Number sense learning at schools (1 Viewer)

[oasfree]

I can see that Australian math exercises tend to lack certain emphasis that I see in the US past papers. Number sense is an area that I see the Americans and Singaporeans putting a lot of focus on. It makes perfect sense to do this. Excellent number sense allows kids to become good mathematicians in the most practical way.

I'd like to get your guys to share your experience about your time in primary schools and early years in HS on this area.

American tests often has questions like

How many tens do you have in 526?
How many tenths do you have in 27?
How many more hundreds 1.2 has over 1.04?
What's the value of 53 in 653478?

Then they give questions for kids to work on decimal numbers but they intended for the kids to use number sense, not algorithms to solve. They don't intend to give you time and working paper. For example, if one shirt costs $3.19, you pay for 3 shirts by $20 bill, what's the change? They then give multiple choices to pick.

They do not intend that you use algorithm to multiply 3.19 by 3 then take that away from $20.00. This way is too slow. You waste much time and cannot complete the long test and try to get a near perfect score. By having great number sense, you will get the problem solved in seconds. By approximating 3.19 x 3 as 3.20 x 3, you can do quick mental math to work out 9.6 then looking at $20, you know the answer is just above $10. So you can pick the answer within few seconds leaving time for much tougher questions along the way.

By teaching this kind of things to very young kids at primary schools, they intend for kids to get a great number sense. This stimulates the young minds to develop the nerve fibre needed for rapid mental calculations.

I don't seem to see this happening at Australian primary schools. In year 4, my own kid told me that the teacher gave a tough test at end of the year before writing up reports. My kid was asked by the teacher to help checking and grading the scores. Most kids got between 15%-30%. Only a few got over 50%. My kid scored about 30% above the runner up! This gap is unacceptable because I think my kid is about average level if I compare with Singaporean tests.

Any comments?

 

[Dumsum]

The state of mathematics (and education in general) at primary and secondary levels in this country is abysmal at best. I blame the advent of calculators. Australians in their approach to making things as simple as possible without regard for consequence, in this case mental agility, have allowed calculators to dominate. In primary school I used to be ace with numbers -- each friday morning we'd have a "multiplication grid competition" where the teacher would read out numbers randomly from 1 to 15 across the top and same for the side, then the first to complete all 225 multiplications would win a prize. Most often I'd take this out, and I owed it to my parents who would always be teaching and challenging me with arithmetic problems.

These days I am guilty of falling into "calculator hell" -- quickly reaching for the calculator to solve any basic arithmetic. Studying tertiary mathematics has taught me that mathematics is obviously much more than all this, but my trains of thought on problems are often interrupted whenever numbers pop up, which is not ideal.

Let it be said that calculators have no place in mathematics.

 

[Trebla]

Oh god, another thread criticising the education of maths....

I'm pretty sure they do teach this 'number sense' at school or somewhere. I know I had to draw upon it in the non-calculator section of the SC exam.

Anyways, these days there are computers and calculators. Real mathematicians don't always have to be number crunchers (that's what accountants do lol ) and even then they have computer software to perform most numerical calculations for them...

 

[oasfree]

Oh god, another thread criticising the education of maths....

I'm pretty sure they do teach this 'number sense' at school or somewhere. I know I had to draw upon it in the non-calculator section of the SC exam.

Anyways, these days there are computers and calculators. Real mathematicians don't always have to be number crunchers (that's what accountants do lol ) and even then they have computer software to perform most numerical calculations for them...

You miss the point. It's about exercising the kids' mind to develop number sense. This development is vital because the young minds are like computers that need the programming. IN early years, this early programming actually develop the brain physically to adapt and compute. Musicians have to learn since 5-6 years old or younger even because of this. They all have a bigger brain because of music training. And they also become very good at mathematics too. If this is not developed early, kids actually lose the ability to do well in mathematics later.

I see that the US tests show a heavy emphasis on this metal math. But the tests here look very soft in this area. Only enrichment materials on the market seem to have some (but still weak).

 

[LordPc]

id have to agree, not just with number sense, but with the mathematical levels in australia as a whole. I've been told stories of children from overseas countries like India who are mathematically years ahead of us, eg, they are learning algebra and calculus a few years before ours kids do.

I did 5.3 (the advanced level) maths from 7-10 and was kind of suprised in year 12 when things that I had learnt in year 9 were being taught in the General maths syllabus for the HSC. really basic stuff like areas. Things I had nearly mastered years ago were being taught to my friends who did not do advanced math in years 7-10

Its really quite remarkable

 

[Templar]

Anyways, these days there are computers and calculators. Real mathematicians don't always have to be number crunchers (that's what accountants do lol ) and even then they have computer software to perform most numerical calculations for them...

I haven't seen numbers in maths for quite a while now. Certainly not much calculation type questions at all.

After all, most of maths isn't about solving some equation with specific numerical parameters. If software can be used as an aid to speed up numerical calculation, then so be it. Unfortunately, many school kids use calculators without understanding how it all works, and that has potential problems (eg telling a kid )

 

[shaon0]

I can see that Australian math exercises tend to lack certain emphasis that I see in the US past papers. Number sense is an area that I see the Americans and Singaporeans putting a lot of focus on. It makes perfect sense to do this. Excellent number sense allows kids to become good mathematicians in the most practical way.

I'd like to get your guys to share your experience about your time in primary schools and early years in HS on this area.

American tests often has questions like

How many tens do you have in 526?
How many tenths do you have in 27?
How many more hundreds 1.2 has over 1.04?
What's the value of 53 in 653478?

Then they give questions for kids to work on decimal numbers but they intended for the kids to use number sense, not algorithms to solve. They don't intend to give you time and working paper. For example, if one shirt costs $3.19, you pay for 3 shirts by $20 bill, what's the change? They then give multiple choices to pick.

They do not intend that you use algorithm to multiply 3.19 by 3 then take that away from $20.00. This way is too slow. You waste much time and cannot complete the long test and try to get a near perfect score. By having great number sense, you will get the problem solved in seconds. By approximating 3.19 x 3 as 3.20 x 3, you can do quick mental math to work out 9.6 then looking at $20, you know the answer is just above $10. So you can pick the answer within few seconds leaving time for much tougher questions along the way.

By teaching this kind of things to very young kids at primary schools, they intend for kids to get a great number sense. This stimulates the young minds to develop the nerve fibre needed for rapid mental calculations.

I don't seem to see this happening at Australian primary schools. In year 4, my own kid told me that the teacher gave a tough test at end of the year before writing up reports. My kid was asked by the teacher to help checking and grading the scores. Most kids got between 15%-30%. Only a few got over 50%. My kid scored about 30% above the runner up! This gap is unacceptable because I think my kid is about average level if I compare with Singaporean tests.

Any comments?

Calculating numbers isn't what makes good mathematicians. It's how one solves a problem. Merely doing arithmetic isn't good.

 

[oasfree]

Oas, alot of the stuff you've listed is actually in the syllabus for stages 2-3.

Correct, but not taught at most primary schools in Australia. The issue is that primary school teachers have to do programming for themselves. If they don't put it in, kids won't learn. This is different from parts of the US and Japan and Singapore where they still use some official textbooks, and that force their teachers to cover.

 

[oasfree]

oasfree - who are you/where did you come from and what do you hope to get out of these threads?

Nothing really, just understanding differences between teaching philosophies and why Aussie kids are not doing great in mathematics. In fact the only reason why selective schools are full of kids from Asian heritage is because these kids do hard math at similar levels to where their parents came from.

 

[oasfree]

Calculating numbers isn't what makes good mathematicians. It's how one solves a problem. Merely doing arithmetic isn't good.

Again you miss my point about the natural development of the young minds. The minds of young kids aren't static. They change each day. Without the constant stimulation to force the brain to adapt, it won't develop certain ability. The ability to "sense" is vital for the creation of geniuses. The reason why we have so many students who only push formulas nowadays is due to lack of "sense". Number sense is a lot more than just mere calculation. It's the ability to group numbers by their properties, the ability to place numbers into the right groups, ... it helps to naturally cut through unnecessary workload saving the brain power for the kind of work that will need hard thinking.

As a practical example, a student wil great number sense will be able to maintain momentum in a long 2 hour math test. But the one without it will be burnt out with the calculations and fail to perform at the end when the problems require more thinking. In financial dealing, a person with great number sense will be able to wheel-and-deal while talking, but others will have to reach for a calculator. Having a good number sense gives people a great advantage in everyday's life. It may even save your life when you decide to cross a highway.

It was such a silly thing when Reagans' aides during the "Starwar" project in the USA failed completely in number sense. After spedning billions, these people were shown the results. At a University they were shown a laser gun shooting a metal pot. Then a University researcher said "We have got to the power 2^10, we need to get the power level to 2^20 to shoot down an airplane". The politicians replied "Oh, my God. You have got half way! We are so pleased". These idiots did not realise that 2^11 is the double of 2^10. They have no number sense at all. And they were leaders in the world's most powerful country.