feli10 / math-coding

Learn Elementary School Math with Coding.

English | 中文

Project Website: https://feli10.github.io/math-coding/

Table of Contents

• What is this?
• Who is this for?
• Project Origins
• Project Goals
• Usage Information
• List of Units and Programs
• Design Principles of Coding Exercises
• Programming Style
• Setting Up the Development Environment
  • Installing Python
  • Code Editor
  • Interactive Interpreter (Python shell)
  • Installing External Libraries
• Useful Resources for Referencing

What is this?

In 2022, my parents entrusted me to help my younger brother learn elementary school mathematics. At the time, he was six years old, and I was a freshman in high school. To tackle this project, I formulated a plan - after he completed each unit in his math textbook, I would design and assign him 1-2 coding exercises, written in Python, that closely relate to the unit's content. Using this approach combining mathematics and coding, we managed to complete an average of one semester's worth of coursework every two months. In about a year, we had finished the Chinese elementary school mathematics curriculum from grades three to five.

The project library contains 60 Python programs that we wrote during the year, including 22 with graphical user interfaces and 38 with command line interfaces. These programs cover all 49 units from the third- to fifth-grade Chinese mathematics textbooks of the People's Education Press. The math_coding_handbook.pdf file contains the main mathematical topics for each unit and descriptions of the corresponding program(s). We have also included detailed documentation and comments within all programs.

Graphical User Interface	Command Line Interface

All programs and the learning handbook have separate versions in English and Chinese. The _en directory contains the English version, with all graphical displays and program comments in English. The _cn directory contains the Chinese version, with all graphical displays and program comments in Chinese.

Download math_coding_handbook.pdf (English version)

Download math_coding_handbook.pdf (Chinese version)

Through this project, my brother and I have proven in practice that learning elementary school math with coding allows learners to efficiently and effectively study mathematics while simultaneously becoming proficient in a programming language.

Who is this for?

To effectively learn elementary school math with coding through this project requires the following:

1. Elementary school students interested in mathematics and coding.
2. People willing to invest time and effort in guiding children through the coding exercises, including but not limited to parents, older siblings, teachers, or community volunteers.

There are two ways to use this project:

1. Following the school curriculum: This project can serve as a supplementary learning resource for school mathematics curriculums, suitable for learners who want to learn math and coding simultaneously.
2. According to personal progress: You can follow the coding exercises in this project to accelerate the completion of elementary school mathematics. For details, please refer to the “Project Details” page of our website.

Project Origins

In 2022, when my younger brother Henry was six years old, my parents asked me to take charge of his mathematics and English education temporarily. At the time, I was ten years older than him and in my first year of high school. The initial goal we agreed upon was that, before I went to college, I would help him complete elementary school math and reach a level of English proficiency where he could continue to improve independently. Since I was the best in the family at English, there weren't many uncertainties about that, but how would I go about teaching him math?

I completed elementary school mathematics when I was nine years old. Looking back, I remember reading many textbooks, doing lots of practice problems, and taking quite a few mock tests. After some consideration, I realized Henry, who was only six, needed a different approach. Based on my learning experience, when someone constantly struggles with a particular type of math problem, it's usually because they lack a deep understanding of the underlying concepts. The purpose of doing practice problems should be to identify and address these weaknesses. However, if one does practice problems mindlessly, the same mistakes will appear again and again. This is why doing a sea of practice problems is often not an efficient way to learn new math topics. Therefore, I aimed to find an approach that would allow Henry to thoroughly understand any math concepts and skills he needs to learn before diving into extensive problem-solving.

The primary inspiration for combining math and coding came from taking high-level math courses as part of a machine learning research project. While taking the courses, I found that using programming tools to assist in learning mathematics at the university level was quite common and highly effective. When learning calculus, linear algebra, and statistics, programming was used to conduct mathematical experiments and solve practical problems. Coupled with the visualization of results, this greatly aided my understanding of abstract mathematical concepts and theorems. Later, I also found a few resources for learning middle school mathematics with the help of programming. However, I never found anything similar for elementary school mathematics.

So, after discussing my idea with Henry, the "Learn Elementary School Math with Coding" project was born.

Project Goals

In addition to the year-long project with Henry, we organized several “programming weekend” events, in which I led groups of 5-10 children to learn mathematics with programming. Because these events were quite successful, I believe this project can benefit more children - allowing them to learn math efficiently with improved learning outcomes while equipping them with programming skills.

For children following the school curriculum, we hope this project can help them enhance their math and programming abilities. We also hope this project allows those who wish to accelerate their math learning, like Henry, to do so. One benefit of accelerated learning is that knowledge of fundamental mathematics can facilitate early interest development. For example, Henry's mathematic abilities greatly aided his music learning, allowing his musical interest and talent to develop early.

I hope this project can provide people with a new approach to learning mathematics and bring more opportunities to those who choose to use it. If you have any questions or suggestions about the project, feel free to contact me at this email: [email protected].

Usage Information

• The organization of the directories is identical to the elementary school Chinese mathematics textbooks of the People's Education Press. For example, for the directory name g311_time, the "g311" at the beginning identifies that the directory corresponds to unit 1 of semester 1 of the grade 3 textbook.

  • The "g" and the digit following it represent the grade.
  • The second digit may be either 1 or 2. 1 represents the first semester, and 2 represents the second semester.
  • The third digit represents the specific unit within the semester.

• The text after the identifier indicates the main learning content of the unit. The G311 unit is mainly about telling time, so the directory name of this unit is g311_time.

• Each directory contains 1-2 Python program files. The names of the programs are indicative of their contents. For example, g311_time contains two programs: clock.py, which displays a functioning analog clock, and digital_clock.py, which displays a functioning digital clock.

• the math_coding_handbook.pdf file in the _en directory contains description pages for all 60 programs across 49 units from grades 3 to 5. Each program description contains the following:

  • File name
  • Graphical command line interface
  • Difficulty rating (1 to 5 stars)
  • Main coding skills used
  • Program description
  • Screenshots of program output

  

• All programs contain a detailed docstring at the beginning and useful comments throughout.

  

• The learning handbook and all programs have separate English and Chinese versions. The _en and _cn directories are organized in the same way but with content in English and Chinese, respectively.

• Some programs in the code library contain references to each other. Therefore, we recommend downloading the entire code library before use.

• A few notes on the mathematical content of the program:

  • All mathematical units are in SI (International System).

  • The display of vertical form arithmetics in certain programs is based on the vertical forms shown in Chinese textbooks.

    

List of Units and Programs

Unit ID	Unit Name	Program(s)
G311	Telling Time - Hours, Minutes, and Seconds	1. Analog Clock 2. Digital Clock
G312	2-Digit Addition and Subtraction	Practice 2-Digit Addition and Subtraction
G313	Measurements	Practice Unit Conversion
G314	Vertical Addition and Subtraction	1. Vertical Addition 2. Vertical Subtraction
G315	Multiplication Word Problems	Practice Multiplication Word Problems
G316	Short Multiplication	Short Multiplication
G317	Rectangles and Squares	Create Rectangle Class
G318	Understanding Fractions	Practice Comparing Fractions
G319	Sets	Set Operations
G321	Orientations	Practice Identifying Orientations
G322	Short Division	Short Division
G323	Tables	Creating and Displaying Tables
G324	2-Digit Long Multiplication	Long Multiplication 1
G325	Area	Improve Rectangle Class - Calculate Area and Draw Rectangles
G326	Years, Months, and Days	Display Calendar
G327	Understanding Decimals	1. Decimal Practice 1 2. Visualization of Decimals
G328	Combinations	Three Common Counting Problems
G411	Working with Large Numbers	Read Out Any Natural Number
G412	Large Area Units	Practice Area Unit Conversion
G413	Measuring Angles	Draw Clock Dial
G414	3-Digit Long Multiplication	Long Multiplication 2
G415	Parallelograms and Trapezoids	Counting Trapezoids
G416	Long Division	Long Division
G417	Bar Charts	1. Creating Bar Charts Using Matplotlib 2. Creating Subclass of Table Class to Draw Bar Charts
G418	Optimization	Counting Game
G421	Order of Operations	Evaluate Arithmetic Expressions
G422	Observing Objects	Three Views of Cubes
G423	Basic Laws of Operation	Solve 24
G424	Meaning and Properties of Decimals	Decimal Practice 2
G425	Triangles	1. Draw Isosceles Triangles 2. Draw Regular Polygons
G426	Addition and Subtraction of Decimals	Addition and Subtraction of Decimals in Vertical Form
G427	Reflective Symmetry	Generate Reflective Symmetric Shapes
G428	Mean Value and Grouped Bar Charts	Mean Value and Grouped Bar Charts
G429	Chicken and Rabbit Problem	Chicken and Rabbit Problem
G511	Decimal Multiplication	Long Multiplication of Decimals
G512	Position	1. Input Coordinates Based on Positions 2. Click on Positions Based on Coordinates
G513	Decimal Division	1. Long Division of Decimals 2. Practice Converting Common Fractions to Decimals
G514	Probability	1. Random Selection with Weights 2. Sum of Two Dice Rolls
G515	Simple Equations	Solving Chicken and Rabbit Problem Using Equations
G516	Area of Polygons	Polygon Classes with Area Properties
G517	Tree Planting Problem	Tree Planting Problem
G521	Observing Objects 2	Three Views of Cubes v2
G522	Factors and Multiples	1. Get Prime Numbers 2. Goldbach Conjecture
G523	Cuboids and Cubes	1. Cuboid Class with Unit Property 2. Practice Volume Unit Conversion
G524	Meaning and Properties of Fractions	1. Greatest Common Divisor and Least Common Multiple 2. Convert Decimal to Simplest Fraction
G525	Rotation	Rotation
G526	Addition and Subtraction of Fractions	Addition and Subtraction of Fractions
G527	Line Charts	Improve Data Class to Draw Multi-Line Charts
G528	Identify the Outlier	Identify the Outlier

Design Principles of Coding Exercises

1. The exercises are closely related to the math content introduced in their corresponding units.
2. Math curriculums are usually organized in a progressive manner, with content in later units connected with earlier ones. Therefore, we also strive to establish connections in our programs, which is primarily reflected in the following aspects:
   • Math units that progress sequentially correspond to programs that also progress sequentially.
   • Coding exercises adhere to the DRY principle (Don't Repeat Yourself), allowing later programs to reuse earlier ones.
   • Later programs often revisit coding knowledge and techniques established in earlier programs.
3. Coding exercises gradually involve more programming knowledge and skills. Programming knowledge covered includes:
   • Basic data types (int, float, string), variables, functions, conditionals, loops
   • Data types containing multiple elements (containers): lists, tuples, dictionaries, sets
   • Classes and objects (object-oriented programming)
   • Common modules, packages, and libraries:
     • Random: random
     • Graphical interface: turtle, tkinter
     • Combinatorics: itertools
     • Data visualization: matplotlib
   • Threads
   • Exception handling (raise/handle exception)

Programming Style

The goal of programs in this project is to translate human problem-solving methods into machine language (i.e., Python programs) as clearly and explicitly as possible. This is mainly due to the following considerations:

1. For beginner programmers, the primary goal is to write a program that can achieve the expected results. This is a process of becoming familiar with the programming language and building confidence. So, the programs must be simple, intuitive, and easy to understand.
2. Programming is gradually becoming an essential skill, but only a small percentage of individuals will pursue careers in computer and software development. Most people don’t need to know how to create the most optimal algorithms or data structures. All they need is the ability to translate work processes into machine language, which will allow them to automate repetitive and precise tasks, mostly involving small amounts of data.

Therefore, we prioritized results above efficiency for most of our programs. However, when encountering scenarios where runtime is greatly affected by input data, learners will be guided to try different programming methods of varying efficiencies.

Setting Up the Development Environment

Installing Python - Choose one of the following three methods:

1. Download the Python installer from Python's official website (suitable for various operating systems). For Windows users, make sure to check the "Add python.exe to PATH" option during installation.

   

2. Install Anaconda or Miniconda (suitable for various operating systems). Conda is an open-source package and environment management system. Installing Conda also installs Python and some commonly used modules.

3. Use Homebrew to install Python (suitable for macOS and Linux operating systems). Homebrew is an open-source package management system. If Homebrew is already installed on your system, you can use the following command to install Python:

   brew install python-tk

Code Editor

1. IDLE (Integrated Development and Learning Environment) is the built-in programming tool for Python. It includes an interactive interpreter and code editor. IDLE only has bare-bone functionalities, so it is recommended to use a more powerful code editor like VS Code.

   

2. VS Code (Visual Studio Code)

   • First, download and install VS Code.
   • After launching VS Code, search for and install the Python extension in the Extensions panel.

   

Interactive Interpreter (Python shell)

A Python interactive interpreter, otherwise known as a shell, is a very useful command-line interface where you can enter any Python expression, and the results will be displayed on the screen instantly. The interpreter is ideal for experimenting with small code snippets, such as testing the usage of built-in data types or functions. It is recommended that when programming, you not only input code in the code editor but also have an interactive interpreter open at the same time. This allows you to experiment and verify the results immediately in the interpreter when the outcome of an expression is uncertain.

You can access the Python interactive interpreter in the following ways:

1. For macOS or Linux users, you can enter python in the terminal to access the interactive interpreter. If the system doesn't recognize python, you can try python3.

   

2. Windows users can access the interactive interpreter by clicking "Python" in the menu or entering python in the Command Prompt window (cmd.exe). If the system doesn't recognize python, you can try python3 or py.

3. The built-in programming tool IDLE in Python directly opens the interactive interpreter when launched.

   

4. You can also access the interactive interpreter through VS Code's built-in terminal or interactive window.

Installing External Libraries

1. Modules or packages like turtle and tkinter are part of the Python Standard Library and come pre-installed with Python, so no additional installation is required.

2. Matplotlib is a popular Python data visualization library and can be installed using the following methods:

   • Install using Python's pip module. If the system doesn't recognize python, you can replace python with python3 or py (for Windows users) in the commands below:

     python -m pip install -U matplotlib

   • If Conda is installed, you can use the conda command for installation:

     conda install matplotlib

3. Pygame is a popular Python game development library. The G512 program "Coordinate Game" uses the sound module from Pygame. You can install it in a similar way to Matplotlib:

   • Install using Python's pip module:

     python -m pip install -U pygame

   • If Conda is installed, you can use the conda command for installation:

     conda install pygame

Useful Resources for Referencing

• W3Schools
  • Built-in Functions
  • String Methods
  • List Methods
  • Random Module
• Turtle
• Tkinter
  • TkDocs
  • Tkinter Reference
• Matplotlib
• Color Names
• PEP8 - Style Guide for Python Code

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