Using the school building as loci for math formulas

I want to work with a Maths teacher in my school (I’m and English/EFL teacher) to use a memory palace for math formulas. I get that really understanding things is somewhat useful for math formulas. And visual maths too. But I do think that using locations in teaching could be helpful. Because there’s a LOT. This is the HK Maths system and it’s very regulated and more intensive than, say, Australian math curriculum.
I’ve tutored a kid who wasn’t great with maths (not in maths, but I was interested in what she was facing in other subjects). She could remember one concept at a time and didn’t know when to switch to a different concept/formula.
How about a locus visual that pulls you into the concept and some context about where you would apply it? And then maybe a trick to remember the formula?
I’m talking junior high school level.
My plan is to get a math teacher to try to teach a unit to me and then see what I can do with it. (My last maths lesson was 1990).

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As a math teacher, I’d wonder why you would put in that much futile effort. Which might sound like a pessimistic stance, but there is a reason.

Math is often seen as a science, with concepts and formulas to memorize and know. However, in reality it is a language.

Memory palaces are often seen as a magical pill to suddenly learn things you would have otherwise forgotten, while in reality, it is spending time to create a visualized book of the subject at hand.

Lets say you do this, you spend multiple hours turning math into a mental grammar book and dictionary. You then have to hope that your student takes the time to recall all the images, and you still have to practice. That is a lot of time, effort and assumption over a subject the student will probably drop as soon as it is possible, unless they want to follow courses where math is definitly needed. Afterwards they need to maintain the knowledge and the practice, which requires self-discipline.

If you think the practice is no big deal, try having a conversation using a dictionary.

The time I mentioned is another thing. Why use the time for mental notes if you can make physical notes in a shorter time?

You could argue that you can take the mental note with you to the exams, and that is true, but it only holds value if you assume that mental notes don’t form if you make physical notes.

One thing I can tell you is that visualizing does work wonders, and barely takes extra time. For example, a question like 5,37 - 8,89 is tough for my students. I can use memory palaces and all for the knowledge of how to do this, or I could say that this is money. You have 5,37 and you have to pay 8,89. How much are you in debt? Answers appear within seconds. Some might be wrong answers, but then you can teach. You can’t teach if there is no answer.

You had another post where you advocated for the use of memory techniques in school. While the basics of that are fine and will probably work -think acronyms, structurizing information, metaphors- the more advanced stuff that you have to train like memory palaces do not have a required place in education if you’d ask me.

The problem with education is not the lack of memory techniques, it is the lack of an outside world. Schools became castles that slowly shot down more and more outside concepts to remain the same since the 1800s. Theoretical. Isolated. If we want to improve it, we have to bring the outside world back.

NOTE: specific points might differ with your situation. What I am mainly trying to show is that when using memory palaces with someone who might not even want to learn memory palaces, you will have a s***load of explaining to do if they fail. And literature is not on your side there.

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That’s a really fantastic answer with a lot to think about. I absolutely agree about the outside world. I’m not racing headlong into this as a cure-all for the deadening deadness of curriculum. I’m very present to that, and at this specific point in my life I’m choosing to work within that system. That’s not my natural inclination. I’m an outsider.

Hong Kong kids do tend to like maths and they do a lot of it and like it or not, it has a big impact on their future as it is a ‘core subject’. There is no easier math stream, everyone does the same exam in Form 6. They like it more than they like English.

Of course what I’m thinking of has a few problems. I speak English and my students don’t. That’s one. I don’t know much about the rest of the curriculum which is all taught in Cantonese. That’s another. I don’t know much about many things, but I’m playing, and this project is having me connect with people in other departments and start finding out (after working here 12 years), so I’m really enjoying it. I’m at the question asking point, not after cheap closure.

Your example of subtraction vs shopping is great. I wonder if a memory palace can be a way to bring in and connect the outside world. Creating vivid images.

As for consequences, I won’t have any questions to answer. I’m not diverting any resources or making any rash promises. School is in such chaos here and the learning so disrupted after 2 years of protests and Covid. 1/4 of our students live over the (closed) border and have spent over a year pretending to learn online. It can’t really get much worse.

Advocating is not the right word. I’m not ‘advocating the use … in schools’. I’m looking at the question ‘why didn’t we learn these methods at school’ that many people have asked, and I know that there are very creative teachers in Australia who’ve taken @LynneKelly’s work and created history timelines and other memory spaces around school buildings. There’s an orality centre! It seems like something that could be possible. And I’m asking how, why, what?

My own kids are in this school system and rather more pro-learning than my students so they’re a good sounding board. I’m trying things out on myself and on them, and then openly sharing my progress with colleagues. And wondering where to go next. That’s what I’m doing. I’m honestly delighted with how pleasurable the whole thing is. I’ve never found memorisation and recall to be without stress.

How do you use memory techniques? Which ones do you use?

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Once, in high school, my Physics teacher asked me how I remembered formulas so easily, so that he teach the method to others.

I said that once you understand how the formula is derived, you will remember it. I think he was a bit disappointed.

I do feel that understanding the derivation, and also what the formula means, is in itself a form of memory technique. Remember how memory techniques work:

  • Associating things with what you already know: if you’re remembering the derivation, you’re doing this
  • Dividing and ordering: When you know many derivations, you tend to build up this “map” - you know that you can go from this equation to that equation. If you forget an equation you can just remember the steps, and know that it must be exactly of a certain form. Also you will learn to go from one formulae to the next.
  • Visualisation: Most concepts can be visualised. Even if you don’t have the formula, you can make one yourself, if you understand the process.
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I get what your saying, and my son who is good at school does something like that. He enjoys dwelling the ideas and playing with numbers and formulas outside set homework tasks.

The thing about teaching, though, (as opposed to designing things for yourself or already-winning learners) is that you have to get into the headspace of someone who isn’t you. I don’t need any overt rules for the weirderies of English grammar. And for most languages, if I’m immersed enough my brain will use its ‘statistical learning’ strengths to do pattern recognition and create an ‘instinct’ for right and wrong. And I can do accents just by copying. But in the school where I teach, kids after several years of English exposure in 7 lessons a week (not my lessons) will still try to read new words using PinYin rules. ie mode will be read as /mor der/. Unlike the types of learners who become language teachers, they don’t have or don’t activate pattern recognition.
For myself, when I am a math/physics student I can get to a point during the lesson where I understand everything. And then when I walk out of the lesson, I lose it. I don’t have a framework to sit it in. I love science, but I’ve never felt any confidence there.

I really get the point that there’s no tricks and shortcuts to actually understanding what you are learning. And that practising is vital. You have to give the neurons time to grow.
But I do think I can find ways to scaffold that process. Attention and engagement also have a big impact on learning and the thing I find interesting with the locations is that it’s enjoyable to revise.

Anyway I’ll work on a history timeline too, and no one will argue with that!

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I love how I see the typos the second I hit ‘send’. *you’re

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Thank you to all these discussions. I am finding it fascinating - there are too many threads for me to mentally deal with them all!

I am intrigued. I am studying Chinese / Mandarin for one of my experiments. Do you use pinyin for Cantonese? I guess it doesn’t matter if you are using traditional or simplified characters.

Very interesting ideas on physics, too. Thank you @Niten. I would always advocate understanding over memory. When I taught physics I found that most formulae could be remembered through the logic and definitions. One day, I will revisit teaching physics now that I know about memory systems. But I have hit overload at the moment, so that must go on the back burner.

Lynne

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Here is a maths project. My daughter got a lot wrong in her end of year math test. Not too surprising, she’s had most of her lessons online, in Cantonese (with English as the home language). I created with her a special project to make a google slide presentation about each question in the exam. Go thoroughly into what went wrong and what’s missing to have power with this type of question.
She’s starting it herself, then discussing it with her brother (who’s 5 years older and also studied maths in Cantonese sans Covid). Then presenting it to the family as a lecture. It’s fun, you’ll have to trust me. We’re weird people.

You will notice that the math terms are ‘wrong’. That’s because she uses Chinese terms and this is a direct translation. Getting the Chinese right is more important that using the correct English term at this point.
And the mnemonics won’t make sense for the same reason. For example numerator and denominator are ‘child-number’ and ‘mum number’ in characters, and she needs to remember both how to read the character and how to pronounce it. So the images of families she knows are representing the chinese characters as well as the fractions.
The three of us create the images (with Olly having final say) as the kids explain everything to me. I have minimal Chinese and I forget my primary school maths, so they really have to teach me.

She chose to put them in the garden as we haven’t set that up as loci yet.

Once we have got the exam’s worth of mnemonics into the garden, we can create a narrative that brings them all together. But it’s early days. This is a Summer holiday project. The P4 Mathematical Garden party.

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This is a very basic mistake, but like ‘left/right’ confusion, one that really needs to be handled. Remembering the characters for ‘odd’ and ‘even’.

We used bad puns (which annoyed her, but her brother promised it would work), and visual cues from the characters. ‘odd’ looks like a pogo stick and kinda sounds like ‘egg’. And we’re also imagining it boings saying ‘daaan daaan’.

‘Even’ kinda contains 2x the counting word for animals ‘jek’ so she thought of the annoying monkeys in ‘along came the doctor and the doctor said, NO MORE MONKEYS JUMPING ON THE COUCH in SEUNG wan’. The full version has the doctor. Sheung wan is her dad’s office so it’s a specific couch.

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I do use pinyin (jyutping or Yale) for Cantonese, but my children don’t - as I self study in a shallow occasional way, and they are immersed and their schools don’t use it. The HK kids do use pinyin to study Mandarin though, as it is mainly a difference of pronunciation and the Cantonese schools need to distinguish it from Canto. In fact I think a lot of ‘learning Mandarin’ is really just drilling how to pronounce pinyin and very uninspiring.

But the pinyin comment I made was actually that my mainland students (who DO learn their first Chinese with Pinyin unlike HKers) then try to apply the pronunciation rules to reading English and it doesn’t work at all.

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Thank you so much for your answers and examples. Fantastic!

Am I right in understanding that there is a system for Cantonese which is also based on romanisation with initials and finals, but it is called jyutping. It is the equivalent of pinyin for Mandarin. But pinyin is used for Mandarin, not for Cantonese?

The memory system I am developing for Mandarin depends very much on the romanisation of syllables, and - critically - that there are a specific set of syllables, with a defined set of initials and finals. I just wanted to clarify about Cantonese, so there is no need for you to read further! But I’ll put it here anyway.

My method is simpler for kids (and adults!), I feel, than the Alex Mullen / Marilyn method (Learning Chinese with Memory Techniques: Part 1 — Mullen Memory).

In my system, you don’t need a complex memory palace upfront, and it handles two and three syllable words with ease, as well as tones just through using images which are set by the system. Individuals don’t need to bring their own set of people and locations to the table.

I then introduce the memory palace with the radicals of characters, and start linking the words to memory palace locations once you have already got the hang of pinyin and the way Chinese vocabulary works.

The character can be memorised with the story / movie method where you make a story out of the components of the characters. Mush as Heisig does (Amazon.com: Remembering Simplified Hanzi 1: How Not to Forget the Meaning and Writing of Chinese Characters (9780824833237): Heisig, James W., Richardson, Timothy W.: Books) but made easier because you already know all the radicals before starting any other characters. I am still testing and testing, but I think it is close to writing up.

If my reading of the Wiki entry for jyutping is right, it works the same way, just more tones. So the same system would work, although it would have to be reworked given the initials are slightly different and the finals are significantly so.

This whole system is dominating my life at the moment, I am finding Chinese so fascinating.

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This is basically right. The difference is that Pinyin is an integral part of how Mandarin/Putonghua is taught. Because it’s a lingua franca and is actually most Chinese people’s second language. So everyone knows pinyin.
Cantonese is taught to local kids without any romanisation system. The romanisation systems were invented by university linguistics departments and each university made up their own and everyone thinks theirs is better and it’s messy. The only Cantonese people who know one of the systems are those who studied linguistics. And then you eventually have to learn all the systems in order to read all the papers or grammar books. >.<
Once you get over being annoyed about that it’s not that hard. Took me about 15 years to stop sulking about how Yale is more intuitive. About 3 days to learn Jyutping. Now I can read Jyutping just fine.
There is not very good NCS/ CAL (Chinese as additional language) support in primary schools and some people are advocating for jyutping enhanced resources.
In summary, yes Jyutping has initial and finals. Cantonese has consonant finals. There are 6 tones for all practical purposes, one is neutral kind of one, and I think Mandarin has 4+1 neutral. They aren’t quite the same tones though.
I’d love to see your system. I could try it out. I’ve never had a Chinese lesson. I just copied my kids’ homework.

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Originally, I want to introduce you Herman To, Herman Yu and
https://youtube.com/c/mathseasy.
They all did a great job in past ten years providing free math education videos.
Especially, Herman To explains maths in daily lives vividly.

After seeing your post about your daughter and son, I know they’re primary student and junior student. So :woozy_face::joy:, in my experience, that’s not much math equations to be learnt.

Back to the track, are you a primary school teacher? If I were your student, I would be grateful for your efforts, trying to bring math easier and memorable. I had an experience tutoring a primary six boy about half year. Though he does well in math, I improved his math a little. What I did most of the time is explain him the questions. Once he understood, what is doing there, he seldom did same mistake.
In addition, he learns math in cantonese.

@LynneKelly I am pretty curious how do you learn Chinese? In speaking, without a tutor, your pronunciation might sound orchid to Chinese people. eg I learn Spanish and Doulingo the bird always warn my pronunciation. In words, Traditional Chinese characters are more challenging than simplified. So my questions are how do you ensure your speaking is fluent and how do you learn the characters effectively?

@TanyaHart
for new comers in mnemonics, body palace is easy startup!

  • Say, when push your :raised_hands: hands in front, only Left hand :raised_hand: can make an L shape, right hand can’t.

  • Oh great! thumbs up representing Odd, you can imagine d as :+1:t2:. Even E as the fingers except the thumb.

  • 真分數 the number is real as the numerator is smaller than denominator. :point_up:.

  • 假分數 the number is false/improper as the numerator is bigger than denominator.:crossed_fingers:

  • 分數 mixed numbers, as it carries all the three parts of a number, eg
    . 2
    1—-
    . 3
    :fist:imagine the things turn into dust in your palm.

Memory technique does not necessarily tell you the logic of everything , it’s more like a hint which links the items you learnt in a sensible direction.
:wink:Keep up fun teachings!

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I’m a secondary school English teacher (NET) in a Chinese (CMI) Secondary school. My undergrad is Fine Arts. I have a Masters in Psychology (a ‘conversion masters’ which means very basic). I love languages science, history, art, all the things. Like most people who end up doing memory crafts, I suspect. I don’t see why anyone wouldn’t be interested in all the things.

Thanks for the mathseasy link. I’ll have a look with the kids. My son is only in S3 but he’s a big math lover and learns above his level for fun. He’ll do extended maths ‘M2’ and physics for his electives (and English literature and mainstream Chinese - because he also loves all the things).

And thanks for the body palace! I haven’t tried that. For Olive, though, she needs some extra links to draw her focus to the phonic and the written character. That’s evident as she managed to get to S3 without being able to read some basic stuff that she must have seen a lot. I’ve also coached a primary kid and found that when I draw his attention to something and explain it clearly, he really can do it. I wish there were more primary school teachers who tried that. Look for the gaps.

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Thank you for that explanation. Much appreciated. I am just starting to write up my system, but checking out other systems online and in books so that I can acknowledge alternative memory systems and where they overlap with mine. I am fascinated by the way Chinese works in such a different way from French, and how the memory systems must be implemented so differently. Such fun to be had!

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Hi Antelex,

Thank you for your interest. I am encouraged to keep working on writing it up. There is way too much to my system to be written here. I will be writing it up in full when I have finished a bit more research.

As for pronunciation, I have a native Chinese speaker to help. She also checks my characters for the way I write them, even though we don’t get to meet often. I am the adoptive grandmother for her daughter, given the biological grandparents are in China. I fill the role for her daughter here in Australia. My speaking is far from fluent. I have a very long way to go!

For the characters, I associate the character, as I learn it, with locations in my memory palace based on the radical of the character. For words of more than one syllable / character, I put the word at the location for the radical of the first character. Then I mentally build the rest of the character using a story. It will take me a bit to explain, because the story has already been started when I learnt the word. The mnemonic image for the word is based on a system I have developed for pinyin. That system involves an animal/person for the initial and an action for the final - and the animals and actions give the pronunciation and the tones. It’s a sort of PAO system using a bestiary. Oh dear - I need to write it out properly.

Sorry that is all a bit vague.

I really need to write it all out in full. I am currently illustrating the animals/people to show how it works. This will take time!

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Nice work :+1:t2:!
My little suggestion, most of the chinese characters in fact is a compound.
So learning the Chinese radical 中文部首 first will greatly improve your visualisation and systemised ability.


https://humanum.arts.cuhk.edu.hk/Lexis/lexi-mf/radical.php
In Chinese we use Chinese radical to look up a specific word, it’s the Chinese way of dictionary.
eg

人 means person. 众 is generated from 人, means people.
Look forward seeing your study summary.

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