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:
Chris Hunter 
Good analogy Chris. As someone who uses screencasting a lot with students, I guess I have to add that I think the purpose of the task comes into play too. I am often capturing evidence of “play by play” kind of thinking…what mental math strategies are you actually using? Can you orally and pictorially show how to solve a problem in more than one way? Those things need be assessed and we need documentation. We don’t always get that info if we ask students to write. Like a vision-impaired Canucks fan who might rely on the play by play to follow the game, a student who has written output difficulties may need the adaptation of screencasting to show what they know. Of course, am already thinking about colour commentary now but must say that I’m not sure screencasting is the most suitable genre of app for capturing big idea/conceptual thinking…I think I’d want to use iMovie or Animoto. Will share when I find an opportunity to play around with that.
Thanks for making me think about this Chris!
Thanks for commenting, Janice. And for reminding me of Jim Robson’s “special hello.” Maybe screencasting isn’t suitable for capturing conceptual thinking: it certainly doesn’t for Sal Khan. Maybe students explain their thinking (if this is indeed the purpose) afterwards. No reason why not. After all, the colour commentator offers analysis between action– with the benefit of slowmotion replay. I watch student-created tutorials and think to myself, “If only a teacher/peer stopped him/her here to ask Why/How do you know?” My frustration with student responses to “Explain your thinking” wasn’t limited to written assessments. I was thinking more along the lines of screencasting as a way to document and share what students explaining their thinking sounds like. These screencasts would probably generate much more conversation between colleagues (within or beyond the school’s walls) than a pdf of the same student’s written response.
This is a great post Chris. I’ve been thinking about this very thing a lot lately. The schools I support often gravitate to “improving communication” as an area of need in their math classes; and these “play by play” type of student responses always dominate. Unfortunately, too often, it’s not noticed or seen as an issue. This will certainly help me with the discussion. As always, you find a great analogy to help us. As a hockey player and fan (go Habs!), I’m just kicking myself for not considering this…. Thanks again!
Thanks, Cam. You’re right. Play-by-play responses can go unnoticed. I think when we do notice them, we often quietly let them slide for a variety of reasons (not wanting to take time to deviate from the lesson plan, not wanting to make the student feel uncomfortable, etc.). Let me know if this does turn out to be helpful in your discussions.
For me, finding analogies is just the result of not being able to walk away from work. Hey, you ever notice how soccer goalies react after being forced to make a save (i.e., their job)? A lot of finger pointing. Completely different in hockey. There’s something similar between this spectacle on the pitch and “Kids in Grade __ don’t know their times tables.”
Linking two of my favourite things was brilliant. Great post.