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• Repaired ideas are the wrong ideas Pip held at the start that the student's explanations fixed. Each topic has four or five. Any still marked shaky is one the student has not yet explained in a way that meets the criteria.
• Explanations that counted are turns where the explanation met every criterion for an idea, in the student's own words. Turns that only stated an answer, or insisted, do not count.
• With an example or picture is the subset that also used a concrete example, a story, or one of the pictures (a fraction bar, a number line or a clock). These are the strongest explanations.
• Quiz scores show each quiz in order. Pip answers from what it believes, so the score tracks the repaired ideas, not luck.

• Ask the student to explain one repaired idea to you out loud. If they can, the understanding is theirs.
• Any idea still shaky is a good next lesson. The idea's label tells you the misconception in plain words.
• A low count of explanations with an example is a prompt: ask for a picture or a story next time.
• The judge's notes are one sentence per recent turn about what the explanation did or still needed. They can misjudge; read them as a teaching aide, not a grade.

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