Posts Tagged 'ipads'

Function transformations: Desmos rocks it

In Algeba 2, we’ve got our growing list of parent functions, and we know how to slide, flip, and stretch them. Some students have developed a pretty deep understanding of the transformation formulas – that is, they know why they work – and I believe they will be able to recall and use them far into the future. Others are able to use the formulas correctly (some more often than others) but maybe don’t really get exactly how they do what they do. These kids may memorize the formulas for the test, and then forget them.

Today I projected a bunch of  graphs of transformed functions, and kids sought to write an equation for each. It’s a classic Algebra 2 lesson, developing more fluency between the algebraic and graphical contexts. When I handed out the iPads and sent kids to Desmos.com, things really got going.

Desmos is so much better than a graphing calculator for this purpose. It provides instant feedback, and you see the equation and graph at the same time. The graph changes while you edit the equation. Or, you can make a copy of an equation and edit that, then compare. I got some great “What would happen if…” and “Why” questions, which I love. In both sections we had a detailed discussion of why translating then dilating a half-circle would yield a different result than dilating then translating.

The lower-achieving kids seemed to do well with this lesson. It was nice to be able to try something, see what happens, then adjust. And because everyone was engaged, I got to spend some more time working directly with them.

Downsides of Desmos: On an iPad it’s pretty easy to lose your work by deleting or navigating away. Also, the parentheses take some getting used to. The downsides were totally outweighed by how immersed the kids were in the algebra-graph environment, and how much they liked it.

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iPads in the high school math classroom

My district invested in several classroom carts of iPads this year. This will allow us to have one-to-one computers in the classroom during selected periods; we sign up for the carts ahead of time, just like booking the computer lab. They are not personal devices for the kids to use outside of class, so we won’t be ditching our textbooks yet. Teachers also received training and their own devices.

I am not particularly interested in apps to practice solving equations or other drill-in-a-fancy-box. (Most of the vainglorious ly advertised “math-teaching” apps seem to fall into this category.) I’m seeking ways to use the devices strategically to get deeper into the mathematics. So far, I have the following uses in mind:

  • Desmos, a free online dynamic graphing calculator that works well on the tablet. It’s easy to imagine using this. I have an in-classroom set of TI-84s, but Desmos is better for many applications. For exploring how the coefficients of a quadratic effect the shape of its graph, Desmos would be smooth as okra in gumbo.
  • Google apps with the iPads as data collection devices, to build spreadsheets of school data for analysis in class. We’ll be doing the data unit in Algebra 2 pretty soon, so this may be my first foray with the class iPad cart. Kids will write their own survey questions, which must be clear, quantitative, and Hemingway-esque. Then they’ll use the iPads in conjunction with a spreadsheet/survey to get data from students around the school.
  • The camera – still and video – with share-ability for a variety of purposes.
  • LogoPlus is a nice, clean Logo programmer which I would like to get kids using. Being good, it is not a free app, which creates a bit of a barrier for the classroom set. I have not found a free Logo app that I like. (Does anybody use Logo in high school geometry? I really want to!)
  • I can imagine students using ShowMe or something similar to demonstrate their understanding or facility with particular procedures. Maybe. Actually this could make a nice assessment, in the right context, but there are some issues with how the files are saved and stored.

That is kind of a short list! In the future category:

  • Geogebra for iPad is in development; I am really itching for this one. Right now the closest thing out there I know of is this: http://tinyurl.com/ggbweb/ but last time I tried it on the iPad many key functions didn’t. (Sketchpad Explorer is a dud for high school IMO – too limited in functionality.)
  • Mathematica folks told me they have an iPad version in the works, which should be interesting to see.

Anybody out there have wonderfully enriching uses of iPads in secondary math classes? Please get in touch in the comments! Thanks.

Blame the avuncular Sam Shah for any Rube Goldberg-ish phraseology in this post!


We are all born into this world, and at some point we will die and that will be that. In the meantime, let’s enjoy our minds and the wonderful and ridiculous things we can do with them. I don’t know about you, but I’m here to have FUN.
-Paul Lockhart

In theory, theory and practice are the same. In practice, they are not.

-Yogi Berra