*Temps de lecture : 10 minutes*

Being nice to your neighbour can apply to everyday, almost anecdotal, situations, like holding the door for the next person or giving up your seat to an elderly person on public transportation, but it also applies to more engaging situations, like sharing information.

To understand what’s at stake here, I’m going to use a specific example. Let’s imagine that three students, Carl, Claire and Clarence, have to solve a math problem.

Here, we can see three excellent ways of arriving at the same result! However, Claire, Carl and Clarence each only have access to one solution… their own. That’s too bad, because as we can see from an outside perspective, each idea is different from the others. Each exploration has something special.

Now let’s imagine that they decide to think about the problem together. What happens?

Everything works!

But I think it could go even further than this! One student could be inspired by the work of another!!!

OK. Imagine, for example, that all of the first ideas inspire the other students to come up with another idea! What would be the impact on the total number of mathematical explorations?

I think that the best way to answer this question is to make a **possibility tree** with all of the students’ ideas!

We can see that there are **3 **ideas at the start, and these ideas inspire **6 **new proposals… for a total of **3 + 6 = 9** solutions to the problem!

Interesting fact: **3 x 3 **is also equal to **9**! There were **3 **students and we have a total of **9 **ideas!

Does this mean that with **4 **students, we would get **4 x 4 = 16** ideas?

** n **students, we’d end up with

So for a class of **30 **students, we would get… wow, **900 **ideas!

It might seem scary for so many ideas to emerge, but trust collective intelligence. After the divergence phase, there is always a convergence phase, where the teacher has a key role to play!

In summary, being open to outside ideas allows us to look at situations in new ways. And like Jo Boaler, author of *Mathematical Mindset*, said, exposure to a variety of points of view enriches the quality of learning considerably. #growthmindset!

This year, we hope we’ll have the opportunity to share more of our ideas and learn from others.

So don’t forget to share this article and review these concepts in class with Netmath!

**Disruption always works at a high velocity. Its impact may take some time, but the generation of new ideas, iteration, and dissemination into society are always moving fast. Just look at what Artificial Intelligence has done in the last few years.**

In 2016, the Chinese game of GO had one of the top players in the world quickly succumb to Google’s *AlphaGo *machine. What was astounding was not the actual defeat, but the strategies employed by the AI machine that ran counter to thousands of years of traditional strategies. *AlphaGo* basically made moves that were unconventional, random, and erratic.

Last year, the AI machine *Libratus* defeated some of the world’s top poker players in the world. Poker with its complex strategies, fragmented information, and use of psychology, was always thought to be almost immune from any technological challenges to this human game.

While these kind of developments are on the cutting edge of technology, every kind of technology–even digital math platforms–feed off of this massive disruption to conventional thinking.

In math education, this innovative speed becomes a complex game of business survival and meeting the high level pedagogical needs of math educators. Ironically, but not surprisingly, changes in math education occur much slower. This is for many reasons, which include, but are not limited to: tradition, historical need for formal education, size, and energy diffused in math debates on teaching practice/philosophy.

Technology also knows its place in the hierarchy of things. Well, *good *technology does.

So, not only does taking technology out of a supportive/reactive role to good pedagogy create a problem, but over-emphasizing its value negates the idea of equity in math education. It’s a tricky balance. However, the companies that understand the picture above will be the ones that thrive. The ones that don’t will be footnotes in the clogged highways of digital platforms.

The larger pedagogical ideas of mathematics, moving forward, are circling around play, sandbox learning, and deep understanding. Digital companies that are acutely aware of this are producing–*will need to produce*–resources that support the seamless confluence of these ideas.

A while back I created a series of short videos looking at the interactive nature of our platform. Here is a link to the popular *Modeling Multiplying Fractions* activity.

This constant pressure to evolve will not only help digital platforms become better in terms of meeting the educational students and teachers, but it will also exert influence on how mathematics has to change and adapt to the learning styles that are native to mathematics–ample space and time–*and* honor the interest/motivation of classroom students and teachers.

But, at the end of the day, teaching mathematics is about connecting with kids in ways that are genuine, human and memorable.

Technology can be a vessel or a barrier for that.