Thank you – much appreciated.

Interesting thought, Pat. With Desmos, it’d be possible to create an activity where the teacher sets the secret number and then every student who has the code to the activity makes their own guesses. I’ll have to give that a try.

Yep, it’s right here.

If you could share the application would be much appreciated
Thank you.

Dick Fuller, the Sapir Whorf hypothesis is what I think you are wanting. I don’t believe that it is true, incidentally — we sure can think about things for which we have no word.

But I’ll put good money that you are extremely careful about your terminology when you teach. I would hope, for example, that you don’t talk about a parabola as a “line”, although students often do, and that you don’t mix the words “expression” and “equation”, although students often do.

Teachers are careful because using the correct words aids understanding, because it limits confusion. Sure you can think about things without the “correct” words, but it’s not a good idea. If a student uses “equation” for an expression, then they are going to struggle when the teacher says “you need an equation before you can solve”.

In my teaching I have two different sets of words, and I make it explicit which group words fall into. The key ones that I expect students to know and use — equation, line, curve, tangent, etc — and the ones that they should recognise when I or the book use them — vertex, coefficient, equivalent etc.

⚠️ Warning: Dangerously high levels of self-regard in this area. ⚠️

But no-one suggested that the way to do it is word lists, especially not at the start of a topic. I don’t teach terms before or after I introduce the concepts. I teach it before, after and during, so they get exposure over time.

This whole modern “we need to teach them to behave like Mathematicians” comes with a cost — Mathematicians are some of the most precise people about terminology in the world! If we allow them to be woolly about key terminology, then we allow them to be woolly about Maths.

Nice!

She didn’t end up actually guessing my number, but there was a lot of great conversation that came out of her guessing process. One of the questions she asked after her first was “Is it a natural number?” Several of her classmates immediately spoke up and expressed their disappointment that she had wasted a question. In the end, most of the students in my class came to understand the distinction between different types of numbers and why that might be important. Thanks for the great idea!

“How are students meant to think about something if they haven’t got a word for the concept?”

What is the word for the concept “to think about a concept requires a word for it”. I don’t know the word but I can think about the concept, and I hope we can talk about it. I confess I can’t see how mathematics, including the learning of it, can happen if the word for a concept must precede the concept. Do children need the name for a counting concept before they count. I don’t know a name for a concept for natural numbers, my “concept” is they are constructed: every one of them has a successor, 0 is the only one them that is not a successor, it starts the whole construction off from nothing. There is lot to think about here, like why not just write them down and put them in a book and be done with it? At least they have to have names don’t they, so write them down. My thoughts, I don’t have a word for them.

Seems to me there is a big education question here. Words before thought require authority. Is that the basis of school education now?