# Top 3 Performers in Engineering Math 1(EMT 201)

Shown below were the top 3 students’ performers in Engineering Mathematics 1 (EMT 201) for the First Semester 2015-16 Engineering 200 level. The Final exam was conducted last March 1, 2016, at Edeh’s Ark Exam Hall, Madonna University, Elele Campus, Nigeria, Africa. Their performance is based on their Cumulative Assessment (CA) and Final Exam result for the semester.

 Reg. Number CA(30% max) Final Exam(70%max) Total Score First Place CHE/14/034 26 65 91 PTE/14/107 26 65 91 Second Place CVE/14/115 25 65 90 EE/14/150 25 65 90 PTE/14/092 25 65 90 FST/14/012 25 65 90 Third Place PTE/14/099 24 65 89 EE/T/14/122 24 64 89 MECH/14/063 26 63 89

Congratulations! Keep up the good work.

VICTOR E. ODARVE – BSME/MEP-ME/MAED/EDD

Professor, Mechanical Engineering Department

# Math Examples that Keep Students Challenge

By Vic Odarve

Solving math examples in different methods but yield the same answer is itself a challenge.  And it works; keeping students at bay!

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, an expert in this field and speak with a 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 yields 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 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!

Working Examples

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 methods; thus, increasing their math knowledge. These environments keep them changing, growing, and learning more 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.

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! It all begins with single math example that keeps the student’s challenge.

# My Math Visitor

By Vic Odarve

Except for private institutions, the country’s federal state universities and colleges were plagued with teachers’ union strike. Students stayed at their homes waiting for trouble to settle and resume their classes afterward. But one student refused to stop her schooling!

So I am lucky to teach in one of the private universities. No teachers’ union strike!

Engineering Mathematics 1

In one of my visit to the university library to read some local newspaper, one of the students approached and requested me to have some explanation on the math solutions previously discussed in the classroom. “Okay, what part of the topic?” I told her. She opened her notes and showed the steps where she got the problems and I did the explanation and discussion. Satisfied, she said, “Thank you, Sir, I understand already”, she said. Then I said,” How was the result of your last quiz?” “I got 90 % score, Sir”, she smiled. “Good, and on next quiz you must get a perfect score”, I replied. Then she slowly walked quietly and slip away. I paid little attention. She got a good score. So nothing to worry!  She may just serious enough and want to do more on her study every day.

Family tour-Chocolate hills, Philippines

Then, the next quiz came. Only 5 out of 234 students in a class got a perfect score. And she was one of them!

It was then that I gave her an attention. I noticed that during the class session, she sat at the end of the last row of the seats in a packed and overcrowded room. She listened intently and focused to my discussion. No friend, no talking even on her seatmates as if she knew none of her classmates! “She must be too shy”, I guessed.

The semester math course was about to finish. I gave the final quiz before the final exam. “This would be the last quiz”, I told the students. Then what was the result? She got perfect score again! She had done it! “She is a good performing student”, I told myself.

The next meeting I returned the quiz scripts. She was absent. For almost two weeks, I could no longer see her. Then I inquired the course representative and her classmates what happened to this girl. To my surprise, none of her classmates knew her. She vanished and I received no word from her and her whereabouts! I am completely blank!

After two weeks my phone rang. The girl informed me that she returned to her school at the federal university since the teachers’ strike was over. She thanked and told me that she learned and enjoyed math during her stint in my class. It was then I knew that she was my math- visitor. She was not my student! She refused to stop schooling! Then she returned to where she belonged!

# Nature Teaches Mathematics

By Vic Odarve

Not everybody loves mathematics! “I don’t like numbers. That’s why I did not take up engineering courses”, said one student. This summed up everything on his schooling! Since kinder up to high school, he has performed miserably in mathematics. But one thing is certain; whether he likes it or not, mathematics is a part of his everyday life. Unknown to many, math already existed in nature the moment we took our first breath of life. What we do is simply marvel mathematics!

The “petals” flower form spirals curve describing Fibonacci’s numbers.

Also nature teaches mathematics! Nature and math works in never-ending harmoniously. From the particle world of billions of stars spreading in our cosmic ocean, mathematical laws seem to work keeping the universe in order. From Newton’s law to Kepler’s Laws of planetary motion and Einstein’s law of relativity, math offers our deep understanding on things around us.

Nature has its own way of expressing mathematics! Patterns such as hexagonal beehives, spiraling Fibonacci flowering trees, fractals flowers and plants, fruits and leaves, and many more are actually mathematics!

FRACTALS, BEEHIVES, AND FIBONACCI’S NUMBERS

Fractals are repeating geometric pattern. They are rough fragmented geometric shapes that can be repeatedly subdivided into parts and that each small portion can be viewed as a replica of the whole. These are geometric designs we teach in classrooms. Since repeated, in mathematics is called iterations or algorithms. Newton’s method, simplex programming, Gauss Seidel, Jacobi, and many more algorithms are among few examples. Some plants exhibit simple recursive operations that after a few number repetitions or iterations their shape can be recognized as a repeated geometric pattern. It is mathematics! Fractals in nature are always pleasing to our eyes – clouds, plants leaves and fruits, galaxies, shells and many more. Plants such as sunflowers, ferns, cabbages, and papaya leaves are among a few of them.

Leaf arrangement suggests repetition

Honeycomb structure is also a nature mathematical exhibition. Look at its hexagonal shape. Its cross-section is made of the comb, a latticework of hexagonal cells made of beeswax. It is an expression of geometry in action. The design might be the most economical in terms of labor and wax; hence expressing least cost in economics and linear programming in mathematics!
Fibonacci number is a simple example illustrating the existence of sequence in mathematics. Just like arithmetic and geometric sequences and progressions. But in the Fibonacci sequence of numbers, each number is the sum of the previous two: 0,1,1,2,3,5,8,13,21, etc. And these numbers are exhibited in various “family trees” and patterns of spirals of leaves and seeds. The image of a nautilus shell approximates the sequence of the Fibonacci’s number in nature. Once again, nature teaches math!

Fractals, Fibonacci‘s shells, and beehives are iconic images that capture the beauty of nature displays in mathematical expressions. These displays are like ornaments to the eyes of the mathematicians. A living math in motion in order for us to love and appreciate nature! Indeed, nature teaches mathematics!

# LEARNING MATH AT CLASSROOM

LEARNING MATH AT CLASSROOM

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!

Students 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

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!

# Working Math Exercises; Tips and Benefits

By Vic Odarve

Mathematics texts/workbooks have something in common: exercise sets are presented at the end of the chapters. That’s why engineering students often wonder what are they for? More so, lecturers often told students to solve some of these exercises and submit the solutions on the next meeting. The message is clear: they are there to be worked out! These exercises are like a passport before students can go ahead to the next chapter. That is it!

Engineering Students

Like a wormhole, it screens whether students are ready for the next topics; also meant to wrap up everything what students are supposed to learn the whole chapter under study.  If the teachers do not give an assignment on the exercises, solve them by yourself for your own benefit. Following are tips on how to work most out of the exercises;

1. As starting point, select one exercise that is similar to your notes or workbooks or the one discussed by your teachers.

2. If you find still difficult and you could not solve anyone of the exercises, go back to the examples from your notes and textbook you are using. Review your example notes and solve without looking the solution. Check if you have a similar answer. If along the way you get stuck up, uncover the solution for a while and see where in the way you get lost. Repeat this process until you can master and understand how it is done. If you are convinced that you comprehend the process, go back to the exercise which is similar to your notes and solve it.

3. Make it a habit of reviewing or checking your work until your final answer. Since most exercises have answers, look and compare your answer only after you thoroughly check yours. If you get one exercise with a correct answer, solve the remaining. This way will build your confidence.

Working math exercises proves beneficial to engineering students. It relates to academic success. Following are common benefits derive from working math exercises;

1. Students who work math exercises perform better on tests or examination. By working exercises, students are reviewing what they cover in class, thus increasing their understanding of the subject concept better.
2. Students develop self-discipline and management skills too.
3. Students feel enjoyment and challenge in mathematics.
4. Students put their new acquired skills into practice. Practice makes perfect.

Math textbooks- a legacy for the next generation of students

Later, students will realize that what they learn in that particular chapter will be used in the next chapter. Mathematics or workbooks subject contents are presented in sequence. Master the first one before the next. Do not skip. If they could not solve the exercises at the end of the chapter, most likely they will be in trouble the next chapter. Follow the tips. Do it now, do not delay! Solve the exercises! Geniuses in mathematics are a gift from God, but skills could be developed!

Simply by following the tips, academic success and other benefits are yours.

# Ask and Learn from your Classmates

By Vic Odarve

It is the simplest thing to do for the students to learn more and pass the course.

Last semester, I had a quiz in Mathematics consisted of four problems. The last problem was the most difficult. Thus, it required an extra mile solution – deeper analysis- so to speak! As expected, the results after marking: only 2 out of 380 students got perfect scores. No wonder, it was difficult. But one of these students who got perfect scores caught my attention. It was intriguing! This student had never been in my list as top performers of the class! After rechecking, I found her script was perfect from the initial steps of the solutions until the very end. The solutions were well presented. Presentation was so detailed that no appreciable error can be seen. When the class resumed, I returned their individual papers or scripts and let her solved the problems on the board. To my surprise she explained very well; discussed  solutions perfectly that the class applauded her. “Thank you, well done”, I commended her after the discussion. Oh my God, I was awed and shocked in disbelief?

Engineering Mathematics

After a week, I happened to meet and talk her in the library how she was able to solve the last problem. “Yes, very difficult sir but I was able to ask help from my classmate few days before the quiz and we discussed together”. That’s it. It was her secret! Asking help from her classmates! She was referring to the other one who always got perfect score in all of my quizzes –a gifted student in Math!

No doubt! She learned by asking help from her classmates during study and propelled her way to get perfect scores! A simple act yet effective in Mathematics! Asking help from your classmates or teachers is one of the options to learn and pass this course.

Every student runs into problems in Mathematics courses from time to time. Even the bright ones! This is a part of learning process. But students who ask help from teachers or classmates appear to move and recover the lessons easily. Problems are likely getting past by asking help. Resourceful students are doing this way.

Classroom lecture!

By asking, students are benefited! The students may ask help from their classmates and get perfect scores during exams! But every student must know the art of asking either from her teacher or classmates in order to learn most out of it. The following tips help students maximize the benefits of asking from their classmates;

1. Do the explanations. Show the way how you come up the solutions until the steps you lose. The reason is clear: the one who does the explaining will learn the most.
2. When you are working in group or sharing some ideas, share your opinions with others. Don’t let only one person do all the talking. Participate!

Just follow the above tips and it works!

# Keep Your Big Mouth Shuts!

by Vic Odarve

When Joseph visited Dr. Martin’s clinic for HIV patients, some of his friends spotted him. So in a party held for the employees a week later, somebody asked him if he had an HIV. Joseph jokingly said, “Yes, that’s why you had seen me at the clinic last Tuesday”. He just talked without bothering it! Joseph actually had no HIV but merely visited the doctor for some business not related to his health. But when he reported to work the next day, almost everybody thought that he was infected with HIV. The news grew rapidly like a wildfire! “It is horrible!” he said. The news amplified and became unpleasant to his ears when somebody asked him on his health. That was it. It started as a joke and appeared out of control!

Keep our big mouth shuts!

In one of a work happy hour, Mary shared her stories to the group that school management approved her scholarship abroad. Then somebody asked her question,”What if you will be hired to teach at that university with much higher salary?”Then she replied without bothering herself,”Well, I have to accept the offer”. That was it! A little rumor developed! But to her surprise the message amplified and spiraled to a proportion that it reached to the management. A few days later, her boss called her to his office. The school management cancelled her engineering doctorate scholarship in London.

So, better keep your mouth shuts next time!

See what happened. Joseph felt irritated when friends asked about his health. It brought an unpleasant atmosphere to his working environment. On the other hand, School management cancelled Mary’s scholarship for no apparent reasons. Their common denominator: Both did not keep their big mouths shut!

Biblical story, too, reminds us that it is better to keep out our mouth shuts. Abraham kept his mouth shut from the day he received the message to sacrifice Isaac until the final moments when the angel intervened.

Life is what we make it. Perhaps some intimate details in our lives are better left unsaid. Keep it from public knowledge! Even to our best friends! Or make second thoughts if we want to divulge! By keeping some vital information to ourselves is a safer option than risking ourselves to the outside world. We will soon realize that this world is much wider than just what we know to be our own.

So, keep your big mouth shuts!

# ENGINEERING MATH 2-STUDENTS PERFORMANCE

STUDENTS PERFORMANCE PROFILE IN ENGINEERING MATHEMATICS 2

Below is the performance profile of the students taking Engineering Mathematics 2 (EMT 202) for the Second Semester 2012-2013 March batch at Madonna University, Elele campus, Riverstate, Nigeria, Africa.

Table 1 shows the students performance that in a class of 399 students, only 310 or 78 % passsd the course.

Table 2 also shows the grade distribution profile and the grading system corresponding to the marking ranges. Surprisingly, number of students who got A grade is almost the same as the number of students who failed to pass the course. That is, 88 students got A grade and 89 also failed to pass the course. Further, 53 students garnered B grade, is nearly equal to those who came up with D grade which is 50. Only 64 students or 16 % got C grade.

Table 1 – Students performance Profile

 Students % Passed 310 78 Failed 89 22 Total 399 100 Table 2- Grades Distribution Profile Grade Marks Students % A 70 – Up 88 22 B 60-69 53 13 C 50-59 64 16 D 45-49 50 13 E 40-44 55 14 Failed below 40 89 22 Total 399 100

As in the previous semesters, passing percentage falls at 70 – 80 % of the class. So, this class performs at the same level.

# EXAMPLE AND HANDS-ON LECTURE METHOD

By Vic Odarve

Do students want a participative kind of lecture in a classroom? Yes, and it is more entertaining in Mathematics! Lectures in mathematics are usually done by presenting problems or exercises. Just by having an illustrative example that catches the students’ attention, all eyes will be on the board and draw their wandering minds to focus on the new lesson for the day. The mind will be put in focus just like a parabola; the focal point will be on the lesson.

Madonna University, Elele Campus,Riverstate, Nigeria, Africa

It puts the students’ engagement to the lesson at high concentration level. This modified traditional teaching method works well if the teacher knows very well the subject matter. Then how to transfer them to the minds of the students in the easiest way is another thing. There are teachers gifted with wisdom and skills to capture one’s mind and power to facilitate understanding. Geniuses are born but skills can be developed. Thus, this method can be developed and implemented in our classroom!

Following are basically the steps on how this method works;

1.    Make an illustrative example of the topics. Usually in mathematics, an exercise or a problem illustrating the discussed principles or theorem can be an example. Make an example or problem that requires the necessary ingredients of the subject matter and its working solution needs deep analyses.

2.     2. Step by step solution. Slowly explain the details clearly on how to solve the problems in a step by step manner. It must be step by step. Step by step discussions must be accompanied along with the reasons and significance. The step must be the prerequisite to the next process. Just like algorithms. Just like climbing a ladder. No shortcut! Complete your discussion until the final answer is done. Remember that we have to number every step! Remember that students learn more by observing how we do the process and imitate it later.

3.  Entertain questions to further the knowledge if something along your discussion students does not understand. Just like open forum. All are free to ask questions.

4.     4.  Highlight the critical steps that must be taken with attention. Your experience will tell you which of the processes the students most likely find difficulty. Review them.

5.      5.Test if they can do it by themselves. Go to your favorite and brightest student. Let him come and discuss the steps written on the board. Add more explanation to emphasize the significance of the step. If you think no more hitches along his discussion go to the next step.

6.      6. Final step.  Make another example and let all the students involve in doing the step by step solution. It is now their turn. Remind them to follow the pattern by following the steps. Start on the students sitting in the first row. That is, first student sitting in a row will be the one to go to the board and work on step 1 of the solution. Then the next one sitting on the same row will be the next to go to the board and do the next step. The process of going to the board and continue the next step by next student is repeated until the final steps are completed or the final answer is achieved. Each student will do each different step in succession! Teacher is now reduced to a mere facilitator. The ball is now rolling to the students. They must do their share.

A two hour period in a course can complete 2 or more topics with the same procedure. In a class of 30-40 students, all can participate by going to the board and do one step each until a problem is completely solved.

It is worth seeing to see students with all the eyes on the board and ears to the teacher. It is because everybody waits his turn to go to the board and write something for the solution or step. All can participate! No student is left behind. Once the teacher is skilled on this system, he can get the attention of the students and add more tricks to make the activity challenging. The class is under his spell when the time of the day is done. Students as well as the teacher are satisfied.

This way teacher and students are doing like a teamwork. It is entertaining and challenging and a learning engaging activity! Students feel the importance of being there by having accomplishment. Perhaps the introduction of this method may result to their lifetime pleasure. We do not know that some students are touched. That is by participation! It is learning by doing… encountering new approach in an exciting ways! A whole new world!