During my research into one of my relatives who was a teacher in the 19th century, I came across some math problems published in a newsletter for teachers. These questions were used during examinations of assistant teachers at elementary schools in 1878. People taking the assistant teachers’ exam were usually around 18 years old, had finished their own elementary school with good results and had worked for several years as a trainee, assisting already qualified teachers.
- Barge versus man
A walker, who walks 5 kilometers per hour, leaves half an hour before the departure of the draw barge from A to B. The barge progresses at 9 kilometers per hour and stops twice for five minutes, while the walker rests for fifteen minutes. If the barge arrives in B 15 minutes before the walker, how long is the road?
- Filling a tub
A tub is filled by three taps. If they are all opened together for half an hour, the strongest tap can fill the tub up in 3.75 hours. If they would be open together for a full hour, the same tap could fill the remainder in 2.5 hours. If the ratio of the strength of the second and third tap is 4:5, in how many hours can each tap fill the tub?
- Selling potatoes
Of a batch of potatoes, 10 percent is rotten and the rest lost 5% to dryness. They are sold for 5.50 guilders and the final profits is 6 7/8 percent. At what price were they purchased?
- Playing with marbles
Herman and Karel have some marbles. Herman has 16 less than Karel. If he gives 24 to Karel, Karel will have five times more than Herman. How many marbles does each boy have?
Can you solve these?
Personally, I think this is pretty advanced math for an elementary school teacher. I like how applied the problems are, so that you first have to translate them to abstract algebra before you can solve them (or maybe that’s just the result of my 20th century education). I’m sure they would have used similar types of problems in class, though probably less complicated. I like how these problems give us a nice glimpse into the level of math expected of these teachers and give us a taste of life in the 19th century to boot.
What do you think? Can you solve these? Kudos to anyone who posts the answers (including proof arguments, of course) in the comments 🙂
“Akte-examens,” De Wekker, 12 June 1878, p. 2, col. 4 – p. 3, col. 1; consulted as digital images, Koninklijke Bibliotheek, Delpher (http://www.delpher.nl : accessed 28 January 2016).