Learning, liking what we do, bright spots, and literacy

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?

Calculator is to Arithmetic as Spell Checker is to Spelling???

Is using a calculator for math comparable to using a word processor for English? Is the calculator an arithmetic checker like the word processor is a spell or grammar checker?

My friend Jeff makes a good point about technology integration (advances) in English. Students that use a word processor must still proof their writing. Do we worry that kids won’t learn to write because of spell check or grammar check? Or, do we think that because of these tools they are free to concentrate on ideas, organization, voice, word choice, sentence fluency, conventions, and presentation? (Okay, conventions have to do with grammar and spelling, but I’m making a point here.)

The grammar or spell checker does not always catch “there” when I mean “their”. A calculator will not catch that I meant (-2)^2 when I entered -2^2. The calculator does not know that I mean 1+(6+4)/2 when I enter 1+6+4/2.

As Peyton pointed out in the Writing Workshop meeting, MS Word will not alert you to your error in writing “warmest retards” when you meant to write “warmest regards”. Your calculator will not alert you to an entry error; it will not know that you entered -3.75 when you wanted -3.57.

The spell checker automatically corrects some of my incorrect spelling. When I type “recieve” it automatically changes it to “receive”. When I type “calcualtor”, the word automatically changes to “calculator”. When I write “I never here anyone…”, the grammar checker alerts me to check my spelling or word choice. The Nspire calculator will autocorrect a little bit, but it assumes what you mean. For example, if you open parentheses, it will close them. However, you must make sure that it closes where you intend to end the grouping.

This is an interesting place for me in my thinking. I know that it has to do with age appropriate learning. I believe that young children should learn their numbers and arithmetic just like they learn their letters and words. I believe that junior high students should learn how to graph and solve equations by hand, graphically, with tables and spreadsheets, and with technology.

How much more could we learn about algebra, calculus, and statistics if we used technology to accommodate 8th graders that struggle to compute? Don’t our students need to spend more time on data gathering, mathematical modeling, and interpreting graphs and less time on mechanics.

Have you seen Conrad Wolfram’s Ted talk Teaching kids real math with computers?  What do you think?

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Just look at any TED talk by Hans Rosling to see examples of how critical the analysis and synthesis of mathematical information is to our future.