To make a program that can do the psychology experiment of arithmetic cognition on human subjects
- Python 3.xx
- Numpy
- Pandas
- Matplotlib
Our user data saved in the directory user_data. In user_data/results, each file contains experiment data from a participant.
- Birth year (Age) :
int - Gender =
{'male', 'female'} - Math ability (answered by a participant) =
{1:'very bad', 2:'below average', 3:'above average', 4:'very good'}
The name of the file means the datetime the experiment taken, birth year, gender(1: male, 2: female), and mathematical ability(1-4). For example, 2018-12-06_04_26_02_1999_1_3.result stands for "This experiment was taken at 04:26:02, Dec. 06, 2018 by a male born in 1999 who had 3-level, above average, mathematical ability."
In the file, its data are organized like below:
| Carry dataset index | Corret | Solving time (sec.) | Answer | True ansewer | Operand digits | Operator | Carries |
|---|---|---|---|---|---|---|---|
| 7 | True | 21.242 | 1001110 | 01001110 | 4 | multiply | 2 |
Each row is separated by '\n', and in each row, each column record is separated by '\t'. In the actual file, there is no header row.
Carry data index refers to the index with which the operation can be retrieved. For example, we can retrieve the operation like below:
from data_utils import *
operand_digits = 4 # operand_digits in [4, 6, 8]
operator = 'multiply' # operator in ['add', 'substract', 'multiply', 'divide', 'modulo']
carries = 2
index = 7
carry_datasets = import_carry_datasets(operand_digits, operator)
op_operands = carry_datasets[carries]['input'][index] # concatenated operands
op_result = carry_datasets[carries]['input'][index]
print(op_operands)
print(op_result)For subtraction, we only deal with the case that operand1 >= operand2 if operand1 - operand2. For division and modulo, we only deal with the case that operand2 != 0 if operand1 / operand2 or operand1 % operand2.
The number of total operations
| Operator | Operand digits | Input dim | Output dim | Total operations |
|---|---|---|---|---|
| add | 4 | 8 | 5 | 256 |
| add | 6 | 12 | 7 | 4096 |
| add | 8 | 16 | 9 | 65536 |
| subtract | 4 | 8 | 4 | 136 |
| subtract | 6 | 12 | 6 | 2080 |
| subtract | 8 | 16 | 8 | 32896 |
| multiply | 4 | 8 | 8 | 256 |
| multiply | 6 | 12 | 12 | 4096 |
| multiply | 8 | 16 | 16 | 65536 |
| divide | 4 | 8 | 4 | 240 |
| divide | 6 | 12 | 6 | 4032 |
| divide | 8 | 16 | 8 | 65280 |
| modulo | 4 | 8 | 4 | 240 |
| modulo | 6 | 12 | 6 | 4032 |
| modulo | 8 | 16 | 8 | 65280 |
Reference this CSV file carry_dataset_statistics.csv.
from data_utils import *
operand_digits = 4 # operand_digits in [4, 6, 8]
operator = 'add' # operator in ['add', 'substract', 'multiply', 'divide', 'modulo']
carry_datasets = import_carry_datasets(operand_digits, operator)How see what kinds of carries exist in the dataset.
carry_datasets.keys()How to access the 2-carry dataset
carry_datasets[2]How to access the input the 2-carry dataset
carry_datasets[2]['input']carry_datasets[2]['input'].shape == (n_operations, 2 * operand_digits)
How to access the input the 2-carry dataset
carry_datasets[2]['output']carry_datasets[2]['output'].shape == (n_operations, operand_digits)
How to access the i-th operation in the 2-carry dataset
carry_datasets[2]['input'][i,:]
carry_datasets[2]['output'][i,:]This work was partly supported by the Institute for Information & Communications Technology Promotion (R0126-16-1072-SW.StarLab, 2017-0-01772-VTT, 2018-0-00622-RMI, 2019-0-01367-BabyMind) and Korea Evaluation Institute of Industrial Technology (10060086-RISF) grant funded by the Korea government (MSIP, DAPA).
When you reuse this implementation, cite the following.
@inproceedings{ChoLHZ19,
author = {Sungjae Cho and Jaeseo Lim and Chris Hickey and Byoung{-}Tak Zhang},
title = {Problem Difficulty in Arithmetic Cognition: Humans and Connectionist Models},
booktitle = {Proceedings of the 41th Annual Meeting of the Cognitive Science Society},
pages = {1506--1512},
year = {2019}
}
MIT License