Integrated studies and a spiraling curriculum…Not only do we need to help our learners make connections between our discipline and other disciplines we need to help them make connections between topics in our own discipline, even when it is about skill building rather than application.

Wow! We’ve learned a lot about our learners this week. Our latest leveled formative assessment has highlighted an additional need for our learners and impacts our curriculum. I’d love for you to see it; I think it’s a really good one. DD and I created it together in her kitchen on our unexpected day off. (Terrible weather here in Georgia knocked the power out all over; no school on Tuesday.)

We are studying quadratic functions. This leveled formative assessment asked our learners to identify x- and y-intercepts graphically in Level 1 and algebraically in Level 2. Virtually no learner got out of Level 2 unscathed. It is illuminating to say the least. Over 50% of my learners did not know how to state the locations of the intercepts in a way that would communicate to a reader an understanding of the intercept location. Often they just plunked down a number. We would see x-intercept: __1__. This might be right (??), but how do I know if they meant (0, 1), (1, 0), x=1, or y=1? Did they know? Talk about an opportunity to discuss conventions and symbol choice!

Over 75% of my learners did not know how to find the x- and y-intercepts algebraically. Over 75%! Many said that they were looking for b in y = mx + b. In the Quadratic Functions unit??? YIKES! Let me say that we have been working on the Zero Product Property and the Quadratic Formula for weeks.

The most illuminating example is from, in my opinion, my very best, most motivated learner. She correctly substituted 0 in for y in y = 3x + 2 to find the x-intercept. So now she needed to solve 0 = 3x – 2. She was stuck, really stuck. She said “I don’t know what to do. I can only use the quadratic formula, and it is not working for me.” Double YIKES!

The assessment changed the course of the content and the instruction as well as the methodology. Today’s lesson, delivered via the TI-Nspire, was still about the vertex form of a parabola, but we also had to decide of the graph or table was linear, quadratic, exponential, absolute value or none of these.

We could check for understanding with a quick poll.  We could check for participation with screen captures.  The learners’ questions were awesome. “I don’t know how to tell the difference between exponential and quadratic. They are both curves.” I rarely said anything. I took lots of notes on the board and asked questions to help them get unstuck. “How do you know if it is quadratic or an absolute value?”

It was a great discussion with real questions being asked and answered by the learners.  The results after the discussion were much better.

The challenge became to document our work.  How am I supposed to take notes when the entire lesson is on my calculator?  Am I supposed to take notes?  What will I use to study later if I don’t take notes?

The graphic organizer was developed through our learners questions.  We first just put L-Linear, E-Exponential, A-Absolute Value, and N-None of these on the board.  As they started sharing their questions and what they did not know, we added notes to the side as a graphic organizer.

We used the technology to deliver the content.  We used the technology to check for understanding and consensus.  We used the technology to guess-test-and-revise.  We used the technology to make sure everyone was taking a swing at each problem.  While your identity could be hidden, our learners requested that we start showing names so that they could help each other and identify resources in the room.

We have no book to lead us down this path.  We used our leveled formative assessment to identify a need, a gap, in understanding.  Our learners and our colleagues are helping us find the path to teach and learn.  Isn’t this the way it should be?  We should struggle to learn, but shouldn’t we struggle to learn together?  Shouldn’t we learn what needs to be learned rather than what is in some book written x years ago?