How To Be A Great Math Teacher In High School Hints For The Teaching Of Algebra

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Hints For The Teaching Of Algebra

Algebra becomes, for some high school students, “the straw that broke the camel’s back.” Students decide that algebra doesn’t make sense to them and therefore math is no longer relevant.

Over my years of teaching, I have developed a few “tricks of the trade” that help mitigate, if not stop, this tendency altogether. Remember that not all of us have a natural tendency to think in a mathematical-logical way. Here are my suggestions for you to try.

Algebra is just the next step in the number chain:

It is important to spend time with middle school classes showing the development of the number system from counting numbers to decimals to common fractions and so on to why we have algebraic numbers. Also, discuss the development of the four operations. Explain that the number system didn’t just happen. It really developed to keep pace with human development. Even the number zero had to be invented.

Algebraic numbers obey the same rules as other numbers:

During these early years of high school, show your students how the rules of the four operations apply to all types of numbers in the same way, for example, you can only add or subtract like terms. Certainly, these rules for the four operations are slowly being expanded to allow new number systems to adapt. Here you can talk about working with power notation as an example.

The answer concept in algebra:

This is the most confusing part for many students. “Sir,” they say, “the answer has no numerical value.” What needs to be emphasized here is that they have the answer. If they had a number value for the variable, they would have a specific answer. What you have to make them understand is that there can be an infinite number of answers depending on what the variable is.

Don’t just use xiy as variables:

Always use a variety of variables in the exercises you give your students to avoid having “x” and “y” be the only ones. Remember that “x” and “y” are used in analytic geometry in your work on functions.

It is more common for students to make algebra mistakes:

Mistakes are made in algebra:

  • By not copying the data correctly;
  • Do not work on the page. (Doing this makes checking easier);
  • Through the incorrect use of symbols; i
  • With a bad start.

So be sure to constantly model the best way to lay out your work to avoid unnecessary mistakes that cause students to lose confidence in their ability to do algebra.

Terms, expressions and equations:

The first formal algebra lessons will bring these three pieces of terminology to students. Spend time instilling these ideas into the minds of your students. Be sure to match the four operations to them as well. I would do a lot of oral work using older traditional textbook material with them. A short quiz at the beginning of a lesson works well to reinforce new ideas.

Equations:

These are the points I constantly stress to my students when working with equations:

  • The goal of solving equations is to find the values ​​of the variables that make the equations true.
  • The left side of the equation is always equal to the right side of the equation and vice versa.
  • When solving an equation, what you do to one side of the equation (in terms of the four operations) you must do to the other side of the equation to maintain equality.
  • When you move a term from one side of the equation to the other as part of the solving process, the sign of the operation associated with that term changes to the opposite sign, for example, plus becomes minus.
  • Finally, the last step in the solving process should be to test your solutions to the original equations.

Factorization:

These are the points I highlight.

  • Don’t just use “x” and “y” as variables.
  • When teaching new factoring rules, show them in different ways, e.g. ex. ax + bx = (a + b)xo xa +xb = x(a + b).
  • I emphasize that, when factoring, you go from a sum or difference to a product.
  • It is important to treat product expansions as important as factorization.
  • I insist that students check their factorization by reversing the process, that is, expanding their answer to see if they get what they started with.
  • There is often more than one method of factoring an expression. So I encourage my students to find other ways and share them with the class.
  • Finally, I emphasize that a simple idea, easy to overlook, can be the starting point of your factoring process. Students often overlook the fact that 1 = 1 x 1 ia = ax 1 = 1 x a.

Confusing power notation products and expressions:

It is important to spend time making sure students understand the difference between a product and a number in index/power form. I explain that a product is a way of expressing a number added together several times, while an index number means that the number is multiplied by itself several times.

Also underline the concept of like terms in relation to power notation.

Many students put algebra in the “too hard basket,” even students who have been successful in the past. They often give up quickly because they can’t see where the question is leading or what kind of answer is required.

The strategies above help give students a better start in algebra so they can get the satisfaction of getting answers they didn’t expect to get.

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