I do not know how to find the square root of a whole number without a calculator. I have number sense; I can estimate that the square root of 21 is between 4 and 5, closer to 5. I wonder if my students’ work with fractions and decimals falls into this category.
From Powerful Learning What We Know About Teaching for Understanding: “Students do not routinely develop the ability to analyze, think critically, write and speak effectively, or solve complex problems from working on constrained tasks that emphasize memorization and elicit responses that merely demonstrate recall or application of simple algorithms (Bransford, Brown, & Cocking, 1999; Bransford & Donovan 2005).”
I worry that our students never get to the solve-complex-problems stage of learning in math. I’m afraid that we assume if they can’t do the “basics” then they are not qualified to attempt sophisticated interesting problems. If we would dare to start with the complex problem, would we interest more students in learning – even learning the “basics”? If we allowed technology to crunch the numbers, would students experience more engagement and attempt more interesting, complex, elegant problems? Would they ask to learn to improve the “basics” that they deem necessary or important? Would they use technology to aid in their learning? Are we brave enough to test this hypothesis?
In Bo’s It’s about Learning blog from June 25, 2010 I read: “We should be recreating more of the moments when things work well, when our strengths are revealed and engaged, when our efforts are at our best.”
Imagine you are sitting in Algebra I looking at one of your papers where every problem is wrong; you do not have one right answer on the entire page. You know that you have done everything the way you were taught. You know and can express that you have used the correct inverse operations to solve the equations? Or, you know the quadratic formula and can correctly interpret the results IF the results are correct? How frustrating!
Think of Gillian from The Element. Gillian did not perform well on tests; her work was difficult to read, and it was often turned in late. She was “a problem” in class. Sound familiar? In Gillian’s case, she needed movement. What if you need technology? What if we could reveal your strengths in algebra by simply allowing you to leverage technology to show your work and effort at its best? Would you find the motivation to work on your deficits if you find your strengths first?