It’s been quite a school year; when the year started in September who among us would have thought we’d be teaching remotely, that some of our friends would be envious of the relative permanence of our jobs, and parents would admit how difficult it is to teach and engage their children for at least 6 hours a day.

We all need a break, and I suggest it’s a great time to challenge yourself and learn something new; something that’ll interest you, positively impact your instruction, and will come in ‘handy’ (especially) if teaching school includes mandatory remote teaching/learning.

I’ll divide my suggestions into two groups; ‘learn’ a math application which will enable you and your students to explore mathematical ideas and ‘learn’ a pedagogical application which will enhance your instruction (I’ll save the latter for another blog post).

**MATH APPLICATIONS**

I’ll recommend three. CODAP, Desmos, and GeoGebra.

I discussed CODAP (Common Online Data Analysis Program) in the March blog post Dynamic Statistics. CODAP is a free, web-based data analysis application for students. It has some built-in data sets or you can use your own, and the application makes data exploration ‘easy’, fun, and very revealing. You can find it at: https://codap.concord.org/for-educators/

Desmos is an advanced graphing calculator implemented as a web and mobile application. That sounds daunting, but Desmos is easy to use and supports the exploration of many mathematical ideas. In addition, there’s a Teacher Desmos and a Student Desmos which contain lessons/mathematical explorations which can be explored by you and your students, and they can modified to fit the needs of your classroom. *Many of these are highlighted on Dan Meyer’s blog https://blog.mrmeyer.com/.* Desmos is a very powerful tool which can change the way you teach mathematics. Take a look at: https://www.desmos.com/

Here’s the description of a proportional thinking learning activity found on Desmos:

And here’s a copy of a typical use of Desmos as a graphing calculator. *Notice I’ve entered the function with a parameter ‘b’, and Desmos helped me set up a ‘slider’ so a student (or teacher) can move the slider, which changes the value of ‘b’, and adjusts the graph accordingly.*

GeoGebra is intelligent graphing software which allows the user to explore both 2D and 3D Cartesian and Euclidean geometry as well as calculus, statistics, and probability. You can find it at: https://www.geogebra.org/

Let’s stick to Geometry for a moment. GeoGebra tools allow you to draw most geometric shapes, lines, points, etc., and you can animate your drawings. You also have the ability to create workbooks and incorporate your drawings. *I even use GeoGebra when I need an accurate drawing of a geometric figure (e.g. a regular octagon) – I draw it in seconds using GeoGebra and then copy and paste it into my handout.* There are hundreds of animated drawings/workbooks saved in a public GeoGebra space which you can use to enhance the teaching/learning in your classroom. By the way, one of my favorite is the animation of the area of circle into a triangle (the radius of the circle is the height of the triangle, and the circumference of the circle is the base of the triangle). So, A_{C} = A_{T} = Cr/2 = πr^{2}

Here’s a typical screen from GeoGebra in which GeoGebra helped me draw a circle in seconds and the corresponding algebra on the left side of the screen.

Have you used any of these in your classroom? How is the teaching learning of mathematics changed in a classroom using these tools? We look forward to your comments.

By the way, this blog will take a break this summer, as my co-author and I will focus on our own professional development. I’m going to catch-up on my professional reading, and I’m going to imbed more of the GeoGebra application into my Geometry Methods course.

Would you like more posts like this or something else? Tell us what would be most helpful right now or for the term following summer ‘break’?

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Have a question for the authors? Email us at: congruentthoughts@nl.edu or tweet us @ProfessorAleksV and @GeorgeLitman1