Standard of Mathematical Practice #3 (SMP3) asks students to construct viable arguments and critique the reasoning of others. Although it’s far from a settled matter, one could argue that SMP3 outsizes the other seven SMPs in importance and is at the heart of what mathematics is. Being able to defend a claim and find holes in others’ is not just an important principle in practically every discipline (law certainly comes to mind), but a principle in which mathematics reigns queen.
Distinguishing correct and incorrect logic allows students to communicate their thoughts and answer the most important question in any math classroom: Why? Boolean algebra gives high school students a way to prove statements as true and false using the clinical laws of algebra. Here’s a Boolean logic activity you can try with your class.
British mathematician George Boole first developed the idea of logic in a mathematical context, hence Boolean algebra. Boole used symbols to represent logical statements and studied the relationships between them. His ideas are used in every computer programming language today, with the Boolean data type (i.e. TRUE or FALSE) as one of the most essential concepts that beginner computer programmers need to learn.
Boolean Logic Gates
When Boolean expressions are evaluated, there are only two possible results: TRUE or FALSE. In computer programming, any series of commands that we want the computer to take requires boiling each step down to a simple 1 (TRUE) or 0 (FALSE). This means an expression cannot be true and false at the same time. Two of the most important logical operators in Boolean expressions are AND and OR. Many programming languages represent these operators using the symbols && and ||.
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