I have always struggled with math my whole life. I was one of those kids who fell behind in math around the 5th grade and never caught up. I’ve failed almost every math class I have ever taken since High School, but somehow squeaked by to get a college degree. I have ADD and also recently discovered that I suffer from dyscalculia. Dyscalculia is a learning difficulty that causes problems in maths ; people with dyscalculia have trouble making sense of numbers and mathematical concepts
I recently stumbled upon the book the “Secrets of Mental Math” by Arthur Benjamin and Michael Shermer which has been a revelation. Why their methods is not taught in grade school, is beyond me… It has taught me to calculate everything from left to right and being able to add/subtract and multiply without carrying any numbers. Even though I feel like I am making significant progress I still struggle with finding a solution to a problem if I have to add/subtract/multiply too many numbers. Last night I was trying to explain the methods to my girlfriend and she just laughed at me because I wasn’t able to get the answer right, even though I knew how to do the problem.
It was
987
x 7
In order to get the answer I multiplied
900 x 7 = 6,300
80 x 7 = 560
7 x 7 = 49
By the time I am at the step of adding 7 x 7, I couldn’t remember that I had added 6300 + 560 and I have to go back to starting the problem over again…
This seems to come down to simple working memory, but are there any shortcuts to being able to keep multiple numbers in your head at once? No matter how much I practice I put in, I still always seem to forget what I was adding in the first place, or even remember what the initial problem I was multiplying was. I have developed a 100 person PAO system but rote memorization is still faster. Any suggestions or advice would be greatly appreciated. I’m beginning to feel like I’m doomed to never be good at math due to my poor working memory.
First of all, you’re not alone, and I work training lots of people who are “good at math” or have a solid career trajectory, and yet find a weekness in mental calculation. Don’t despair!
You’ve identified the main reason, which is working memory—the human analogue to a computer’s RAM. It turns out that humans all have a pretty uniform working memory size (written by me), and it doesn’t seem that we can change it easily.
What we can do, is to use it more efficiently. This can be approached in a few ways:
Use methods that don’t need so much memory. My favourite way to solve this question, 987 × 7, was already explained by Bjoern.
Memorize the key mathematical facts, like the times tables, single-digit additions and subtractions, and others. This means that you can focus on the difficult part of the problem. If we use your method for 987 × 7, if you know 8 × 7 = 56 easily, then you won’t lose track of the other numbers. And if you happen to know 7 × 13, then you can also use BJoern’s method more easily.
Get more used to working visually with numbers. There are lots of techniques for doing this that are outside of a forum post, but you want to be able to do mental math without needing to repeat numbers to yourself. I still use my verbal working memory for some calculations when I run out of RAM, but when I train to avoid that, my speed typically increases.
Alice, Bob, and Eve concur… especially, when ‘others’ includes semiprimes.
Alternatively, if you know that 91 is a semiprime, you can just find the question (13 and 7) to the answer (91) rather than the answer to the question.
…and then next time you can introduce her to Alice, Bob, and Eve whilst explaining public-key cryptography to her.
Great, why don’t you combined that with the above and create a memory palace for square free semi-primes and store them as n=p*q; where n is the semiprime in question and p and q are the two prime factors. So in one particular location you’ll find…
Person 91 is doing action 13 to object 07… followed by
Person 93 is doing action 31 to object 03… etc.
…this way you’ll know the semiprimes up to 100 and its prime factors as well. Comes in handy in problems other than cryptography as well, so it’s a nice memory palace to have.
I believe that maths can be expressed phonetically: the first number of a sum can be stated as consonants. The second number can be stated as vowels. Merging the two, you get syllables. The thing to rote learn is the result of each syllable.
I haven’t had time to prove it’s a great method.
I overview the idea on my site but I should not advertise on this site.