19 Pitfalls of Mathematical Communication
When communicating mathematics, it is essential to remember that knowing mathematics and are different skills. A mathematically correct explanation can still be ineffective if it is inaccessible, poorly structured, or mismatched to the audience. Here are a few pitfalls to be wary of:
Skipping steps
A common pitfall is assuming knowledge that a learner has - just because something is obvious to you, does not necessarily mean it is immediately obvious to the learner.
Example: Writing \(x^2 - 9 = (x-3)(x+3)\) may be sufficient for an experienced mathematician, but a learner may not understand why this factorisation works.
Always introduce unfamiliar notation or terminology. Always identify the prerequisite knowledge. If uncertain whether your learner has the required contextual understanding or comprehend certain steps, always ask and clarify.
Overusing mathematical jargon
Using precise mathematical language is important, and unnecessary terminology can create barriers to comprehension.
Example: A sentence like “consider the bijective mapping induced by the isomorphism …” may make sense to an experienced learner, but would confuse and overwhelm learners encountering the concept for the first time and otherwise unfamiliar with the technical terms.
Good means using mathematical vocabulary deliberately and concisely.
Overloading the audience
Similarly, trying to communicate too much mathematics at once can overwhelm the learner and increase .
Example: Too many examples, excessive notation, lengthy explanations, complicated diagrams, introducing many new concepts simultaneously.
Effective considers not only what information is presented, but also how much information the learner is able to process and grasp.
Explaining what, not why
A common mistake is using an explanation that only instructs a learner on what to do, as opposed to helping them develop of why the method works.
Example: “Multiply both sides by 3, then subtract 5.” is a procedural explanation, while “multiply both sides by 3 preserves the equality because we are performing the same operation on both sides” explains the behind the step.
Explaining the underlying reasoning allows the learner to develop mathematical intuition, as opposed to simply memorizing methods.
Assuming one explanation will work for everyone
Different learners possess different needs, requiring different representations, examples, and levels of . Mathematical ideas can often also be represented in multiple ways, from verbally, to graphically and computationally. Using only one representation may prevent some learners from accessing the underlying concept.
Effective and accessible requires .
Failing to check whether communication has worked
Perhaps the most important pitfall is assuming that an explanation was successful simply because the communicator thought it made sense.
After communicating an idea, reflect upon ‘what evidence do I have that the learners understood it’. This could involve asking learners to explain an idea in their own words, applying it to a new example, or asking a learner to identify an error. This also strengthens dialogue between the communicator and the learner, as opposed to purely talking at the learner.
Correcting mistakes without exploring them also hinders communication, as a wrong answer can provide valuable information about a learner’s thinking. Simply dismissing a wrong answer, for instance by saying “no, that’s wrong” ends the mathematical conversation. Rather, a trigger question such as “tell me how you got that answer” can reveal and create opportunities for .