How does it fit?

At the beginning of the semester, I wrote a post about using the history of the LEGO company as a cautionary tale for innovation in education reform. The idea came from a Diane Rhem interview with the author of Brick by Brick. But there was another idea presented in book that also caught my attention - clutch power.

When a child snaps two bricks together, they stick with a satisfying click. And they stay stuck until the child uncouples them with a gratifying tug. And therein lies the LEGO brick's magic. Because bricks resists coming apart, kids could build from the bottom up, making their creations as simple or complicated as they wanted. … it is clutch power that makes LEGO such an endlessly expandable toy, one that lets kids build whatever they imagine. (page 20)

It was the last sentence that got me thinking. How might I design learning experiences that use clutch power - allowing learners to "build whatever they imagine?" In particular, I had one of our math courses for preservice teachers in mind. It explores a variety of mathematical topics that students often see as disconnected: algebra, geometry, measurement, and data.  Was there a way to treat concepts in that course as building blocks that learners could use across the domains to build new understandings instead of simply following the instructions I provide?

I am still working on that question, but I did start experimenting with simple problems that allow learners to add their own ideas while demonstrating their content competency. The following is one problem (modified) from the final I just gave. I would be interested in your feedback.

Plot the points (2, 2) and (2, 4) on the coordinate plane. Pick two other points that could combine with these first two to be used as the vertices of a trapezoid. Use this context to develop items that would align with the following targets (be sure to justify your alignment using the indicators):

• Graph points on the coordinate plane to solve real-world and mathematical problems (5GA1, 5GA2)
• Classify two-dimensional figures into categories based on their properties (5GB3, 5GB4)
• Solve real-world and mathematical problems involving area, surface area, and volume (6GA1-A4)
• Draw, construct, and describe geometrical figures and describe the relationships between them (7GA1, 7GA2, 7GA3)
• Solve real-life and mathematical problems involving angle measure, area, surface area, & volume (7GB4, 7GB5, 7GB6)

Because this was a new assessment for most of my students, this time around I offered some example items to pick from:

1. Define the term "trapezoid" and then use that definition to identify what other names apply to your shape.
2. Find the area and perimeter of your shape.
3. Extend each side (creating 16 angles) and find all the angle measures.
4. Write your own question for this context.

I still expected them to align the item with the targets, justify their alignment, and come up with a correct response.

Can innovation be a bad thing?

And there's lots of ideas about innovation, theories of innovation, rules of innovation, like you should open up your innovation more. You should think about all these different types of innovation, you should practice disruptive innovation. There's all these theories out there about how you boost innovation. And when I went into do my initial interviews at LEGO, they hadn't read all those books. In fact some hadn't been written then, but they had done all those things that consultants and academics say you should do, and it almost put them out of business. And I thought that was really interesting. You know, how can we be so wrong?

This quote comes from an interview with David Robertson on his book Brick by Brick. I have been trying to share ideas from the interview with anyone interested in education reform. Given that innovation is such a buzzword in education these days, I think Robertson's book might serve as a cautionary tale for those trying to reform education.

So why did innovation nearly destroy this popular toy? Robertson explains:

what had happened is that when they'd innovated, they just came out with a whole lot of toys that weren't very LEGO-ey. They weren't very popular. ... 

I got the sense that the toy-designers in the 90s were allowed to be as creative as they wanted. As a result, LEGO put out a slew of new toys but the new toys did not fit together the way the old LEGOs did; this limited the creativity of the users. So the kids disengaged.

I sometimes wonder if we are in danger of doing the same thing in education. We see teachers being very creative in designing their lessons. For example, using technology to innovate the way they deliver content. However, by focusing on innovation in teaching are we sacrificing students' ability to be innovative? When I shared this question with a colleague, he said, "I know that those times when I thought I created the perfect, creative lesson - those were the times when students seemed least likely to be engaged."

There are several other ideas I took from the interview that might apply to education but it feels like I dropped a pretty big bomb in that last paragraph. Perhaps this is a good place to stop and see if some of you might want to add your two cents. I look forward to reading your thoughts.

What do you want to do?

Early this week, John Hunter was interviewed on the Diane Rehm Show. So this seems like the perfect time to move another exhibit from my Learning Museum blog to here. It's a short one, so take the time to watch his amazing TED Talk.

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"The work will teach you how to do it." 

Estonian Proverb

New Teacher (just hired for first job - teaching gifted children): "What do I do?"
School Administrator: "What do you want to do?"

John Hunter was that new teacher, back in 1978, and that administrator's response "set the template for the entire career [he] was to have after that." It provided him space to explore - space that he decided to pass along to his learners as they tried to create meaning of the world. To that end, he created an activity, The World Peace Game, intended to help players "explore the connectedness of the global community..." This has been documented in the film World Peace and Other 4th-Grade Achievements by Chris Farina and in the following TED Talk:

What would happen if all teachers were offered the opportunity to answer the question: "What do you want to do?" Can you imagine what people might learn?

Where does it hurt?

Me: (after a fairly lengthy description of open questions) So what did you hear? What are you thinking?

Teacher: (long pause) I don't know what you want me to say.

Exchanges like this happen more often than I like. People have been trained to believe that when a teacher asks a question, he or she is looking for a particular answer. We want to be good students which means providing the expected answer. It reminds me of a book discussion on Diane Rehm about how patients and doctors fall into a routine that can result in mistaken diagnoses and unnecessary tests.

Proud parents with Dr. Hilary at MSU COM graduation

This book came to mind when the teacher responded as she did. You see, I have tried to get in the habit of asking questions I do not know the answer to; it ensures that I avoid falling into an educational rut, and it makes my job as a teacher much more interesting. I tried to explain to the teacher that my question was an attempt to gather some information about what she had attended to in order to make a decision about our next steps. I said something like, "Think of me as a doctor trying to make an accurate diagnosis of your 'health' in regards to understanding of this topic. It's like I'm asking, 'Where does it hurt?'" She laughed and then went on to describe what she had understood about open questions. As the discussion went on, I would stop every now and then to ask, with a smile, "Where does it hurt?"

This is one of the ways we might use warm-ups more appropriately (see last week's post for my perspective on this problem). We could treat it as a way to diagnosis the readiness of the learners to move on or determine what issue we might need to address. (Here is an example of the latter.)

I saw an example of this earlier in the week. Students worked on some scale drawing questions, and after giving the answers the teacher asked if there were any of the questions students needed help on. A student called out a number. So far, so good. However, instead of doing more of a diagnosis, the teacher fell into the rut of showing the student how to find the answer. After a couple of minutes, the teacher stated, "That means the answer is 1/2 an inch. Okay?"

Fortunately, the student responded, "So 6 centimeters, right?"

Now the teacher could do an accurate diagnosis. The problem was not in finding the answer - it was interpreting the answer. "This is 1/2 an inch (holding his thumb and index finger close together). 6 centimeters would be more than two inches (expanding the distance between his thumb and finger). I wonder - were you thinking that 6 inches is half of a foot, so half of an inch is 6 centimeters? (She nods yes.)"

How often do we jump into treatment before doing an accurate diagnosis? I know that it seems inefficient to spend time listening to the student explain "where it hurts," but is it? Drs. Kosowsky and Wen found that it was important for physicians to take more time listening to their patients in order to get their diagnoses and treatments right. The same could be said for teachers.