Nobody Becomes Rich in Teaching

                       By Vic Odarve

Yes. Nobody becomes rich in teaching simply because teachers are low wage earners, the profession requires full time and dedication, and ever increasing cost of living. Across the globe worldwide, various bills are pending in congress and legislature asking for increases in educational funding where salaries and wages for teachers are often connected with. It requires a full time work, dedication; hence income is largely dependent on the remuneration. In today’s complex living environment, the rising cost of daily commodities overtakes the salary increases; hence putting the meager wage earners like teachers in a hand to mouth situation. Therefore, nobody got becomes in the teaching profession.

Classroom lecture in an African university

Classroom lecture at an African university

Traditionally, teaching has been one of the lowest-paying jobs available in the market today. Though salaries vary from country to country, most well developed countries, for example, teachers receive significantly better salaries and benefits than do teachers in the developing nations. In most African countries as well as third world countries, teachers often have prestige, but their salaries are often meager. That is why teaching jobs are less inviting for most qualified college graduates because there are more lucrative positions in commerce and industry. This sentiment seems to be becoming more and more prevalent. Today, teachers’ salaries are often subjected to debates in congress by lawmakers in almost all countries around the globe; hence resulting in a turtle paced increases. With a low paying job, nobody becomes rich in teaching!

A Math exam

A Math exam

Teaching job requires full time commitment. As teachers devoted their time in the classrooms, earning other extra income is limited. Opportunities to earn more outside the profession appears difficult. The meager salary is just enough to meet daily needs. When a member of a family got sick, problems multiplied. These explain why most teachers are victims of usurers and other shark infested loans. What are left of the take home pay are not barely enough for electric bills, tuition fees, hospital bills, etc. Nobody got rich in teaching!

Math textbooks- a legacy for the next generation of students

Math textbooks- a legacy for the next generation of students

Compounding lower salary increases is the spiraling cost of living. The price of the daily commodities often increases exponentially while the salary goes linearly. This adds to the pain they feel. This is a growing concern in almost all countries. Cost of living is rising and outpaces the individual income. In most cases, teachers runs out of money before the end of the month. However, some seem to manage to have car or big houses, but it could just be a façade to hide a mountain of debt in banks and money lender.

Conducting lectures at international convention

Conducting lectures at the international convention

 What drew to the teaching profession are the passion to teach and love to build the characters on our students for life. Teaching touches lives and a noble profession. Teachers help us who we are today and steer the course of civilization of mankind. But teaching profession could not make us rich, but it is the legacy that matters.


EMT 202 Engineering Math 2 Quiz 2

Our second quiz will be on Monday, June 22, 2015. Please review the following matrix methods in solving unknowns for sets of linear equations.

  1. Cramer’s rule. This method makes use of the determinants in finding the solutions. Using the minor’s method, determinants can be solved easier. Very important for the minor’s method is the use of the conventional signs. Any rows or columns can be utilized as long as conventional signs are observed. Then use the formulas for the unknowns.

2. Gaussian Elimination method. This is the most used among the upper triangular matrix system in solving sets of linear equation. Of course transform first three sets of equation into the augmented matrix form. Any legitimate row operations can be used to achieve the required upper triangular matrix. Then, finally, back substitution will solve the unknowns.

3. Gauss Jordan. This method is just a continuation from Gaussian elimination by making the diagonal line into 1’s and zeros upper and lower matrices. Row operations are used to attain the form. Since the diagonal elements are 1’s, unknowns can be solved readily.

4. Inverse Method. This is derived from the AX= b equation. Of course, A is a coefficient matrix, X represents the unknowns, and b, are the constants. Transforming such equation into X = A -1b, may solve the equation where A -1 is the inverse of A.


Try the sets of linear equations below. Solve the following sets of equations by

a) Cramer’s rule b) Gaussian elimination

c) Gauss Jordan method d) Inverse method

                       2x – y + 2z       = 7

                        x + 3y -3z        = 10   

                        3x – 2y + 3z    = 5

Answers:        x = 1                y= 11               z= 8

  1. Victor E. Odarve, BSME/MEP-ME, MAED, EDD

Mayana, Jagna, Bohol, Philippines, Southeast Asia



Let us learn from plants! It is the nature’s way. Just like learning math at classroom! Plants make use of the quantum physics superposition theory. They harvested packets of light energy and converted to chemical energy with remarkable efficiency. Experts found that photons come in and see many energy paths and the effect called “coherence” helps determine which path is the most efficient to follow. That is it! Plants, the receiving end, maximize the conversion process!

IMG-20131003-00161Students studying mathematics are like plants harvesting the light energy. If students do not find the most efficient way to capture the wisdom of the classroom discussion, they are not converting efficiently the best knowledge that supposes to be imparted by the lecturers. Everything they do from the start to the end of the lectures has something to do with their own learning method.
Classroom lectures work on the same idea as plants do. Students, being the recipient of knowledge, must learn it with remarkable efficiency. Teachers always find the most efficient means to impart the subject to the students the best that they can deliver. Teachers feed them different ways how to solve mathematical problems by breaking these into its components slowly

Engineering Mathematics 1 students batch 2013 First Semester

Engineering Mathematics 1 students batch 2013 First Semester

and slowly. Then finally problems are transformed to its basic operations. This is basically the features of the classroom lectures!
Still classroom lectures are the best means for students to learn fast in mathematics. Teachers are there to instruct, discuss, assist, and show different approaches in mathematics by working out examples and illustrations. Classroom lecture offers opportunities for students to ask questions, offers suggestions and presents ideas, and shares knowledge with others.
In order to help students, the following are tips on how to maximize learning on classroom lectures;

1. Take an advanced reading of the topic for discussion before going to the class. Just read and picture out the new subject matter even you do not have clear understanding. Just a glimpse of the new topic! The idea is to let you feel as if you are in a review mode when you are in the classroom.

2. Listen carefully the discussion done by the teachers. Make notes on important points! This keeps you alert for the whole session. This avoids feeling sleepy or daydreaming. Sometimes teachers could share their own knowledge on things that may not be found in your textbook. Be an active participant.

3. Ask question if you fail to grasp some important points during class lectures. This keeps you from guessing and spending time later on your review. By asking questions, you learn and solidify important points. Understand the why behind every steps of the solution.

High-achievers undoubtedly do more efficient way to maximize their learning in classroom. Though not all students are endowed with wisdom to learn quickly like King Solomon, above suggested tips will help the slow learners in Mathematics. Remember there is no day in our life without mathematics!


Addition and subtraction of matrices do not offer much difficulty to the student. Basically the operation follows the usual arithmetic operation. But multiplication of matrices is a different matter. It is quite difficult as some rules are to be followed. The difficulty of operation increases as the size of the matrices to be multiplied also increases.

MS Excel becomes a valuable tool in obtaining a solution for matrices multiplication. The program saves time and effort. For purpose of illustration, open the MS Excel and solve the following matrices;

EXAMPLE: Find the product of matrix AB.
If matrix A= 4           2         3
1            1         2
2           1          3
and matrix B =    2         4
1           0

1           2

Find AB.

Highlight vacant cells for the product. The product
is a 3×2 size. Then move the cursor to the formula bar and put = sign.
Then at Formula heading, browse for function MMULT. Dialogue box
appears. On array 1, highlight data of matrix A. On array 2, highlight
data of matrix B. Then press F2. Then press Ctrl + Shift + Enter
simultaneously. Answer appears at the space provided for the product, as follows;

13          22
5           8
8           14

Below is a dialogue box as shown in the spreadsheet.

Dialogue box where you enter the matrix data.

Dialogue box where you enter the matrix data.



By Vic Odarve

 Let’s take a look on how the students performed last semester. This class of 440 students was undoubtedly large.

 As in most African universities this school has its own grading scheme. Components composing the final grade are continuous assessments (CA) and final exam. Maximum marks for CA is 30 while for Final exam is 70. Total is 100 marks or points. Students must get at least a total of 40 points in order to pass the course. It can be from CA or Final exam or both. Table 1 shows the grading scheme and its equivalent score range. Continuous assessment or CA generally consists of assignments, attendance, and class participation. Final exam score is the one obtained by the student during final examination.

Table 1. Grading Scheme

Table 1. Grading Scheme

 Table 2 showed the percent profile of the grade distribution in the last semester. Out of 440 students in the class, only 320 passed (73%) and 120 failed (27%) Majority of the students who passed the course obtained a C grade or its total equivalent marks of 50 – 59.

Table 2. Grades distribution

Table 2. Grades distribution

 Table 3 showed the different contributing factors why students failed to pass the course. As shown, majority failed to pass the course due to poor performance during final exam (48%) and followed by no assignments (40%).

Table 3. Failing grades distribution

Table 3. Failing grades distribution

 Teachers are like gardeners planting seeds in the fields. They planted wisdom to the minds of the students in the classroom. Some learned the lessons quickly while others did not! Even Jesus, the greatest teacher of all time, lamented on the outcome of his preaching through parable from Matthew 13: 4-8.

 4 Jesus said, “The sower went out to sow and, as he sowed, some seeds fell along the path and the birds came and ate them up.

5 Other seeds fell on rocky ground where there was little soil, and the seeds sprouted quickly because the soil was not deep.

6 But as soon the sun rose the plants were scorched and withered because they had no roots.

7 Again other seeds fell among thistles; and the thistles grew and choked the plants.

8 Still other seeds fell on good soil and produced a crop; some produced a hundredfold, others sixty and others thirty.

 This happened 2000 years ago! Today the same thing happens in our classroom. We plant seeds to the students. Some may sprout and others do not.

 And what is on the statistics? The statistics demonstrates that the grade distributions are scattered. This shows that students are struggling to obtain good grades. Why? Because grades are earned and are not given! But as always be in the minds of the lecturer, if there are winners there are also losers. The trend seems to fit the parable.

Kneel and Ask Forgiveness?

By Vic Odarve

Uniquely African practice!  Kneeling and asking forgiveness for violations or mistakes is a common practice among college students.

It was a final examination day in Mathematics! Amid a hot and crowded exam room, I saw two students copying answers with each other. Without warning, I confiscated their papers. Then they knelt before me and said,” Sir, we are sorry”.

Engineering students

Engineering students

 I have not yet decided on what punishment would I take, but they were there kneeling before you! Then I told them,”Stand up, do not kneel before me, stand in front of the class until I tell you to sit down”.

I was caught by surprise as I have not experienced students kneeling before me for several years of teaching in university/college in our native soil. But this is an African country! They have their own way of practice.

In most parts of the world, it is one of the customs to kneel to a person who is older or in authority as a sign of respect. Kneeling is often associated with reverence or submission. In religion, kneeling is associated with worshiping. It is an expression of submitting yourself to the Almighty.

 But college students are kneeling here! Students kneeling before the teachers are  a common sight in African colleges and universities, according to one of my colleagues, an African lecturer. This could be the practice since time immemorial as this continent was once ruled by kings and queens who were revered like God by the constituents. These constituents are kneeling before them for some reasons.

Final Exam

Final Exam

 Perhaps there are no other more profound forms of pleading or asking forgiveness or help from a person in authority than kneeling. When you see college students kneeling before a teacher and pleading for forgiveness for the mistakes they committed, the teacher simply cannot ignore. We have to balance our assertiveness in exercising our authority in the classroom at the same time being approachable. That is establishing a limit, a boundary or red lines!

  Even Jesus, seeing a woman kneeling before him, did not simply ignore since he sees the action comes truly from her heart. Read the  Matthew 15;22-28;

 22 Now a Canaanite woman came from those borders and began to cry out, “Lord, Son of David, have pity on me! My daughter is tormented by a demon.”

23 But Jesus did not answer her, not even a word. So his disciples approached him and said, “Send her away: see how she is shouting after us.”

24 Then Jesus said to her, “I was sent only to the lost sheep of the nation of Israel.”

25 But the woman was already kneeling before Jesus and said, “Sir, help me!”

26 Jesus answered, “It is not right to take the bread from the children and throw it to the little dogs.”

 27 The woman replied, “It is true, sir, but even the little dogs eat the crumbs which fall from their master’s table.”

28 Then Jesus said, “Woman, how great is your faith! Let it be as you wish.” And her daughter was healed at that moment.

Madonna University,Nigeria,Africa

Madonna University,Nigeria,Africa

 Are these college students using kneeling as a smart way of admitting the mistakes and needing immediate forgiveness? Does kneeling, an action asking forgiveness or reverence, come true from their hearts? Are these new generations of college students redefined kneeling on their favor? Nobody knows!

Kneeling and asking forgiveness… its African way of life.


Zip line- Adventure

Zip line- Adventure

Garden of Eden

Garden of Eden



These are the areas of concentrations. Try to solve by yourself as part of the review on the Final Exam in February 2013 . Similar problems will be coming out.

  1. Bacteria are growing at the rate equal to 10.60 % of its population each week. If in the beginning there are 2000 microorganisms, how many organisms are present after

A) 4 weeks           b) 2 months

2. An engineering student deposited N400, 000.00 at an annual rate of 18.55 % compounded continuously, how long will it take the account to triple in value?

3. A tank contains 222 liters of water. A bitter lemon solution containing 3 kg/liter of sugar enters the tank at the rate of 6 liters/min and runs out at 5 liters/min. The tank has a paddle that keeps on stirring in order to keep the mixture uniform. Find the amount of sugar in the tank after 1 hour.

4.       Determine the value of current I flowing in a resistor R= 100 ohms, an inductance L = 7 henrys and a battery E = 100 volts connected in series.

5. A Madonna University canteen serves a cup of tea at 96C   to an engineering student. After 3 minutes, the tea has cooled to 78C . If the canteen temperature is 18C , how many minutes that the student must wait to cool the tea to 46C?

6.Solve y” + y’ -2y = e 3x    using a) undetermined coefficient method

b) Variation of parameter method

7. Solve y’ + 6y = 0,          y=2    when t=0.  Solve by Laplace transform.

8. How much will be left after 600 years for a radioactive element carbon 14 which has a half life of 5750 years if the initial amount is 50 grams? Solve by Laplace transform.

9. Determine the equation of motion of a 40 kg mass suspended to a coiled spring with k = 2000 N/m, initially displaced a distance of 1 meter from equilibrium position, and released with zero velocity and subjected to no damping or external forces. Solve by Laplace Transform.

10.  A student deposited N200, 000.00 at an annual rate of 8.25 % compounded continuously, how long will it take the account to double in value? Solve by Laplace.

11.Find the area bounded by a parabola y=x2 from x =0 and x=6 by vertical and horizontal elements methods.

12.Determine the accumulated amount of N22000.00 after 12 years if invested at a nominal interest of 4 % is compounded continuously?

13. A hemispherical tank 8 meters in radius contains mercury to a depth of 4 meters. Find the volume of mercury in the tank.

14. The watermelon is ellipsoid in shape with major axis 44 cm and minor axis 36 cm. Find its volume.

15. Solve  y” + 5x (y’)²=0.

Good luck!



The Game of the Math Professor

                                                 By Vic Odarve

Some students find it frustrating that they cannot make sense of the lesson, and that’s why they feel tired inside the classroom. As a result, they miss the point the professor wants to emphasize. Failure to grasp clearly on the lectures may give its toll in the next succeeding topics. Worse, students are bound to fail the Math course they are taking. But not for a wily mathematics professor! He is bringing his students to his own world… playing his game in a tricky way. It’s a professor’s game.

Working Examples at the classroom,UIC-Davao city, Philippines

Working Examples at the classroom,UIC-Davao city, Philippines

Picture this one out! The professor started his game this way. After a detailed discussion on how to solve the example math problems and sensing that there were no more questions, the professor pointed to the board and said to the students” Alright class, it’s now your turn, work out the following problems in your seats”. To catch their attention, the professor made a simple problem. It was just similar to the example discussed. Just a trick!  If the students understood the discussions, the problems were as easy as eating peanuts. Looking for the students with a big smile, he asked, “Any volunteer to solve this problem?” Surely, almost all students raised their hands. But to the dismay of the students, the professor pointed to students not raising their hands.

A Math exam

       Caritas University, Inugu State, Africa

Then the professor made a second problem on the board.  It was  a difficult one. “Is there any volunteer?” he asked again. Only a few raised their hands. Then the professor told one of the volunteers to solve the problem with the board. Lastly, he made a difficult one. Since nobody raised hands, the professor looked to his best and brightest student. “Just try to solve this one on the board’’, he said. Commanding but supporting words to his favorite student. A bright student is a teacher’s pet! Moments later, silence engulfed the class. Students were very busy wrestling out the steps by steps in solving the problems. Then afterwards, the professor instructed the students working on the boards to explain their works to the class.

Engineering students

Engineering students-Madonna University, Nigeria,Africa

So, what was the next picture? It was a lively discussion. Just like an open forum. Students discussing their solutions on the board and entertained questions, comments, and suggestions. Professor acted as a facilitator. Almost everybody shared the ensuing discussion. The lesson was like a hot cake in which customers were in line waiting for their turn to buy! Unknowingly, the class was slowly and slowly drawn by the spell of this wily professor. That’s how the game works. Students are falling for the line, hook, and sinker. The professor is playing his game in the classroom.

The scenario is quite easy and simple. Yet these simple sequences of drama demonstrate how this professor is playing the minds of the students in the classroom. Unknowingly the professor has opened student’s senses under his spell. Aligning students’ minds with the professor’s mind! Living in harmony! One world, one mind in focus… solving mathematics. He is building a ladder for his students to challenge mathematics.

This is the trick that works! Never a dull moment! A vibrant discussions and lively environment in the making! No frustration! No more tired students. Everybody enjoys the class and dreams when will be the next session. It is the game of the professor.