Hey! I remember you. You were the one thinking about not taking Algebra. I'm glad to see that you've changed your mind. Now, we must make sure you stay successful and don't regret your decision. Remember that the failure rate for first year Algebra is approximately 50% and this isn't because 50% of our students are dumb! There are many different reasons for this miserable state of affairs--some as simple as having weak multiplication skills. (I trust that if your multiplication skills are weak, you will practice those before the school year starts.) What I am going to give you here are some of the big philosophical reasons students fail (sorry about the word "children") and then a list of the really goofy mistakes kids make.
The 5 BIG Issues Behind Student Algebra Failures:
1. Not understanding what Algebra is. Algebra is the set of basic skills that will be needed for all future math classes. Students tend to view Algebra as they do History, meaning that they study for the test and then promptly forget everything they just studied. You simply cannot do this with Algebra because the skills you just learned will keep coming back again, and again. Many of the early skills will form the foundation for other skills. It is a HUGE mistake to think you can study for the test and then just forget everything. The skills of Algebra must be ingrained in your brain. You must learn them the first time you see them and then you must keep reviewing them.
2. Not bothering to memorize properties. I'm not sure why students think the many sets of properties are included in the textbook, but the majority of students consider them a nuisance factor and never bother to understand them or memorize them. This is another very serious mistake. The properties are your guidelines--the rules--of what you can and can't do in different situations--for the rest of mathematics! They must be learned--not forgotten.
3. Sign mistakes. These could almost be listed in the "goofy mistakes" to follow, but sign mistakes happen more frequently than any other type of mistake, so I decided to give them their own category. You have already learned to deal with positive and negative numbers, and what will get added to this are the rules of negation. These rules are not hard. They just require practice. You must put in the necessary practice. And NEVER forget to distribute the negative sign: - (2 - 7) = -2 + 7 = 5.
4. The GOOFY mistakes. Each of these is at first glance somewhat logical, but just a simple check with numbers will show you these are wrong. Learn these rules the correct way and don't do the DUMB versions!
(a) (x + y)^2 is NOT x^2 + y^2. Let x = 2 and y = 3: (2 + 3)^2 = 5^2 = 25 but 2^2 + 3^2 = 4 + 9 = 13 not 25.
(b) 1/(x + y) is NOT 1/x + 1/y. Again, let x = 2 and y = 3. 1/(2 + 3) = 1/5 but 1/2 + 1/3 = 3/6 + 2/6 = 5/6 not 1/5. NOTE: Had the original fraction been 1/xy then it would be OK to separate it as (1/x)(1/y), but you cannot do so with addition on the bottom of the fraction.
A similar situation occurs with radicals: sqr(x +y) is NOT sqr(x) + sqr(y). Let x = 9 and y = 16. sqr(9 +16) = sqr(25) = 5 but sqr(9) + sqr(16) = 3 + 4 =7 NOT 5. Again, multiplication under the radical sign can be separated, but not addition.
(c) Reducing fractions. You may NOT cancel any number next to an + or - sign. ONLY multiplication. (x + y)/(2 + x) is NOT y/2. Again, let x = 2 and y = 3. (2 + 3)/(2 + 2) = 5/4 NOT 3/2. However, (xy)/(2x) DOES reduce to y/2.
(d) Confusing the Rules for Exponents. (x^2)(x^3)(^4) = x^9. ADD exponents when multiplying terms with like bases. (x^4)^5 = x^20. MULTIPLY exponents when raising a power to another power.
(e) Not checking solutions when you've solved an equation. Yes, even you might have made a mistake; or there might have been an extraneous root you need to find. Always check your answers!
(f) Forgetting that x^2 = 9 has two solutions: both 3 and -3. Remember that the degree of the equation states how many solutions there will be. x^2 = 9 is degree 2, so there will be 2 solutions: +3 and -3.
(g) Division by zero is undefined. This becomes a problematic issue with algebraic fractions. For 2/(x - 3), you must remember that denominators may never be zero. So you must look at (x - 3) from the standpoint of are there any numbers that would force x - 3 = 0. The value 3 would do that, so 3 must excluded from any possible solution.
(h) Raising a product to a power. Many students forget about the coefficient. (4x)^2 = 16x^2 NOT 4x^2
5. Not knowing how to study math. Math needs to be read and studied differently that you study history. Math should be read and studied OUT LOUD. You need to make your homework a study tool with problems copied, all work shown, and additional notes to yourself that will help later when studying for the final.
If you understand the big issues and avoid the silly mistakes, you will find Algebra to be surprising easy. That doesn't mean it doesn't require effort; but your efforts will lead to success rather than frustration.
0 comments:
Post a Comment