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Category: Math for Elem Teachers

TMBG Polygon Song

I saw this posted over at 36o and I thought it would be a really clever addition to the geometry section in Math for Elementary Teachers. However, I wasn’t crazy about the 1-minute introduction, which was obviously intended for a younger audience. I figured that there MUST be a video on YouTube of just the song (about polygons, and featuring the nonagon especially) … sure enough … there is! 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...

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...

Listening to the Rationals and Irrationals

Earlier this year I shared an application with you that would play a song based on the digits of the decimal expansion of pi. After I suggested that playing rational and irrational numbers could be a nice learning activity, one of the readers discovered a Wolfram Demonstration that also plays the irrational numbers called “Math Songs.” I’m pleased to report that Michael Croucher (from the blog Walking Randomly) has obliged us with the requisite companion Wolfram Demonstration that plays the RATIONAL numbers (any rational number with a numerator between 1 and 1000 and denominator between 1 and 1000). His demonstration is called “Music from the Rationals.” Now that we have both, what can we do with them? As you are, no doubt, aware, many students have great difficulty with the distinction between the rational and irrational numbers. Now you can play each number song-style and ask the students to identify whether the song ends, has a repeating element, or contains a random pattern. I was playing several fractions with denominators of 7, and then some with denominators of 13, when I made an interesting observation (well, maybe an obvious one). The same elements of sound patterns repeat, even as the numerators change. With so much calculator use today, I wonder if students realize all the patterns in the decimal expansions. Many students have probably never done a long division...

Why Subtraction Algorithms are Hard to Learn

Once you learn the algorithms for doing multidigit subtraction, then it might be difficult to remember why it’s hard to learn. If you’re teaching math for elementary teachers, this video might help your students to see why this is so hard for elementary students to learn the subtraction algorithm (or any other algorithm for that matter). 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...

Creating 3D Geometry with PowerPoint

I find this to be a handy trick in PowerPoint. Although there is certainly better software for graphic design (for example, Adobe Illustrator), most instructors have a copy of Microsoft Office on their computers and so it makes a convenient graphics and layout program. You may need 3-D graphics for Calculus, geometry, or math for elementary teachers and you can create those graphics pretty easily in PowerPoint. Here’s my 2-page tutorial. If you’re going to label these figures, I recommend using the equation editor (or MathType) and then grouping the figure with the labels to create a single object. Copy and paste the graphics into a Word document using “Paste Special” and “Enhanced Metafile.” It doesn’t always look crystal clear on the computer screen, but it will print beautifully. Possibly Related Posts: Bringing the Real World to Your Math Class Every Day Getting Graphs to Instructure Canvas Discussions History of Numeration Systems Collection of Math Games Signed Numbers: Colored Counters in a “Sea of...