When designing a task, I strive for a simple premise.  Try this:

The two fraction bars below are mislabeled.  Explain how you can tell they are mislabeled.  Then drag the big black point until the fraction bars are correctly labeled.  Test your solution by checking the “Reveal Solution” box.

Dan Meyer has proposed a new hashtag to use for posts aimed at our community of math educators. The hashtag he proposes is:

#iteachmath

It has many features that make it a very strong identifier. It is clear, direct and non-threatening to newcomers. It is also refreshing for veterans of teaching. In an age where we are not always getting the respect we deserve, declaring #iteachmath in such an open way gives me a surprising feeling of pride.

Dan’s reason for proposing a new hashtag is to provide a better experience for our members. He argues specifically that the #iteachmath hashtag allows an easier entry for newcomers because of its clarity and non-threatening nature. This will lead to more members who feel comfortable participating, he argues, and all members will benefit.

We need people who can make tangible changes to our world using mathematics. This post outlines a framework for achieving that.

The modern world is a mechanical symphony. Our days are rhythmically organized into time slots where we interact with systems that have been designed using mathematics. We wake up to the sound of a programmed clock and make coffee with a machine that precisely regulates the temperature and flow rate of water. Our mail comes like clockwork, efficiently finding its way to our homes because our address is one element in an efficiently nested set: house numbers within streets within towns within zip codes within states. We drive to work in moving, mathematical sculptures. Our cars are intricate systems of metal and electronics that are designed almost entirely in mathematical software programs and fine-tuned using statistical analyses of performance.

Graphs of functions seem like they should provide great insight into the behavior of the quantities they describe. I mean, c’mon. They’re visual ways to view the relationship. And that’s how humans experience and understand the world primarily: visually. Graphs seem perfect, then. So what’s the problem?

The problem is that graphs don’t look like the quantities they describe. For example, let’s say the number of birds living in a particular area increased at a relatively constant rate from 10 to 20 over the course of 2 months. What does this look like? It looks like a mini-movie that has 10 birds on the screen. Then, over a period of time, additional birds get added to the movie, one-by-one, until there are twenty. In other words, it looks something like this:

Like many of us, I read and watched Fawn Nguyen’s story about Lillian. I won’t say much here. Only that it has certainly made me feel and think. I have three children and I love them deeply. They are are in pre-school, kindergarten and 2nd grade. Although Lillian is in 9th grade, I realized that only a short number of years ago, she was the age of my daughter. This really affected me. I’m not sure what to do about the whole experience or what it means. I made a short film to help deepen my relationship with the story and better understand my feelings about it.

In 2015, Graham Fletcher posted an article centered around what he calls “Multiplication Subitizing Cards”. Each card displays a visual representation of a multiplication sentence.

Today, Michael Fenton wrote a blog that posed the question "How many squares fit inside an m x n rectangle?"  Here is a link to Michael's article: How Many Squares? And here is the solution to his problem: where $latex m$ and $latex n$ are the lengths of the sides of...

Mathematics is a tool for storytelling. To see this, consider my brother. He is an applied mathematician. One of his current areas of study is groundwater. He tries to understand, and help other people understand, what happens to water that is deep within the ground. He collects data about the water’s behavior at different locations within the ground and then uses mathematics to stitch that data together into a story about what the water is doing. He’s a story teller.