Posted by: Alexandre Borovik | August 12, 2008

## I need your personal stories

This is my first attempt to appeal to the wider public for their personal stories of difficulties they experienced in (early) learning of mathematics. I find that such stories could provide a fascinating insight into psychology of mathematical thinking and are frequently linked to astonishingly deep issues of mathematics. I’ll give you a few examples what I am looking for.

Story 1. A girl aged 6 who could easily solve “put a number in the box” problems of the type

$7 + \square = 12,$

by counting how many 1′s she had to add to 7 in order to get 12 but struggled with

$\square +6 =11,$

because she did not know where to start. Worse, she felt that she could not communicate her difficulty to adults. Her teacher forgot to explain to her that addition was commutative.

Story 2. A girl aged 6 who was also afraid of subtraction. She could easily visualise subtraction of 4 from 100, say, as a stack of 100 objects; after removing 4 objects from the top (by reverse counting: 100, 99, 98, 97), 96 are left. But what will happen if you remove 4 objects from the bottom of the stack?

Story 3. A boy aged 9 who could easily factorise two-digit numbers and knew that, say 42 is 6 times 7, but had difficulties with the times tables and could not answer what was 6 times 7. In his learning of mathematics, division preceded multiplication.

Please send me your stories. You can write at borovik <<at>> manchester [dot] ac [dot] uk or leave your comments at this post. Please also give me the following details:

3. What was the language of mathematical instruction? Was it different from your mother tongue?

4. What is the level of mathematical education that you have eventually got? If your occupation is mathematically related, what is it? Are you a teacher?

Do not be afraid that your story perhaps repeats an already told one. In the examples above, Stories 1 and 2 are interesting exactly because they deal with the same underlying mathematical difficulty.

My warmest thanks! Alexandre Borovik

## Responses

1. I was about 4 or 5 or 6.

Male.

English.

Master Degree. Part-time teacher.

I recall my friends and I trying to figure out whether it was faster to cross a rectangular park by traversing the diagonal or going around the edges. I forget how the issue was resolved or the reasons employed. I recall, though, that the problem was far from easy for us.

2. Thanks! This is the kind of stories I need.

3. 8 years old

Female.

English

Master’s in Special Education; high school special education math teacher

In third grade, we regularly had timed single digit operation tests, with 100 problems on a page and 60 seconds to complete them. I believe there were single operations on a page, though I imagine it probably became mixed as the school year went on. I was slower than my classmates on this task, to the point where the teacher used to send blank copies home with me to memorize them. I didn’t have a misunderstanding of any concept; I was just slow. Later, I found long multiplication and division with regrouping to be a similarly exhausting grind (5th grade).

I viewed myself as bad at math, and I viewed math as an unpleasant grind based on these experiences until geometry, precalculus, and calculus in high school. At that level, my ability to quickly carry out basic calculations wasn’t no longer the definition of my math success. And I loved it.