The relationship between reading comprehension (understanding what we read) and solving mathematical problems is crucial in education, especially during the early school years. In this article, we explore how developing reading skills can become a fundamental pillar for understanding and solving mathematical problems. We provide resources and tips, emphasizing the role of language, teaching strategies, and teacher mediation.
Language as the Foundation of Communication and Its Connection to Mathematics
Language is more than a tool for expression; it is the primary means of understanding the world and sharing knowledge.
In schools, alongside everyday language, specific languages such as literary, scientific, and mathematical languages are used. Mathematical language, characterized by its symbolic and concise nature, requires constant practice to master its symbols and rules.
Mathematical Language
Mathematical language is universal—it is understood in the same way across all cultures and languages. To comprehend it, we must become familiar with specific terms and unique structures. This language includes:
- Symbols: Examples: + – × ÷ %
- Specific terms: Phrases like “greater than,” “less than,” “equal to,” “total,” “difference” …
- Graphical representations: Diagrams or tables that complement mathematical texts.
Why Is Reading Comprehension Key in Solving Mathematical Problems?
Interpreting the Problem Statement
Reading comprehension allows students to break down the statements of mathematical problems. Often, difficulties lie not in numerical operations but in correctly interpreting keywords like “in total,” “remain,” or “distribute.”
Examples of Mathematical Vocabulary and Its Use
- Adverbs of Quantity: Words such as “more,” “less,” “enough,” “too much,” or “how many” form the basis for comparing and describing quantities. A simple question like “What is the most popular animal?” or “How many are there in total?” already connects language to arithmetic operations.
- Adverbs of Position: Terms like “in front,” “behind,” “above,” “below,” “between,” “right,” or “left” are essential for locating objects (useful for geometry and measurement) and fostering spatial skills
- Terms Related to Data and Probabilities: Concepts such as “frequency” or “counting table” help interpret graphs. Example: Reading pictograms to identify preferences.
- Basic Operations: Common verbs: “add,” “combine,” “increase” (addition); “remove,” “take away,” “decrease” (subtraction); “share,” “distribute” (division); and phrases like “each” (frequent in multiplication). Example: Problems like “Maria has 3 more pencils than Juan” reinforce comparisons.
Teaching Strategies for Parents and Educators
- Paraphrasing the Problem: Asking children to explain the problem in their own words helps verify their understanding.
- Highlighting Keywords: Identifying important terms like “total” or “remaining” guides students toward the correct operations.
- Using Concrete Materials: Physical objects (e.g., tokens, blocks) help visualize abstract problems.
- Polya’s Method: A structured method that guides children through problem-solving in four steps:
- Understand the Problem: Read it multiple times. Highlight keywords and questions. Identify known and unknown data.
- Plan a Solution: Relate data through diagrams or visual representations. Determine if addition, subtraction, multiplication, or division is required.
- Execute the Plan: Perform necessary calculations. Write a complete and clear answer, always including units (e.g., meters, kilograms, pieces).
- Verify Results: Check if the answer makes sense and aligns with the question asked. Encourage children to review their solutions and explain their reasoning.
Children often do a pre-reading of a problem, but by the time they reach the middle of the statement, they may no longer remember what they’ve read. This is why it’s crucial to get them accustomed to working on a “scratch paper” and motivate them to read the problem while dramatizing the questions as if it were a play. Buy a highlighter and encourage them to underline the important information. For example:
“Dad went to the market and bought 5 apples for 3 euros, 2 pears for 1 euro, and 4 bananas for 3 euros. How many pieces of fruit did he buy, and how much did the purchase cost?”
We create a diagram to promote comprehension. We use the “scratch paper” and underline the important details:
“Dad went to the market and bought 5 apples for 3 euros, 2 pears for 1 euro, and 4 bananas for 3 euros. How many pieces of fruit did he buy, and how much did the purchase cost?”
In this exercise, there are two questions. It is very common—and perfectly normal—for students to only notice one question and respond solely to it. Here, dramatization is highly recommended. Teach them to exaggerate the question.
“Dad went to the market and bought 5 apples for 3 euros, 2 pears for 1 euro, and 4 bananas for 3 euros. HOW MANY PIECES of fruit did he buy, and HOW MUCH did the purchase cost?”
Remember, this is a long-term process. We need to help children develop a habit of identifying keywords so they can truly UNDERSTAND the problem.
The Role of Teachers and Parents
Our role as teachers or parents is to provide activities and scenarios that encourage children to develop their own strategies and paths for learning. It’s not about giving students pre-processed solutions but guiding them so they can create their own.
To achieve this:
- Reformulate the question.
- Encourage classroom discussions.
- Dramatize problems.
- Use physical objects or manipulatives.
- Explore resources that help them learn how to ask themselves the right questions and solve problems effectively.
- Recommended Resource
Common Errors in Problem Solving
- Incorrect Interpretation: Reading too quickly without identifying key data.
- Wrong Operations: Failing to justify results with proper reasoning.
- Incomplete Answers: Not verifying whether the final response addresses all parts of the question.
- Calculation Mistakes: Especially in addition or subtraction involving carrying/borrowing.
The relationship between reading comprehension and solving mathematical problems is undeniable. As we’ve seen, mathematical language is a specific code that requires decoding skills. The ability to read, interpret, and understand mathematical texts is essential for translating words into symbols and operations. Reading well is like having a map that leads you to the solution.
Benefits of Strengthening Reading Comprehension in Mathematics:
- Greater Autonomy: Students who understand problems are better equipped to solve them independently.
- Increased Confidence: Understanding problems boosts students’ motivation and confidence in seeking solutions.
- Critical Thinking Development: Mathematical problem-solving fosters logical, analytical, and creative thinking.
- Improvement in Other Areas: Reading comprehension is a transversal skill that benefits all areas of learning.
In summary, reading comprehension is the foundation for building mathematical thinking. By developing strong reading skills, students will be better prepared to tackle mathematical challenges and achieve academic success!
