The Compulsive Gambler

 This is our newest publication, authored by Piirkor Francis, one of our young authors at Tee Series. 

ABOUT THE BOOK

Frank, a brilliant and hardworking young man who just completed high school, had always aspired to

become a medical doctor.

The once hardworking and trustworthy Frank had now turned into a serial gambler. He would defraud and dupe anyone at the slightest chance to get something to gamble. Upon all this, Frank held his reputation in high esteem and would not sacrifice it for anything. What was so fascinating about his cheating lifestyle was how his shenanigans were usually well orchestrated. He would always find a way to squeeze money out of people and still receive laudatory for it. 

How did he get involved with gambling in the first place? Was he able to perpetrate his furtivity on all the innocent victims and get away with it? What could have caused the sudden change in Frank’s character?

Frank, starting to turn over a new leaf after realizing he was treading the wrong course, managed to obtain a scholarship to study medicine in Cuba due to his intelligence and hard work as a pupil-teacher. What happened to his scholarship? Will he become that medical doctor?

ABOUT THE AUTHOR

Piirkor Francis is a teacher of Integrated Science at Lighthouse Junior High School, located at Atimatim, Kumasi, in the Ashanti Region of Ghana. He hails from Nandom in the Upper West Region of Ghana but was born and bred in Sunyani in the Bono Region.

He is a young author at Tee Series who is the brain behind this powerful book. Francis always creates intriguing stories from the happenings and experiences of himself and others to tackle social issues. He is a great teller of fictional chronicles.

INFO

A copy is GHS20.00 

Whatsapp or call Tee Series on +233553226200 / +233208740869 to grab your copy now. 

You can also purchase it directly from Booknook.store and it will be delivered to you right at your doorstep. 

SIMPLE MATHEMATICS TRICKS FOR JUNIOR HIGH SCHOOLS

Simple Mathematics Tricks for Junior High Schools is our first publication authored by John Bagiliko. This book sold about five hundred (500)  copies in a matter of two weeks. He wrote this book while in his second year pursuing BSc. Mathematics at the University for Development Studies (UDS) Navrongo, now CKTUTAS.

ABOUT THE BOOK

The book is presented in a way that will arouse the interest of the reader to learn arithmetic. For example, 11 × 35 can be computed by placing the 3 and 5 as 3….5. The 3 and 5 are again added and placed in between 3….5. This becomes 385. This is very amazing and confirms that arithmetic computation can be very interesting. In the book, there are many of these which will help the reader to know how to compute similar ones. The book also presents to the reader various simple tricks to be used in computing many arithmetic questions.

This book is targeted at the Junior High School pupils and below who are required to write their mathematics exams without the use of calculators. It presents them with fascinating tricks to ace their exams with ease. 

What will the reader be able to do after reading this book? The author presents the book in such a way that, after the reader has gone through it, he or she should be able to perform some operations such as multiplying two numbers using the fingers and estimating square roots. 

These are all things the reader will be able to do without the use of a calculator. The reader is also expected to practise these things well to be able to give out answers to any of those computations within a few seconds. The book is actually a must-read since we all need arithmetic in our daily activities.

ABOUT THE AUTHOR

John Bagiliko is a data scientist and software engineering consultant. He is also the Zindi Country Ambassador for Ghana, and co-founder and team lead of AI Ghana. John holds MSc. Mathematical Sciences, with a specialty in Big Data and Computer Security,  from the African Institute for Mathematical Sciences, AIMS Senegal. He is passionate about mathematics and its application in solving real-world problems. John is a phenom as far as artificial intelligence, mathematics and general tech is concerned, and he has won multiple awards in the past two years, including a Google grant that flew him to attend the Deep Learning Indaba 2019 in Nairobi, Kenya. He has been an advocate of simple mathematics right from high school. John loves to teach what he knows and had his alias, Tee, from his peers and students. He also loves to read and write at his leisure. 

J

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MATH TRICKS

SOME FALLACIOUS MATH PROOFS

 Math has a lot of proofs. Some of these proofs prove statements that we all know cannot be true. When a fallacious statement is proven in math, then there is a violation in the process.

We should note well, some of these violations so that when they appear in a proof, we can easily point them out:

Ø  Dividing a number by zero: Dividing a number by zero is undefined and hence is a violation.

Ø  Any number multiplied by zero yields zero

Ø  If a² /b² = c² /d²  then a/b = ± c/d .This means that either the positive is true or the negative is true and so one should not always be quick to pick the positive as the answer.

Let us now proceed as more violations will be noticed in the process.

PROVE THAT 1 + 1 = 0

Step 1: a = 1

  Step 2:  b = 1

Step 3: a = b

Step 4: a² = b²

Step 5: a² -  b² =o this becomes (a – b)(a + b) = 0

Step 6: (a – b)(a + b) /(a – b) = 0/(a – b)

Step 7: 1(a + b) = 0

Step 8: a + b = 0

Step 9: 1 + 1 = 0 (this is because of step 1 and 2) and this end the proof that 1 + 1 = 0

Why is this a false  proof?

In step 6, (a – b)(a + b) was divided by (a – b). (a – b) is 0 because a = b. The division by (a – b) in step 6 is the same as dividing by zero which is undefined. In the same step 6, (a – b)(a + b) is 0 because (a – b) is 0. Any number multiplied by zero yields zero (Spencer, 1998).

PROVE THAT 2 = 1

Step 1: a² = ab( let a = b)

Step 2: a² – b² = ab – b² ( that is subtract b² from both sides)

Step 3: (a – b)(a + b)/(a – b) = b(a – b)/(a – b) ( that is dividing both sides by (a – b)

Note: ab – b² = b(a – b) (that is, b factorized out)

Step 4: (a + b) = b

Step 5: But a = b

Step 6: b + b = b

Step 7: 2b = b

Step 8: 2b/b = b/b

Step 9: 2 = 1

Which step makes this proof a fallacy?

We should note that a = b.

 In step  2, a² – b² = 0 , ab – b² = 0 and so 0 = 0 which means there is nothing to prove.

In step three ( a – b) = 0. (a – b)(a + b) = 0,

(a – b)(a + b)/(a – b) = 0/0 which is undefined.

In the same step, b(a –b)/(a – b) becomes b(0)/0 which is also undefined. Upon all these “violations”, the proof still continued and that makes it a fallacious proof.

 TO PROVE THAT 1 = 0

1.       Let x = 1

2.       Multiply both sides by x

          x² = x

3.       Subtract 1 from both sides

x² -1 = x – 1

4.       Divide both sides by x – 1

(x² – 1 )/(x – 1) = 1

5.       Simplify

(x – 1)(x + 1)/(x – 1) = 1 note that x² – 1 = (x – 1)(x + 1)

 x + 1 = 1

6.       Subtract 1 from both sides

X = 0   

Substitute the value of x from step 1

1 = 0

The fallacy here is subtle in step 2,

Multiplying both sides by x introduces an extraneous solution to the equation of x = 0. Then in step 4, there is division by x – 1 which is an illegal operation because x – 1 = 0 and you cannot divide by zero.

SEE THE FOLLOWING:

^1.                y = 100, z = 0

               x = (y + z)/2

              2x = y + z

              2x(y –z) = (y + z)(y –z)

              2xy – 2x² = y² – z²

              Z² = 2xz = y² – 2xy

             z² – 2xz + x² = y² – 2xy + x²

             (z – x)² = (y – x)²

              Z – x = y – x

              Z = y

             0 = 100

            Shaun; (December, 2008)

Then 1 + 1 = 3 becomes x + x = 3

2x = 3

2x/2 = 3/2

X = 1.5

Substituting into the expression we get 3 which imply that 1 + 1 = 3 as required.

Are the above two fallacious proofs? If they are, point out the wrong steps and explain why they are are wrong. You ideas will be appreciated.

WHY DO SO MANY PEOPLE HATE MATH?

I hate being the first to tell you that mathematics has never been liked by many people since the beginning of time. I hope, also, that I am not the first to tell you this. Why have many people out of the many subjects thought in schools just decided to give hatred to math? I used to hate math at the primary school too. Now math is the subject I like best. I think that is the reason why I offerred BSc. Pure Mathematics at the University. I have always been researching hard to find an answer to this question and have ended up having more than one answer. I am convinced I am not the first person to take up this task upon myself. 

Math is poorly taught at school  

Math is poorly taught in schools of all levels. Some teachers read out what they have also read to students. Sometimes without any explanation, probably they do not also understand. If that is the case, then I will say that is hypocrisy on their part to pretend to know what they not know. Gordon Barker on March 7, 2013, said, most math teachers should be put against a wall and shot. He argued that math is taught badly at all levels (including first Year University) with no connection to real world. Not a quote though. This really kills the desire of most students to pursue math in higher levels and also increasing their hatred for it.  

Passing of antipathy on to kids by parents and role models

It is sad to know that the perception of most people that math is difficult is as a result of antipathy passed on to them by parents or role models. A woman told the daughter who failed a math paper in the open air, not to worry at all since math is difficult and that she herself wasn’t good at it when she was in school. This woman, indirectly, has killed the daughter's zeal that she may have had to learn this subject. So it is evidently clear that no matter the effort of the teacher, this girl cannot make an effort to make it in math. She will always be consoled by the fact that her mother was not also good at it so what’s the big deal. There was a case, back at the primary school, where a math teacher was solving a math problem and made a mistake along the line and when it was pointed out to him, he simply said “adwen no nnye mma 'maths'.” This is Asante Twi, meaning the brain is not good for maths. It is laughed over but the pupils may have been consoled that after all, their math teacher said the brain is not good for it, why should they make an effort?

Absence of constant practice

Math and constant practice are synonymous. Due to laziness or other reasons for people to constantly practice math, they end up forgetting the basic things in math that are must-know to the problem to be solved. I think I now know why I did not like math at the basic school. In the Senior High School, I started learning math regularly and I made sure I was always ahead of my math teacher. Within some few months in the Senior High School, my interest in math started increasing and I eventually became one of the best students in math in my class. So most people do not practice constantly and so forget the basic concepts in math and end up hating it because they lack the basic concepts to solve any math problem.

Poor preparation on the part of some teachers before going to teach a lesson

It sometimes baffles my mind why some teachers enter the class to teach without doing any good preparation or having a well prepared lesson notes with them. This constant practice in math applies to everyone, whether a teacher or a student of any level. Some teachers go to the classroom having done barely any preparation. They end up in the class not being able to solve a certain math problems. When the students become fully convinced that their teacher could not solve it, they also relent in their effort to learn math since even their teacher could not do so too.

Lack of good fundamental preparation

Luck of good fundamental preparation is factor to most people hating math. Most people do not like mathematics because they are not good at it. They are not good at it because they may not have had the basic preparation. As stated earlier, people begin to hate math if they do not have knowledge on the basic concepts of math. Children are not thought basic concepts in math as the way they are thought poems. If basic math concepts were made known to basic school children as poems in the basic schools, the issue of someone growing to hate math would reduce. For instance, I do not know the number of days in the months of the year off head. I can only tell you the number of days in a particular month of the year by reciting a poem in my head. There are some things I do remember now only by singing a song or by reciting a poem. Math has not been taught that way. I wish I could come out with a song or a poem containing most of the basic concepts in math which would be taught in basic schools to children, so that as they grow physically, they also grow mentally with math concepts. I am sure someone is good at writing songs or writing poems and is reading this blog post of mine. This person I hope will be touched and will come out with a very nice song or poem that will make children like math. Nonetheless, I recommend to use of simple arithmetic tricks for arithmetic calculations for these basic school pupils and teachers. This will get kids to like the subject from their infancy. For example, it is possible to perform some multiplications using the fingures. See also my article on this.

Is math a language? 

 This I came across, in a comment by someone to a blog post. This is from John Giano, March 8, 2013, “I think you hit the nail on the head. Math is a language. It is a set of symbols and concepts that relate and work together. Why everyone hates math is probably because the language is not spoken from birth and its rarely spoken in a dialect that people can understand. For most people, it will be like trying to learn Japanese; reading it as a native English speaker, and having the instructor pronouncing with a Russian accent.” A Nigerian comedian also joked about this issue of math in one of his comedies using a scenario; a teacher giving an expression like 2x +3 = 4 and asking the students to find x when x is already in the expression. His argument is valid. The math language used is not understood by many and is barely made to be understood. 

  

No sense of application of math

Math as thought in most cases is not pointed out what the application of that topic in real life situations is. What math seems to be doing is prepare the individual and providing him with the basic concepts to be applied in the next difficult topics. Math for example, prepares an individual in pre-calculus for calculus. Maths is thought as if we were going to be students forever without having to apply the concepts in normal life activities. I remember one student once asked a math teacher what the importance of construction was. He was given a bogus answer. He was only told, “You will know its importance as you go higher.”

Who likes to told openly that he’s wrong

If you are the type who hates to be told the simple truth that you are wrong, then, you will think math is not your field. Math has a unique answer to a particular problem and you cannot have two different answers to the same math problem. All these answers are expected to be proven, some in a somewhat simple way, some too, very abstract. In any given math problem, one is expected to follow some specific procedure in coming up with that answer, if not, wrong!! Math is unlike those other subjects where you may be asked a question and you are expected to share your ideas. Your , matter what, cannot be totally wrong.

This math issue is a problem of the whole universe.


Your comments to this article will be very necessary for coming out with a solution to it.  I also recommend the article titled, “Six Easy Ways of Performing Arithmetic Computations” and also a book titled “EASY WAYS FOR PERFORMING ARITHMETIC COMPUTATIONS BY: BAGILIKO JOHN”. They seek to prove to readers how computations in arithmetic or math can be made so easily and interesting.