# ‘Low barrier, high ceiling’ and the Maths Arcade

I’ve been catching up with the TES Maths Podcast. I just listened to episode 7, towards the end of which guest Brian Arnold shares ‘the Frogs puzzle’. You probably know this, but if not Brian points to the NRICH interactive version which explains:

Imagine two red frogs and two blue frogs sitting on lily pads, with a spare lily pad in between them. Frogs can slide onto adjacent lily pads or jump over a frog; frogs can’t jump over more than one frog. Can we swap the red frogs with the blue frogs?

You know the one? You can play it with coins or counters or people. Anyway, host Craig Barton refers to this as “low barrier, high ceiling”, in that

anyone can do a few moves. So there’s your low barrier, but you can take that, the maths that that goes into! You can extend it to different numbers on either side, everything’s in there.

Much as I dislike the term because it sounds jargony, I realise it describes something I’ve been explaining all week.

This week has been induction week at work, so we’ve had 120-or-so new undergraduates taking part in a programme of activities. On the list has been three two-hour sessions of the Maths Arcade. This means I’ve spent six hours of my working week playing games with students (yes, it’s a hard life).

Most took well to the idea, and some were outright enthusiastic. Many of them wanted to know, though, what was going on. One even said “I’m struggling to see the maths here”. To the latter, I asked “what do you think maths is?” “Numbers”. So I explained how maths is logic and problem-solving, and the games had been specifically chosen (by Noel-Ann Bradshaw, whose suggested games list we used) to be simple to learn but capable of developing strategic and mathematical thinking. I explained that some students will attend the Maths Arcade simply because it is fun and a nice way to socialise, while others will start to think about the best strategy for a particular game. Some might even ask “does the first or second player have an advantage?” At the other end of the spectrum, some might even choose to do a final year project in game theory. ‘Low barrier, high ceiling’, it turns out.