Sequencing examples

Using multiple examples to build depth

Author

Peps Mccrea
27 Apr

Hey đź‘‹

How’s your week going? Did you manage to squeeze in (m)any asks for advice? This week we’re pivoting to a new topic: using examples in explanation…

Big idea 🍉

As teachers, one of our primary tasks is to help students grasp new concepts. This can be particularly tricky when dealing with abstract or highly technical topics. In such situations, one of the most effective tools at our disposal is a carefully designed sequence of examples. Let’s dive in:

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Examples are useful because some concepts can be difficult to convey adequately through words alone. Sometimes, definitions require technical vocabulary or involve other abstract ideas that can be hard for students to grasp.

Take this this definition of a triangle: a closed, 2-dimensional shape with three edges and three vertices.

If we relied solely on this definition, students might easily end up developing shallow or distorted understanding. Such as thinking that all triangles must have at least 2 sides of equal length. Or that the 'bottom side must always be on the flat'.

Misconceptions often arise from a lack of exposure to diverse examples. If students are presented with a definition of a triangle and only exposed to isosceles triangles with horizontal bases, then it’s entirely reasonable for such misconceptions to arise.

"We understand new things in the context of what we already know."

— Daniel Willingham

To harness the full power of examples, we can:

  1. Identify the critical and non-critical features of the concept we are teaching. For triangles, critical features include having three straight sides and being a closed shape, and non-critical features include side lengths, angle similarity, and orientation.

  2. Present multiple examples that ideally change only one non-critical feature at a time (or as few as possible). This helps draw attention to how a concept can change and yet still remain an instance of that concept. See image for example.

  3. Perceiving differences can be hard, especially when it comes to the subtler variations required for more refined understanding. Where possible, make it easier for your students to spot the difference by presenting examples side-by-side.

  4. Introduce definitions to add precision to student understanding after they have begun to develop an intuitive understanding of the concept.

When we provide multiple examples in ways that orient student attention to critical features, we help students develop a deeper and more robust understanding of a concept, and increase the likelihood of future knowledge transfer.

Note that using examples is not limited to maths(s)—it can be a valuable strategy for any topic targeting abstract or technical understanding. Such as the appropriate use of apostrophes or the position of verbs in a sentence.

That said, providing examples is not necessary or even appropriate for every concept, especially where concrete definitions can be given (partly because careful exemplification can be time consuming).

Challenge → How intentionally do you approach your use of examples? Consider an abstract concept you are due to teach, put some extra thought into your sequencing of examples, and see how it goes.

Summary

• Examples are powerful tools for helping students grasp abstract or technical concepts.

• When we provide multiple examples that highlight critical and non-critical features, we build deeper and more transferrable understanding.

• In relevant cases, definitions are more useful when introduced after exemplification.

Till next time.

Peps đź‘Š