Logic and Formulas The Core of High School Math

Monday, October 6, 2008

In The Washington Post's review of math education, staff writer Nelson Hernandez today explores high school geometry

and algebra skills needed to earn a diploma.

A New Angle On Geometry

The third-period geometry class at Paint Branch High School began one day not with a proof or a series of triangles, but with a lesson on two famous debaters in U.S. history.

To introduce the Montgomery County students to the concepts of truth and validity in logical arguments, teacher Colin Reinhard displayed pictures of 1858 Senate candidates Abraham Lincoln and Stephen A. Douglas.

Both men made what they considered logical statements. Lincoln said that if slavery continued to expand, then it would endanger the Union. Douglas argued that if states' rights to determine the slavery question were ignored, then the Union would break up.

Reinhard pivoted to statements familiar to students: If you miss your curfew, then you're grounded. If I am hungry, then my stomach growls. "If" is the antecedent, he said; "then" is the consequent.

Students drew Euler diagrams, which look like a circle inside a square. The "if" statement is drawn within the circle, the "then" drawn outside the circle but within the square.

It was basic stuff for the outset of the school year. Lessons in logic would set them up for triangles and proofs to come.

"That's all logic is -- the rules of the game," Reinhard, a former engineer, said. "To be able to communicate your ideas thoroughly, accurately. Most of our students, they're enjoying the logic the most, because they can use it."

Diploma Standards

Maryland: All students must pass basic algebra and geometry, although credit requirements vary by county, with some requiring the equivalent of four years of work and others three. Students must also pass the High School Assessment in algebra and data analysis.

Virginia: To receive a standard diploma, students must earn three standard credits, one of which must be a verified credit, of classes in basic and advanced algebra, geometry or higher-level math courses. A standard credit is earned when a student passes a course. A verified credit is earned when a student passes a course and its Standards of Learning exam. For an advanced-studies diploma, a student must earn four math credits, two of which must be verified credits.

The District: Students must take four units of math -- each unit is equivalent to two semesters of study -- and must pass basic algebra, geometry and advanced algebra. Students are also required to enroll in algebra no later than ninth grade.