PhET is a collection of approximately 100 interactive simulations in science and math developed and maintained at the University of Colorado at Boulder. You can find PhET at https://phet.colorado.edu/

I’ll focus on the math simulations which make up less than half of the simulations. If you’re interested in STEM applications, the ‘other’ simulations can help you connect science and math using engaging activities.

One of the important characteristics of this entire website as well as the individual simulations is that they are available in dozens of languages and, importantly, many have multiple accessibility features such as alternative entry, sound, magnification, and voicing.

In addition, there are many videos and pdf guides to help teachers use these simulations in the classroom. Included among them is “How to Use PhET in a (Lecture) Demonstration.” Interactive demonstrations enhance the instructor’s ability to communicate ideas and are usually much more effective than drawings on the board.

Sometimes I use interactive simulations in my classroom as part of a demonstration of a concept or mathematical activity, then I expect students to use the simulations individually (or small groups) to continue their investigations/inquiries.

Finally, there’s a 4 – 7 hour virtual workshop for teachers which introduces PhET and many elements of lesson building using these simulations. Though many of the simulations are at the secondary level; there are some designed for elementary and middle level students. For example, the following is from Area Model Decimals (https://phet.colorado.edu/en/simulations/area-model-decimals)

This sample screen shows the options and thoroughness of the simulation. On the bottom right the student (or teacher) has the option of limiting the rectangular area to 1×1, 2×2, or 3×3. The student (or teacher) has the option of showing partial products within the rectangular area and/or the area model calculations. As you can see above, the ‘size’ of the rectangle can be changed using the blue and red arrows, AND the size of the four partial products can be changed by sliding the red and blue triangles in the grid. The other PhET math simulations are similar; there are many opportunities to explore a concept by dynamically varying the parameters within the simulations, and then playing a ‘game’. In the following example, the student must build a polygon with a specific area (A = 40 sq units), perimeter (P = 26 units), and specific ratios of light and dark squares (1/4 vs. 3/4). By the way, the figure below DOES NOT meet all these expectations; it’s a work/game in progress.

As you can see, the simulations are designed to allow the student to explore the concept. I hope you’ll try them at https://phet.colorado.edu/

Mathigon is another website worthy of your examination and consideration. As you can see, Mathigon identifies itself as The Mathematical Playground. You can find it at: https://mathigon.org/

Mathigon contains 4 sections; Courses, Polypad, Activities, and Lesson Plans.

Selecting Courses leads you to 3 choices: Foundations (grades 6 – 8), Intermediate (grades 9 – 10), and Advanced (grades 11 – 12). Each of these has many topics, subtopics, and ‘lessons’. Though identified, only 1 has been completed at this time. The Activities section contains mathematical investigations. One of them, for example, is P-adic Numbers which, as you can see is composed of a topic identified as Exploding Dots which contains 3 subtopics. https://mathigon.org/course/exploding-dots/p-adic

Polypad comes ‘closest’ to an organized set of manipulatives. Here, for example, is the Algebra Tiles manipulative (https://mathigon.org/polypad/r8guTEhOhtugmQ). This is but one of three dozen manipulatives and digital games in the Polypad section of this website.

Finally, the Lesson Plans section contains Professional Development which provides access to webinars, a library of tutorial videos, and more. The section of Lesson Plans contains standards based lesson plans, teaching ideas, etc. using the digital activities on the Mathigon website.

The Lesson Plans section allows teachers, students, and parents to create accounts, and all of the above is free. And, all of Mathigon is available in more than a dozen languages. Finally, there are dozens of User Guides, Polypad Webinars, Short Video Tutorials, Guest Speaker Series, and Special Events; all of which can be found at: https://mathigon.org/pd

In today’s blog we’ve explored both PhET and Mathigon; two mathematics focused websites which feature much more than manipulatives. I’m sure if you spend a bit of time with some of these mathematical investigations, you’ll find many which will engage your students and enhance their learning (as well as your own).

Do you use any of these in your classroom? Would you use these to enhance and/or extend the learning of mathematics?

Would you like more posts like this – reviews of math websites, or something else? Tell us what would be most helpful right now or for the future.

Subscribe to the blog and never miss a post! If you like a blog, tell your friends and colleagues.

Have a question for the authors of this blog? Email us at congruentthoughts@nl.edu or tweet me @GeorgeLitman1