A month or so ago, I wrote a post asking if we needed a new mathematics association. The dearth of replies suggests that you guys are happy with what we have. Whatever. To quote Johnny Rotten, This is what you want … this is what you get:
One of the things you get is MERGA. In particular, you get the 2025 MERGA Conference, which has just begun. And which brings us to our latest competition. In 2022 we ran a MERGA competition, and this is the 2025 version.*
The new competition is to name, and to briefly argue for, the 2025 MERGA paper-talk that provides the genuinely greatest benefit/insight/whatever into mathematics education. So, the challenge is, what of genuine and significant worth can people find. The conference homepage is here, the list of scheduled talks is here, and the draft proceedings is here.
The best and best-argued answer will win the competition, and the winner will receive their choice of a signed copy of either A Dingo Ate my Math Book or Putting Two and Two Together.
Good luck.
*) I just realised that I never wound up the 2022 MERGA comp, and there is also the AAMT comp and ATSI comp to wind up. (For finalised competitions, which do occur, see here.) I’ll wind up all the previous comps together with this comp.
When I did my master of teaching, I was rather discouraged. We humans have been teaching maths for at least 5000 years, but they couldn’t tell me how to do it well? But now, finally the solution: Session 10.1 RT-How do people learn mathematics? (Peter Grootenboer)
I am a bit sceptical. Why do I think I will find this session a disappointment?
This one, also caught my eye: Session 5.5 RP-Top Number or Numerator? Teachers’ Choices of the Mathematics Register in Mathematics Teaching Talk
I talked with one of my daughters who had been taught ‘d – denominator is on d – d bottom’, but not that the base word in denominator is ‘nom’ meaning to name and that the denominator names the fraction in a way to tell it apart from fractions of different sizes.
Benefits of Cognitive Offloading Tools in Mathematics Education – this is a critical topic, rather surprisingly the abstract seems to have missed rote memorisation and pen and paper as key cognitive offloading tools. Extremely surprising!
Um, have you guys read the goal of the competition?
Yes – but it’s not exactly easy! Why couldn’t you just have asked us to prove Fermat’s Last Theorem!
This is probably one of the most difficult tasks I have undertaken in a long while. The very high probability of a prize was what drove me – my best sporting award was third in the shot-put at an athletics meeting. I even got my name read out over the loudspeaker. Fortunately they did not read out the number of contestants in the event!
The papers go a long way to highlighting what is wrong with at least this part of academia – bearing no relationship whatsoever to good maths teaching! My methodology was to highlight 7 articles from the contents that at least looked like they might have something worthwhile in them. All 7 were pretty useless – the closest I could find to anything I might actually use was that mother-child analogy for a function.
Here’s a more detailed explanation – which came from AI following Googling as it explains it better than another research article I found. Note that the MERGA paper did NOT even explain it!
Input (Child): In a function, the input is the value you are putting into the function. This is analogous to a child in a family.
Function (Machine): The function is the process or rule that transforms the input. It’s like a machine that takes the input and performs a specific operation.
Output (Mother): The output is the result of the function’s operation on the input. It’s analogous to the mother who is related to the child.
Key aspects of the analogy:
Uniqueness: Just as a child has one biological mother (in most cases), a function ensures that for each input, there’s only one corresponding output.
Mapping: The function maps each input to a specific output. This mapping is the core idea of what a function does.
Examples: A simple example is a function that doubles a number: f(x) = 2x. If the input (child) is 3, the output (mother) is 6. Another example is a function that squares a number: f(x) = x^2. If the input is 4, the output is 16.
Variations: Just as there can be different types of relationships between mothers and children (e.g., adopted children, step-mothers), there are different types of functions in mathematics (linear, quadratic, etc.)
In essence, the mother-child analogy helps visualize the relationship between input, process, and output that defines a function.
Here is the quote that prompted my googling “The most popular analogy in the former group is the conventional ‘machine’ analogy, while it is a novel ‘child-mum biological relationship’ analogy in the latter group (for more details, see Hatisaru, 2022).”
So on the basis that more analogies are better to have in one’s repetoire, this is at least somewhat useful. Though I will continue to use the sausage machine analogy I was taught in the early 80s!
Thanks, JJ. You are indeed winning.
What is the title and the author of the MERGA paper?
Analogies to the Concept of Function and Their Affordances
Vesife Hatisaru
[EDIT]
Ok I’ll look.
I also deleted the contact information. That was gratuitous, and silly.
Jesus. If that nonsense is the best MERGA has to offer then we are doomed. Nonetheless, you are currently winning.
“affordances”. FFS.
I wouldn’t say best, I would say least worst
“Least worst” still doesn’t capture it.