One recent semester I permitted my Algebra students to use apps on their cell phones and a program on my computer to solve every numeric or algebraic problem on the tests. My tests contained all the usual questions for an Algebra test and then on another portion of the test I asked questions that addressed

# Tag: deductive reasoning

# What Should We Teach?

In arithmetic we use and manipulate numbers to create concrete answers to specific numeric questions. Algebra is the theory of arithmetic. The two main tools used to create this theory are abstraction and generalization. First, we try to describe abstractly, without reference to specific numbers, the manipulations and processes that are used in arithmetic. The