Can We Can Improve the Learning of Mathematics?

There is, I think, sufficient data to indicate that, for both students and teachers, mathematics is the least popular subject in elementary schools, and this has been true since before I entered mathematics education over 40 years ago.

After a life time spent in mathematics education I have come to the conclusion that, despite the improvements in our understanding of how children learn, and new methods of teaching mathematics, students still leave school with a low level of numeracy. To be clear, numeracy is the ability to reason with numbers and other mathematical concepts, and includes number sense, operation sense, computation, measurement, geometry, probability and statistics. Numeracy also requires that students have an intuitive or emotional feel for mathematics that gives them confidence in predicting or calculating answers.

Many people would argue that there is no emotional aspect to mathematics, just obey the rules, get the right answer and move on. However most adults have a strong emotional response to anything related to school mathematics; unfortunately these responses are usually negative!

Intellectually students can deal with everyday calculations (after all, they are rarely without a calculator), but many lack the emotional understanding that gives confidence in predicting and calculating answers.

The problem does not lie directly with the teachers but more with the way we recruit and train potential teachers. We have a self perpetuating cycle; students don’t enjoy mathematics in school, graduate and go to university where they tend to avoid mathematics courses. They enroll in teacher education programs where they may or may not take a course on how to teach mathematics. Even if they do take a course on teaching methods for mathematics it lacks value if the participants have serious gaps in their knowledge and understanding of mathematical concepts. It is like a course on how to coach basketball if you have no knowledge of the game and the skills involved.

The student, totally unprepared to teach mathematics, now enters the teaching profession and the cycle continues.

The dilemma facing educational leaders, politicians, and society in general is figuring where and how to break the cycle.

One possible solution, which could address the problem fairly quickly, would be to have a series of courses addressing both mathematical understanding, and teaching methods for specific topics or strands of the curriculum. On successful completion of each course participants would be given a certificate to say they had been trained in that topic and were qualified to teach that topic. Over time teachers would become fully qualified to teach mathematics.

This, like most solutions to problems in education, would require financial commitment by governments, education authorities, faculties of education, and a time commitment from teachers.

At the same time the mathematics requirements for entry to teacher education programs could be made more stringent to ensure that students entering these programs will have greater mathematical understanding thus ensuring that methods courses in mathematics will be more relevant and useful.

Until we improve the entrance requirements and the qualifications of potential mathematics teachers, mathematics will be poorly taught, too many students will not achieve the numeracy skills necessary to function in today’s society, and the work done by teachers will not be given the respect it deserves.


College and the Mathematics Prodigy – What Career Should You Take?

There are many super up and coming math student in our time, for some reason, perhaps due to increased population, we are discovering more and more anomalies. And yet, we need so many more. It’s great to have the super-stars of humanity and these unbelievable mathematical prodigies, but we are going to need more to run our ever increasing complex and technologically advanced society.

If you are good at math, you should work to excel and see where it leads, as there are excellent jobs and careers available if you go for it. What sorts of jobs could you take? Well, many of the very most important jobs and career paths that our nation relies on include math. For instance; There is a whole lot of math that goes into a Missile Defense Shield system.

Oh speaking of math and careers, why don’t we also mention “Computer Science” as a potential academic choice, if this interests you maybe you should set your sites on a technology school – Virginia Tech, MIT, Cal Tech, Stanford, Carnegie Mellon, they have AI, VR, Robotics, Computer science degrees, perhaps with your name it. Don’t give up on math and science, we need you for America’s future.

If you are gifted in math, or love the subject we need you and you can enjoy a good career in the area of mathematics. Everything in the world we know is made up of math, without it, everything would fall apart. Why not be part of that master plan, and help us use this knowledge to write the next chapter in human evolution. Please consider this.


Remember the Simple Mathematics of Pay Per Click

Some have the PPC experience of a geriatric turtle whilst many are only just starting out with testing PPC campaigns, landing pages, ad-copy, and fine-tuning all of these factors as a means of maximising profit. With this in mind, one thing that never fails to amaze me is the frequency of which I speak to affiliates who have not thought through the raw figures of the campaign they are spending their hard-earned wonga on.

Let me give you an example.

I recently spoke to an affiliate who was using PPC to promote a videogame store on a sales campaign. The store paid out 5% commission and he had been told that the average order value was £26. So, it doesn’t take ‘Arnold Cleverbugger’ to calculate that every successful conversion will be worth, on average £1.30 in commission to him.

Now, videogames retailers have more competition than the Olympic Games, so there is a fair chance that conversion rates (unique visitors/number of sales) wil be no higher than, let’s be really generous, 3%. (TOP TIP: this is the conversion rate to PPC traffic, not other types of traffic that may have higher conversion rates and distort the figures.)

So, following our example, every 100 clicks purchased will yield £3.90 in affiliate commission.It follows then that the affiliate must be buying clicks for less than 3.9p per click to be showing an operating profit.

Can this be done? Possibly, but the affiliate I was speaking to had his maximum bids (all of them, as he hadn’t heard of keyword tracking/identification) set to 10p per click, paying on average 9p per click. So, for every 9p he spent, he would earn, on average, 3.9p.

Now that is a very quick way to fall out of love wth PPC, not to mention your bank manager who wants his pound of flesh and your new lady-friend who has her eye on those new Jimmy Choo footwarmers.

So, the moral is to look at the simple mathematics first and select campaigns from there. Then, with split-testing, accurate tracking, and ongoing optimisation, the rest will follow.

It really is all just very simple mathematics.


On Mathematical Proofs,Problems and Impossibility

Geometric constructions captivate one and all and is one of the areas of mathematics that is highly preferred by a high school student. Although easy to comprehend and fun to do, a few geometric constructions defy completion with a ruler and a compass. This article takes a look at the confusion in the mindset of many people regarding these ‘impossible’ constructions.
The following are the most famous of the impossible constructions with a ruler and a compass:
Trisecting an angle
Doubling the volume of a cube
Constructing a square equal to the area of a circle

A Proof:
What is a proof? For those of you who are wondering about that, here is the definition for a proof:
‘A proof is that which has convinced and now convinces the intelligent reader’ Who is an intelligent reader? In this context, those people who are known to be mathematicians by the society are the intelligent people.
Also a major requirement for a proof is that,a proof should be in complete harmony with another proven fact.

The ‘Impossibilty of a Problem’:
One often confuses the impossibility of a problem with an unsolved problem. A few problems are unsolved, that is, they have not been solved as of yet, whereas some other problems are insoluble,that is, they cannot be solved.The problem is proved to be impossible to solve. There is no question of anyone coming up with a construction for trisecting an angle because it has been proved mathematically that no one can trisect an angle.Whereas if someone were to claim that he/she (no discrimination) has found a proof of the Riemann’s hypothesis or the Goldbach Conjecture ( famous problems that have not yet been solved but have not been proved to be impossible either), mathematicians shall look into the claim. However for those of you who are itching for a claim to fame by solving one of the unsolved problems, let me remind you the path to success is not a bed of roses.


Easy and Fun Mathematics Or Why Can’t You Do Math in Your Head?

How many times have you been cheated simply because you did not had time to calculate the sum of what you bought? How many times have you trusted the seller but got cheated?

How many times have you suffered and felt shame just because you could never understand all the romance behind the numbers? If none, congratulations – you are a lucky person. If several or many times, welcome to the club! – you must know that there is a cure, actually more than one.

A traditional, but a difficult method – you could simply study all the mathematic books again. Does not sound lucrative? Not, I agree! That’s why I would like to share with you The Easy Way out of this problem. This is especially important nowadays when each cent counts.

Knowing these simple secrets you will be able to calculate faster in your head than most of us with a calculator. Wouldn’t that be exciting? Many people, just like you and, me have taught these important but extremely simple math secrets and they are shocked and keep asking themselves: “Why no one taught me this when I went to school? Why were I not given these amazing tools?” I like to compare it this way – you were taught to walk up the street backwards, now it’s time to walk forwards.

If you are going in school now – this is your shortcut to Fast Math calculations giving you an advantage over the others.If you are an adult – missing these simple secrets is the reason why you can be easily cheated.

The secret of Fast and Easy Mathematics was rediscovered after 3000 years !!! Todays methods taught at school are not simple, in fact they are blocking your potential not releasing it.

How simple is this multiplication 43 by 38? Do you need a calculator? Wrong – all you need is simple knowledge and you will be able to multiply these and other number faster that you could type them on your calculator. What about adding and subtracting fractions in seconds? All those tests what they give to pupils at school are just taking them further and further away from the simplest truth there is – mathematics is simple if you have the right tools.