Digital learning tools – Desmos

May 3, 2019

This week we put our digital learning tools spotlight on Desmos. Officially Desmos is a free online graphing calculator, but in reality, it is so much more. I started using Desmos four years ago when the only device in the class was my computer. Other apps have come and gone, but I still use Desmos in almost every maths lesson.

Demos consists of 5 different products:

  • Desmos Online Graphing Calculator (desmos.com) is the primary product underlying all the Desmos products. This allows users to quickly draw many functions like parabolas, log graphs as well as non-functions like circles or the inverse of a parabola. In addition to graphing both equations and inequalities, it also features lists, plots, regressions, interactive variables, graph restriction, simultaneous graphing, piecewise function graphing, polar function graphing and two types of graphing grids.
    Desmos
    Four function calculator
  • The Four Function Calculator (desmos.com/fourfunction) is precisely that, an online calculator that can add, subtract, multiply and divide (and calculate square roots). While not groundbreaking it is surprisingly useful to have access to a calculator that you can easily project onto a screen so that learners can see what you are doing.
  • The Desmos Scientific Calculator (desmos.com/scientific) has all the most commonly used features in high school and then some. The app is free, works offline and can be downloaded onto any smartphone. This means that if you can download the app, you do not necessarily need to fork out hundreds of rands to buy a scientific calculator.
  • Desmos – Geometry (geometry.desmos.com) is a new addition to the Desmos family and allows you to draw and model how lines, angles and shapes interact with each other.
  • Classroom Activities (teacher.desmos.com) enable a teacher to set up an interactive slide deck where learners can draw, experiment, explain their thinking and interact with each other’s thought process in a guided and structured way.

Desmos vs Geogebra

When I introduce Desmos to teachers, the first thing they ask me is, “What is the difference between Desmos and Geogebra?” The short answer is nothing really; it is like the difference between Apple and Andriod, Google Apps or Microsoft. Both are free graphing calculators with a bunch of extra features.

Making a detailed comparison will be a blog post on its own. Personally, I love the ease of Desmos especially when it comes to functions. But it is the fantastic classroom activities that bring me back to Desmos time and time again.

I think when it comes to geometry, Geogebra might still have the edge. The geometry functions in Desmos is still very new but improving by the day. If you do not have a stable internet connection in your class, the fact that you can download Geogebra on your computer, on the other hand, is a big advantage.

Using Desmos with only a teacher computer

While Desmos classroom activities are ideal for the one-to-one classroom, it doesn’t mean that you cannot get lots of value from Desmos with only a teacher computer. I started using Desmos long before I even dreamt that one day each of my kids would be able to work on Desmos by themselves.

Graph everything

I have a suspicion that until I started using Desmos my learners thought that the only functions that can be graphed are linear, quadratic, cubic and exponential functions. Now we might be busy with algebraic fractions and learners will ask me if I can quickly Desmos it so that they can see what it will look like. Or when I introduce the degree of an expression in grade 8, I will show them how the degree changes the way the graph looks. Graphing other equations creates connections between the different sections of maths and gives learners a visual way to understand the work we are doing.

Use sliders to save time.

When I started using Desmos, my colleagues could not believe how much quicker a could teach the characteristics of the different functions, which freed a lot of time for practising. Sliders meant that I have multiple examples of each graph at the tip of my fingers. But the best part is that when learners start asking, “What would happen if you change this or that?” I can show them immediately and in the process give learners ownership of the maths they are learning and encourage curiosity.

Using Desmos in a one-to-one class

But the real power of Desmos is released when you let the kids loose on it. Without even trying you tick the one learning box after the other. All the learners are actively involved with the maths; they are discovering things without being told what to do; they share ideas and talk maths.

For me, the most significant advantage of Desmos is the Classroom activities. Classroom activities are like an interactive slideshow, that guide learners through their task. On each slide, you can provide learners with information, show them an example, give them a task to complete or ask questions. You have the option of allowing learners to work through the slides at their own pace, or you can manage the pace from the teacher dashboard by limiting them to a specific set of slides. But the best part is that you can keep an eye on what each learner is doing right from the teacher’s dashboard. Or if you want to assess the activity, you can do it in a single glance instead of opening 30 different websites or documents.

And while setting up your activities is really easy to do, the best news is that there is a collection of ready-to-use, pedagogically sound activities available. You can either use them as is or adapt them, especially for your class.

What makes Desmos different from other digital learning tools?

Teachers are often amazed that learners, who spend hours on their devices outside the classroom, dislike doing online school activities. But outside the classroom-context, people use their device in social and creative ways. They create all kinds of media – text messages, videos, photos, etc. – and they share that media with their peers via social networks. In the typical classroom-context learners are only required to provide multiple choice and short answers that are either right or wrong. They share those answers with an algorithm, or in some cases, their teacher. In the case of most digital learning tools, the teacher will only ever sees the grade the algorithm gave them. The fact that a lot of the most used edtech is generally anti-social and uncreative might explain why learners are so easily distracted when they work on personal devices in the classroom.

Typical personalised online programs let students work through a set of problems or concepts at their own pace, isolated from the rest of the class. This eliminates the best element of learning in a classroom-context versus learning online. When you find something like Desmos that is not just skill, drill and kill, but rather encourage deep conversations and creating, testing and formulating hypotheses, it gets your attention.

5 Reasons to use Desmos

  1. Desmos encourage learners to create their own mathematical ideas and share it, not with a computer algorithm.
  2. By making maths visual, Desmos helps learners to understand what they are working on and making connections between different maths topics.
  3. Desmos has a collection of well thought-out, pedagogical sound, ready-to-use activities that you can adapt for your classes.
  4. Desmos is free and always on hand and very easy to use.
  5. Demos makes maths fun while diving into some very complex concepts.

Desmos in non-maths classes

If you are not a maths teacher and still reading, kudos to you, so I will share a secret with you, while Desmos was designed for maths teachers, with a little creativity other teachers can also make use of a lot of the features. For example, card search can be used as a way to test definitions in any subject.

If you are not convinced, have a look at this collaboration between Desmos and The New York Times called What’s Going On in This Graph?

Get inspired by these Desmos activities

Created/Edited by me

Grade 11 – Trigonometric functions

https://teacher.desmos.com/activitybuilder/custom/5aba29952fa00346673c519b

I created this as a revision exercise to use at the beginning of Trig functions in grade 11. It allows learners to refresh their memory and prepare them for the new work.

Grade 10 – Trigonometry functions

https://teacher.desmos.com/activitybuilder/custom/5b62a17c2485be6648b356d0

In this activity, learners test their understanding of the range of trigonometric functions and how that is affected when the amplitude change or the graph shift. I adapted this activity from a pre-exciting one, changing it from radians to degrees for South African schools.

Grade 11 – Functions

https://teacher.desmos.com/activitybuilder/custom/5c73b6ed8917474b9a242eb5

In this activity, learners use sliders to see how a change in the discriminant will change the number of x-intercepts of a parabola.

Grade 11 – Revision of grade 10 functions

https://teacher.desmos.com/activitybuilder/custom/5a72fbb5edc7a644f2864ca0

This activity reminds learners about the functions they learned about in grade 10 and lay the groundwork for grade 11 functions.

Grade 10 – Functions

https://teacher.desmos.com/activitybuilder/custom/573eb542827691d10e1c6ca7

This activity can replace the worksheet you have about determining the equation of a parabola.

Grade 10 – Analytical Geometry

https://teacher.desmos.com/activitybuilder/custom/57cd19e2ea94591609226a08

This is a perfect activity to use as an introduction to analytical geometry.

From the Desmos catalogue

Grade 11 – Functions

https://teacher.desmos.com/activitybuilder/custom/56e0b6af0133822106a0bed1

A great introduction to the concept of parabolas and how functions can be used to model real-life situations in order to make predictions.

Grade 8/9 – Numbers

https://teacher.desmos.com/activitybuilder/custom/57d9fdc6ebf48f73093807b2

Learners often come to high school with a lot of misconceptions when it comes to inequalities. This activity clears up these misconceptions early in high school before it becomes a problem.

Grade 9 – Probability

https://teacher.desmos.com/activitybuilder/custom/59233c9aefd17610dbbd684e

This activity makes is easy and quick to do a lot of chance experiments in a short time, connecting probability to real life.

Grade 9 – Financial maths/Straight line graphs

https://teacher.desmos.com/activitybuilder/custom/56c7457e11c7724106e683b1

In this activity, learners compare exponential growth with linear growth, while at the same time being introduced to modelling equations as graphs.

Grade 12 – Statistics

https://teacher.desmos.com/activitybuilder/custom/58cc26d4c722f106146a8310

This one activity covers basically everything learners need to know about scatterplots and line of best fit.

Grade 11 – Functions

https://teacher.desmos.com/activitybuilder/custom/566b31784e38e1e21a10aade

This is the activity that first got me hooked on Desmos, and it is still one of the best. Challenge learners to apply their knowledge of parabolas in a fun and competitive way.

Author: Renate

Renate is a resource developer, blogger and technology integration specialists for schools. Starting her career as a maths teacher in 2006, she quickly became interested in the opportunities technology can bring to the learning process. For four years Renate was in charge of managing the introduction of 1-to-1 devices at Rhenish Girls’ High School in Stellenbosch before she decided to venture out on her own and offer her experience to other schools. Renate now provides professional development and consult on planning and implementing digital learning on a freelance basis. Read more…

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