Math Exercise: Multiple Approaches to Problem-Solving

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 support their choice will increase their comfort levels. Th is process also builds math logic, intuition, and reasoning skills that extend into other academic subjects and real-li...

 Ways of Being "Good at Math"

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 solvers, able to come up with nonroutine ways to approach an unfamiliar problem. Still others may be good at visually representing relationships or problems or translating from one repr...

 Intellectuals Must Engage the Public, Not Hide From It

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 books like "mathematics for the millions" (which made mathematics intelligible to millions of people), participating in and speaking for popular organizations, etc., are now large...

 Satisfying Work Requires Clear, Actionable Goals

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 aren’t sure how to go about achieving it? Then it’s not work—it’s a problem. Now, there’s nothing wrong with having interesting problems to solve; it can be quite engaging. But it d...

 Common Core Math Standards

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 and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem ...