Teaching

Teachers and Content Mastery

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.

By patrick honner, 12 years12 years ago

Resources Teaching

Storytelling, Teaching, and Mathematics

This short list of “Pixar Story Rules” from Pixar story artist Emma Coats offers a fun look into the mind of a story-teller, as well as a surprising source of mathematical problem-solving and teaching advice!

These particular story rules sound remarkably similar to techniques of mathematical exploration.

#7 Come up with your ending before you figure out your middle.

#9 When you’re stuck, make a list of what WOULDN’T happen next.

#10 Pull apart the stories you like.

#11 Putting it on paper lets you start fixing it.

#20 Exercise: take the building blocks of a movie you dislike. How would you rearrange them into what you DO like?

Working backwards, proof by contradiction, taking apart things you understand and trying to put them back together, getting your hands dirty by working out the details–these are all common and useful techniques in exploring and understanding mathematical ideas.

And as a friend pointed out, writing a story is indeed a kind of problem-solving; maybe it’s not so surprising how much that process shares in common with mathematics.

And as a teacher, the following two really resonate, for obvious reasons!

#2 You gotta keep in mind what’s interesting to you as an audience, not what’s fun to do as a writer. They can be very different.

#1 You admire a character for trying more than for their successes.

By patrick honner, 12 years9 years ago

Challenge Teaching

On College Rankings

This essay from the President of Reed College discusses what it’s like to live outside (and inside) the world of college rankings, essentially asking “Are these rankings meaningful?”

https://www.reed.edu/apply/college-rankings.html

It’s a familiar story to anyone who has ever contemplated teaching to the test. As rankings/ratings/grades become more and more important, colleges/schools/students (and teachers) tend to focus more and more on those metrics, perhaps at the expense of what’s really important (whatever that might be).

A perfect rating system, presumably, would compel the rated parties to meet and expand the standard of excellence. But in practice, it seems difficult to come to a consensus about what comprises excellence, and even harder, then, to construct an appropriate rating system.

So how should we measure a college or university?

By patrick honner, 12 years4 years ago

Math-Intensive Majors

The MAA and David Bressoud released a report about the current status of math intensive majors in the U.S. (which you can find here).

Bressoud starts with the encouraging news in the STEM fields–Science, Technology, Engineering, and Mathematics. In the past fifteen years, colleges have seen a 33% increase in students in these majors. However, those numbers may be dominated by particularly large increases in Biology and Psychology.

As a mathematician, Bressoud is interested in math-intensive majors, and so he looks more closely at mathematics, engineering, and physical sciences. As total college enrollments and STEM majors have increased, these math-intensive majors attract a consistent percentage of students. In fact, Bressoud notes that this percentage has been stable for the past 30 years, as math-intensive degrees have shown no growth as a percentage of overall college degrees.

This is curious, given the increasingly quantitative nature of modern society, industry, and academia. Are greater percentages of students in other countries pursuing such degrees? Or do we only need 0.5% of our college students studying math-intensive fields?

By patrick honner, 12 years4 years ago