Many students perceive their teachers to know more than they really do (Math teachers in particular). If a Math student who just observed a teacher solve a problem at the board is asked "What do you think was going through the teacher's mind as they solved that problem?", I suspect the average answer would be something …

## Keep Your Eye On The Variable

The following equations all have a similarity: $latex y = |x - 8| + 5\\*~\\*y = 4(x - 6) - 7\\*~\\*(x - 3)(13x + 11) = 0\\*~\\*y = (x + 1)^2 - 9&s=2&bg=ffffff&fg=000000$ The similarity is that they all have expressions like (x- 6) or (13x + 11), which are often either translations or factors. …

## Procedural vs Intuitive Approaches

Both procedural and intuitive approaches to problem-solving are useful and important. As students begin to learn algebraic approaches to solving problems that feel very procedural, the challenge is to help students maintain their intuitive problem-solving skills while also developing an intuitive sense of why algebraic approaches work.

## Life Skills Learned In Math Class

Descriptions of life skills (skills useful in daily and business life) learned in elementary through high school mathematics courses.

## Analyzing Linear Equations: a summary

Explanation of key linear equation concepts: slope, intercepts, and equation forms. Discussion of how slope-intercept form, point-slope form, and standard form are related to one another. Includes general descriptions of the various starting points a student is likely to encounter in problems, and how to proceed from there.

## Equivalence Deserves More Attention

Most students taking courses in Algebra or higher seem quite comfortable with the idea of "equivalent fractions": improper or unsimplified fractions all of which evaluate to the same decimal value. An example would be $latex \dfrac{2}{3}=\dfrac{4}{6}=\dfrac{12}{18}=\dfrac{60}{90}=0.\overline{666}&s=2&bg=ffffff&fg=000000$ To create such fractions, multiply whatever fraction you wish to start with by 1 (the multiplicative identity) in the …

## On the origin of algebra problems

As you are solving a math problem, have you ever wondered how textbook authors come up with algebra problems that have simple answers? Just as you use inverse functions to solve an algebra problem, problem authors reverse the solution process to create a problem: they start with the answer. From there they use the same …

## Word Problems… !#$%@;*!!

Word problems can be... frustrating. Most of their reputation arises from their use of words to describe a quantitative problem. And if the problem's author did not choose their words very carefully, you've got Trouble (with a capital T). So why are so many word problems assigned? Because they are more similar to the quantitative …

## Problems fall into four categories

Description of a useful way of categorizing math problems: easy, medium, ugly, and hard. When studying for quizzes or tests, make sure to seek out "ugly" problems if you have not solved many yet.

## Lost points on a problem? What to do…

People don't like losing points for errors in their solution of a problem. So, what can you do to insure you won't lose points again the next time you are given a similar problem? Most folks seem to look through the corrections, then perhaps ask the teacher to solve the problem for the entire class, …

## Getting the most out of standardized test (SAT, ACT) practice books

How to get the most out of your time studying for standardized tests like the SAT or ACT.

## Operations are taught in pairs

Many High School students I have worked with have not spent much time pondering the sequence in which math topics were taught to them. So, it can be interesting to step into the "waaay-back" machine and investigate this question a bit: What was the very first arithmetic operation you were taught (probably in first grade)? What …

## Improve Your Math Grade: Use Scrap Paper

Scrap paper is an important tool when learning and doing mathematics. Every student should be using it to solve math problems from Algebra 1 on.