Desmos is another great math tool

Yesterday I wrote about g(Math), a tool for adding formulas and graphs into Google docs, like an equation editor on steroids. Today I’m going to talk about Desmos, a full-featured, web-based standalone graphing calculator.

Desmos can be run from the website, or installed as an app in Chrome. You don’t need an account to use it, but if you create an account you can save your work – even saving a copy to Google Drive, which is nice. The interface is clean, with the list of functions down the left side, and a large central grid (which can be switched between Cartesian and polar) to display functions. It responds well to double touch, so using it on an interactive whiteboard is easy.

There are many, many saved examples on the Desmos site which highlight it’s capabilities – including animation and drawing pictures with multiple equations.

I’ve started using it to illustrate the parabolic functions of acceleration, finding the roots, intersection of functions (solving two equations and two unknowns), and illustrating standing waves and beat frequency. I’ve just scratched the surface – there is a lot more that can be done with it, I just need to find the time to figure out what all else it can do. But for teaching transformations of functions? Just throw in a function with sliders and watch what happens. It is a very user-friendly interactive tool.

It’s teacher friendly, student friendly, works beautifully on the interactive white board, it runs animations, and it’s fun. What’s not to like?

Why can’t we follow a recipe?

Chances are you know someone who can’t follow a recipe. When they try your favourite recipe, it comes out as a disaster. Why is that? Why is it that someone following step by step instructions can mess it up so badly?

I don’t know the answer for sure, but I suspect it has something to do with lack of familiarity. It seems perhaps ironic that in order to follow a set of step by step instructions you need to know what you are doing already, but I think that is what is required, and here’s why: If you don’t know what you are doing, you won’t know if you made a mistake, whereas if you have an idea what you are doing, you can recognize mistakes and correct them along the way.

The same is true for lab activities. Many of them are cookbook style, with step-by-step instructions. And foolishly we think, well, how can they possibly screw up? And the answer, I’m afraid, is very easily. Step by step instructions instil a false sense of confidence. Students, like cooks who can’t follow a recipe, assume that they have done each step correctly, because they don’t necessarily have the experience to recognize missteps.

The other day in Biology class we were using the popular pop-beads to simulate mitosis and meiosis. They are good in that they give students a tactile, visual representation that they can manipulate and see the process as dynamic, as opposed to series of discrete steps. But it was a disaster. The set comes with very explicit, step-by-step instructions. But either they could not follow the directions, or they were so focussed on the directions they virtually ignored the beads, or they simply skipped the beads altogether and drew the results from memory, rather than observation.

Next time I try this lab, I will do it very differently. I will introduce them to the beads one day, have them plan out exactly how they would represent the steps, and then on lab day have them make a stop-motion animation of the sequence of events in Meiosis. That way they are responsible for planning it out, and will have an idea what it should look like, so they can recognize mistakes when they arise, and then the videos can be critiqued afterwords to see if there are any glaring (or subtle) errors or omissions.

Now I just have to keep this in mind going forward, and plan ahead knowing that cookbook activities (not just labs) have a built-in human flaw.

Helium Frog Animator

Stop motion animation can be an effective way for students (and teachers, for that matter) to demonstrate a phenomenon. It requires some planning, but mostly it requires a thorough understanding of the sequence of events in the process – which is exactly what we are trying to achieve.

I am by no means an expert on stop-motion animation, but I have learned a few techniques – such as onion-skinning – to improve the quality of the end product. My current stop-motion software of choice is the Helium Frog Animator. This is free software for Windows that seems to have all the necessities, and several luxuries as well.

I don’t have any sample videos to show at the moment, but I will post some when I can. In the meantime, I am curious to see what others might be doing with stop motion animation in the science classroom.

Indispensable PhET

PhET is one of my go-to resources for teaching Science. There are dozens of science simulations in Physics, Chemistry, Math and Biology that are research based and designed to demonstrate and simulate specific phenomena. While some have a very narrow focus, others are others that are more open ended. The electric circuit simulator for instance, is sufficient to act as the focus for electricity unit of my grade nine Science class – it can even load and save files, so my students can create circuits and send them to me. For those who have not explored it, go there now.