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Category: Math Ed Research

Signed Numbers: Colored Counters in a “Sea of Zeros”

The “colored counter” method is an old tried-and-true method for teaching the concept of adding signed numbers.  However, to show subtraction with the colored counter method has always seemed painful to me … that is, until I altered the method slightly. Now all problems are demonstrated within a “Sea of Zeros” and when you need to take away counters, you can simply borrow from the infinite sea.  Voila!  Here’s a short video to demonstrate addition and subtraction of integers using the “Sea of Zeros” method.  You can print some Colored Counter Paper here. Video: Colored Counters in a Sea...

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: Contemporary Algebra Collection (new resources 2/4/2019) Teaching in Higher Ed Podcast about ESIL Lens Add Graphs In The World to Courses Bringing the Real World to Your Math Class Every Day Taking the Algebra Out of College...

Prime Number Manipulatives

For those of you who are curious what we were actually doing in class in yesterday’s post (Record with a Document Camera and a Flip), we were “fingerprinting” the factors of composite numbers with their prime compositions. The wooden “prime number tiles” are created using the backs of Scrabble tiles and the white tiles you see on the board are the student version of the prime number tiles (each of them cut out a sheet of their own prime number tile manipulatives at the beginning of class).  Just for the record, I would like to confess to destroying more...

Wolfram Alpha for Inquiry Based Learning in Calculus

Now that all my Calculus II students know about Wolfram Alpha (I showed them), I have to make sure that the assignments I ask them to turn in can’t just be “walphaed” with no thought.  In Calc II, our topics list includes a lot of “techniques-oriented” topics (integration by partial fractions, integration by parts, etc.) and because of the need to keep this course transferable to 4-year schools, I can’t really get around this.  So now I’m in the position of having to reconcile the use of technology that easily evaluates the integrals with making sure that students actually understand the techniques of integration.  There are two ways I’m tackling this: 1. CCC (Concept Compare Contrast) Problems: I’m writing problems that focus on understanding the mathematical process and the compare/contrast nature of math problems.  While Wolfram Alpha can evaluate the integrals for them, the questions I’ve asked require (I hope) a deeper level of understanding about what happens when the techniques are used.  Here’s an example from my recent problem set: There are two pairs of problems below that are exactly the same. You won’t see why until you do the integration, showing all the steps. Find the pairs and then explain how the matched integrals are fundamentally the same. 2. Inquiry Based Learning: One appropriate use for any CAS (computer algebra system) is to use it as a...

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