patrick honner

Math teacher in Brooklyn, New York

Math and Weaving — Belt Weaves

Here are some examples of what I call “belt weaving” (I’m sure there’s a better term).  The basic idea is to begin with long strips of construction paper, oriented perpendicularly, and then weave and fold your way down.

Here are two examples of 2×2 belt weaves.  In both cases, the same kinds of strips are used,  but in a different initial configuration.

The 3×3 belt weaves offer more initial configurations, and show more complexity.

There is a rich and interesting structure to explore in these “belt weaves”.  For example, these two weaves look similar, but are indeed different.

My students and I had fun exploring the mathematical relationships between the various belt weaves.  I will share some of our ideas and results in my series on Weaving in Math Class.

By patrick honner, ago

Differentiating Consumer Quantities

One thing I’d like to see more of in math education is an appreciation for practical consumer math.  For example, suppose your favorite cereal brand unceremoniously starts arriving in a smaller box.

Students should learn to be on the lookout for things like this.  They should develop a quantitative curiosity, exploring the various ways that quantity can be disguised.

And ultimately be able to put together a real quantitative analysis that helps them make good decisions.

This is math that everyone can use!

By patrick honner, ago

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, ago

The Trouble with Burger a la Carte

I appreciate the simplicity and elegance of this build-your-own-burger a la carte menu, but it does create some real problems.

From an ordering perspective, it’s nice that all toppings are a uniform $1 in cost.  But is it fair?

A burger’s worth of applewood bacon is probably worth a buck; a fried egg is reasonably priced at a dollar.

But how many bread-and-butter pickles would I expect to get for a dollar?  Or pickled jalapenos?  Way more than I could put on a burger, I suspect!

By patrick honner, ago
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