
i was a math major but a poor student . i was excited at start of each course but quickly became frustrated . somehow i graduated . many years later it occurred to me mathematics is discovered not as was often stated by my most hated math Perfessor invented like boring tax laws just as the laws of nature are of course discovered and not invented by a bunch of boring accoutants . i then restudied Calculus and was able to solve every problem in the book . for a demonstration of mathematical discovery i direct you here viz. HACKENBUSH: a window to a new world of math  YouTube[^]





Great story, thanks for sharing. I too like the idea of "discovery of math".
Once my mindset changed (from fixed mindset to growth) I discovered that what we see in schools is often the filtereddown results of bunches of people who summarize everything.
It makes most subjects boring and distant.
As soon as you discover that mathematical concepts are just really great patterns that super smart people have learned then you begin to see that you can:
1. go back to the roots of it and discover what the original people discovered  it will just take a long while and you may not get a huge breadth of understanding.
2. understand that those smart people have shortcut a lot of learning and discovery to give us what we have but we all need to remember that even those giants who we stand on the shoulders of were picking their way through the challenges too.
It's kind of like seeing into the subject and being a part of it instead of just "another thing to memorize."





I never understood that last part but you made it sound easy.
Bastard Programmer from Hell
"If you just follow the bacon Eddy, wherever it leads you, then you won't have to think about politics."  Some Bell.





Game my mother played with me and I played with my children.
Usually while driving somewhere.
just have a conversation
25 divided by 5 times 4 times 5 minus 1 divided by 11 is what?
Nothing about order of operands in this. Just in linear order. But it makes one think instead of using a calculator or sheet of paper. You can make it as easy or hard as you want. But it causes the person to work thru things in their head. It worked wonderfully for math.
9
To err is human to really elephant it up you need a computer






I apologize beforehand that my reply is colored by my personal experience. Why not try to teach him something else than basic arithmetic? There are so many branches of mathematics you can choose from: geometry, sets theory, algebra.
For me, the first 5 years were absolutely horrible. I had (and still have) no inclination for arithmetic and struggled to get mediocre grades. Luckily, in grade 6 I started basic synthetic geometry (triangles and stuff) and a bit of algebra. All of a sudden I discovered that math is about reasoning and first "reductio ad absurdum" proofs seemed like intellectual martial arts. Got hooked for life.
Mircea





Mircea Neacsu wrote: in grade 6
Mircea Neacsu wrote: a bit of algebra
Were you in a class for gifted students?
The difficult we do right away...
...the impossible takes slightly longer.





Richard Andrew x64 wrote: Were you in a class for gifted students? No, that was the standard curriculum at that time in Romania. We were starting school at 7 so they probably had to cram more stuff in our little heads. Anyway, at 13, the idea that you use a letter for a number that you don't know how much it is, didn't seem too difficult to grasp.
A year latter I was reading George Gamow's "One, two, three, infinity..."[^] and discovering Cantor's diagonal method and Moebius bands. As I said: I've got hooked. Once a nerd, always a nerd
Mircea





The issue is that we've to adhere to the school syllabus schedule, because tests and homeworks are as per their schedule. And Integers, Addition, Subtraction come first.





Tell him that there is really only one operator: addition. The other three just all reduce down to that.
"One man's wage rise is another man's price increase."  Harold Wilson
"Fireproof doesn't mean the fire will never come. It means when the fire comes that you will be able to withstand it."  Michael Simmons
"You can easily judge the character of a man by how he treats those who can do nothing for him."  James D. Miles





David Crow wrote: Tell him that there is really only one operator: additionIncrementation. The other threefour just all reduce down to that.
FTFY
(In fact, incrementation, addition, subtraction, and multiplication all reduce to set operations. I'm not sure how to represent division using set operations, other than as repeated subtraction.)
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
 6079 Smith W.





Exactly, that's what I'm doing. Transforming a Subtraction problem to an Addition problem. Need to continue this with Multiplication and Division also.





If your student has learnt a bit of programming, why not write a calculator with him/her that takes two numbers represented as strings (one digit per character), and operates on them using the basic multidigit arithmetic operations?
I did that with my daughter, and it was fun for both of us.
Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.
 6079 Smith W.





Yes, perhaps need to introduce Programming to this kid.





I try to explain things in a way that the kid can see it as something to understand, not to memorize. For example:
Kid trying to count to 100 and you hear "forgetting" numbers. Explained:
You only need to repeat from 0 to 9 (and you already know that)
Once you get to 9, you move back to 0 and add 1 to the tens
then I told the name of all the tens and once I got to 100 I just said,
and now we repeat again, but with 3 numbers instead of 2,
and told the name of the hundreds until 1000
and when the numbers behind the first one are not zero... you go back to the previous "scale" and add it
so
234 = 200 + 30 + 4
The kid learned how to count to ten thousand in one afternoon.
For arithmetic I use examples on everyday routines, i.e. preparing the meal box...
How many pieces of apple do you want? 5, Ok... If I only pack 2 how many are you missing? And if I pack 9, how many additional pieces do you have?
Multiplications... writing down the equivalent in times added on the side and saying, multiplication just save time and pencil. Question back, but daddy, 3x1 you need more pencil than writing only 3... me
If the kid is curious (and that's almost by definition of Kid), you only has to find the way that particular kid needs. Playful, logical, by heart, laws of nature... whatsoever. If you find it, the kid learns way faster.
Just try to find it.
M.D.V.
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.





Thanks. Could do many of these things if the kid were in front of me. This kid is in a different city, and I am doing Skype sessions, so need to adapt this method to an online teaching session.





A very long time ago I found a book in the school library and read it. It was called "Quick and Easy Math" by Isaac Azimov (1964). Give it a read.
David Wright





Great book. Thanks for sharing.





Whatever you do, don't use some beans[^].
Quote: BA: Right Baldrick, let's try again shall we? This is called adding. If I have two beans, and then I add two more beans, what do I have?
B: Some beans.
BA: Yes... and no. Let's try again shall we? I have two beans, then I add two more beans. What does that make?
B: A very small casserole.
BA: Baldrick, the ape creatures of the Indus have mastered this. Now try again. One, two, three, four. So how many are there?
B: Three
BA: What?
B: And that one.
BA: Three and that one. So if I add that one to the three what will I have?
B: Oh! Some beans.
BA: Yes. To you Baldrick, the renaissance was just something that happened to other people wasn’t it?
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
 Homer





Richard Deeming wrote: ape creatures of the Indus
Looks like my country India





Looks like the modern local name is the Sindh: Indus River  Wikipedia[^]
"These people looked deep within my soul and assigned me a number based on the order in which I joined."
 Homer





According to traditional scholars in India, Sindh is the name of the geographical region towards the east / south of the Indus river (Sindhu river). This Sindh became Hind, because the S sound became difficult to pronounce for some people. So, Sindh > Hind. (Rather Sindh was the name given by people from other countries to this geographical region. The original name was Bhaarata, and earlier Ajanaabha. This is what is told in our age old Sanskrit scriptures).
This further became Hindu, and India (because H sound also had some pronunciation difficulties).
modified 18Aug23 5:23am.





I taught all of my kids math using several methods because learning differs. Here are some:
I made worksheets with hands on them to demonstrate making 5 (fingers up + fingers down), making 10 (same concept but with both hands), and adding to 5 (using the same diagrams as for making 10)
I got a curriculum called Math U See with blockstyle manipulatives. This system comes with a great scope and sequence as well, the blocks are colorcoded, and the lessons are all centered around "Decimal Street" which focuses on place value.
Another curriculum called Life of Fred puts math into the context of daily life in an engaging and compelling way. This is great for those who ask "When will I ever use this?" and for those who love a silly story. There are other lessons embedded in the stories as well, mostly academic, but also critical thinking and philosophical thinking.





When we learned our multiplication tables in school, we had to stand in front of the class and recite them to a vinyl record with background music.
2 times 2 is [pause]
2 times 3 is [ pause]
…
2 times 10 is [ pause ]
We had a “tracking dog bone” with 2 thru 10 or 12.
If you recited them all correctly, then the teacher would use a hole punch to mark the number off. It was on a volunteer basis, but in hind sight, each student was super attentive to see if the reciter messed up or succeeded so the whole class was reinforcing each recital. Even people who never recited in front of the class were proficient by the end of the year.
The next year we did a 3 minute timed test everyday progressing through addition, subtraction, multiplication, and division.
Once you aced 3 tests, you moved to the next operation.
Once you aced 12 tests, the teacher would call “pro time” at two minutes.
The tests were very simple, basically a folder that you would wrap around a sheet of paper. It had holes to write your answers. Flip it the other way and it became the grader.
I remember that my weak spot was 7x8. I would always answer 48 or maybe 54? Blocked me for weeks!
Memorize memorize memorize!





Math Blaster
Also.. Numberblocks (youtube)



