Teaching as an Apprenticeship

I’ve always favored an apprenticeship (epistemological) model for teaching. Not so much learning facts, but learning how people with long experience in an area approach problems to be solved. So to have students do what scientists do (or historians for that matter), and to model how these experts think.

David Brook’s, The Social Animal, expresses this philosophy in a more narrative form:

Of course, Ms. Taylor wanted to impart knowledge, the sort of stuff that shows up on tests. But within weeks, students forget 90 percent of the knowledge they learn in class anyway. The only point of being a teacher is to do more than impart facts; it’s to shape the way students perceive the world, to help a student absorb the rules of a discipline. …

She didn’t so much teach them as apprentice them. Much unconscious learning is done through immitation. She exhibited ways of thinking through a problem and then hoped her students participated along with her.

She forced them to make mistakes. …

She tried to get students to interrogate their own unconscious opinions. …

She also forced them to work. …

— Brooks, D., 2012: The Social Animal.

Finding Where Two Lines Intersect: Khan Academy Lessons

Khan Academy videos on how to solve systems of linear equations:

Use a graphing calculator to double check your lines, or use WolframAlpha, or use my simple line grapher.

by Graphing

Video: Solving Linear Systems by Graphing

Most algebra texts have good problem sets for practice (Khan Academy does not – as yet).

by Substitution

Moving from the more intuitive, visual, graphical method of solution to the more exact algebraic methods, we start with solving by substitution.

Video: Solving Linear Systems by Substitution

Practice Set: Practicing Systems of equations with substitution

by Elimination

Video: Solving Systems of Equations by Elimination

Additional Video: Solving systems by elimination 2 (on YouTube).

Additional Video: Solving systems by elimination 3 (on YouTube).

Practice Set: Practicing Systems of equations with simple elimination