Daniel Henderson, Millington, MD, danielhenderson@cpm.org
I have been thinking about the best structure for a math lesson. In one powerful simile, a lesson is like a cruise, a mission to Mars, or a vault in gymnastics. In each of these cases, you launch, have a special journey in the middle, and then you land. Launch. Journey. Land. For most of my career, I focused way too much on the first two parts and not nearly enough on the last part. The landing is critical.
Before you @me for my simplistic simile, I am aware of all the acronym models taught in teacher preparation programs – MARGE (Motivate, Attend, Relate, Generate, Evaluate), PERMA (Preview/Present, Explore, Refine, Master, Apply), IEEA (Invite, Experience, Examine, Apply), EMPOWER, GEMS, CRA, CPM, CPR, BRICK, FAANG, KAROLI, TACOS. I might have made some of those up. I have built lessons and units around several of these acronyms. I know they are helpful as structures. Even still, these acronyms do not pump my intuition the same way this launch-journey-land simile does.
To me, the lesson-as-journey simile clarifies a lot about what matters in a lesson and why. The launch matters because it gives me access to the journey. It quickly propels me from where I am onto a path of discovery. Sometimes there are stages to a launch, and the simile carries forward. Maybe I burned up on the launch pad because I failed to generate enough student interest to lift off. Maybe I never reached escape velocity because I did not take time to properly fuel up the knowledge tanks. Maybe I got us into low Earth Orbit but then flubbed the ejection burn that (CPM author) Dr. Leslie Deitiker might call a plot twist. Maybe I scrapped the whole lesson before I even started the launch because of bad student weather. Launches of any kind are tricky – they need a lot of forethought and meticulous preparation. Being off by just a degree here can mean missing the landing by a significant distance.
Like the launch, the journey itself is shared between students but experienced differently by all of them. We are all headed in the same direction but maybe doing and seeing different things. The skills my students bring to the journey can make their voyages unique: If the lesson is a cruise, everyone can enjoy it even if some swim and others parasail; if the lesson is a gymnastics vault, some students simply bound over the vault while others do a Yurchenko with a twist. If the lesson is a mission to Mars, some students measure the position of the stars while others focus on deploying solar panels. There are twists and turns and complications along the way. The journey is really about seeing and experiencing new things, smelling the flowers, and noticing things you had not before. In class, as on a cruise, at a gymnastics meet, or on a mission to Mars, there is a crew making sure you get where you are going safely and helping you choose interesting experiences along the way. In my class, I, the teacher, am the crew, and my curriculum is my guide book.
At the end of your journey, you absolutely must STICK. THE. LANDING. If you miss this critical piece, the entire journey can be for naught. Here are a few famous missed landings to prove my point: Titanic, Hindenburg, Mars Climate Orbiter, Olympic gymnast Francis Samir Ait Said (youtube it), and me in about 40% of my lessons. More than half of all US missions to Mars have failed at the landing stage. (NASA named their recent attempt Perseverance for a reason.) The Produnova, aka the death vault, has ended more gymnasts’ careers than that old show The Apprentice because it is incredibly hard to stick that blind landing. When you fail at the landing, much of what came before is wasted, sometimes disastrously, and anything you wanted to do after is…limited.
Perhaps unsurprisingly, all of NASA’s failed Mars landings have math-class counterparts. My classes have missed landings because I came in too steep and burned up student interest by mathematizing too quickly or because I came in too shallow by letting the students be too self-directed so we bounced off the target without actually landing. More than once, I have turned off the burners a little too soon and left my students to plummet an unsurvivable distance to their target. An embarrassing number of times I have crashed headlong into the rocks by not leaving myself enough time for a proper descent. I have failed to properly convert student work into mathematical notation and wrecked in the confusion that followed. I have not properly oriented the heat shield against too-broad generalizations and burned up on approach. I have safely reached an endpoint only to lose contact 20 seconds later. I have gotten to the time I set for the landing only to realize that I should have redirected students a half-hour earlier to better approach the planned landing site. Sticking the landing is hard, and it does not happen without proper preparation and thought long before the launch. Sticking the landing is the hardest part of the journey, and it does not happen without constant monitoring and adjustment throughout the journey.
One thing that became clear to me as I thought through this launch-journey-land simile is that the Karolyis and NASA administrators of the world are right to assert that the landing is the most critical step in any journey. We would do well to listen to them. If we do not stick the landing, we have failed in our mission, no matter how things were going up to that point – see the Hindenburg for a case in point. Most of you may not recall that the Hindenburg had just successfully crossed the Atlantic ocean before ending the era of airships. Interestingly, the flip side is also true: if we stick the landing, especially after a rough journey, we become real-life heroes. Even when things go sideways, sticking the landing has amazingly positive outcomes! Hi, Apollo 13! Hi, Kerri Strug! Hi, Captain Sully! I see you all!
I love what this simile has helped me see about teaching. I love its power to elucidate why each part of the lesson is important. I love its power to illuminate all the parts of a lesson that need enough attention and preparation to make it come together. And I love that in exploring it, I developed a further appreciation for the masters who stick the landings in their own fields. I hope that you find this simile as helpful as I do. If so, then I stuck this landing: BRICK!*
*Brick is what gymnasts shout when their friends stick a landing.