Hey š

Hope your week is going well and that youāre been exploring the power of *non-examples* (alongside examples). Today, weāre wrapping up this series with a related idea around reducing student confusionā¦

## Big idea š

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? Letās dive in:

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When we first introduce a new concept to our students, itās 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.

This can lead to conceptions which are both *flawed*āfor example, students who initially see triangles presented in a certain orientation often think this is a defining feature of a triangleāand resistant to *transfer*āfor 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.

"The learning of an object is not possible if we cannot first discern the object from its context."

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: āyou multiply or add the sides, but I canāt remember whichā.

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 donāt 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 confusedāsuch as *climate and weather* in science or *conjunctions and transitions* in Englishāare worthy candidates for initial separation.

**Challenge ā** 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.

**Summary**

ā¢ When we first learn a new concept, we can easily get it mixed up with similar concepts being introduced around the same time.

ā¢ To avoid this, we can teach similar concepts separately, before bringing them back together to further refine understanding.

ā¢ This might seem obvious, but many curricular materials donāt incorporate this principle.

## Little links š„

**On topic ā**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 ā**Fab new paper on strategies for helping students make sense of ideas (āgenerative learningā), and another fresh one contrasting novice/expert teacher use of content knowledge during pedagogical reasoning.

Stay crunchy.

Peps š

PS. I ran a poll last week on whether folks wanted to hear about the origin story of *Snacks*. **75% of you said yesā¦** BUT only as long as it didnāt detract from the core stuff. And so, Iāll throw together a short vid in the next few weeks and add it as a small optional link at the end.