Teaching

Arguments that suggest we over-emphasize mathematics in education don’t bother me.  I love math and see its utility in every aspect of my life, but I understand not everyone feels this way.  Also, when someone says we shouldn’t teach math, or we should teach less, it encourages me to reflect on my own beliefs about math and teaching.  This is usually a valuable experience.

So I read “Is Algebra Necessary?“, Andrew Hacker’s OpEd in the New York Times, knowing that I probably wouldn’t agree with much of it, but still prepared to examine my beliefs.  Hacker offers up a few of the standard reasons why students shouldn’t be forced to take “Algebra” in high school (“it’s too hard”; “it turns kids off”; “not everyone’s going to be an engineer”), but he doesn’t really bring anything new or substantial to the discussion.

One thing I did find interesting, however, was Hacker’s suggested fix:  instead of “Algebra”, we should be teaching courses like “Citizen Statistics”.

It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.

This is indeed a good idea.  Ironically, exploring the mathematics of the CPI is largely an algebraic activity.

Discussing which items should be included means creating a mathematical model and declaring variables for the unknown quantities we wish to investigate.  These fundamental skills are taught and emphasized in high school algebra.

Determining the weights that these items should be given essentially amounts to finding the coefficients of some function of those variables and exploring the consequences of those choices.  In their basic forms, these skills are also taught and developed in high school algebra.

Thus, it seems to me that Hacker is suggesting we replace Algebra, with, well, Algebra.

There are worthwhile discussions to be had about what we are teaching, why we are teaching, and how we are teaching.  But those discussions should be led by people who really understand what’s going on.  If Andrew Hacker thinks we should replace Algebra with Algebra, then someone else should be leading the discussion.

Related Posts

• Why Are We Listening to Andrew Hacker?
• Replace Algebra With … Algebra?
• N Ways to Apply Algebra With the New York Times

On her blog, Diane Ravitch posted a reader quote about the importance of content expertise for teachers.  Here is an excerpt:

There is nothing more important, especially in the HS classroom, than a teacher who is an expert in his/her respective field. The “tricks of the trade” are second nature for those truly called to this noble profession. A teacher needs passion and patience, but more than anything else she needs to know what she’s talking about. That is what gives the teacher authority. 

And here is a slightly edited version of my response, originally posted as a comment on Diane Ravitch’s blog.

I disagree with the sentiment expressed by your reader.

First, it’s impractical to expect all teachers to be masters of their content. If we need 200,000 math teachers in the US, we aren’t going to find 200,000 math experts for those positions, unless we dramatically redefine what we mean by ‘expert’.

Second, content expertise is not the source of a teacher’s authority. Being a teacher is more about being a leader than being an authority, and leadership is earned through a combination of respect, effort, enthusiasm, caring, and expertise.

Lastly, subject-specific content delivery is one aspect of teaching that can obviously be streamlined by technology. As education evolves, we teachers need to make our case by emphasizing the variety of other tools and expertise we bring to students, not just content.

The original post can be seen here.