Mathematics often involves ideas that we can’t physically touch or see. These abstract concepts can be particularly challenging for visual learners, individuals who thrive when information is presented graphically or spatially.
If a student understands best through charts, diagrams, and demonstrations, how can they grasp seemingly invisible mathematical ideas?
This post explores why visualizing maths is important and why visual learners with their personalized tutors can bridge the gap between seeing and understanding even the most abstract concepts.
Understanding the Visual Learner in Maths
Visual learners process and retain information most effectively when they can see it. In a typical maths class, which might rely heavily on lectures, symbolic notation (numbers and letters), and verbal explanations, these learners can sometimes feel lost.
They might excel in geometry where shapes are obvious, but struggle when:
- Concepts become purely symbolic (like in algebra).
- Multi-step problems require mental tracking without visual aids.
- Understanding relationships between abstract quantities is needed (e.g., ratios, functions).
For these students, simply hearing or reading about abstract concepts isn’t enough. They need to see them in action.
The Power of Visualizing Maths
Visualizing maths is the practice of translating mathematical ideas, including abstract concepts, into visual representations. Beyond drawing pictures, it involves using:
- Diagrams and charts
- Graphs and number lines
- Colour-coding
- Physical manipulatives (like blocks or tiles)
- Mind maps
- Digital simulations and models
The benefits are significant:
- Deeper Comprehension: Visuals make abstract concepts more concrete and relatable.
- Improved Memory: Visual information is often easier to recall.
- Enhanced Connections: Learners can see how different mathematical ideas link together.
- Reduced Anxiety: Making math visible can make it feel less intimidating for visual learners.
While visualizing maths can benefit all students, it’s an essential toolkit for visual learners.
How Tutoring Makes Visualizing Maths Effective
A classroom teacher managing many students might find it difficult to consistently provide tailored visual aids. This is where one-on-one or small-group tutoring shines, offering unique advantages for visualizing maths:
1. Personalized Strategies
A tutor can quickly identify a student’s visual learning preference and adapt their teaching methods accordingly. They aren’t bound by a single curriculum delivery style and can focus entirely on the visual learner’s needs.
2. Hands-On Tools and Manipulatives
Tutors can effectively utilize tools that bring abstract concepts to life. They have the time and focus to guide the student in using;
- Base-ten blocks for place value
- Fraction tiles or circles for comparing and operating with fractions
- Algebra tiles for understanding polynomials
- Geoboards for exploring geometric properties
3. Custom Diagrams and Models
Need to explain solving equations? A tutor can draw a balancing scale on the spot. Struggling with numbers? A quick number line or thermometer diagram can be created instantly. This responsive visualizing maths approach addresses misunderstandings in real time.
4. Technology Integration
Tutors can leverage digital tools perfect for visual learners:
- Interactive graphing calculators (like Desmos)
- Dynamic geometry software (like GeoGebra)
- Educational apps and simulations that model abstract concepts visually.
Bridging the Gap to Abstract Concepts
Importantly, tutors use these visual tools not just as aids, but as bridges. They help the visual learner connect the concrete representation (like blocks) to the symbolic notation (like the written equation), gradually building comfort with abstraction.
Visualizing Abstract Concepts in Tutoring
How does this look in practice? Here are ways tutors help visual learners by visualizing maths;
1. Algebra (Variables)
- Concept: Using ‘x’ to represent an unknown value.
- Visualization: Starting with empty boxes or containers in equations (__ + 3 = 7) before introducing ‘x’. Using physical balancing scales or drawings to show that whatever you do to one side of an equation, you must do to the other.
2. Fractions
- Concept: Understanding fractions as parts of a whole or points on a number line.
- Visualization: Extensive use of fraction bars/strips and circles to compare sizes (e.g., visually showing why 1/2 is bigger than 1/3). Placing fractions on a number line alongside decimals and percentages to show equivalence.
3. Negative Numbers
- Concept: Numbers less than zero and operations involving them.
- Visualization: Using a vertical thermometer model for temperature changes. Employing number lines that clearly extend left of zero. Using analogies like money (debt vs. assets) or movement (steps forward vs. backward).
4. Geometry Proofs
- Concept: Logically demonstrating geometric truths.
- Visualization: Using color-coding to highlight corresponding angles or sides. Employing dynamic software where students can manipulate shapes and see properties remain constant. Breaking down complex diagrams into simpler parts.
Tips for Parents and Tutors Supporting Visual Learners
- Encourage Drawing: Ask the student to draw the problem or concept.
- Use Graph Paper: Helps organize numbers, equations, and graphs neatly.
- Colour-Code Notes: Use different colours for different steps, concepts, or variables.
- Seek Visual Resources: Look for apps, websites (like Khan Academy with its visual explanations), and books that emphasize diagrams and visual explanations.
- Make Real-World Connections: Point out geometry in architecture, graphs in news reports, fractions in recipes.
- Communicate: Ensure teachers/tutors know about the student’s visual learning preference.
Making Maths Visible
Math doesn’t have to be purely abstract. Through the deliberate practice of visualizing maths, even complex ideas can become clear and understandable, especially for visual learners.
Tutoring provides an invaluable, personalized space where these techniques can be tailored and applied effectively, helping students not only conquer abstract concepts. It will also build lasting confidence and appreciation for mathematics. By making math visible, we make it accessible.
