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# Using Precise Language to Boost Math Skills: Strategies and Examples

by **Connie Warren** on Jul 19, 2024 11:51:18 AM

Using mathematically precise language helps students understand math concepts better and improve their problem-solving skills. When students explain their reasoning and solutions with exact math terms, they show their understanding and get better at sharing complex ideas. This practice is key for developing critical thinking and analytical skills needed for school success and solving real-world problems.

The Importance of Mathematically Precise Language

The Importance of Mathematically Precise Language

Using mathematically precise language helps students internalize and apply mathematical concepts more accurately. By encouraging students to describe their problem-solving processes with exact terminology, we can ensure that students grasp the nuances of mathematical operations, properties, and relationships. This precision in language reduces ambiguity, clarifies thinking, and promotes a more structured approach to solving mathematical problems. Moreover, it enables students to engage in meaningful discussions about their work, receive constructive feedback, and build on their understanding through collaborative learning.

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Research Evidence

Research Evidence

Research supports the positive impact of using mathematically precise language on students' mathematical achievement. Studies indicate that students trained to use accurate mathematical vocabulary and syntax perform better in problem-solving tasks and standardized assessments. For instance, a survey by Kotsopoulos (2007) found that students who used precise mathematical language significantly improved their ability to solve complex problems and articulate their reasoning clearly. Another study by Siegler and Ramani (2008) demonstrated that precise mathematical language use is linked to better understanding and retention of mathematical concepts.

Furthermore, incorporating precise language into mathematics instruction aligns with recommendations from leading educational standards, such as the Common Core State Standards for Mathematics (CCSSM). The CCSSM emphasizes the importance of mathematical communication, stating that students should be able to "construct viable arguments and critique the reasoning of others" using appropriate and precise terminology. This approach enhances individual learning outcomes and prepares students to participate in mathematical discourse at higher academic levels and in professional contexts.

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**Strategies to Develop Precise Mathematical Language**

To support students in using mathematically precise language during their verbal and written explanations, we should integrate specific strategies into our teaching practices. By adopting these methods, we can create a learning environment that prioritizes clarity, precision, and effective communication in mathematics.

**Model Precise Language:**Demonstrate how to use accurate mathematical terms during explanations.**Vocabulary Lists:**Provide students with lists of key mathematical vocabulary relevant to the topic.**Sentence Starters:**Offer sentence starters to help students begin their explanations using precise language.**Mathematical Journals:**Encourage students to keep journals where they practice using precise mathematical language.**Peer Review:**Have students review each other’s explanations and provide feedback on using mathematical language.**Word Walls:**Create a word wall with important mathematical terms and definitions.**Anchor Charts:**Use anchor charts to display examples of precise mathematical explanations.**Explicit Instruction:**Teach specific vocabulary and how to use it in context.**Discussion Prompts:**Use prompts that require students to explain their thinking using precise language.**Error Analysis:**Analyze errors in mathematical language and discuss how to correct them.**Think-Pair-Share:**Encourage students to discuss their problem-solving process with a partner using precise terms.**Sentence Frames:**Provide sentence frames to guide students in structuring their explanations.**Interactive Word Walls:**Use digital tools to create interactive word walls where students can add examples and definitions.**Scaffolded Practice:**Gradually increase the complexity of tasks requiring precise language use.**Feedback:**Provide constructive feedback focused on the use of precise language.

## Examples of Precise Mathematical Language

Using Correct Terminology

- Incorrect: "I added these numbers."
- Correct: "I added the two fractions by finding a common denominator."

Describing Processes

- Incorrect: "I made the shape bigger."
- Correct: "I made the shape twice as big by multiplying its size by 2."

Explaining Reasoning

- Incorrect: "This answer looks right."
- Correct: "This answer is correct because when I substitute it back into the original equation, both sides are equal."

Defining Terms

- Incorrect: "These shapes are the same."
- Correct: "These polygons are congruent because they have the same shape and size, with corresponding angles and sides."

Clarifying Operations

- Incorrect: "I times these numbers."
- Correct: "I multiplied the base by the height to find the area of the rectangle."

Elaborating on Steps

- Incorrect: "I solved for x."
- Correct: "I isolated the variable x by subtracting 3 from both sides of the equation and then dividing by 2."

Providing Justifications

- Incorrect: "It's a triangle."
- Correct: "This is a scalene triangle because all three sides have different lengths."

Using Symbols Appropriately

- Incorrect: "I used the 'equals' sign."
- Correct: "I used the equality symbol (=) to indicate that both expressions represent the same value."

Describing Geometric Properties

- Incorrect: "The lines go the same way."
- Correct: "The lines are parallel, meaning they run equidistant from each other and never intersect."

Articulating Algebraic Steps

- Incorrect: "I moved the numbers around."
- Correct: "I applied the commutative property of addition to rearrange the terms and simplify the expression."

Explaining Fractions

- Incorrect: "I split it up."
- Correct: "I decomposed the fraction into smaller fractions to make it easier to add."

Clarifying Graph Interpretations

- Incorrect: "The line goes up."
- Correct: "The graph shows a positive slope, indicating that as the independent variable increases, the dependent variable also increases."

Specifying Measurement Units

- Incorrect: "The answer is 10."
- Correct: "The perimeter of the rectangle is 10 centimeters."

Detailing Patterns

- Incorrect: "The numbers go up by 2."
- Correct: "The pattern is arithmetic, with a common difference of 2 between consecutive terms."

Explaining Probability

- Incorrect: "It might happen."
- Correct: "The probability of this event occurring is 1/4, or 25%, based on the ratio of favorable outcomes to possible outcomes."

Describing Transformations

- Incorrect: "I flipped the shape."
- Correct: "I performed a reflection over the y-axis, resulting in a mirror image of the original shape."

Articulating Comparisons

- Incorrect: "This one is bigger."
- Correct: "This triangle has a greater area than the other because its base and height are larger."

Expressing Equations

- Incorrect: "I got this equation."
- Correct: "I derived the quadratic equation by setting the expression equal to zero and factoring."

Elaborating on Volume Calculation

- Incorrect: "I filled it up."
- Correct: "I calculated the volume of the cylinder by using the formula V = πr²h."

Clarifying Statistical Measures

- Incorrect: "The average is 5."
- Correct: "The mean of the data set is 5, calculated by summing all the values and dividing by the number of data points."

These examples and strategies can be integrated into daily instruction to help students develop the habit of using mathematically precise language in both verbal and written forms.

Using mathematically precise language is an important part of effective math teaching. When students learn to explain their math thinking clearly and accurately, they understand concepts better and improve their problem-solving skills. This also prepares them for future success in school and their careers. By making precise language a regular part of lessons and using proven strategies, teachers can help students reach these educational goals.

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