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In 1998, as California was in its first year of a counter- revolutionary mathematics curriculum framework thanks to efforts led by anti- progressive mathematics education groups like Mathematically Correct and HOLD, Richard Rothstein's THE WAY WE WERE? The Myths and Realities of American's Student Achievement was published as a Century Foundation Report. The first chapter should be required reading for anyone who thinks s/he knows about the history of American public education. It explores and debunks many widely-believed myths about "falling" achievement in literacy, general academic knowledge, and the whole notion that our public schools are failing us, kids today are far less competent in basic skills than were those of previous generations, and that our lousy schools are paving the road to hell for our kids and our nation. In particular, Rothstein examines two currently hot-button topics - social promotion and bi-lingual education - and reveals many surprising r...

Last time, I explored some ideas about what comprises good mathematical questions in mathematics classrooms taken from MAKING SENSE: Teaching and Learning Mathematics With Understanding, by Hiebert, et al. In this entry, I want to introduce ideas from a book by Peter Sullivan and Pat Lilburn: Good Questions for Math Teaching: Why Ask Them and What to Ask [K-6] Sullivan and Lilburn's Criteria In the introduction to their book, Sullivan and Lilburn list three main criteria for good questions: a) They require more than remembering a fact or reproducing a skill; b) Students can learn by answering the questions, and the teacher learns about each student from the attempt; and c) There may be several acceptable answers. The first of these features, while not something everyone sees as important in all mathematics classrooms, is essential to non-routine questions. It takes no teacher skill to come up with questions that only ask for students to show that they have memorized a fact (e.g...