And why does your child need it?
In a general way, Number Sense is being able to play with numbers. Play is pleasure, so if you have Number Sense, you are sure to enjoy Mathematics.
You gain Number Sense through experience, experimentation, discovery – in a word, adventure. The teacher, the parent, the mentor is there to guide, not to inflict dogma upon the learner.
In the past, many people’s Number Sense remained undeveloped. It was like a seed in the dark earth that did not have enough energy to sprout through to the beauteous sunlight.
In the past, mathematics was taught in an authoritarian manner. This meant that facts, facts, facts, had to be drummed into the child. The possibility that a child could be shown why said facts were interesting, indeed, thrilling, did not occur to the curriculum-makers. For the child was not a subject whose curiosity and awe and sense of personal power should be sparked. Rather, the child was an object upon which must be imposed strict, lacklustre facts and moth-eaten algorithms.
I remember as an eight-year-old calculating miles per gallon. I was a bit young to get my licence at that point! It did not occur to text-book composers that arithmetic lessons should be designed to be useful, to be relevant to the child’s experience. This would have made the lessons meaningful. The problem is, when learning is meaningless, none of us takes in very much, no matter what age we are. Passive learning is boring to the point of tears. Passive learning requires constant assessment. Active learning requires very little assessment because the teacher knows exactly where each student is. This is because rather than requiring 90% pencil-and-paper tasks, or 85% onscreen work, active learning involves the following socially dynamic self-expression of a student: discovery, discussion, argument, proving, team collaboration, experimenting with different strategies, getting things wrong and discussing why, building with a variety of math tools and construct systems, drawing visual representations, teaching peers, presentation, videoing, and application to a real child's experience.
In this way, every child gains a solid Number Sense. Did you know that Number Sense makes math a whole lot easier? In the old way, a student obeys instructions rigidly. Rigid calculations can be laborious. With Number Sense, thinking is fluid and flexible. Let me give you an example:
Your 2 invoices say you have spent $97 and then $16. Do you have enough money to pay them?
Now, we could grab a pencil and make an algorithm: $97.00
+ $16.00
But oh dear, what if you were in a restaurant and had to do it quickly in your head? 97 + 16
You could take 3 from the 16 to make the first number 100. To the 100, add the number left over, which is 13. The answer is $113.00 You have just decomposed the number 16! And you have recomposed the number 97! Is the calculation less formidable now? Simples.
Computation has become suddenly easier. You have not ‘learned’ more in the formal sense. You have not memorized a number fact, no way, José! You have merely seen numbers differently. An analogy of this difference is the Japanese concept of ma: 間
Ma tells us to look at the negative space and then we may think differently. You can see what I mean by this image:
In Sydney Math, from their youngest years, children are taught to see numbers in such a way that they can decompose numbers and compose new numbers not only with ease, but with glee! That is what you did above – you decomposed the second number to make a first number that was much easier to work with (100) and then you only had to look and see that the second number was now 13, and add. Or, if we put 97 + 16 in terms of the ma 間, what happened is that you saw that the number 97 had a negative space of 3. If that was filled in, you would be able work with the number 100 as easy as pie. What you had left was 13, and swiftly, you knew the answer: $113.00 Imagine if you regularly decomposed and recomposed numbers. How natural your mental computation would become! How pleased you would secretly feel with yourself!
After running a ‘joust’ in Sydney Math class, we sometimes take a 3-minute break with the 8-year-olds to dance out our happiness - to music such as Abba’s Dancing Queen.
When we do subitizing (the skill of recognizing numbers within one second, without counting them) with pre-schoolers, we ask the child to notice not only how many, but sometimes, how many are missing? We use the word ma, and often children are in the mood to paint the Japanese character 間. This is the first step in teaching children to think about and to see numbers flexibly.
I will quote the brilliant UK professor, Jo Boaler, to drive home how crucial is the need for Number Sense (The Elephant in the Classroom, Jo Boaler, 2015, Souvenir Press, UK, page 135):
“What we learn from research is that the high achieving students don’t just know more but they work in very different ways – and critically, they engage in flexible thinking when they work with numbers, decomposing and recomposing numbers.
The researchers drew two important conclusions from their findings. One was that low achievers are often thought of as slow learners, when in fact they are not learning the same things slowly, they are learning a different mathematics. The second is that the mathematics that low achievers are learning is a more difficult subject.”
What is Number Sense? Number Sense is the ability to be flexible with numbers. It is the ability to see the relationships between numbers, and to be eager to discover new ways of manipulating these relationships in order to make math easier and exciting.
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