## Saturday, November 29, 2014

### TT-TNG (F14 edition)

 Teaching Tips (from) The Next Generation
Presenting the inaugural edition of... Teaching Tips (from) the Next Generation: a summary of semester-end blog posts written by graduating secondary math teachers at Grand Valley State University.

They share their greatest areas of personal growth and their most powerful teaching strategies from their recently completed student teaching experiences.
(I will continue to add more as they come in. Last update: 12/1/14 at 12:55pm)

## Wednesday, November 19, 2014

### The Equity Principle

Here's a clip from NCTM's webpage on the Equity Principle:

So Equity does NOT mean that every student is treated the same.

That can be tough for new educators, especially here in America where all men are created equal is taken as a "self-evident" fact in our founding documents. (Except...)

## Monday, November 10, 2014

### Pocket strategies: Purposeful Incredulity

Think back to your school years. Think of that one teacher who managed to make every lesson fun and engaging, the one who had a canny way of making even the driest of topics seem worthwhile and interesting.

How did they do it?

Personality? Sure, probably. But I think this short post from Dan Meyer may have something to do with it, too. They made the content interesting, somehow. And it wasn't usually by embedding it into a game or puzzle or activity -- it was because they tapped into something genuine. They didn't just pose questions and show us how to find the answers, they made the questions seem worth investigating.

Dan's post calls it "developing the question."

A lesson I observed recently involved the theorem that "the sum of the vertex angles in any triangle is 180 degrees." The lesson involved an informal proof--an activity, wherein students created a triangle of arbitrary size and shape, cut it out, tore off the corners, and rearrange them to form...  a...

"What are we supposed to do with the pieces?" A student asked, mid-lesson.

Just see what you can notice.

Eventually a few kids got the corners to form a straight angle. Word spread quickly, and before long everyone found they could do it. It's a nifty trick if you haven't see it:

 Source: cutoutfoldup.com

But... now what? Because the question was never really developed, there wasn't much of a climax to build to, nor was there much relief when kids had figured out what to do.

But Dan's post got me thinking about that lesson again. How could we develop the question? One way I like to do it is by using what we might call 'purposeful incredulity'. I include it on my list recyclable "pocket strategies" for enriching, extending, or enhancing a traditional lesson.

## Wednesday, November 5, 2014

### Quadrilateral Hierarchies - Productive Struggle

An overarching goal for the semester is to help my pre-service teachers grow more comfortable with "productive struggle" and with persevering on challenging tasks. We worked at it for a long time earlier this semester on problems like the Chessboard Problem, the Cheesecake Task, and many others.

Last week, we moved into Geometry. After spending some time exploring the Van Hiele levels of geometric thought and the kinds of activities that help children progress to higher levels, it was time to put their own geometry knowledge to the test.

In this two-stage lesson, I first divided the class into five teams (of four) and assigned each team a shape class: rectangles, kites, rhombuses, parallelograms, trapezoids (inclusive definition). They were directed to produce a poster with a 2x2 grid with space for examples and properties of general and special members of their shape class.

Here's an example: