A draft hinge question for a Grade 3 lesson on two-digit addition with regrouping: 24 + 18. Before you meet, he writes the predicted wrong answers first, explains the misconception story behind each one, and sketches a three-level fading plan.
Work through each one as a diagnostic signal, not a grading category.
Ask Jordan: what would you say to the student who wrote 312 that you would not say to the student who wrote 32? That question makes the diagnostic function concrete.
Contingent support (Wood, Bruner and Ross, 1976) is read from the student, not imposed by the plan. The fading levels are a starting position. Jordan needs to know he can move up a level if the student stalls — that is not failing, that is reading the room.
Jordan knows his students’ world in ways no pre-service textbook reaches. In conversation 3 he showed you that a trap line of 24 lobster traps plus 18 more lands as clearly as any classroom addition problem — and more truthfully for his students. Ask him to walk you through two or three of those contexts. Let him run that segment of the conversation. Tell him plainly that you are taking his examples into your pre-service seminar. That is not a compliment; it is a fact. He teaches you here.
In three conversations Jordan has moved through the ZPD for formative assessment at a pace most first-year teachers do not manage. He can construct a hinge question, anticipate misconceptions, and now articulate the fading principle. What remains in his ZPD: reading a mixed-misconception whiteboard set in real time and adjusting mid-lesson without freezing. That is the MKO function for conversation 5 — scaffold real-time responsiveness, then plan your own exit from the mentoring relationship.
Watch for: does Jordan differentiate his response to 312 versus 32, or does he treat all wrong answers the same way? Does he return to level 1 when a student stalls, or stay at the planned level? Does he read when to pull a small group versus re-teach the class? These are the in-the-moment formative assessment moves Black and Wiliam (1998, “Inside the Black Box”) describe as requiring responsive, not scripted, teaching.
Note: Jordan already reads his community with precision. Do not scaffold what he already does.
About Jordan: relied on show-of-hands confirmation; interpreted universal nodding as understanding. Exit task revealed 50% had not followed. Classic false-positive problem with low-stakes, undifferentiated checking.
So: shifted to an all-response system (mini whiteboards). The hinge question gave him a tool he could use the next morning — theory anchored to his classroom worked. hinge questions all-response system
About Jordan: once he had the data (whiteboards with mixed answers) he froze. The formative loop collapsed at the response step. He had the diagnostic; he lacked the contingency plan.
So: introduced pre-planned responses — each wrong option predicts a specific misconception; plan the response before writing the question. (Dylan Wiliam’s formulation of the hinge question principle.) contingency planning formative loop
About Jordan: over-scaffolded until students were copying his steps. He named the principle himself: “the help should get smaller on purpose.” That phrasing is a marker — he can now articulate the concept, not just follow a procedure.
About you: Jordan knows his community in ways that pre-service textbook cases do not reach. Fishing, forestry, small trades — these provide richer, more culturally grounded maths contexts than your current seminar materials.
So: introduced contingent support and fading explicitly (Wood, Bruner and Ross, 1976). Agreed to learn the community contexts from Jordan. contingent support fading ZPD
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After conversation 4 with Jordan. He arrived with a solid hinge question draft and two distractors he could explain. We worked through the misconception story for 312 (place-value gap) and 32 (lost carried ten) and he named the difference clearly. Fading plan: he moved away from the sequential view once I asked "what does the student show you right now?" That question landed. Community contexts: Jordan walked me through lobster-trap counting and cord-wood stacking as addition contexts. I'm taking these into my pre-service seminar. What I noticed: he is ready to start noticing fading opportunities in real time. Conversation 5 could be an observation visit with that lens. What surprised me:
Paste this into your own AI chat to think through the conversation before it happens.
I'm mentoring a first-year Grade 3 teacher. In our next conversation he is designing a hinge question for two-digit addition with regrouping (24 + 18 = 42). He predicts wrong answers and explains the misconception behind each.
Useful distractors: 312 (column addition without regrouping — place-value gap) and 32 (partial regrouping — the carried ten is dropped).
He's also building a three-level fading plan: model it together, then a prompt card, then a single phrase ("check your tens"), then nothing.
Help me think through: What question should I ask if he can explain a distractor but doesn't know what to do differently for each group? What's the clearest way to distinguish contingent support from scripted instruction when I explain fading?
Three conversations done. Here’s what’s next, what you’ve built, and some things to try.
Write these out before you meet with Dinah:
If you want to practise on something concrete first:
24 + 18 = ?
The answer is 42. Two answers show up often on whiteboards:
Different answer, different problem, different next step.
You don’t go 1, 2, 3 in order. You start where the student is today. You watch for when to move. This has a name: fading. The help gets smaller on purpose, because the goal is that they get there — not that you got them there.
You asked: 24 + 18 = ? on mini whiteboards. Here’s what you see. Pick your next move.
Tap a support from the list, then tap the slot where it belongs. Most help at the top, least at the bottom.
Slots (1 = most help, 4 = least):
Tap one to select, then tap a slot:
If more than half the class wrote a wrong answer, re-teaching the whole group makes sense. But be specific about what you’re re-teaching — not “the lesson” but “the part where you carry the ten.” A vague re-teach doesn’t fix the specific gap.
Then you have two groups with two different problems. Re-teaching the whole class will reach one group and talk past the other. It’s worth splitting them — even briefly — so each group hears what they actually need.
Watch for: they stop asking what to do next. They slow down before a tricky step — that’s thinking, not waiting. They start checking their own work. Any of those is a signal to step back.
Normal, and fine. Move back to the level that worked — maybe the prompt card again, maybe one phrase. You’re not starting over. You’re just at where they are right now, and you’ll try stepping back again later.
When you’re at the front of the class with twenty-two whiteboards in the air, you have about two seconds to decide what to do. If you’ve already thought it through, you know what you’re looking for. If you haven’t, you freeze — exactly what happened in conversation 2.
No — just the likely ones. Two or three is enough. If a student writes something unexpected, ask them to show you their thinking. The plan is for the predictable mistakes that show up again and again.
You can, and sometimes that’s exactly right. But if the amount of help never changes, students practise doing it with you rather than on their own. The goal is that they do it alone — so they need practice with a little less each time.
There’s a difference between a struggle that moves and one that goes nowhere. Fading means staying close, watching, and stepping back in if they hit a real wall. You’re not walking away. You’re stepping back with your eyes open.
Your students’ families fish, work in the woods, and run small businesses near Miramichi. Dinah teaches teachers at a university — she has never seen a trap line become an addition problem the way you have.
In conversation 4, you run this part. Walk her through how you’d say: “24 traps out, 18 more added this morning — how many traps total?” and why that lands differently than “a store has 24 apples.”
She’s writing it down for her university class. That’s not flattery — she said so plainly. You’re teaching a teacher.
These aren’t just “fun” examples. They land because your students have watched their families count this way. The numbers mean something before the maths starts.
Real examples she can use with teachers-in-training who will work in communities like yours. Not a textbook case — your actual classroom, your actual students’ world.