Engage Students in Math with Exploding Dots


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Fiumicino airport – Passport control – Discussion with passport control officer

  • Why do you want to be in Roma?
  • I’m going to a project meeting.
  • What kind of project are you talking about?
  • It is a school/ Comenius project. There are four schools from different European countries working together on the same topic.
  • So – you are a teacher!?
  • Yes, I’m a teacher.
  • And what do you teach?
  • I teach mathematics.
  • Ooooooohhhhhh …. I never liked mathematics and, in school, my poorest academic results were in math.

I have had similar conversations several times. Each time I wondered why people so easily confess to an unknown person that they didn’t like math and/ or they weren’t good at math. People usually share their successes with everybody – so probably they think that not liking math is a success; they are, somehow, proud of not being successful in math – which is not the case when people talk, for example, about their reading or writing competences.

Over the years, I have noticed that students don’t engage with math when they don’t understand it. Why don’t they understand math? Good question! Probably, the teacher focuses on teaching them algorithms, formulas, etc. In many cases, this means that the students memorize the algorithm / the formula and use it over and over – and I’m not sure how much they do understand out of it. Teachers have no time to ensure that students understand why they have to follow some specific steps in the algorithm, why a formula looks like it does. They have no time to develop their mathematical thinking …. You know: one has to take final exams in math, sometimes under family and school pressure, students have to have good scores in math to ensure whatever future they want for themselves, the math curriculum is vast, the final exams do not assess student thinking (or at least, not in Romania). … So what can we (math teachers) do to engage more students in math?

I found the exploding dots story (Tanton, n.d.) and I was really excited. Please see below the beginning of the exploding dots not-true story:

“When I was a young child I invented a machine (not true) that was nothing more than a series of boxes that could hold dots. And these dots would, upon certain actions, explode. And with this machine, in this non-true story, I realized I could explain true things! In one fell swoop I explained all the mathematics or arithmetic I learnt in grade school (true), all of the polynomial algebra I was to learn in high-school (true), elements of calculus and number theory I was to learn in university (true), and began to explore unanswered research questions intriguing mathematicians to this day (also true)!”  (Tanton, n.d.)

Why was I so excited? First, because I found an excellent way to explain number operations. I teach secondary-school students, and no student asked me why we add numbers as we do – they learnt it in primary school and took it for granted. My son, when he was in first grade, asked me the why question.

And my explanation was so complicated! Second, because operations with polynomials can be easily explained with the dots-machine.

I was curious if students would engage with the exploding dots story. So, I tried it with the 11th graders. I explained how the   machine works.  During the lesson, the students did: addition, multiplication, subtraction, division in base 5 (by using a  machine). They thought about how to do it, in groups, and they shared it with their peers. Every student engaged in this activity – regardless of their math academic results – as the work didn’t make use of ‘hard’ mathematical concepts; it was just about thinking. We actually covered, with the 11th graders, the five lessons from the exploding dots website (Tanton, n.d.) in 50 minutes. Please see below some samples of the students work:

Figure 1: Addition in base 5

Figure 2: How a student thought to do division in base 5

Figure 3: Addition and subtraction in base 5

Students understood that exploding dots challenges involve both mathematical and computational thinking.

I can’t wait until October, when during the Global Math Week, we’ll continue our exploding dots experience with the polynomials and infinite sums.

Exploding dots is the topic of the Global Math Week, which will be held on 10-17 October 2017. The Global Math Week is organized by the Global Math Project which aims to connect millions of students around the world through a shared experience of mathematics. See www.theglobalmathproject.org/gmw for details.

The project aims to generate a fundamental paradigm shift as to how the world perceives and enjoys mathematics. The project initiators want each and every person on this planet to see mathematics as human, relevant, meaningful, creative, uplifting, and joyful. They want to show how conversation about the play and wonder of mathematics transcends borders and truly unite communities.

The project initiators are providing all the teaching guides, lesson videos, written materials, and an interactive web app. Teachers can use full, minimal, or no technology in the classroom.

If you share the project aims and like the exploding dots story – visit the website https://gmw.globalmathproject.org/ and register for the Global Math Week!


Tanton, J. (n.d.). Exploding Dots. Preluat pe 22 June, 2017, de pe G’Day Math!: http://gdaymath.com/courses/exploding-dots/

Key words: mathematical thinking, computational thinking, math, engage, innovation, exploration, Global Math Week, Global Math Project

Article written by: Ariana Vacaretu, Scientix Ambassadors 

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