To many, Explain your thinking = Tell me your steps.
Which got me thinking about hockey.
In sports broadcasting, the play-by-play announcer gives a detailed account of the action. The colour commentator provides expert analysis and insight. The sideline reporter does this.
Listen for the difference (play-by-play vs. colour commentary) here:
From ‘Doc’ Emrick, play-by-play announcer, we learn:
- Sidney Crosby tries to split the defence
- Ryan Miller steers the puck into the corner
- Crosby “crunches” the puck along to Jarome Iginla
- Crosby scores
- the game is over
- Canada wins the gold medal
Emrick’s enthusiastic call certainly added to my enjoyment of the broadcast, but it did little to add to my understanding of the events. It’s the stuff of who, what, where, & when. I didn’t really need ‘Doc’ for this; I saw it for myself.
From colour commentator Ed Olczyk, who comes in at 0:50, we learn:
- a two-on-two turns into a one-on-nothing
- Sidney Crosby beats Ryan Miller under the pads
- Jarome Iginla, as he’s falling down, makes a beautiful pass to Sidney Crosby
- it’s man-on-man coverage in overtime
- Crosby gets offensive position on Brian Rafalski
Olczyk answers how & why Crosby scores.
Back to the math classroom…
Explain your thinking.
Two fictional responses at two extremes:
Doc: First, I minused 5 from both sides. Then, I divided by 2 and got x equals 3.
Ed: We modelled open & closed using red & yellow counters. We looked for a pattern and noticed that the first three open lockers–1, 4, & 9–are perfect squares. We tested 24 & 25. Switching has to do with factors. Only the perfect squares have an odd number of factors: you only count the 5 for 25 once.
In many math classrooms (mine included), student explanations can sound more like the former than the latter; more detailed account of the calculations on the page than insight into mathematical thinking.
Math teachers can work backwards and determine that Doc completed a practice exercise; he solved 2x + 5 = 11 for x. They’ll also recognize that Ed solved a problem–the well-known locker problem. Students are more likely to explain their thinking if they are being asked to think.
But practice or problem, creating a culture of why–consistently asking “Why?”/”How do you know?”–can also insert colour.
At first, I thought this analogy might be helpful to students–a small part of conversations that also involve post-game analysis of shared student responses (formative feedback, exemplars, etc.).
Whiteboard apps, such as Explain Everything or Show Me, can be used to capture and share student thinking. Student-created videos shared with me (so far) are more play-by-play than colour commentary. There is a place for a description of events as they happen. In fact, I just used a step-by-step video tutorial to help me repair my dishwasher. But we’re talking about mathematics, not home appliance repair. Behind the bench of each student-created tutorial that gets a “meh” from me, there’s a teacher passionate about mathematics and/or technology. I think we have different gameplans. Maybe the sports broadcaster analogy would be helpful to teachers, too?
Got a student-created video that’s more colour commentary than play-by-play? See you in the comments.
And just for fun, the finer points of hockey: