Saturday, May 13, 2017

WHY MATH IS A DIFFICULT SUBJECT

       I was once a mathematically phobic student. I really ignore anything that involves math. From daily work up to sports,assignments to quizzes. Math really told me that I am not part of the elite group inside the classroom. I excel in other subjects except math. There were times that I have to got an early headache, stomachache, etc, all illnesses suddenly arrives when there is an announcement for a math quiz.  I suffer this academic feeling since I was in my elementary days and up to high school.

      In my college days, although math was still my phobia in academe, I enrolled mathematically inclined course. This is to face my fear in the said subject. First semester was a brutal experience. I failed in my three math subjects. Second semester was a little good to me, I passed them all because it was a retake.  In my second year same thing happened, all in all I have five failures in my college history.
   
      And why I became a mathematics teacher now?

      I do not know why in my Algebra class, the equation x + y = 2 by the teacher's discussion is not the same with the Algebra book which is x + y = 5. I checked with the other author and the equation became x + y = -7. This is so crazy. Why the answer in every x + y became different? How would I know that my answer is correct knowing that every x + y has different answers? And I keep on wondering why my classmates got correct answer except me. why those classmates of mine has the same guess to the answer?

      I keep on researching in silent knowing that I don't want those people knew that I don't know how to treat those simple  equations. I read a lot, guess if my answer will be correct.I still don't understand. I suffered anxiety, I was a attacked by extreme inferiority feeling by the fact that I was the only one in the class knew nothing but myself drowned into the sea of dreadful feeling. Every night was my most comforted moment. Nobody would ask me how to solve this and that by students of other courses who believe that I am a  mathematically brilliant by my course. I simply stay in my comfort zone just pretend I am okay but actually was not.

      Days passed, my readings and  personal research develops very little. I almost gave up, and sometimes thinking that better to shift another course without math. I keep on searching what particular course without math but all courses has mathematics as part of the curriculum. I decided to stop the course to end the shame but whether I like it or not, this is the requirement to be in a professional circle. I never gave up in searching the answer to my big problem but simple to others. I don't know one day what happen to my daily routine just to heal my dilemma but it happened, really happen to me. I was able to distinguish the difference between "expression" and "equation" accidentally. I noticed then that every expression has different equality which is also a expression. I thought before that x + y = 2, x + y = 5, and x + y = -7 is just a simple addition with "guess what is x and y values" to have an answer of 2, 5, and -7 respectively. It was then an opener to my idea that mathematics is not a "subject" but  a "working subject". It told me that I cannot understand this subject by reading alone. It should be with extra papers, a pen and effort to solve every math problem. There is a building of ideas and information happens inside the human brain while solving each problem. More students did not discover about this. It is really a daily exposure to a "thing" to know that "thing" well. Imagine you are in a  new place where it is your first time. You can not have an access to any streets and avenues because you don't knew it. Your radius towards your knowledge to the place is very short. Check yourself after one year to the said place. You notice that you can simply explain all details within it. Daily living with that place communicates well for your development up to mastery. It is also the same as your first walk. At first, you fall because you find your balance hard to master. It is by constant need by your daily requirement for living to master the balance. Then by having the balance, you can walk perfectly, and run lately.

      Mathematics is not a subject but a working subject. Do not study your math, live in it, dwell with it.



   

WHYMATHISADIFFICULTSUBJECT

Saturday, February 13, 2016

ADDITION OF FRACTION


Fraction is always a quite hard to deal. Dealing fractions with MDAS (Multiplication Division Addition Subtraction) as basic operation is really a big deal. Students seems to be helpless in solving problems involving fractions. By the use of calculator, fraction can be  done easily without understanding how did the answer arrived.

Fraction by definition is a part of a whole. A piece of something. It is very laborious to add fraction when it is dissimilar. (a fraction with no the same denominator). The process requires finding the LCD (Least Common Denominator). Finding the LCD alone is herculean. If you can not find the LCD, you can not end to the right solution. But there is an alternative way to add fraction the easily There is a formula provided below how to deal addition of fraction without finding the LCD.


In the formula "a and c" are the numerator.The "b and d" are the denominator. In this formula, simply get the product of "a and d" added by the product of "b and c". For the denominator, just multiply "b and d".The result would be the answer if it is reduced to lowest term. We will give a numerical example to better understanding. See the illustration below.


We will substitute each values of the given formula to each numerical proportion. In this illustration "a=2", "b=3", "c=4", and "d=5". We get the product of 2 and 5 which is 10, added to the product of 3 and 4 which is 12. The sum of 2 and 5 which is 10 and 3 and 4 which is 12 as the numerator is divided by the product of 3 and 5 which is 15 as denominator (see illustration). 


Notice that the result is improper fraction(a fraction whose numeration is higher than the denominator). We will convert the result into mixed number (a whole number and a proper fraction). In this illustration, the final result is 1 7/15 as final result (see below).



ADDITIONOFFRACTION

MDAS OPERATION

MDAS OPERATION


In mathematics,logical operation is the most important to consider. It is by its gradual order where the final answer can reliable. Constant daily practice is the most advice by many to master mathematics. By basic operation, it should be the Multiplication should be the first in the series of operation, followed by Division, Addition, and Subtraction. Majority got stuck on this because some do not understand how to handle the operation. Multiplication will be treated at first and should not be intervene by Division at the same time. After treating the Multiplication clearly then that is the time for Division. Again do not manipulate them together. The result of the two gradual operations should be then followed by Addition and Subtraction. Let's check with the given illustration.

Based on the description, Multiplication is the first to operate followed by division, addition and lastly subtraction.


Illustration.


1. 12*3/4 + 5 - 3 = 36/4 +5 -3

                           = 9 + 5 - 3
                           = 14 - 3
                           = 11

From the example above. 12 and 3 should be treated because they have "multiplication" as operator. And 12 of 3 is 36 (see the initial result). After multiplication was completely done, division will be the next, and that is to say 36 divided by 4 which gave us 9. The next thing to do is addition to be followed by subtraction. Hence, our final answer is 11 and that is 36/4 +5 -3 = 9 + 5 - 3 = 11.

2. 4*4 / (2*2) - 2 + 3 = 16 /4 -2 +3

                                 = 4 -2 + 3
                                 = (guess what is the final answer)

Our second example was intentionally made for you to finish. What is the answer to this simple math with MDAS operation? Is it 5? Some say its negative one (-1) So what is then is the final answer?

3. 5 + 4*3 - 6 / 2 * 3 = ? (try to fill out the solution,remember the MDAS rule)


The third example was leaved for you to finish. Follow the simple steps of the operation. Check where is the multiplication as operation located. So it is between 4 and 3. Followed by the division which is 6 and 2 but it is multiplied by 2.  Next is the 5 added to the product of 4 and 3. 

Let us try the other two problems.

4. 15/3 + (4*2)/4 - 16 / 3 * 2 + 1 =

5. 2*3 + 6-2 * 3 + 6/2 - 1 =



MDASOPERATION

Friday, February 12, 2016

QUADRATIC EQUATION









This is the formula for quadratic equation. This equation is only for one variable with second degree of order. The general form of quadratic equation is ax2+ bx + c =0. For a derivation reason we arrived what is in the photos above.This is used usually if factoring seems so not a perfect square to get the value of x.

Sample graph of a quadratic equation:

1. A graph of single quadratic equation.




2. A graph of double quadratic equation.


3. A graph of multiple quadratic equation.


These are the illustrations of different graphs of quadratic equation looks like in different form of quadratic equation, may it be single, double or multiple.

LINEAR EQUATION















This is the form of linear equation in two unknowns. It shows a single straight line. This is different from quadratic equations. The arrow of the line means continuity. Meaning the line is extended infinity. The illustration only shows where the line was made. It is from the origin or center (0,0) of the Cartesian plane. The vertical axis is labeled by y and the horizontal axis was labeled by x. In this photo of linear equation, x was only limited from -1 to 5, and y to -3 and 2. It is not required really to extend those grades of the line to higher number. That only depends on how less or great the given of the equation is presented. The green dot shows the exact location of the point, of a line of course. The green dot above shows the point has the (4,1) vertex and the green dot below shows (0,-2) vertex. There are a lot of linear equation in different form, not only from the photos above.

Thursday, February 11, 2016

VENN DIAGRAM
















This the Venn diagram presentation. It shows logical presentation of a set(s). The red color in between signifies common parts of two sets. First circle and second circle are two different sets. There are several types of sets. They are one-to-one correspondence as a set, equivalents sets, equal sets, proper subsets,overlapping sets, and disjoint sets.

On set operation, we have unary operation and binary operation.  Unary operation is operation only for one set. And for the binary operation we two or more sets to form another set or sets.

CLASSROOM SET UP












This is the actual set up in the classroom where students are more interested in new mathematical learning. The topic being discussed here is linear programming.