## June 17, 2019

### Can’t do maths? Try Fermi problems instead! – Jeremy

I talk to Jean - an intelligent, articulate Glaswegian who left school with no qualifications - over the internet. I told her about my essay on re-engaging students who are “switched off” to maths.

“I can’t do maths.”

“Perhaps you could if you were taught using Fermi problems.” Being keen to try this approach, advocated by some of the literature, I told her how Enrico Fermi solved problems such as “how many piano tuners are there in Chicago?” without any data, using his knowledge to supply defensible estimates.

“I don’t care about piano tuners in Chicago.”

“Fermi problems can be about anything,” I said. “The teacher should choose a problem which is meaningful to their students.”

“How?”

“You’re interested in cycling, so … how long would the averagely fit person take to cycle from Land’s End to John o’ Groats?”

“I don’t know. Two weeks? Three weeks?” Jean was engaging with the problem, but she was guessing. She needed some scaffolding.

“Don’t guess: use your knowledge. How many hours a day will they spend in the saddle?”

“Eight.” This sounded too high but I didn’t want to discourage her, so I said nothing.

“What will their average speed be?”

“40 mph.”

No way! That’s the speed of a world champion, not the averagely fit person. I challenged it, and after discussion Jean settled for 15mph.

“How many miles will they cover each day, riding at 15 mph for 8 hours?”

“120” was Jean’s instant response: she was “doing maths” without even realising it!

“What’s the distance from Land’s End to John o’ Groats?”

“I don’t know. About 1,000 miles?”

The actual answer is 874. I would have accepted 1,000 as an estimate, but she had guessed. You mustn’t guess when solving Fermi problems.

“Don’t guess. How can you estimate it?”

“I don’t know.” Jean was slipping into “maths lethargy”, but I was not going to let her give up.

“Suppose I tell you there’s a sign outside King’s Cross saying Edinburgh 401 miles? So London to Edinburgh is about 400 miles.”

“1,000 miles is two and a half times that.” Jean was re-engaging, and we were back in the hunt!

“Think about the map of Britain. Is Land’s End to John o’ Groats two and a half times London to Edinburgh?”

A pause, then: “Yes, it’s about that.”

“Good. So you can defend your figure. How many days will it take to cycle 1,000 miles at 120 miles a day?”

“Eight.”

“What’s 8 times 120?”

“960. Oh! So nine.”

“Yes,” said Jean. Then, “No! Some days they might not do 120 because of punctures, or hills. So, ten.”

“Yes.”

“Yes.”

“OK. Let’s check it.”

I consulted Wikipedia. Land’s End to John o’ Groats cyclists normally take 10 - 14 days. Jean’s sense of accomplishment when I shared the link was palpable: she had just solved a Fermi problem and absolutely nailed it! In doing so she had multiplied 8 by 15 and 120 by 8; divided 1,000 by 400; estimated comparative distances; and identified and applied an appropriate rule of rounding. She had “done maths”; and I intend to incorporate Fermi problems into my teaching practice.

You are not allowed to comment on this entry as it has restricted commenting permissions.

## June 2019

Mo Tu We Th Fr Sa Su
May |  Today  | Jul
1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

## Galleries

• Very interesting, thank you for sharing. Great CPD reflection. by Joel Milburn on this entry
• Hi Lucy, Thank you for sharing the highs and lows of diverse assessments. I hope you have inspired o… by Anna Tranter on this entry
• Hello Lucy, I totally agree with everything you have said here. And well done for having the energy … by Natalie Sharpling on this entry
• Thank you for setting up this Learning Circle. Clearly, this is an area where we can make real progr… by Gwen Van der Velden on this entry
• It's wonderful to read of your success Alex and the fact that you've been able to eradicate some pre… by Catherine Glavina on this entry