Lessons In How Not To Teach Math

Fortunately I didn't attend a traditional university program for obtaining my teaching credential, I went through an alternative route.  That route didn't have any "teaching methods" classes, for which I am eternally grateful.  This author, though, did have such a methods class:

According to the establishment, students should be “led” to their discovery of the answers. Providing explicit instruction is considered to be “handing it to the student” and prevents them from “constructing their own knowledge.”

“Discovery learning” isn’t bad. Most teachers use some discovery learning and group work in their classes. Also, staging problems so that they vary slightly from the worked example—so that the students are essentially applying prior knowledge in a new situation (called scaffolding)—has the “look and feel” of discovery. The problem is that the reigning education theory focuses mostly on discovery, with only a nod to direct instruction. That’s mistaken.

The worst class I took in education school was on “math teaching methods"...

Educators who promote “authentic learning” mistakenly believe that novices learn the same way that experts do. They believe that students construct their own knowledge by being forced to make connections with skills and concepts that they may not have mastered. The theory is that they learn what is needed in a “just in time” manner, thus providing the motivation for learning, which they assume would otherwise be a tedious and soul killing exercise...

The ed school approach to teaching math seeks to minimize “inauthentic” learning by replacing it with so called “authentic” exercises. But presenting students with a steady diet of challenging problems that neither connect immediately with their prior knowledge, lessons and instruction, nor develop any transferrable skills results in poor learning.

It is like children playing “dress up” in their parents’ clothing. The education establishment may believe they are producing “little mathematicians"....

This style of pedagogy is being foisted upon us under the guise of Common Core.

Update:  Check out this post of mine from 5 years ago on teaching calculus as described above.  The more things change....