Basics of Pre-algebra

 

Keywords: Finger Math, Abacus, Number sense, Classroom math activities, Math learning for kids, Teaching tools, Interactive math, Hands-on math

“Finger Math and Abacus: A Comparative Study”

Overview:

Mathematics, the foundation of all sciences and technology, plays a fundamental role in our everyday lives. Yet many students find the subject challenging, causing them to shy away from it altogether. This reluctance is often due to a lack of confidence, a misunderstanding of unclear concepts, a move ahead to more advanced skills before they are ready, and ineffective learning methods. However, with the right approach, math learning can be both rewarding and empowering. This post will explore different approaches to learning math, strategies for success, and cutting-edge tools to help you achieve your goals.

Math Learning:

Math learning can take many forms, including traditional classroom instruction, online courses, and self-directed learning. A multifaceted approach to math learning can improve understanding, engage students, and promote subject mastery. A 2014 study by the National Council of Teachers of Mathematics found that the use of multiple representations, such as visual aids, graphs, and real-world examples, supports the development of mathematical connections, reasoning, and problem-solving skills.

What is Number Sense?

Number sense is a group of skills that allow people to work with numbers. These skills are key to doing math — and many other tasks. 

Number sense involves:

Understanding quantities

Grasping concepts like more and less, and larger and smaller

Understanding the order of numbers in a list: 1st, 2nd, 3rd, etc.

Understanding symbols that represent quantities (7 means the same thing as seven)

Making number comparisons (12 is greater than 10)

Recognizing relationships between single items and groups of items (seven means one group of seven items)

Some people have stronger number sense than others. Kids and adults with poor number sense may struggle with basic math operations like addition and multiplication. They can also have trouble with everyday tasks and skills like measuring, handling money, and judging time.

Trouble with number sense often shows up early, as kids learn math. For some people, the difficulty lasts into adulthood. But with time and practice, these skills can improve.

Example:

I teach number sense through fun and easy activities. Students find numbers, clap and count, and learn big and small numbers with the alligator game. They use sticks for place value and sort odd and even numbers. We skip count, guess numbers in jars, and enjoy shopping games. Tasbeeh counting helps connect math with faith. My students learn numbers with joy and understanding. 

Finger Math – Concept and History

Finger Math is a mathematical technique that uses fingers as a visual aid for performing calculations. It is commonly used as a tool to teach basic arithmetic concepts, particularly addition and subtraction, to young children.

Finger Math helps children develop number sense, improve their counting skills, and gain a conceptual understanding of basic arithmetic operations. It engages their tactile and visual senses, making math more tangible and accessible. It is often used as a foundational learning tool before children progress to mental math strategies.

The Sumerians were the first civilisation to have developed a counting system. It is a common belief amongst many scientists that some of the oldest and most basic mathematical functions, such as addition, subtraction, multiplication, and division, have been used for over 4,000 years.

Indeed, Mushu's research showed that the fingers' origins go back to Ancient Greece and Rome.

Abacus – Concept and Historical Background

The abacus, an instrument to calculate or count by using sliding counters and rods, is indeed the world's first calculator. The abacus was in use in Europe, China, and Russia. The old version of the Abacus was a shallow tray consisting of sand, and numbers could be erased easily when needed, but the modern abacus is made of wood or plastic. It is a rectangular box consisting of nine vertical rods strung with beads. A horizontal crossbar that is perpendicular to the vertical rods divides them into unequal parts. The beads above the horizontal crossbar are called Heaven beads, and the beads down the bar are called Earth beads. Though the Abacus originated in Babylon, it had traveled a long way from the Middle East to Japan and China. When it traveled from one country to another, it also transited. In China, it is called Suanpan. In Suanpan, it has 25 decks.

The famous Japanese mathematician Seki Kawa replaced 25 decks with 14 decks and called it Soroban. The modern-day abacus, which we use today, ay is the Soraban type of abacus.

We can use an abacus to solve all kinds of arithmetic operations, such as addition, subtraction, multiplication, and division. It consists of rods, and each rod contains some beads. There are many kindabacusesbacus present, but the Japanese abacus or soroban is the widely used one. It has 4 beads at the bottom deck and 1 bead at the upper deck. Each rod can represent any number between 0 and o, which is 10 numbers. The beads above the horizontal crossbar are known as Heaven beads, and the bottom one is known as Earth beads. We have to count or calculate by moving the beads up and down.

5. Finger Math vs Abacus – Comparative Study 

Feature	Finger Math	Abacus
Tool Used	Fingers	Beads and frame
Learning Style	Hands-on, natural	Visual and structured
Place Value	Basic understanding	Clear understanding
Calculation	Small numbers, quick thinking	Big numbers, faster calculation
Flexibility	Can use anywhere	Needs an abacus tool
Mental Skills	Memory, coordination	Focus, visualization, mental math
Speed	Moderate	Fast
Best For	Simple, everyday calculations	Complex calculations and practice

How Both Methods Build Number Sense

 I use Finger Math and an Abacus to help my students understand numbers. With Finger Math, they count and group using their fingers. This helps them see numbers clearly and think fast. With the Abacus, they use beads to show numbers and place value. It helps them do bigger calculations and focus better. Both methods make students confident with numbers. They also improve memory, mental math, and problem-solving. Together, these activities build strong number sense in my class.

Islamic Perspective on Learning Mathematics (optional)

Learning math that is integrated with Islamic values means creating continuity between school math material and the values taught in Islam. This is because math can help Muslims to practice one of the sciences taught in the Qur’an. However, the internalization of Islamic values in the learning of math in various educational institutions has not been implemented optimally. There is no formulation of an internalization strategy and model of integration between Islamic values (Al-Quran) and math that can be used as a reference. The integration of math and Islamic values is not a process of Islamizing math, producing Islamic math, or giving religion to math. This integration is one to make people more religious through math. It can be said that the integration of Math and Islamic values aims to make math a means for humans to carry out the purpose of their creation.

Use of Both Methods in Modern Classrooms

In my classroom, I use Finger Math and an Abacus to help students understand numbers. With Finger Math, students count, add, and subtract using their fingers. For example, 

for 7 + 5, they use their fingers to find the answer quickly. It is simple and can be done anywhere.

With an Abacus, students use beads to show bigger numbers and place value. For example, 234 + 158 is solved by moving beads, which helps them see numbers clearly. An abacus also improves focus and mental math.

I use both together. Finger Math is for quick, small calculations, and the Abacus is for bigger, structured practice. This makes my class fun, interactive, and helps students learn numbers confidently.

Conclusion

Both Finger Math and the Abacus are very useful in the classroom. Finger Math is simple, quick, and helps with small numbers. An abacus is structured, shows place value, and helps with bigger calculations. Using both makes learning fun, interactive, and helps students understand and calculate numbers easily.