Introduction to Communicating Mathematics

In the IB MYP, being a "mathematician" is about more than just finding the right answer. It is about how you share your ideas, explain your steps, and prove your findings to others. This is what we call Criterion C: Communicating.

Think of mathematical communication as a bridge. On one side, you have a complex problem; on the other side, you have your solution. The bridge is the notation, representation, and reasoning you use to get there. If the bridge is weak, people won't understand your work, even if your answer is correct!

1. Mathematical Notation: Using the "Secret Code"

Mathematics has its own universal language. Using the correct symbols (notation) makes your work clear and professional. It also helps you avoid long, messy sentences.

Common Notations You Must Know

For your eAssessments, you are expected to use specific notations correctly. Here are the most common ones used in the MYP:

  • Functions: Instead of just writing "the equation," we use function notation like \(f(x) = 2x + 3\) or \(f: x \to 2x + 1\).
  • Probability: We use \(P(A)\) to mean "the probability of event A." For combined events, we use \(P(A \text{ and } B)\) or \(P(A \text{ or } B)\).
  • Sets: When working with groups of numbers, we use symbols like \(\cup\) (union/all together), \(\cap\) (intersection/overlap), and \(\in\) (is an element of).
  • Algebra: Always write your final rules clearly, such as \(y = -0.05x^2 + x + 6\).

Quick Tip: Don't worry if these look like a different language at first! Just remember that \(\implies\) is a great symbol to use between steps. It means "this leads to" or "therefore."

2. Forms of Representation

Communication isn't just about symbols; it’s about how you show your data. A good mathematician uses different "views" to explain a single idea. The four main types are:

A. Tabular (Tables)

Tables are perfect for Investigating Patterns (Criterion B). They help you organize "Inputs" (\(x\)) and "Outputs" (\(y\)) so you can see what is changing.

B. Graphical (Graphs)

A graph tells a visual story. It shows you the "shape" of a relationship—is it a straight line (linear) or a curve (quadratic)? Note: Always label your axes (\(x\) and \(y\)) and include a scale!

C. Symbolic (Algebraic Rules)

This is when you turn a pattern into a general rule or formula. For example, after looking at a table, you might communicate the relationship as \(n^{th} \text{ term} = 3n + 2\).

D. Diagrammatic (Diagrams)

Sometimes a picture is the best way to communicate. This includes:
- Venn Diagrams: To show relationships between sets.
- Tree Diagrams: To show sequences of events in probability.
- Geometric Sketches: To show angles, side lengths, or 3D shapes.

Key Takeaway: In an exam, try to use at least two different representations (like a table and a graph) to explain your answer. This shows you have a deep understanding!

3. Mathematical Reasoning: Explaining the "Why"

Reasoning is the logical "glue" that holds your communication together. It is how you justify why you chose a specific method or why a pattern works.

How to show good reasoning:

1. Show your steps: Never jump straight from the question to the answer. Write down the intermediate steps.
Example: To solve \(2x + 5 = 11\):
\(2x = 11 - 5\)
\(2x = 6\)
\(x = 3\)

2. Use "Connecting Words": Use words like "Because...", "Therefore...", or "Since the pattern increases by 3 each time, the rule must be...".

3. Verify and Justify: If you find a rule, test it with a new number to verify it. Then, explain why it works based on the structure of the pattern (this is justification).

Common Mistake to Avoid: Don't just describe what you did ("I added 5, then divided by 2"). Explain why you did it ("To isolate the variable \(x\), I performed the inverse operation...").

4. Accuracy and Conventions

Communication also includes being precise. In the MYP, you need to follow certain "rules of the road":

  • Degree of Accuracy: Unless told otherwise, give your answers to a sensible level of accuracy (usually 3 significant figures).
  • Units: If a question is about meters or seconds, your answer must include \(m\) or \(s\).
  • Estimation: Sometimes, communicating that an answer is "roughly" a certain amount using the \(\approx\) symbol is better than using a long, confusing decimal.

Quick Review Checklist for Criterion C

Before you finish a math task, ask yourself:

[ ] Did I show all my working out clearly?
[ ] Did I use the correct mathematical symbols (like \(f(x)\), \(\cup\), or \(\implies\))?
[ ] Did I use different representations (Tables, Graphs, Formulas)?
[ ] Are my axes labeled and my units included?
[ ] Did I explain why my answer makes sense in the context of the problem?

Remember: You are telling a story with numbers. Make sure it's a story that someone else can follow!

Next Steps: To see how this communication is used to find rules, check out the chapter on "Investigating Patterns: Selecting Techniques and Describing Rules."