I’m a big fan of manipulatives. Make no mistake, symbols and formal language are part of math, and we have to get students there. But I see students for whom mathematical words and notation are a foreign language. They get dragged through a conveyor-belt curriculum, expected to understand a language for which they don’t have enough meaning.

There are rightly concerns about tech in the classroom, but when it comes to manipulatives, screens offer real advantages.

Yes, getting students onto devices can present logistical challenges. But a class set of manipulatives is also a lot of plastic to buy, distribute, and return to a store cupboard.

Concrete–pictorial–abstract is often seen as a natural progression. But both concrete and pictorial have limitations: physical objects can’t easily change, and pictures can’t be manipulated. Screens offer the perfect middle ground of pictures that tiny hands can manipulate into new pictures. Four 2s can change into an 8.

With physical manipulatives, tasks often need explaining using the very symbols and language students are struggling with. On a screen, we have clever ways to present tasks without words or symbols, lowering the cognitive barrier to entry.

But here’s the most exciting reason. With each manipulative task, it takes time to get a class to the starting arrangement for their manipulatives, and then more time to explain the destination arrangement they’re expected to reach - a minute or two or more. On a screen, it’s instant. In NumberClub, we know that, on average, students make a move every 9 seconds. That’s potentially an order of magnitude more mathematical thought in every lesson, and that is a very significant win.