We are, as a rule, skeptical of the promises of the EdTech world. When so many students (young students especially) need hands-on materials, why put them on screens? And why do so many of the supposed breakthrough technologies seem like worse versions of what already exists in an analog format?

Of course, the pandemic has created a new impetus for online materials, since so many of us can’t meet in person. When all meetings are on Zoom, online manipulatives are better than none at all. That’s one reason we put our new Multiplication by Heart cards online, with a little help from Mathigon.org.

In times other than the extraordinary present, there tend to be two compelling reasons to move online. The first is that online materials, even if they are similar to what might be in a workbook or block set, are less expensive, more easily disseminated, and can sometimes be automatically assessed by teachers, without having to spend hours and hours on grading. That’s all pretty nice.

The second is that sometimes you can do things online that you can’t offline. You might have a better experience playing with blocks online, but what if you want to design new types of blocks? What if you want to automatically know the angles and side lengths? The best virtual manipulatives can actually do things that would be ungainly, impractical, or impossible to do offline.

I’m here to tell you about two of these. Both, as it happens, depend on the color structure we developed for our board game Prime Climb. And both let you go beyond—way beyond—the numbers on that board.

Prime Line

I collaborated with KnowledgeHook to create the #PrimeLine. This synthesis of the Prime Climb factor circles with KnowledgeHook’s dynamic number line is… well, it’s just really cool. You can go WAY beyond double-digits (check it out yourself!), and the patterns and questions that emerge are fascinating.

If you’re not familiar with the color-coding, orange = 2, green = 3, blue = 5, purple = 7, and all other primes are red. The dots provide a nice dot pattern to make the coding legible for those with color-blindness too.

Polypad’s Prime Factor Number Circles

After collaborating with Mathigon to produce Multiplication by Heart online, there’s a question of what else can be done with the graphic structure once you have it. So I was thrilled to see that the team there had produced a dynamic new way to drag and drop factors. You can build numbers with multiplication and division, and see how the prime factorizations impact what the numbers are and how they relate. This came out last week, and teachers are already playing with it to see what else you can do (GCDs! LCMs!).

You can, of course, use the virtual tools as sandboxes, and just play. That’s not a bad time to start anytime you’re got a new tool. The real question is, can we keep our skepticism (more screen time? Don’t kids’ brains just turn off?) and also some clear-eyed hopefulness about how we can create experiences that might use these tools and others like them to produce authentic learning.

The best of these experiences, in my opinion, should actually encourage students to turn away from the screen at some point. For example, I noticed that if I put pins down arbitrarily at some high enough stretch of the number line, there always seems to be a red sector (i.e., a prime factor greater than 10) in that number. Can you find one that doesn’t have that red section? How many can you find between, say, 9000 and 10,000?

You could click a bunch, but it probably wouldn’t help much. At some point you need to stop clicking and start thinking. When you think you’ve answered the question, you can turn back to the tool and see if you were right.

No matter the tool, it’s going to take teachers, educators, and thoughtful, persistent work for any of the EdTech tools to live up to their promise, and not fall prey to the dangers inherent in their use.

But I’m more hopeful now than I’ve been in the past. Skeptical still, but hopeful!

LINKS

• Prime Climb
• Multiplication by Heart online
• Prime Line
• Polypad