My short stories

I propose the following problem to primary school teacher candidates:
A worker can do a job in 15 days. The second worker can do the same job in 10 days. How long will it take for the workers to complete the work, if they work together?
– What do we need to do to solve this problem?
– Add up?
– Subtract?
– Cross-multiply?
I announce the correct answer: “We need to analyze the problem mathematically!”
Analyzing mathematically… What is the place of analysis in a mathematical activity? In teaching mathematics? In learning mathematics?
September 2017
Daniel, my 6-year-old son, is doing his homework. He is leaning over the notebook, absorbed completely by the work.
– What are you doing?
– I’m doing a mathematical problem.
Curious, I look over his shoulder. Daniel draws flowers, all in color, with round petals. He is putting a considerable effort in making the flowers look colorful.
– Can you explain what you are doing?
– There are eight flowers. Each flower has four petals.
Daniel draws another flower and colors the petals. Another flower … It takes him about 15 minutes to draw, to color, and to count the petals, and another minute to re-count all 32 petals. He gets distracted in this long counting and starts over.
I wonder, “What did he learn? To draw? To count? Did he try to analyze the problem mathematically?”
These are the questions that fascinate me.
October 2005
Maya, 3 year-old, and I are having tea with cookies and sweets
Me: – Maya, if you put one cancy in each of your pockets, how many candies will you have? (Maya has two pockets on her dress).
Maya: – I do not like these candies.
Me: – OK. You will put one cookie in each pocket. How many cookies will you have?
Maya: – I do not want cookies now.
Me: OK. We are going to the park. In the park you will get hungry. Let us put one cookie in each pocket. How many cookies do you need to take from the table?
Maya: – Two. Let’s go to the park!
July 2018
Maya, 3 year-old, is having dinner.
Maya: – Mommy, give me like this (shows 4 fingers) tomatoes.
Masha puts 4 small tomatoes on Maya’s plate. Maya rapidly eats 3 of them.
Me: – Look Maya, there were 4 tomatoes and now, you have only 1. How many tomatoes did you eat?
Maya shows 3 fingers.
Masha to me: It is by chance!
Maya: – Mommy, give me like this (shows 4 fingers) tomatoes and one cucumber.
Masha puts 4 small tomatoes and one piece of cucumber on Maya’s plate. Maya rapidly puts 2 tomatoes in her mouth.
Me: – You had 4 tomatoes and now, look, there are only 2. How many did you eat?
Maya: Rapidly puts one more tomato into her mouth, already full, and shows 3 fingers.
September 2018
Maya, 3 year-old, is at the table with her three uncles eating pancakes.
Maya: You should take only one pancake, each of you! If you take two, it will be very bad!
December 2018
Maya looking at my belly: granny, you have two bellies and me – only one!
December 2018
Me: “Maya, let us count your grandmas.” [I take her hand holding the fingers straight and bending down her fingers one-by-one starting with the pinky finger).
Maya: “Granny Lena, granny Musia, granny Assia, granny-Farida.”
I point at her 4 bent-down fingers: “Look, you have four grandmas.”
Maya holds up her thumb: “this is Biggy (our dog)! I have five!”
December 2018