We tend to think of teaching formulas as in the domain of math and science teachers only, when in reality, there are very few areas that can be said to have no involvement with formulas. Many courses, like photography, economics, all the sciences, and all of mathematics, are heavily dependent on formulas; but since formulas are simply statements of relationships that exist in the real life, virtually all subjects have some connection to formulas. It becomes the responsibility of all teachers to help their students understand where formulas come from, why formulas are important, and help students to learn and use them correctly.
5 Ways to Help Your Students Better Understand, Use, and Memorize Formulas:
1. Always explain where the formulas you encounter come from. There are some math students who think formulas as just "made up" examples the author of the textbook included. It takes explaining many times and giving many examples to get across the concept that formulas represent relationships already known to exist in real life; and not only is that relationship "real"--it is ALWAYS true.
Ideally, we should teach who discovered the relationship, when it was discovered, and how it was discovered. I hate to admit this, but it is a rare occurrence for this to happen in a math class. Science classes seem to do a good job of actually showing physical relationships, photography relationships almost become obvious and automatic, economics seems to be "showable" just by looking at the world, but in math classes we tend to describe relationships and show them in a two-dimensional sense if we can, like c = "pi"d with a circle on paper. Making visual, understandable sense out of the derivation of the quadratic formula is a challenge!
2. Always explain the importance of formulas. Students often do not "get" that because formulas are always true, they can be used to find a missing value if all the others are known. Knowing that one needs to drive 400 miles in the next 5 hours means driving __?__ miles per hour. Knowing the relationship rate times time equals distance (rt = d) or changing that to rate is equal distance divided time (r = d/t), we can calculate that we would need to drive 400/5 or 80 mph. Well, maybe we should change plans.
3. Encourage students to make and use flash cards out of each new formula. Flash cards may be an old teaching/learning technique; but that doesn't make them any less effective. These new flash cards need to include the formula AND the individual parts; and they need to be specific about what each part stands for. For example: in c^2 = a^2 + b^2, "a" represents a leg of a right triangle, not just a side of a triangle; "c" represents the hypotenuse of a right triangle, not just hypotenuse.
4. Practice in class. If possible, for several days after each new formula is introduced, take about 5-10 minutes to quickly have the students: (a) name what each symbol represents, (b) give the various possible wordings for the operation symbols (plus, increased be, added to, etc.), and (c) say the entire formula in words as a complete sentence.
5. Give suggestions on how to memorize formulas at home. These should include: (a) speaking out loud, (b) pointing at parts on a diagram if that is appropriate, (c) practice only about 10 minutes, take a break, and then try again, until it is memorized, (d) check again in 30 minutes, and (e) any other hints you or your students have.
Be sure that you always stress the importance of studying out loud. The ability to verbalize what a formula is for and what its parts stand for is critical to understanding, and understanding the formula is critical for using it.
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