Category: Schema Formation

Celebrate the Errors in Math Practice

Dear math students, As you work through your mathematics practice, I’m going to challenge you to embrace making errors in an entirely new way.  Many students believe that every problem in math homework should be perfectly constructed with no errors. It might look something like this:   But when it’s time to study after the initial problem run-through, what does this perfectly constructed problem say? Does it coach you on remembering how you struggled? Does it remind you where you made an error? No. When you make an error as you’re working a problem, please don’t erase it from the face of the...

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Algebra is Weightlifting for the Brain

This was my presentation on Friday in Austin, Texas at the Developmental Education TeamUp Conference. The process of learning algebra should ideally teach students good logic skills, the ability to compare and contrast circumstances, and to recognize patterns and make predictions. In a world with free CAS at our fingertips, the focus on these underlying skills is even more important than it used to be. Learn how to focus on thinking skills and incorporate more active learning in algebra classes, without losing ground on topic coverage. Algebra Is Weightlifting For The Brain from Maria Andersen   I’ve loaded the uncut, unedited video that I took of the presentation to YouTube.  I’m not going to claim the video recording is great (recorded with a Flip Video Camera sitting on a table), but you’ll get to hear the audio and more of the details.  View “Algebra is Weightlifting for the Brain” here. Possibly Related Posts: Group Exploration in Math Elaborations for Creative Thinking in STEM Better to be Frustrated than Bored Video of AMATYC Keynote Celebrate the Errors in Math...

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Hammer and Nail Problem

Believe it or not, I have been at MathFest for three days and have only managed to attend four sessions (besides the one I presented in). But I talk to a lot of people and talk to a lot of the exhibitors and because MathFest is a lot more research-oriented and focuses more on upper level math, there are actually not a ton of sessions that I am interested in – although, as is always the case, the sessions I did want to go to were all scheduled for the time I was speaking. I haven’t seen Kien Lim since graduate school – I saw him walking down the street one night in Madison and recognized him. Kien and I used to be involved in some great discussions about how students learn. He invited me to his talk on the “Hammer-and-Nail Problem in Mathematics.” His talk (10 minutes) was briefly about his interest in math education and his experiences with students in Math for Elementary Ed. What he’s seen in teaching future teachers, is the same problem that I think we’ve all seen in different courses. Here are some examples that I’ve seen in math classes: After you teach algebra students how to multiply polynomials, some can suddenly no longer add polynomials and will multiply an expression like (x + 3) + (x – 4). In Calc II, I...

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