaching conceptual knowledge. It is, as its name implies, a memory device only. Keeping Bloom's taxonomy in mind, I always tell my students, "Memorization is the easiest form of learning." Given the choice between memorizing Quadratic Formula, or recognizing and applying its applications, I believe the latter has greater significance.
Sandra said...
I like the mnemonics as an additional teaching/learning tool. Sometimes when a student says, "Move this up and this down" and they have no idea what they are doing, I groan inside....however it does allow a weak student to continue and perhaps reach a point that does make sense conceptually to him. When I teach a student who strugges greatly with math, I appreciate anything that helps him move forward....even if it causes me to groan silently!
A student once told me that you couldn't divide by zero because if you put the eggs in the bottom of the grocery bag they would break. It was okay to have the eggs on top. He would always get this correct but thought it was all about eggs......groan....
Anirban said...
While I was a stuudent in class-3,I remember the mnemonic BODMAS (Big Old Dot Made A Shot ) while approaching Simplification sums to remember the seuence of function from left to right.
BODMAS -----> Bracket, Open, Division, Multplication,Addition, Subtraction.
Girishkumar said...
There is one to remember the conversion
King (Km)
Hitler (Hecto metre)
Died in (Deca metre)
Mumbai ( Metre)
Due to ( Decimetre)
Cholera and ( Centimetre)
Malaria (Milimetre)
Teaching in Harmony said...
I know EXACTLY what you mean, Sandra! *L* ...it's just another tool, though for me, teaching so that students truly understand the concept is most important! I have a friend who teaches students that the "sun shines ABOVE the horizon" and not "below the horizon" to show that division by zero is undefined! *shaking my head* In my geometry classes, I have reserted to pointing out the "SOS" in the word "iSOSceles" to show that help (SOS) is here to show that two Sides are congruent, the two l's in the word parallel to show 'two sides parallel," etc. ....so many others come to mind now that I am facing the beginning of another school year...and am once again in teaching mode!
Lim Ee Hai said...
I believe this form of teaching using songs, poem or otherwise is to trigger the left and right brain similar to mind mapping concept. We can always use or try whatever methods that the students can accept as long as they like them and enjoy them. It is indiectly reducing the anxiety for those facing problem in math. Triggering all senses is the objective, if possible.
But I like this method of poem to excite the students.
Teaching in Harmony said...
I have always told my students that the more they inolve their senses in learning, the easier it becomes....definitely thinking VAKT (visual, auditory, kinesthetic, and tactile) on this one!
Jerry said...
For the trig formulas sin(x+y) and cos(x+y) we had a cheer:
SINE COSINE, COSINE SINE
COSINE COSINE, SIGN SINE SINE
What do you think about mnemonic devices?
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