The Evolution of Vocabulary in Maths Education

# MathsConf19 ‘The development of vocabulary in mathematics education’ is a blog preview of Jo Morgan’s #MathsConf19 session/workshop being held at #MathsConf19. Languages change all the time. Words become obsolete, words are replaced, words are no longer fashionable. Through my research into math textbooks from the last 500 years, I have discovered all sorts of interesting and surprising vocabulary. Come to develop your subject knowledge and (hopefully) be entertained and amused. What’s up with vulgar fractions? My Longman math textbook from the 1960s told me about the ‘fraction tree’. Its members are the brothers Vulgar Fraction, Decimal Fraction and Percentage, and of course the illegitimate son Ratio, whom we don’t want to talk about. Profanity fractions are just two whole numbers (the numerator and the denominator) placed above and below a fraction bar. They are also called ‘common fractions’. I knew the vulgar terms and common fractions from my childhood, but I never said them in my own classroom. A textbook by Bostock and Chandler from the 1980s tells us that “Usually we refer to common fractions as simply fractions and decimal fractions as simply decimals”. This alludes to the fact that in the latter part of the 20th Century the terms ‘vulgar fraction’ and ‘decimal fraction’ fell out of common usage in schools, leaving us with ‘decimal fraction’. number’ and ‘decimal’. With this lexical change, I don’t think we’ve lost any precision – the terms fraction and decimal are both fit for purpose. So even though some of the math vocabulary lost saddens me, I don’t mourn the loss of the vulgar word. The vulgar term fraction was used for centuries before it disappeared – it can be found in mathematical texts from the 1500s onwards. Here, we can see it appearing in a fascinatingly titled textbook from 1741: Textbooks from the 1700s and 1800s not only show the commonly used vulgar term fractions, but also provide some interesting definitions and explanations. For example, in “A Treatise on Arithmetic, Theory and Practice” (Loomis E, 1856), we explain it like this: Read more: difference between windows xp and windows 7 That last part that I particularly like: “This mode of representing decimal fractions is used to avoid the inconvenience of writing the denominators”. I never thought of it like that. Just as the percent sign is used as a shortcut to avoid writing the denominator as 100, the decimal notation is just a shortcut. All this vulgar gossip makes me wonder about the word vulgar. It’s a rather odd word to use in math. A dictionary gives us the following definitions: 1. lack of sophistication or deliciousness. 2. explicit and derogatory mentions of sex or bodily functions; rude and rude. 3. [DATED] characteristic of or belonging to ordinary people. Now I’m pretty sure that fractions don’t go around relating to gender and bodily functions. Definitely not in my class. Obviously the third definition is the one that is relevant here – the usual or common idea. It turns out that the word vulgar comes from the Latin word vulgus meaning ‘ordinary people’, and it was first used in English in the fourteenth century. It then refers to something that is commonly or commonly used or something that is customary or done as a matter of fact on a daily basis. The meaning of the word profanity changes over time. It began as “relating to common people” but meant “ordinary”, and by the seventeenth century it had become “lack of finesse or good taste”. One of the only places where the word goes on to mean ‘normal’ is in math. I think it’s a bit sad when a word meaning “of ordinary people” is combined with crude, rude, and obnoxious. But I’m not sad when I don’t have to say the word ‘vulgar’ to a room full of teenage kids! That’s a troublesome request. In other news, did you know that it is completely useless these days to call a fraction incorrectly? Obviously it’s a bit insulting for larger fractions to assume that they don’t fit… Who knows? Come to my workshop at #mathsconf19 to hear more about how vocabulary has changed over the years – lost math vocabulary can be profound, sometimes interesting, and always engaging. You can watch Jo Morgan talk about “Vocabulary Development in Math Education” in #MathsConf19 at Penistone Grammar School on Saturday, June 22 Make your reservation Don’t forget in July we also have specials ‘FREE’ Math Teachers Network event in association with Oxford University Press and AQA. We look forward to seeing you at our next La Salle Education Event if you haven’t already, follow us on Twitter @LaSalleEd Read more: What’s hotter: Mild or Medium? (Full Breakdown) | Top Q&A