Detangling similar concepts

Hey 👋

Hope your week is going well and that you’re been exploring the power of non-examples (alongside examples). Today, we’re wrapping up this series with a related idea around reducing student confusion…

Big idea 🍉

When we teach our students concepts that are similar, they can easily end up confusing them. Why exactly does this happen, and what can we do about it? Let’s dive in:

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When we first introduce a new concept to our students, it’s not always clear to them where the concept ends and its context begins. As a result, aspects of the context often get encoded in their understanding along with aspects of the concept. Aka, confusable categories.

This can lead to conceptions which are both flawed—for example, students who initially see triangles presented in a certain orientation often think this is a defining feature of a triangle—and resistant to transfer—for example, many students can often happily rearrange formulae in a math(s) classroom but struggle when asked to do the same in a science lab.

However, when we first encode a new concept, not only can it easily get mixed up with the local context, but it can also get mixed up with any similar concepts being introduced around the same time.

For example, if we introduce the concepts of area and perimeter close together in our teaching, it is entirely possible that students will mix up aspects of each when encoding their understanding.

When asked to explain how to find the area of a rectangle, students taught this way will often say something like: “you multiply or add the sides, but I can’t remember which”.

We can reduce the opportunity for our students to confuse similar concepts by simply not teaching them together to begin with. And instead, helping students to develop a robust understanding of each one independently, ideally, with a gap in between, before pulling them together to highlight their differences and unpack their relationship.

Now, this might feel like an obvious strategy, but many curricular schemes and materials don’t heed this principle, and so unless we are intentional about what we teach and when, we can easily fall prey to less effective practices.

Note that this is not limited to math(s). Any concepts which overlap and are often confused—such as climate and weather in science or conjunctions and transitions in English—are worthy candidates for initial separation.

Challenge → How intentional is your sequencing of similar concepts? Identify some concepts your students often confuse and explore ways you might initially separate them even more in future.

Little links 🥕

• On topic → Check out these studies on similarity and difference and the cognitive costs of context, and this blog by Bruno Reddy where I first encountered the idea of separating similar concepts.

• On trend → Fab new paper on strategies for helping students make sense of ideas (‘generative learning’), and another fresh one contrasting novice/expert teacher use of content knowledge during pedagogical reasoning.

Stay crunchy.

Peps 👊

PS. I ran a poll last week on whether folks wanted to hear about the origin story of Snacks. 75% of you said yes… BUT only as long as it didn’t detract from the core stuff. And so, I’ll throw together a short vid in the next few weeks and add it as a small optional link at the end.