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The three ideas that do the heavy lifting. The full article goes deeper , free, no gate.
The same diamond shape works for addition, subtraction, multiplication, and division, students see how the operations are related, not four separate procedures.
The empty cell forces the question "what do I know, and what does it tell me?", reasoning first, computation second.
Kindergarteners compose and decompose with it. Fifth graders use it for fractions and factors. Same puzzle, deeper numbers.
Teachers who watched understanding arrive, and said so.
“I saw light bulbs turn on and thinking turn on that I had never seen with math.”
“This is it. This is how to teach math.”
“These kids aren't just saying math words anymore. They can explain them and show models to back it up.” (Rosie Ashcraft · and Ms. Hochstrasser's 4th graders made dramatic gains, the kind you can point to on the assessments and see in how students talk about the math.
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The Diamond Problem , the article, with the research and the classroom takeaways.
Read it free →
DMT INSIGHT · The Diamond ProblemWatch the lesson taught, models, questions, and the language, on tape.
Watch it free →The activities and demo lesson that go with this idea, open now.
Open the free lesson →The people behind 40+ years of classroom research don't hand you a binder and disappear. They're in the portal, on the weekly calls, and, when you need it, building a plan for your students with you.
Coach in the room, number line up
PD that respects your time
Fraction questions? He's got them.
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Tell us about one student who's stuck, or one lesson that keeps falling flat, and we'll help you build the plan for it. That's the partnership: teacher-led, expert-backed. We don't push a system downward; we listen, advise, question, and support.
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