Understanding Symbol In Mathematics
A Closer Look At Symbols
In mathematics, symbols are notations or representations that stand for numbers, operations, and relationships. They serve as a bridge between concrete ideas, such as physical objects or actions, and abstract mathematical thinking.
For example the numerals 5, 12, and 3.5 represent quantities, the operation symbols like +, −, ×, ÷ represent specific mathematical actions or processes, and the relational symbols such as =, >, and < show relationships between quantities.
Symbols allow for concise and universal communication in mathematics, but they must be connected to meaning to be effective. Without understanding what they represent, symbols can lose their meaning and become just random marks.
Common Symbols in Early Mathematics
Students encounter a variety of symbols in their early math education. Each symbol represents a specific mathematical operation or relationship, and helping students understand their meanings builds a strong foundation for problem-solving and reasoning.
| Symbol | Name | Meaning / Use |
|---|---|---|
+ | Addition | Combines or adds amounts together. |
- | Subtraction | Represents taking away, comparing, or finding the difference between two numbers. |
× | Multiplication | Represents repeated addition or combining equal groups. |
÷ | Division | Represents separating a total into equal parts or groups. |
< | Less Than | Indicates that the first number is smaller in value than the second. |
> | Greater Than | Indicates that the first number is larger in value than the second. |
= | Equal Sign | Shows that two amounts have the same value. |
| ≠ | Not Equal | Shows that two amounts do not have the same value. |
( ) | Parentheses | Used to group parts of an expression, especially in multi-step problems. |
⁄ or — | Fraction Bar | Represents division or part-whole relationships (e.g., ½). |
. | Decimal Point | Separates whole numbers from fractional parts (e.g., 3.5, 2.75). |
% | Percent | Represents parts per hundred (e.g., 50% = 50 out of 100). |
... | Ellipsis | Indicates a pattern or sequence continues. |
Introducing Symbols In Mathematics
Connecting Symbols To Meaning
Symbols should not be introduced as arbitrary marks. Research highlights the importance of developing number sense and conceptual understanding alongside symbols. For example, writing the symbol 5 should be connected to counting five objects, recognizing a group of five, or understanding five as part of a number line. Using the + symbol should be tied to combining quantities physically or visually before transitioning to written equations.
Using symbols in meaningful ways allows students to learn to share their thinking and communicate math ideas clearly, which is an important skill for understanding math.
Symbols As Communication Tools
Symbols allow students to express mathematical ideas efficiently, but their meaning is enhanced through language and dialogue. Talking about mathematical actions strengthens the connection between the symbol, the idea it represents, and the action it describes. For example, while writing 3 + 2 = 5, students might say, “Three and two more make five.” This verbal explanation reinforces the meaning of each symbol and connects it to the process of addition.
Encouraging students to explain their reasoning out loud, while modeling the writing of symbols, helps clarify the relationship between mathematical operations and their representations.
How To Support Students In Understanding Symbols
Modeling The Use Of Symbols In Context
Students first need opportunities to explore mathematical ideas using manipulatives and visual models before introducing symbols. This gradual progression ensures that symbols are grounded in meaning, reflecting the actions and relationships students have already explored.
Start with Hands-On Activities: Begin with manipulatives, such as counters, blocks, or Unifix cubes, to represent mathematical actions. For example, to show 3 + 2, students can group three counters and two counters together, observing how the groups combine to form a total of five. Encourage students to describe their actions aloud, such as, “I added three and two together to make five.”
Transition to Visual Representations: Move from physical manipulatives to drawings or diagrams that represent the same actions. For example, students can draw three circles and two circles, then combine them into a group of five. At this stage, introduce the + symbol to show the combining action visually:
- Draw three circles, write the + symbol, and then draw two more circles.
- Finally, write the = symbol, followed by the total: 3 + 2 = 5. Encourage students to talk about what the symbols mean: “The plus sign shows we’re adding the two groups together, and the equals sign shows the expressions on both sides of the equal sign have the same value.”
Introduce Abstract Notation: Once students are comfortable with physical and visual representations, use symbols as a way to summarize their actions. Write 3 + 2 = 5 and connect it back to the objects and drawings they used earlier.
Following this progression, students see how symbols represent the ideas they’ve already explored. This approach builds a strong foundation for mathematical reasoning, helping students use symbols confidently and accurately.
