Which way does it turn
9
Waist band
An elephant
Leave this one to your imagination!
10
Between your knees
Computer
Is it a laptop or desktop?
11
Under your feet
Tree
Stand firm on the branch
How to develop Memory Pegs further
Begin with each peg which then becomes its own body of 10 pegs; you can start to build a memory palace!
Now try this with a theme based on facts or information you really want your group to learn well. Try it out with your shopping list and practise at the supermarket. How about French vocabulary or the planetary system?
By the time you have reached this point you have probably already installed the Memory Pegs in your brain. Speed improves the technique, so act fast and enjoy!
Although there is a vast amount of information stored on computers, machines are infinitesimal compared to your brain. One of the best medical diagnosticians Richard knew could rattle off 5 symptoms and every disorder that fitted would pop into his mind. Then he would go and check them. You could load that into a computer and it would find the disorders connected to the symptoms, but the human brain does it better. This is because the human brain can sort and select for relevancy. When this doctor was in front of a person, he picked up on signals such as smells, breath patterns and skin temperature unconsciously, as well as his knowledge of symptoms.
Think of those people who learned to programme computers 40 years ago. Compilers learned to translate one computer language into another computer language. They don’t even have compilers anymore. If the compilers only learned that one thing, they would all be out of a job now. But their ability to know how that was done meant that they could think about other problems and find solutions. In years to come, all the knowledge taught now may no longer be relevant, but the process of remembering, encoding, decoding and pleasing yourself when you get something right will enable everyone to learn new things.
summary
In this chapter you have learned the key components of a good memory, including how to encode (remember) information so that you can decode (recall) it in a range of ways and contexts. You have explored two strategies for remembering which you can apply and adapt to any subject area for yourself or your students.
references
1. Samuel Johnson: Idler #74 (September 15, 1759)
2. Willis J. MD, 2006,Research-Based Strategies to Ignite Student Learning: Insights from a
Neurologist and Classroom Teacher, ASCD
3. Diamond M. Hopson J., 1998, Maic Trees of the Mind, New York, Dutton
4. Nash J.M., 1997 (February 3) Fertile Minds, Time 48-56
activities
Activity 1
it’s all in the name
Do you have a good strategy for learning names? If not, work through the steps for learning names methodically and thoroughly with a group of 10 people. If you have a great strategy, elicit your own strategy and compare it with the one in this chapter. Which steps are the same and which differ? Remember Caroline, the Teaching Excellence student who learned the names of 200 new students within the first week and had a competition with the students at the end of the week to prove she can do it? The students loved it and felt very special because she remembered their names every time. Can you challenge yourself to do the same?
Activity 2
teach a group memory pegs
Test them first and then record the results after teaching the strategy. Compare their recall on the next test with their previous test. Here is the list to remind you. You can of course vary the body positions to suit your group of learners.
BODY -PEG
ITEM
1
Top of the head
2
Up your nose
3
In your mouth
4
Hanging from
your ears
5
Right shoulder
6
Left Shoulder
7
Right hand palm
8
Left hand palm
9
Waist band
10
Between your knees
11
Under your feet
Tap to download Resources
Extension activity
Do you know someone who has a terrific memory for something special? Elicit their strategy for remembering and try it on for yourself.
This eBook is licensed to Dominic Luzi, [email protected] on 10/18/2018
Chapter 6
How to teach anyone to calculate:
Strategies for Mathematics
TAP THIS TO SEE THE VIDEOS
‘In mathematics you don’t understand things.
You just get used to them.’ (1)
John von Neumann
In this chapter
Developing your ‘Mathematical Mind’
Counting and Skip Counting
Attractive Addition
Sublime Subtraction
One day, we were discussing a strategy a little boy used to prepare for his SATs test in Mathematics. The school Kate had visited was one of the few schools in the UK where all the staff are trained in NLP. The little boy explained to his teacher how he went into his very own maths room in his mind and all the answers to the maths questions were on the walls of this room. His teacher said to the whole class, ‘let’s all have a maths room so maths is easy’ and set about teaching each child how to have a room in their minds too. Richard began to laugh as he explained that when he had elicited the strategy of a genius mathematician some years before, he had discovered that the mathematician had a maths room where all the equations were calculating automatically on the walls. Both this child and the mathematical genius had mathematical minds!
The poor literacy level in the USA and the UK (Chapter 4) are nothing in comparison to the percentage of people who have difficulty with numeracy and mathematics. Up to 40% of people in the UK are functionally innumerate, nearly one in three adults in the USA have only low level numeracy skills, and in some ways, being no good at maths has almost become a badge of honour (2) . Often, the primary emotion associated with mathematics is fear. This is the opposite of the feelings we want to associate with numbers – the feelings of comfort and certainty.
Many people think of maths as complex and difficult. Sadly, the unpleasant feelings that adults have about maths directly affect children. When mothers express to their daughters that they are no good at maths, their daughters’ grades go down(3) . We want to reduce the process to the simplest and easiest way of doing maths, so that everyone feels great about making it simple.
When a group of students complained to their teacher that they couldn’t do maths, the teacher responded by saying ‘that’s OK, neither can I, so I’m going to show you the tricks to get around it’ . He was telling the truth, because the solutions to mathematical problems are processes and procedures which resolve problems or puzzles in the simplest way possible; they are the tricks of the trade!
Learning maths in a sequence and making sure all the pieces are in place will ensure people are confident and enjoy maths. Missing a few steps along the way often leads to the confusion that makes people move away from maths rather than towards the fun of solving puzzles and problems. So to be great at maths and to enjoy learning it’s helpful to begin at the beginning and make sure each stage of learning connects to the next stage, and that the steps at each point are explicit in that they clearly show the learner what to do on the outside and what to do on the inside of their mind.
We want to do even more than this though. We want to create a Mathematical Mind . When you learn to have a mathematical mind, it is full of numbers that are pleasing and comfortable to have in your head. The numbers move by themselves, automatically finding simple and easy solutions and th
e quickest way to find answers to all kinds of problems. A mind that enjoys the magic of maths is filled with numbers and patterns, so that a problem reduces logically to the simplest and easiest level, so maths becomes natural and comfortable.
It may be that you want to teach a small child to begin learning maths, or you want to help an adult to improve and enjoy Mathematics. Either way, the key stages to building a mathematical mind are Counting, Addition, and Subtraction. Later you may want to teach fractions and percentages, or ratio and proportion, or statistics. However, each of these disciplines requires the fundamentals of counting, addition and subtraction, so let’s start with these. Here are some approaches to Mathematics that are based on how the brain works, so you can start to adapt and create your own strategies based on sound neurological principles and NLP.
When we learn to ride a bicycle or a scooter we don’t just learn to ride. We learn to balance, steer, and push with our feet on the pedals. The activity becomes ingrained or encoded. So much so that, even after years of not riding a bike, it comes straight back to you at that magical moment when you sit on the saddle; the foundations are laid in just the right way and with just the right state attached to the learning. We want to encode Mathematics in the same way.
As with other strategies such as reading and spelling, you know that if you are to remember something visually in your mind, it is best if it is big and bold. It is the same with numbers. When children start at school, numbers are made bright, bold and big. As they progress through school, more and more numbers appear on the page, they get smaller and smaller and are usually reduced to black and white. Fortunately, the inside of your mind is not limited in this way. We want the look and feel of numbers to be interesting and engaging. Have a go at this exercise for yourself to discover how you can change the submodalities of numbers so they are pleasing to you. Once you have this experience for yourself, it will be easy to create comfort and fun around numbers for your learners.
Think of a number you are certain about. Look at it in your mind and know it is right. See it in a certain place, a certain size or colour. The bigger it is in your mind, the easier it is to be sure of, so make it at least 20 centimetres tall. Make it just the right size so it feels comfortable. Now move on to another number and do the same thing. Is it a different colour? Is it in a different place? How big is this number? There are only nine numbers plus a zero - so there are not that many to remember and not that many to make every one of them special, developing a great feeling of certainty and comfort with each number.
Whether you are starting to teach little people or helping adults with numeracy, this is a good place to start, because if you are going to fill your head with numbers, it’s a good idea that you enjoy having them inside your mind!
Counting
We have a vast heritage of counting songs and the internet offers endless animated versions of these songs. Songs that count up and count down help to encode the sequence with feelings of fun and laughter, laying the foundations of a mathematical mind filled with number certainty, pleasure and comfort. Do you remember singing ‘1, 2, 3, 4, 5 once I caught a fish alive’ , or ‘10 green bottles hanging on the wall’ , and ‘there were 10 in a bed and the little one said ‘roll over, roll over’ ? Were you singing along as you read those phrases? Combining the internal visual representation of the numbers with the auditory sound of the numbers and the good feelings associated with the activity are the foundations of enjoyable numeracy and magical maths .
The unconscious mind repeats this learning over and over and very quickly encodes the learning. So whatever the age of your learners ensure that you count up and down, not just to 10, but on and on to higher and higher numbers, running the sequence over and over. Unlike the monotony of rote learning, this is best done as fast as possible, so make it a race. The brain learns quickly and the patterns form effectively when it happens all at once. Think of the metaphor of the little books with one picture on each page, which you flip with your thumb to make a little movie. You are encoding numbers in the same way!
Skip Counting
Once a person can add any combination of numbers together and race through them up and down, all the combinations they need become encoded and automated. Counting leads to addition. When someone can add up numbers they can easily learn to subtract, and are ready to learn to multiply and divide.
The next step to learning to add numbers is to count and add at the same time - sometimes called Skip Counting . The more fun the counting game is, the better it feels. Einstein and other great mathematicians paid more attention to how the numbers made them feel than focusing on just the visual images.
Start with sequences that are easy for the learner. Often, small children will find counting in 2s easiest, but older learners and adults will often find 5s and 10s easier. Ask your learners which sequences are easiest for them and remind them of the feelings of certainty and comfort about the numbers they have in their mind before you begin. Beginning with the easiest sequence enhances these feelings, so you can build the belief that all the other sequences are easy too.
Now the game to play here is to see how quickly you can count in sequence. Have a competition to see who can get to 100 or to another specified number first. Your learners may not know all the numbers to start with, so have them write out the sequence in a long list to start with, so they are not burdened with trying to remember the numbers and they have all the information to keep up with the game. Very quickly, the learners will stop using the list as the number sequence becomes easy to remember.
Some people may think this is an odd thing to do, as you are giving the answers to the learner. But remember - we want the learner to have certainty, and this certainty feeling is connected to what will quickly and easily be memorised – the sequence of numbers.
As an example, start with counting-up and down in 2s: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 … all the way to 100 and then count back down again.
Or in 10s:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100 and then count back down again.
Now move to 3s: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 all the way to 102 and back again.
Repeat this with each set of numbers so you have the complete set of sequences up to and including 10s, which will be so easy for your learners now.
Each time the learner succeeds, ensure that you reinforce how easy this is and how fast they are getting. Remind them that the bigger the number they are counting with, the fewer numbers are in the sequence and the less there is to remember; the bigger the numbers, the easier it gets! Whether you use this strategy for yourself or with your learners, the more you repeat this process, the more your unconscious will identify the patterns emerging in your mind.
The wonder of the human brain is its plasticity. Children find this so easy and so much fun. Adults are surrounded by numbers and sequences - phone numbers that just pop into your mind, email addresses, money and change. Just those 10 digits that match your fingers and toes create exquisite patterns in your learner’s mind.
Once you have had fun running each sequence in order, continue to play this game by mixing up the number sequences. For example, do 4s followed by 7s followed by 3s and 5s and 8s etc. It’s not about being able to understand mathematics, but about being able to take the steps to build a more organised and more numbered mind.
These games encode the number sequences so quickly that you will see rapid improvements when you begin to teach addition and subtraction, multiplication and division. These are great games for the car or on school trips and can involve, ‘let’s get to 100 before the next petrol station’ , or ‘can we do the 6s before we get home?’
Moving to addition
Once your learners are confident and comfortable with skip counting, you can move on to a range of skills to make addition fun and easy. You can experiment with these:
double-up
Once your learners can count and skip count, they already have some addition skills. Now they can e
asily move on to how to double up numbers:
Double two: 2+2 is 4
Double six: 6+6 is 12
When they have all the double numbers encoded the next step is easy!
double plus 1
This strategy uses the information they already know and builds on it.
Take 5+6 - the learner already knows 5+5 = 10, so add 1 more and the answer is 11.
Continue with each of the doubles and add one more.
counting-up
The first step is to add two numbers together. Look at the two numbers in the sum and choose the biggest one. So in the sum 4 + 3; the biggest number is 4.
Start with the number 4 and count up the same number of times as the smallest number – in this case 3 times.
4 (count up 3 times): 5 - 6 - 7
Now the learner knows 4 + 3 =7 and 3 + 4 = 7
Move on to bigger numbers such as 8 + 5.
8 is the biggest number, so count up from 8, five times
8 (count up 5 times) 9-10-11-12-13
Now the learner knows 8+5 = 13 and 5+8 = 13
Continue practising with other sums, counting up from the big number by the small number so that all the sequences become familiar. Very soon the learner will automatically remember the sequences and see the patterns in the numbers.
getting to 10
Remind the student of all the nice pictures and feelings they have about the numbers, then begin to use the counting-up strategy to work out all the numbers that make 10. Begin with the biggest ones: 9 +1=10, 8+2 =10, 7+3=10, 6+4=10, 7+3=10, 6+4=10, and look - now 5+5=10 and so does 4+6! So, once they see the pattern they realise they already know the rest! Once your students know ‘getting to 10’, all the other additions become easy with this next game.
Teaching Excellence Page 9