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.

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…… Continue reading Equivalence Deserves More Attention

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…… Continue reading On the origin of algebra problems

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…… Continue reading Word Problems… !#$%@;*!!