Life is full of alternatives. Would like fries or coleslaw with your meal? Should you put on your right or your left shoe first? Should you attempt to solve a math problem using algebraic procedures, or your intuitive sense of the situation?
Life is also full of false choices: there are many occasions when you do not have to make a choice unless you wish to. You could have fries with a side order of coleslaw. If you wear loafers, you could slide your feet into both shoes at the same time. And many math problems can be solved quite successfully using Continue reading Procedural vs Intuitive Approaches
One of the hardest questions for many math teachers to answer in a way that is relevant to students is: “why do I need to know this?” “For the next course you take”, the easiest answer in many cases, does not answer the question that was usually being asked. My answers to this question obviously depend on the topic being studied at moment, and I don’t have “good” answers for all topics… but here is my list of key life skills I learned directly or indirectly from math class, with Continue reading Life Skills Learned In Math Class
Towards the end of the unit(s) on Linear Equations and their graphs, students can feel a bit overwhelmed. The following is an attempt to summarize and link the key concepts you need to be comfortable with.
What is the least amount of information you need to Continue reading Analyzing Linear Equations: a summary
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
To create such fractions, multiply whatever fraction you wish to start with by 1 (the multiplicative identity) in the form of a fraction whose numerator and denominator are the same:
The key concepts here are that
a) an infinite number of equivalent fractions can easily be created, and
b) while all these equivalent fractions sure look different, they all represent the same decimal value or simplified fraction.
Turning to algebra, the very similar concept of “equivalent equations” is helpful in Continue reading Equivalence Deserves More Attention
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 you might encounter in life than many of the practice problems in your textbook: you have to supply some insight and organization in order to arrive at a solution.
Just about every level of mathematics, not to mention chemistry and physics, seems to Continue reading Word Problems… !#$%@;*!!
Math and science problems fall into four categories: Easy, Medium, Ugly, and Hard.
Easy Problems are ones you can solve with no difficulty in a short time. An example from Algebra I might be:
The problems that come at the beginning of each group of problems in a textbook are usually Easy Problems. If you had Continue reading Problems fall into four categories