The discovery approach is closely associated with the investigatory approach in teaching mathematics. Discovering patterns in mathematical computations come as a result of this approach. One can discover many patterns in mathematics especially when doing fast and quick computations. As one tries to discover more patterns, he develops reflective and creative thinking.
Speed in computation is generally acquired through constant correct practice and through development of mathematical skills. These are developed when one can discover patterns for shortcuts. When one acquires the habit of discovering patterns, it will be easy for him to work out combinations, make analysis and logical approaches, decipher shortcuts and better ways to attach or solve problems. It can lead one to varying techniques and ways in solving problems as one becomes open to the many avenues for solutions of the problem.
Some people nurture the idea that those who are gifted with mathematical skills are really different. This is not so. Anybody can become a “math wizard” at any one time or another. If one knows some patterns for short-cuts which others are not familiar with, he can give the impression that he is skillful in mathematics.
There are several instances when teachers in mathematics have exhibited “magical tricks and formulas” to their students, leaving them amazed and awed at the teacher’s dexterity. They asked questions in bewilderment: “How did you get the answer so quickly even without solving for them”; “What magic formula did you use to solve the answer much quicker than our calculators?”; “How did you do it Sir/Ma’am? Can you teach us your secret?”. These are many more questions from the students only proved their intriguing admiration to their teacher’s “expertness” in computation. But the students did not realize that in many instances, the skill for giving quick and accurate responses in mathematics sprang from discovering patterns and techniques for short-cuts in computation.
Students can be trained in discovering patterns especially in computation. Once they have developed this skill, they could be lead to do more discovering of patterns which probably teachers will be amazed. Encouragement from the teacher should also be handy, so that students will be motivated to do more discoveries. For example, it is amazing to note that the very basic multiplication by 9 could lead students to discover the variety of mathematical patterns.
Teachers who can help or lead the students to discover patterns may find it rewarding in the sense that their students can do the computations quickly. Consequently, they can cover the prescribe topics as scheduled or planned. Students who can discover patters in computations may be inspired to do better in the subject. They can be motivated to think that they have contributed new ideas and can share these discoveries to others. If as a mathematics teacher you can inspire your students to discover patterns in mathematics, who knows, someday a famous “math wizard” may surface from your class.