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!