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For example, if the problem was to fi nd the answer to 8 × 6, students may suggest three options: memorizing the multiplication table for 6, knowing that 8 × 5 = 40 and adding another 8 to equal 48, or adding a column of six 8s. Allowing students to personally choose among approaches all confi rmed as correct and to…
It’s a common misconception that someone who’s good at math is someone who can compute quickly and accurately. But mathematics is a broad discipline, and there are many ways to be smart in math. Some students are good at seeing relationships among numbers, quantities, or objects. Others may be creative problem…
A final point, something I've written about elsewhere (e.g., in a discussion in Z papers, and the last chapter of "Year 501"). There has been a striking change in the behavior of the intellectual class in recent years. The left intellectuals who 60 years ago would have been teaching in working class schools, writing…
Satisfying work always starts with two things: a clear goal and actionable next steps toward achieving that goal. Having a clear goal motivates us to act: we know what we’re supposed to do. And actionable next steps ensure that we can make progress toward the goal immediately. What if we have a clear goal, but we…
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution…
am enthusiastic over humanity's extraordinary and sometimes very timely ingenuities. If you are in a shipwreck and all the boats are gone, a piano top buoyant enough to keep you afloat that comes along makes a fortuitous life preserver. But this is not to say that the best way to design a life preserver is in the form…