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High school mathematics teacher Katie Sinnott presents multi-tiered probability problems to her 11th and 12th grade AP Statistics class, in this media gallery from WGBH.

Katie Sinnott asks students to draw on prior knowledge to develop a solution strategy for a multi-tiered problem. She prompts them to use maximum effort. Students team up and Ms. Sinnott circulates through the classroom, assessing student struggles before offering questions and explanations to help.

Ms. Sinnott explains her goals for the day, which center on helping students formulate different strategies for solving a difficult probability problem. She defines a good problem as challenging for most students but not so hard that no one can solve it.

Ms. Sinnott describes her strategies for assessing what students know and getting students to persevere. These include “eavesdropping”—observing students and making mentor notes—as she circulates in the classroom to learn what students are discussing in group work.

Ms. Sinnott explains the importance of perseverance in problem solving and the idea that students should rely first on themselves and their notes, and then on their classmates, before asking the teacher for help.

Ms. Sinnott discusses why even high-performing students struggle in her statistics class. She instills in her students the importance of explaining their answers and emphasizes that teachers must also demonstrate persistence in giving students direction.

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