Building concept maps is harder than it looks

I'm having students create a concept map as a summative assessment for our Complex Numbers unit and... w o w — there is all kinds of learning going on.

 

Students are working in groups and can use all their notes and assignments from the unit. Some kids jumped right in and started hacking away. Others whined and asked why we couldn't just have a normal test.

We are using Post-Its, scissors, pencils, and paper to do our constructions.

In-process projects range from amazing to struggling, but what impresses me most is how much the work reveals about what students are figuring out and how each student is understanding and constructing meaning in their learning. It also demands that learners own their own learning.

Because this is so revealing, I am probably going to use concept maps both as formative assessments before and during the unit as well as using them as a 'ways of understanding' tool to help them consolidate their learning.

BREAKING: OK, this activity is definitely a keeper. Students are really digesting their learning, talking about it, debating how to represent it, and clarifying areas of confusion for themselves. Here is an outstanding example from today:

Oreos, Barbies, and Essential Questions: framing projects for differentiated learning

The Oreos lesson/unit has been going swimmingly. Students loved the project and the poster, though I'm feeling a little bored with my project ideas right now. Not every project culminates in making a poster. I have a bunch of other ideas I want to write about in another blog post, but that is not where I am headed in this post.

What I want to ponder is, I wonder if we have not been making our Essential Questions (EQs) in mathematics too small. Too narrow. Ever since my Global Math presentation (the one where I had the epic #micfail that left me playing Harpo to Daniel and Tina's Groucho and Chico), I have been thinking about Understanding by Design more and more, and that has led me to ask myself if I don't need to make my Essential Questions in math lessons a whole lot bigger and deeper. There are so many ways to bring the real world into my math classroom, and one of those ways is to frame our work using questions that adolescents are obsessed with thinking about in their everyday lives — questions such as, How dangerous is too dangerous? How do we define what is fair? truthful?

These EQs can form a frame around the activities we do to connect the mathematics to the real world around us. They help provide a situational motivation for learning — and for wallowing in — the mathematics that starts from a place where all students are naturally. And they also make the work we do more, well, essential.

Some of my "major" Oreo lesson EQs blossomed into, Are Nabisco's claims about their Double Stuf Oreo products fair? Are they truthful? just? And my "minor" EQs started revolving around, How can systems of linear equations in two variables help us to model and assess the validity of this claim in the real world?

I am finding more and more that when I frame our work in this way, I hear less and less of the question, "When am I ever going to use this?" And frankly, that's less wear and tear on my soul as a teacher.

With Barbie Bungee, in addition to creating an occasion for more practice in reading aloud and practicing decoding and interpretation skills, I used my situation set-up to raise the EQ, how dangerous is too dangerous? This is a question every adolescent has had to wrestle with since the dawn of time (or at least, since the dawn of puberty as a social construct). In their effort to keep him safe, Siddhartha's parents built him a golden cage of pleasure palaces and theme parks so he would marry and have a life there and never want to leave home. And I can only imagine what Moses' parents must have gone through ("Put down that rod! You're going to put someone's eye out with that thing!").

And the things that matter about that question are (a) the assertion you come up with and (b) the way you marshall concrete evidence and interpretive scaffolding and support to persuade someone else (such as your parents) of the validity and rightness of your assertion.

Coming from a writerly and an entrepreneurial background, I often find that the math of a thing — the essential mathematics of a thing — comes down to what I can persuade someone else of. 

For example, How dangerous is too dangerous? 

Well, it turns out that 28 rubber bands can be empirically demonstrated to be one rubber band too many. With 27 rubber bands, Barbie can have a thrilling — but still safe enough — ride, but at 28, she cracks her head open on the sidewalk, the lawsuits begin, and her parents return to her graveside frequently to tell her "I told you so!" throughout eternity.

And isn't that something we ALL dread?

With the Oreos experiment, the EQs were, Am I being cheated? Are Double Stufs, in fact, double? Is this fair? Is this a good deal? and of course, also, "Does this seem universally and predictably true?"

These are questions every adolescent wallows in every day of their lives. How many times a day do YOU hear, "But that's not FAIR!" or "Mr. C decided such and such. Do you think that is FAIR?"

Fairness is about our own personal beliefs and interpretations of the evidence in light of our own experiences in our world. And only you can answer a question like that for yourself.