How to Participate in Mathematics Competitions in Primary Schools

Taking part in a mathematics competition allows students to sharpen their problem solving skills and serves to generate interest for mathematics amongst them. Annually,there are various mathematics olympiads which primary school students can participate in and some of the more prominient ones are listed in this article.

The Asia Pacific Mathematical Olympiad for Primary Schools 2009 (APMOPS 2009) is organised annually in April -May by the Hwa Chong Institution-Aphelion Consortium. There are two rounds to this mathematics competition for 6th graders.

The first round of the competition is usually held in April and is conducted across the different centres across the Asia-Pacific region. The contest held in Singapore is commonly known as Singapore Mathematical Olympiad for Primary Schools (SMOPS).

Awards for SMOPS
Students compete for the following awards in the SMOPS.

1) Top 10 individual prizes, awarded to the top 10 scorers.
2) 3 Honourable Mention Team Awards and 5 Honourable Mention Individual Awards.
3) Top 3 school awards, given to the three schools with the highest combined score of its top three students.

In addition, students who are ranked amongst the top 10% or top two hundred participants(whichever is lower) will be invited to write the second round of the contest known as the Asia-Pacific Mathematical Olympiad (APMOPS) 2009. This year’s contest was held on a Saturday, 30 May 09.

During APMOPS, students get the opportunity to interact with other mathematically talented students from the various countries. They also compete for the forty individual prizes which will be given out on afternoon of 30 May 09.

Format of the APMOPS Contest
The APMOPS contest challenges students to complete six questions within two hours.
No mathematical tables or calculators are allowed for the contest. Students have to show all the workings for each question. Each question carries 10 marks and the total score is 60 marks.

National Mathematical Olympiad of Singapore (NMOS)
The NMOS is a competition organised by the NUS High School of Mathematics and Science. This competition is designed to spur interest amongst students for mathematics. This competition is usually held in the months of July-August and welcomes students in Primary 5 and below to participate to challenge their mettle with other mathletes. Various awards are given to students who managed to achieve quality scores in competition. Usually the registration begins in May of every year.

American Mathematics Contest 8(AMC 8)
The American Mathematics Contest 8 is the first of a series of mathematics competitions organised by the Mathematical Association of America and is administered by Maths Oasis Pte Ltd in Singapore. This International competition welcomes students who are interested in mathematics and enrolled in grades 8 or Secondary 2 and below to participate.

Students get to challenge themselves with mathematics that is beyond what they usually encounter in school and they can experience a wide spectrum of topics available in Middle School Mathematics. The multiple-choice format of this competition makes it attemptable by many students. Students need to complete 25 questions within a forty-minute period and there is no penalty for wrong answers.

Annually, more than a hundred thousand students participate in the AMC 8 contest.High scoring students in this contest can look forward to challenge themselves in higher levels contest such as the AMC 10. AMC 12 or American Invitationa lMathematics Examiniations. These are the various mathematics competitions and olympiads students in Singapore can participate in annually from the primary school levels onwards

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Learning Mathematics by Heart – A Questionable Approach

Have you ever tried learning mathematics by heart or memorizing a large amount of mathematical information? Though the course of action is tough-going, the outcome may be good and even fabulous. This approach of learning by heart may suit basic mathematics education or knowledge-based subjects, for example, history. However, does this approach suits learning at a higher level of education?

As mentioned, when the mathematics education is at elementary level, the amount of facts to grasp with may not be large enough to warrant attention and concern. With the good results that it sometimes shows, the approach of learning by heart can even be accepted. But is that the correct or suitable way forward in mathematics education? For mathematics learning at the higher education level, given more complex concepts and mathematical expressions, memorizing information and numerous steps become a challenging chore. The performance of many students of mathematics, who practiced the learning-by-heart method, has been known to suffer drastically. This causes them to fear mathematics lessons and led them into the undesirable mathematics anxiety situation. Their confidence over solving mathematics questions declined as a result. Mathematics at a higher level calls for a mixture of mathematical solving tools and detailed analysis of the solving strategy. Selection of a suitable tools and its associated strategy to solving a given mathematics question cannot be accomplished through memorizing as the combination is too wide to cover. Learning at that education level, therefore, takes on a different platform.

A better platform to learning mathematics is to understand mathematical concepts as opposed to placing facts as the focal point. Learn and focus on the why of the solving approach instead of the how, although both complement each other. This is a generic approach whereby practice can start from day one of mathematics lesson. The habit formed to understand mathematical concepts will do them good when advanced mathematics comes into the learning picture. Mathematics is a special subject that differs from the rest of the knowledge-based subjects in that its language is embedded in its mathematical variables, expressions and equations. There can be many twists and turns in asking a simple mathematics question. Without understanding the underlying concepts of the mathematics topic, it will be difficult to move forward or solve the mathematics questions, unless applying the dreadful memorizing approach.

Learning, especially in mathematics, can best be obtained by linking mathematical facts with thinking skill where conceptualization is part of it. The linkages formed will be strengthened over time with many mathematics practices. The ability to solve any mathematics problems at any given time is therefore a true reflection of one’s ability to handle mathematics. Learning mathematics by heart will not achieve this target as memory fades with time and quantity. Retention of knowledge goes hand in hand with the depth of understanding.

Albert Einstein once said “Education is what remains after one has forgotten everything he learned in school.” Learning through linkage of mathematical facts with concepts will remain for a long time since true understanding is achieved. Purely memorizing facts, which has negative impact, causes the meaning of mathematics education to be lost when one forgets the knowledge learned.

Therefore, in conclusion, learning mathematics is best taken with focus in concept understanding compared to the pure rigid way of memorizing mathematical facts, since the outcome will last longer with true comprehension of mathematics and its applications. Foster a habit to approach mathematics lessons and tutorials through understanding the concepts involved instead of the numerical facts and specific steps in any given mathematics examples. This habit formed will ease acceptance of complex mathematical concepts later on in higher level of mathematics education.

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Natural Limitations of Mathematics

Scientists, especially Physicists and many others respect Mathematics as the last evidence of anything. It’s often held that after a proposal can locate some mathematical argument in its service, it’s termed settled and proved once and for all. Physicists have invented the expression”Mathematical-logical derivation and raised it to the degree of rhetoric fact. The present cosmic perspective preserved by Physicists is a glaring case of where mathematical-logical derivation may result in, if implemented in interpretation of unprocessed occasions, without due concern of pure constraints of Mathematics. As a consequence of uncontrolled mathematical-logical derivation, the Physicist’s cosmic perspective has landed into a cosmos that is outside sensory perception and is consequently not there. Strings of this series theory and M-Theory are outside sensory perception – indirect or direct.

This leads us into the wonder of pure constraints of Mathematics in comprehending normal events, matters along with the cosmos as a whole.

1) Math isn’t all actual: For instance Sophisticated numbers and Boolean algebra aren’t grounded in normal events. These can be regarded as mathematical visions, can be helpful as techniques and tools in some specific scenarios.

He maintained that using Schwartz Distribution Rule through committed applications to the data that was available, it might be possible to forecast incidence of ground quakes. He explained that the main reason behind his belief that ground quakes can not be forecast on the basis of available information simply due to inaccuracy of accessible data that may be rectified by using Schwartz Distribution Rule and then accurate forecast of prevalence of ground quakes could be manufactured.

But, I discovered it beyond and past understanding. Mathematics isn’t enjoy a magician’s hat which could seemingly produce things from nothing. Until and unlessone obviously understands what information is to be gathered and the way the applicable info is to be translated, how mere use of a mathematical instrument or procedure can ever result in prediction of a pure event is beyond understanding.

Ultimately, these digital elements of Mathematics are applicable only as techniques and tools so much as they contribute to outcomes harmonious with actual world. When it’s otherwise, then their usage is obviously unwarranted.

2) Character is hierarchically organized and principles vary from a hierarchical level to the next. Rules related to cosmic dust might not be exactly the exact same as principles related to celestial bodies like planets, stars etc.. Thus, infinite mathematical extrapolation can not be appropriate and appropriate. By way of instance, by providing heat to a block of ice, then it’s possible to convert it into a liquid and vaporize it into water vapor. But principles related to liquid, solid and gaseous state of matter change and therefore mathematical computation related to water from solid condition can not be legitimate if applied to water from liquid condition and so forth so on. Natural events frequently involve reversal of condition and change of period with significant changes in related rules. Thus boundless mathematico-logical extrapolations are completely unwarranted before and unless it’s shown that principles being applied are valid throughout alter of hierarchical degree, change of stage, change of condition .

3) Character isn’t mathematically-logically ideal: Nature awakens in non-linearties. All acts of pure origin and production are nonlinear in nature. All stage shifts and change of condition are nonlinear in nature. A few of those nonlinear functions are known as singularities from Physicists. A singularity in design usually means a odd point because Physicists neglect to employ Laws of communicating over a singularity.

No more unconstrained mathematical-logical extrapolation could be valid throughout a nonlinear act. These nonlinear functions are determinate but in the current level of human comprehension are logically indeterminate. For instance decay of Uranium in to direct is an empirically specific event but its incidence can not be called on the basis possessions of Uranium and understood laws of Physics.

Thus, we must be directed by Nature in use of mathematical instruments and methods towards interpretation of organic events. Application of mathematical instruments and methods is legitimate only so much as it evolves with observations/ experimental outcomes / expertise.

Notwithstanding the aforementioned, mathematical instruments and techniques are rather helpful in discovering hidden requirements underlying events and things. Mathematical reconciliation of detected data suggests adequate and acceptable comprehension of the specified subject matter.

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The Reality And Non-Reality Of Mathematics

There’s little doubt that mathematics rules the reality roost when it comes to the laws, principles and relationships within the sciences in general and the physical sciences in particular. Further, mathematics plays a dominant role when it comes to the purely economic aspects of our lives and where would sports be without statistics? However, when it comes down to brass tacks, how much of really real reality is actually reflected in our mathematics?

The Reality of Mathematics.

Mathematics is just a shorthand mental concept that simulates reality, or approximates reality or a possible reality or even an imaginary / impossible ‘reality’. Mathematics is NOT reality itself. You can mathematically manipulate the alleged extra dimensions in String Theory but that doesn’t mean of necessity that these extra dimensions actually exist.

Mathematics is a tool that at first approximation tries to reflect upon the nature of really real reality. Mathematics is not reality itself. Further, our mathematics are structured to reflect our version of reality based on our observations not of necessity what really happens. The perfect example is Quantum Mechanics. For example, we may not know, even cannot know even in principle, exactly where a particle is as well as at the same time where it is going with 100% precision. So we invent a form of probability mathematics like the Schrodinger Equation or the equation that governs the Heisenberg Uncertainty Principle. Those equations are for our edification but they don’t alter the really real reality fact that the particle has actual coordinates and is going from A to B. Probability in Quantum Mechanics, and the mathematical equations associated with it, are just reflections on the limits of the human observer and human instrumentation, not a reflection on Mother Nature’s really real reality. Our Quantum Mechanical equations are imposed approximations to really real reality much like Newton’s equation for gravitational attraction was really only in hindsight an approximation.

There can be multiple models of reality, each based on mathematics, but they can’t all be right. Cosmology is a case in point.

The phrase “but the mathematics works” means absolutely nothing. Just because mathematics predicts the possibility of some kind of structure and substance, or some law, relationship or principle that the Cosmos might have, does not of necessity make it so. A prime example where the mathematics worked but the Cosmos didn’t go along for the ride was the ad-hoc piling on those epicycles upon epicycles in order to explain the motion of the planets. It finally got so unwieldy that the baby was thrown out with the bathwater and a new baby conceived, that being that the Earth was just another planet and not at the center of life, the Universe and everything. Once it was postulated that the Earth went around the Sun, planetary motion fell into place – mathematically into place as well.

Take a more modern example. The mathematics works in String Theory, but to date String Theory remains a theorists’ theoretical dream (accent or emphasis on the word “dream”).

Probability theory is that branch of mathematics that interposes itself between the macro human and human comprehension and abilities and the micro world of quantum mechanics. That has way more to do with the macro than with the micro since the absolutes of the micro aren’t visible in the realm of the macro; they are beyond the realm of the macro to resolve through no fault by the way of human comprehension or abilities.

A prime example is that there is no probability in quantum mechanics, only probability introduced by the limitations of the conscious mind to get down and dirty to the level of detail required to eliminate the concept of probability from quantum mechanics.

Mathematics serves no purpose, useful or otherwise, outside of the context of the human mind (specifically) or outside of the intellectual conscious minds of other sentient species (in general), thus making allowances for E.T. and maybe the terrestrial great apes; whales and dolphins; and perhaps other advanced minds – perhaps elephants as well as some birds.

In the absence of any conscious minds, what use has the Universe for arithmetic, geometry, trigonometry, calculus, topology, statistics and the multi other branches of mathematics? Now 1 + 1 = 2 might be universally the case and logically true even in the absence of any conscious mind, or before any life form ever came to pass, but so what? That cuts no mustard with the Universe! There was nobody around to conceive of that or to make use of that or to equate the manipulation of numbers as a reflection of universal reality (or even non-reality*). There was no conscious or intellectual mind around to appreciate any mathematical utility or usefulness or beauty or elegance.

Mathematics in fact is not a reflection on or of reality, only that reality as observed or defined once having been filtered through sensory apparatus thus pondered over by the conscious mind. Reality as perceived in the mind is several transitional layers of processing removed from whatever pure external reality there happens to be. There’s even an additional layer if instrumentation is a middleman. So the conscious mind is thus limited in terms of its ability to come to terms with the full scope of really real reality.

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Restoring Ancient Ethical Mathematics to Guide an Ennobling Government

In 2010, the American Mathematical Society published Ruben Hersh’s Experiencing mathematics: What Can We Do When We Do Mathematics? The book argued that no code of ethics existed in pure mathematics but the author felt concern that “mathematicians can enter a mental state that is rather inhuman, totally cut of from humanity.” His concern is warranted. Ethical mathematics has long been banished from global society as a pagan heresy. In particular, wars are still being fought to the death over which Deity provides permission to research the mathematical nature of infinity.

Mathematics has certainly entered into a state of inhumanity when it is politically acceptable for it to be programmed into poker machines to bring about states of financial and emotional bankruptcy. Mathematics, in collision with harmonic artistic sound and colour frequencies can indeed induce emotional states of inhumanity. When this deception is used within the global stock market this process of illusory anticipation provides entertaining global excitement. The current battle for the Presidency of the United states of America, without any mathematical thought or feeling of the eventual outcome, is a good example of this. Government appointed epidemiologists are well aware of the existence of a global epidemic transmitted by dysfunctional global mathematical information systems, but making money no matter what, is the predominate objective in today’s mathematical world.

Mathematical science was not always like this. In 3rd BC, pagan Greek science had a completely different mathematical mental state being taught at two Athenian Universities. The mathematics of emotion was fused to the 28 day cycle of moon movement affecting the female fertility cycle. Harmonic colour frequencies associated with this process were held to resonate with the atoms of a mothers spirit. Instead of anticipating some illusory financial reward, the artistic expectation of dressing up children in colourful costumes and to lovingly care for them was an ethical joy of life. But over the centuries the various war-like gods of modern day religion banished such emotional mathematical logic from being developed for the betterment of the human condition.

To obtain the antidote to this sad state of affairs is not a problem. If the dysfunction money making mathematical expertise is fused with the ethical mathematical logic and programmed into a computer, designed to generate human survival blueprint simulations then we will quickly obtain substantial survival guidelines. This is not an idle proposition. China’s most highly awarded scientists, Kun Huang, in 1979, proposed this research methodology by using sacred Greek geometrical logic to measure the mathematical life-force governing seashell evolution over their fifty million year old fossil record. He noted the similarity of ancient Greek ethical mathematics with ancient Chinese ethical philosophy.

Huang is famous for introducing such ideas into the work of the Nobel Laureates, Neils Borh and Max Born. What is lesser known is that Australia researchers used his research methodology to actually measure the mathematical existence of the life-force governing the evolution of seashell life-forms. In 1990 the world’s largest technological research institute, IEEE in Washington, reprinted this discovery as an important one of the 20th Century, placing it alongside such names as Louis Pasteur and Francis Crick. Unfortunately the logic used belonged to infinite fractal logic, forbidden by global religion and politics to be used to obtain the human survival blueprint.

Kun Huang’s belief in the ethics of ancient Chinese philosophy and its association with ancient Greek atomic physics has now become an integral aspect of a new neurological quantum biological medical science. At some future time, when human tribal persuasions causing injury to the human species can be seen as belonging to a carcinogenic global mindset, Kun Huang’s mathematical perspective will be hailed by a technology well beyond the limits of our present thermodynamic scientific culture. The fact that this global subculture demands human extinction, is by its own definition, carcinogenic.


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