Math Examples that Keep Students Challenge

By Vic Odarve

Working math example and solving it in different methods, but yield the same answer, are itself a challenge. Students learn three or four math techniques with a single example. And it works; keeping students at bay!

Math workbook

This approach allows the students to learn the principles of each method of solving same examples and develop mastery. As they master the different methods, students can readily compare the results with ease and build confidence. As confidence builds up, they challenge math problems by doing themselves; hence math becomes easier and simpler. 

Solving math problems by different methods can surprise many students, even the stupid ones. Math teachers, expert in this field and speak with power of persuasion, keep students’ eyes, glue to the board; ears listen to every discussion, and silence throughout the classroom. For example, in Algebra, find the value of x in a quadratic equation by factoring, by completing the square, and by the use quadratic formula. These three methods of finding the solution work differently, but result to the same answer. This way the students learn three math principles in just one example. Furthermore, they can spot the differences, and mimic the teacher’s steps in arriving to the final answer. Students feel great, satisfied, and enjoyed by learning three different approaches. This develops mastery of the course. Of course, a surprise and challenge!

Math students

Solving single math problem and obtain the same result using different methods also allows students to check and compare the final answer; hence the process builds up their confidence. Students turn this great opportunity to learn more of the methods; increasing their math knowledge. These environments keep them changing, growing, and learning more in math; thus becoming them to be an expert. Since all the methods yield the same results, they are motivated and making great grades… one of the top class math performers. The approach does build their confidence.

Henceforth, as confidence develops, students challenge themselves in solving math exercises and problems. They practice solving math more often. Teachers, too, can apply the same technique in a higher math. For instance, last semester, a lecturer gave an assignment to his students as a follow up in a classroom discussion, shown below;

Solve the Differential Equation    y’ -2y = 0,           y (0) =1.   Find y (0.8)      by

a) Ordinary Differential Equation method

b) Laplace Transform

c) Power series

d)  Euler’s method with n = 4.

One exercise, but to be solved by four different methods!

What were the results? Some students came to the office smiling and showed their solutions confidently; others wanted to discuss how they got their final answer. Sounds great and fulfilling!

Engineering students

The experience teaches lessons that will never be forgotten; the process builds strong math students to prepare for international competitive careers. That’s why some teachers notice that all workbook exercises left for the students to work out as homework have been solved with incredible correct solutions and approaches. Some solved by three or more methods with accuracy. It is a perfect challenge! It all begins with single math examples.

Math is difficult but teacher gives illustrative example that looks like hitting three or four birds with one stone!

Loosen Your Toxic Friends

                    By Vic Odarve

If they amplify problems to your life instead of giving solutions, it is now time to loosen these toxic friends; they are opportunistic, disrespect, and insecure.

Toxic friends are opportunistic; looks so pitiful and sorrowful when asking help. But once your help is over, he abandons your friendship and never looks back. He is on your side when you have something to give, and do opposite when you have nothing to share. He never feels obliged to render help when you need him most.

Loosen your toxic friends

They treat your friends with disrespect. They exploit the mistakes of others, even pointless; often make unsolicited remarks about others shortcomings during group meetings, acquaintances, and associations. They want your friends to become a target of ridicule for a sole purpose of propagating jokes; make them as a source of the enjoyment. It is their pleasure to see their friends committing mistakes or misfortunes. But if somebody will do the same to them, say, joke on their error or mistake, they will confront the person like a wounded tiger. If your friend does this to others chances are he will not respect you too. A good friend will treat everyone with respect.

Friends together

Toxic friends are jealous and insecure. He cannot sleep comfortably if he cannot fit your new iPhone, iPads, I-pods, etc. He feels being left behind. In a society, where bigwigs and famous personalities are adorned, they also want to be the chosen, the beloved, and the esteemed. If they failed, the natural instinct is to tear the friends down. Though act as a good friend in the daily meeting deep down in his heart he feels devastated that you’ve overtaken him in some areas of your life. These friends take the pride in relating how he did successfully in some illegal activities, putting their friends down, and idolize the corrupt and famous personalities.

If these telltale signs are clear to you it may be the time to loosen your partnership with them gradually. If you could not ward off getting rid of the group association for some reasons, the best way is to minimize your acquaintances.

Friends are like sunsets. It has an end.

These demonstrate the dark sides of human nature. Toxic friends may just bring you heartaches, sickness, and endless misery. It may bring you unwanted drama in your life and may end yourself in a disaster. Spend with your friends, which you think are your model whose solid character as true friends brings you a positive outlook in your life. These toxic friends wicked and living in the darkness must be loosened. The Bible tells us so, 2 Corinthians 6:14-15

14 Do not make unsuitable covenants with those who do not believe: can justice walk with wickedness? Or can light coexist with darkness,

15 and can there be harmony between Christ and Satan? What union can there be between one who believes and one who does not believe?

 Get rid of toxic friends. Cut them loose! They are not meant to be a member of your tribe. Toxic friends drag you down.

Copy Blindly and Understand Later

                                        By  Vic  Odarve

Failed to understand and behind in a math discussion? Just copy blindly and understand your notes later.

This is an engineering student’s way of life – abounds of mathematical theorems, formulas, principles, transformations, and a lot more. What a life! So, anybody would like to become an Engineer? And adding to the pain, once students behind in a discussion, teachers just told them boldly,” Just copy blindly and understand it later”. Copying without understanding? That’s it. This is the picture painted inside the classroom. The lecturer did no longer explain the details of the steps on how the previous course of mathematical principles and techniques are done. “These steps are supposed to be learned in your previous course, and the class is running out of time,” lecturer told the students. That’s why students who did poorly in the previous math are frustrated. Sounds hopeless? Not at all; just copy blindly and understand the notes later!

Math lecturer

 Copying blindly simply means noting down whatever the steps the lecturer has done in the classroom, even without complete understanding on what you have copied. This is the common scenarios in an engineering classroom. The lecturer is a lecturer and nothing more. He knows how to weigh things, whether to review or not, otherwise he will be behind or may not complete the topic before the semester ends. So as a result “just copy blindly “. It is the students’ initiative; teaching them that to become an engineer is not a bed of roses. Math professors like Einstein, work and solves worded problems lightning speed that only few can fully understand. Since math is like a ladder and if students had poor performance in their previous courses, this time it takes its toll. As a result, students just copy without understanding. But this is a significant step…first step to develop how the students can catch up the tremendous pressure to pass the course.

Madonna University

However, this scenario is not so horrible. This message” copy blindly and study later” encourages the students to study more. This means that students must revisit their notes and lessons after the class. The phrase “understand later” lingers in their memory urging them to review on what happen to their notes or else next meeting they do the same.... Copy blindly and completed the bachelor’s degree in six to eight years instead of five. Most often students will find that after a little review in a discussion that initially baffled them will all of a sudden make sense. Thus, like a gravitational pull exerted by dark energy in the expanding universe, “copying blindly and understand later” challenges the students.

Copy blindly and study later

Subsequently, the students develop a habit of opening the notes and review everything there on what was discussed by the teacher every after the classroom session. Believe it or not, that slowly and surely, the students develop the habits of doing these practices every after the class session. The turn of events is now clear: students find themselves loving mathematics! The phrase “copy blindly and understand later” becomes the thing of the past.

When the Baby Smiles

When the Baby Smiles

By Vic Odarve

When a baby smiles, it brings more than a smile. It is a smile that develops a feeling of attachment and bonding. Unlike all other smiles, a smile from a child is more powerful and appealing. It is contagious, that is, it has an ability to make others also smiling. Children are gifts from God and their smile captures the tenor of your day.

A smile can change your mood of the day

When a baby smiles we can’t help but smile back at them. There is something strange developed within your heart; a feeling of connection and bonding. This sensation plays an important role in their development. They felt secure and safe. Smiles are their way of communications and relay some important information. Your payback smile, too, helps the babies learn and understand about the world around them. Thus, slowly and surely, connection and bonding develop…a bond more powerful when two atoms share one or more pairs of electrons form a molecule.

Innocent smile

What makes their smiles more powerful and enchanting are their innocent and fascinating faces to look at. Their simple, sincere, and straightforward smile can attract more than admiring looks. Their cheeks rise and the skin around their eyes bunches up…a true feature of a true smile. Their smiles are also bliss for all those seeking happiness of other people. Unlike adults whose smiles are often fakes and superficial, children offer perfect smiles. Going back to our old pictures while we were still young and carefree, and eager to explore the world is itself a source of entertainment. Our smiles, then, were once powerful and fascinating… showing to the world our innocence!

Children have an ability to make others also smiling. Their gestures and smiles are very interesting, especially to observe if they are doing funny things in a crowd. It can make your day smiling and forget the daily toxic stresses. It alters your depressive mood to happier one and sets the tenor of your day. “To see the kids' smile on their face, it brings a smile to my face too," said Hagler, who has been involved with the

Young and carefree

foundation for children for over a decade. Over the long term, smiling can have a positive effect on our well-being; improve our health, perception at work, social life, and feel happier and less stressed. A good smile can help release emotions, especially those emotions that might bottle up inside our heart.

Therefore, children’s smiles are something that connects us together to their world; so unique and interesting that it makes also others smiling. Their smiles are more than a smile! 

Simple Joys That Nature can Offer

By Vic Odarve

Mother Nature has, and always be, offers her inexpensive entertainment. From the forested land and mountains, an orchestra of birds doing choir. In the sky, canopy of clouds is drifting above our heads doing a military drill and at night stars are twinkling in unison like an entertainment in the heavens. Back to our sandy beaches and rivers, beautiful sights will stick in your mind for the rest of your life. Nature has, and forever be, gives pleasures free of charge to everybody!

Dining at Floating restaurant in Loay,Bohol

It is always a joy to visit farms with our family and kids as weekend retreat area. Nearby are mountains, dense forest, and a pristine river. What we do there! Feel the earth. We feel like walking through mist and clouds along the mountain ranges, meet all the fairies and magical creatures, and watch the birds doing orchestra along the canopies. By remembering our good old childhood days, it is sort of feeling that cannot be captured on camera and more than the old pictures hanging on the wall.

Mayana Village, panoramic view - borders Boctol and Bangwalog

During daytime, clouds can be seen drifting above our heads. At nighttime, it is a joy to see the canopy of stars twinkling in all the heavens; stretching like an enormous spider’s web scattered in all directions across the vastness of the cosmic ocean. Feel the presence of our Creator; we owe our lives to these stars. By thus doing, we feel the joy the Nature gives.

Walking alone or with your love ones along the sandy beaches or take a ride on a floating restaurant alongside in a river is a joy by itself; spend some moments watching fireflies at the banks of a river or the thrill of observing trees decorated with bird’s nests or dined with your family seeing the

Tree flowered bird's nests

beautiful panorama underlining the river upstream open our eyes to the outside world. For a moment, we feel the tranquility of our lives from the toxic city life.

As we see it, Natur gives pleasure free of charge to everybody; from forested lands and mountains, clouds and stars, to sandy beaches and rivers. It is all given unconditionally… to the poor, the rich, and the mighty!