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What is WJETT?

The WJETT blog or 糖心TV Journal of Education - Transforming Teaching blog is designed to encourage staff and students to disseminate good practice and to engage with their peers on academic cultural critique or areas of research that they find interesting. With the increased focus on 鈥榯eachers as researchers鈥 in the sector, many qualified teachers are expected to publish the outcomes of any action research projects they undertake. The WJETT blog can be the first step on your journey towards publishing and enables you to experience publishing and reviewing in a friendly and supportive environment.

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Can鈥檛 do maths? Try Fermi problems instead!

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 鈥渟witched off鈥 to maths.

鈥淚 can鈥檛 do maths.鈥

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

鈥淚 don鈥檛 care about piano tuners in Chicago.鈥

鈥淔ermi problems can be about anything,鈥 I said. 鈥淭he teacher should choose a problem which is meaningful to their students.鈥

鈥淗辞飞?鈥

鈥淵ou鈥檙e interested in cycling, so 鈥 how long would the averagely fit person take to cycle from Land鈥檚 End to John o鈥 Groats?鈥

鈥淚 don鈥檛 know. Two weeks? Three weeks?鈥 Jean was engaging with the problem, but she was guessing. She needed some scaffolding.

鈥淒on鈥檛 guess: use your knowledge. How many hours a day will they spend in the saddle?鈥

鈥淓颈驳丑迟.鈥 This sounded too high but I didn鈥檛 want to discourage her, so I said nothing.

鈥淲hat will their average speed be?鈥

鈥40 mph.鈥

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

鈥淗ow many miles will they cover each day, riding at 15 mph for 8 hours?鈥

鈥120鈥 was Jean鈥檚 instant response: she was 鈥渄oing maths鈥 without even realising it!

鈥淲hat鈥檚 the distance from Land鈥檚 End to John o鈥 Groats?鈥

鈥淚 don鈥檛 know. About 1,000 miles?鈥

The actual answer is 874. I would have accepted 1,000 as an estimate, but she had guessed. You mustn鈥檛 guess when solving Fermi problems.

鈥淒on鈥檛 guess. How can you estimate it?鈥

鈥淚 don鈥檛 know.鈥 Jean was slipping into 鈥渕aths lethargy鈥, but I was not going to let her give up.

鈥淪uppose I tell you there鈥檚 a sign outside King鈥檚 Cross saying Edinburgh 401 miles? So London to Edinburgh is about 400 miles.鈥

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

鈥淭hink about the map of Britain. Is Land鈥檚 End to John o鈥 Groats two and a half times London to Edinburgh?鈥

A pause, then: 鈥淵es, it鈥檚 about that.鈥

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

鈥淓颈驳丑迟.鈥

鈥淲hat鈥檚 8 times 120?鈥

鈥960. Oh! So nine.鈥

鈥淚s that your answer? Nine days?鈥

鈥淵es,鈥 said Jean. Then, 鈥淣o! Some days they might not do 120 because of punctures, or hills. So, ten.鈥

鈥淚s that your final answer?鈥

鈥渊别蝉.鈥

鈥淎re all your numbers defensible?鈥

鈥渊别蝉.鈥

鈥淥K. Let鈥檚 check it.鈥

I consulted Wikipedia. Land鈥檚 End to John o鈥 Groats cyclists normally take 10 - 14 days. Jean鈥檚 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 鈥渄one maths鈥; and I intend to incorporate Fermi problems into my teaching practice.

Thu 01 May 2025, 15:24 | Tags: PGCE, Reflections, Fermi_problems, Teaching

Writing guidance

Can I write about anything in my blog post?

Yes pretty much. Academic cultural critique (Thomson and Mewburn, 2013) is always a good source of content for academic blogs. This can include (but is not limited to) comments and reflections on funding; higher education policy or academic life. You might also want to consider blogging about:

  • Academic practice (Saper, 2006)
  • Information and/or self-help advice
  • Technical, teaching and careers advice
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No, this is a reflective piece so it does not need to include citations (but you obviously can include them if they are relevant).

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We would encourage you to include links to any articles that you have considered whilst writing your blog post. We also welcome the use of images (as long as you have permission to use them) as they can often help to illustrate a point and obviously will not be included in the word limit. Please remember this is a public site so if you want to include images of your students in your classes then you will need permission to do this.

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Your blog post should be emailed to A.Ball.1@warwick.ac.uk. Once the submission has been reviewed it will either be uploaded at the beginning of the next available week or sent back to you for editing if it requires amendments. You should then send the amended work to me once again and I will then upload it.

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