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A solution to improve students’ achievement in maths

Decline in maths of Australian schools – the fact

Achievement of Years 4 and 8 students in maths over the past 20 years has flat-lined, while many other countries have improved.

According to the latest findings from the 2015 Trends in International Mathematics and Science Study (TIMSS), Australian schools continue to fall behind in maths and science.
TIMSS, conducted every 4 years, has measured student achievement in maths and sciences at Year 4 and Year 8 in Australia and many other countries since 1995. The report shows that Australian Year 4 students were significantly outperformed by students in the other 21countries in mathematics. At Year 8, Australian students were outperformed by those in 12 other countries in mathematics(1).

Since 2011, the report (2) shows Australia plunging from 18th to 28th on Year 4 mathematics, and from 12th to 17th on Year 8 mathematics. The 2015 TIMSS report also shows that Kazakhstan, a Central Asian country with a small population (≈ 17.8 million), has smashed Australia in all 4 categories(3) :

                           Kazakhstan         Australia
Year 4 maths              12                         28
Year 8 maths                7                         17
Year 4 science             8                         25
Year 8 science             9                         17

Federal Education Minister Simon Birmingham said beating by nations like Kazakhstan is a wake-up call. He also said ‘I think Australia should be seeking to be among the best in the world and declines like this are unacceptable and that we need to be working hard to turn it around.”

Another report , the Program for International Student Assessment(PISA), shows that Australia schools are in ‘absolute decline’ globally (4). PISA is an internationally standardised assessment that was jointly developed by participating economies and administered to 15-year-old in schools. The main differences between TIMSS and PISA include:

About 630,000 students from more than 60 countries participated in TIMSS in 2015. In Australia, more than 570 schools and more than 16,000 students were involved.

About half a million students from 72 countries took part in the PISA in 2015, including more than 14,000 Australian students.(5)

Results from PISA 2015 showed the ten top countries in maths are :

Singapore (564), Hong Kong (548), Macao (544), Taiwan (542), Japan (532),
China (531), Korea (524), Switzerland (521), Estonia (520), Canada (516).

Australia ranking is 25 with 494 points, above France (493), United Kingdom (492), and United States (470). Australia was significantly outperformed by Asian countries, ranking just below New Zealand, well below Singapore, Hong Kong, Taiwan, Japan.

The results again raises questions about the global competitiveness of the Australian educational system. Dr Sue Thompson from the Australian Council for Education Research (ACER) said local academic performance was in “absolute decline”. “The proportion of high achievers is decreasing and the proportion of low achievers is increasing”, she said.
Federal Education Minister Simon Birmingham said the country could not afford to “continue to slip behind”.

Causes of the decline of Australian schools.

According to TIMSS and PISA reports, the absolute decline of Australian schools is an urgent issue that needs to be investigated and resolved.

This document will not discuss the tangible causes of the issue like school funding, school curriculum, teacher competence, teacher training, and the role of families.

The intangible causes include:

a) The advance of electronic technology.
Nowadays, almost all students at schools have an iPhone or iPad each with full capacity to perform all services relating to mathematics.
b) The advance of electronic games.
The deep passion of young people for electronic games has disoriented their minds, resulting in a dislike of mathematics.
c) The lake of an educational game challenging, competitive, and interesting enough to attract students’ attention.

Can Chess improve mathematical ability of students ?

Benefits of Chess

Chess is a two-player game that happens on a 64 squares board. Each player has 16 pieces of different types (one king, one queen, two rooks, two knights, two bishops, and eight pawns).
Each type of piece can make a specific set of moves; those moves can be described by mathematical rules and moves of the full game can be described by a formal tree.These trees can be analysed and studied by mathematics in a branch called ‘game theory’. Therefore, the chess game has a clear mathematical nature.

In the document “Teacher’s Guide: Research and Benefits of Chess” (6), the author, Dr. Robert C. Ferguson, reports many experiments carried out in the period from 1970 to 1990 in many countries: Zaire, Belgium, HongKong, USA, Venezuela. These experiments investigated the correlation between chess playing and math skills development. The document shows a number of benefits from playing chess as follows:

• Chess is a game for people of all ages.
• Chess develops memory, improves concentration, and develops logical thinking.
• Chess promotes imagination and creativity, teaches independence, and inspires self-motivation.
• Chess develops the capability to predict and foresee consequences of actions.

For the correlation between Chess and Mathematics, Chess involves a great number of calculations, such as counting the number of attackers and defenders in the event of simple exchange. All these calculations need memory, concentration, logical thinking, and decision-making. Theoretically, the correlation between Chess and Mathematics exists. However, the relationship between thinking mathematically and thinking in the game of Chess are different. Enrique Diaz G. discussed this issue in the document “Mathematics and the games of chess” (7).

In Mathematics, the method of obtaining knowledge is reasoning under several forms. One can reason by analogy, conclusion is based on similar situation or circumstance. Another method of reasoning is induction, commonly used in experimentation. The third method of reasoning is deduction where the conclusion is a necessary consequence of certain statements called premises.
Mathematics must not be considered only as a system of conclusions drawn from premises or postulates. Mathematicians must also discover what to prove and how to establish the proofs.

A Chess game is a war of two sides. The game finishes when one of the Kings is captured.
Chess is not necessarily a game of elimination but rather a game of tactics. The attributes a person must possess in order to become a good Chess player are:

Visual imagery
Before making a move, the player has to visualise how the board will look afterward, and how it will be changed by the opponent’s response.
Patience and restraint
Good memory
Memory has two components: ability to retain, and ability to recall.

The reasoning in Chess consists of joining the above attributes in order to give an appropriate response to any move.

Some facts relating to Mathematics and Chess are:

• Will a good mathematician become a good Chess player? One of the greatest mathematicians, Henri Poincaré, denied this possibility.
• The common belief that expert chess players are good mathematicians is fiction.
• The Chess process, being intuitive, is not mathematical in the normally accepted sense of that term. The fact that the Chess players are controlled by rules does not make them comparable to those who explicitly use rules which are created deductively.
• There is not any valuable reason to support the theory that a Chess player must possess abilities related to Mathematics.

Does playing Chess improve Math ability ? 

This question at high school level arises often in the social media, like the following:

“I am a student in high school and I aim to become an engineer, however math is quite hard, I’m fairly certain I can handle the math, but if I improved my mathematical ability then it would make things much easier. A friend of mine told me that playing chess once a day could make me better at math. I don’t know if this is true or not. That’s why I decided to ask the experts. Could playing chess improve my mathematical ability?”.

Almost all replies to this question are similar to the following:

• Nope. It won’t help a bit.
• I don’t think it does help with math (I’ve done Calculus I, II, and III and played chess
for two years)
• In my experience, it does not help at all. People are often strong in both fields, if they practice enough and if they have the ability. I think the two go hand in hand. However, one does not facilitate the other.
• Many years of studying math taught me that the best way to improve at math is doing math.
• Use your chess study time for math directly. Much bigger payoff.
• If you find difficulty learning math, you need a good math tutor or at least a study companion. Playing chess does not help.
• At the very least, I’ve noticed that transitioning from a poor to a strong player because of improvements in discipline, focus and thought process translate to all other mental activities one engages in life. I became a better engineer because I started learning to play this game better.
• I believe chess improved my attitude towards math by a great deal. I used to be very bad at math. Then I came to chess, which is considered a game that needs talent. I said to myself, if chess, which is such a complicated, can be learned, then math cannot be much more different. So a few weeks ago, I sat down with my high school math book again and put a lot more effort into trying to understand concepts. Now I can solve some problems that I have never been able to do before.

The answer to the question “Does playing Chess improve Math ability? is clear: “No, it doesn’t directly” or “Yes, but indirectly only”.

In a paper published recently in Learning & Behavior, there is a report on an experiment focusing on math ability. Two hundred and thirty three (233) third and fourth graders were given 25 hours of chess instruction and tested on mathematical problem-solving task, against a passive group. The experiment showed no statistically significant differences in the active and passive groups. The authors conclude: “These results suggest that the effects (if any) of chess instruction, when rigorously tested, are modest and that such intervention should not replace the traditional curriculum in mathematics” (8).

A solution to improve students’ achievement in maths.

It is well known that:

• Chess has many benefits as memory improvement, concentration, strategy planning, decision-making, perseverance, observation, analysis, and organisation skill.
• Chess games are difficult and time-consuming.
There are over 9 million different possible positions after three moves each. There are over 288 billion different possible positions after four moves each. The number of distinct 40-move games is far greater than the number of electrons in the observable universe.(9)
• Chess cannot be a subject in school curriculum.
• Math ability at primary and high schools includes numerical skill, speedy calculation, mental arithmetic, memory, analysis, strategy planning, observation, and organisation skill.
• Math skills can be learned with methods easier and simpler than Chess.
• Young people like interesting, challenging, and competitive games.
• Electronic games have damaged the minds of young people with hatred of mathematics.

The solution to improve students’ achievement in maths is to find out a way to incorporate the benefits of Chess with the requirements of Math ability in an easy, simple, and non time-consuming, but challenging and competitive, educational game, suitable for all students at all levels in primary and high schools.

These are the aims of the game “Mathematical Chess”, invented by Dr George Ho, recently published by Xlibris.

Mathematical Chess is a two-player educational and entertaining game played on ten digit pieces (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and six operator pieces (addition, subtraction, multiplication, division, power, and root). The chessboard is a grid made up of nine vertical and nine horizontal lines. The game has ten definitions and twelve rules. It is flexible and suitable for all students from middle and high schools to universities.

Link to the book in Amazon:


(1) “Australian schools continue to fall behind in maths and science”, ABC news,

(2) “Australia crashing down international leader board for education, falling behind
Kazakhstan”,ABC News,

(3) “More than Borat: Here’s what you need to know about the country beating us in
education”, ABC News,

(4) “Australian schools are in ‘absolute decline’ globally, says PISA report”,ABC News, http://www.abc.net.au/news/2016-12-06/australian-school-performance-in-absolute-decline-globally/8098028

(5) “The latest ranking of top countries in maths, reading, and science is out — and
the US didn’t crack the top 10”, ABBY JACKSON, ANDY KIERSZ, Business Insider

(6) “Teacher’s Guide: Research and Benefits of Chess” by Dr. Robert C. Ferguson:

(7) “Mathematics and the Games of Chess” , Enrique DiazG. ,

(8) “Does chess instruction improve mathematical problem-solving ability?Two
experimental studies with an active control group”,Sala, G. &Gobet, F. (2017),
Learning &Behavior.

(9) “Number of Moves in Chess”, Source:

Sydney, 17 July 2017
Dr George Ho

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