Common Opener

I really like where we are going here.  Our video production class has been broadcasting daily announcements live for a while and now we are really starting to take advantage of this time to establish some campus habits of mind. Recently, we started a series of "Common Opener" segments airing on Tuesdays and Thursdays focused on Flexible Thinking.  Math was up first and we used the Number Talk as the vehicle.

Basically, we are asking students to deconstruct and reconstruct numbers by looking for ways to find the answer that may be different than what they're used to.  We want them to leave their comfort zones just a bit.

Once the announcements are finished, teachers send their "exit slips" up to the office (or a student aide will pick them up) and I end up with a delivery of ~500 index cards/half slips of paper with student responses.  I quickly go through them and look for patterns.  It's been interesting to say the least.  Many students have started to look for new ways to work with numbers while a large majority still stick with the standard algorithms, but I'm optimistic that students will become more comfortable with the uncomfortable.

Hopefully, this acts as a vehicle to further the student/student, student/teacher and teacher/teacher conversations about learning on our campus.  What really encourages me is the opportunity we have to show how big ideas show up in all over the place.  Once the other content areas have a chance to interpret Flexible Thinking, we may see some real aha moments with our students.

You can find the announcements here.

Hypothetically...

What if we could design a project-based class for middle school students that integrated math and science-- that provided context for math and gave instructional minutes back to science?  What if this class capitalized on the natural correlation between the Practices For K-12 Science Classroom and the Standards for Mathematical Practice.  What if students were asked to design investigations, used modeling to move from the concrete to the abstract and then presented their findings for peer review?  What if they used technology to take snapshots of their learning along the way and kept a running journal of the process?

What if...

The Comma

If [this], then [that].  We talk a lot about [this] and [that] in the math classroom. Teacher supplies [this], student responds with [that]. They even have names:  hypothesis and conclusion.  But, what about the comma?   All the power of the entire process is summed up with a tiny little "," that is all too often ignored.

No more.  It's time to give the comma a voice.

We were getting ready to add rational expressions and I wanted my students do have a workable rule for adding fractions with like and unlike denominators.  My goal was to develop the idea that when adding fractions with unlike denominators:

A lot of students don't see this very clearly.  They do what they do to jump from [this] to [that].  And most of the problems end up looking a lot like

with no real understanding of what's taken place between the hypothesis and conclusion.  And up to this point, no one has really cared because Johnny was able to find the correct answer on multiple choice scavenger hunts with a great deal of accuracy added fractions like a champ in 6th and 7th grade. However, when Johnny gets to algebra, and sees

for the first time, you'd think he's never worked with fractions before.


Time to talk about the comma.  It was actually a pretty simple adjustment to a simple question, but the conversations it generated made all the difference in the world.

This quickly became

See, the beauty here is that the process became the outcome.  The numbers become the variables and we get a good grip on how one-third plus two-sevenths becomes thirteen-twentyfirsts.  The abstract isn't so abstract and the easy part is swapping out the 1, 2, 3, and 7 for a, b, c, and d.

Mission accomplished.  Now, lets hope they remember it tomorrow.