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Lesson by lesson podcasts for teachers of Illustrative Mathematics®.
(Based on IM 9-12 Math™ by Illustrative Mathematics®, available at www.illustrativemathematics.org.)
Alright. Ready to dive into something a little bit different today?
Speaker 2:Always up for a challenge. What do we got?
Speaker 1:We're tackling a pretty crucial concept, actually, causation versus correlation.
Speaker 2:Oh, getting into some deep waters there.
Speaker 1:Right. But it's way more interesting than it might sound at first. We're talking about those moments where you start to see through misleading statistics. Yeah. Like, you know those headlines you see sometimes that make you go, wait, Really?
Speaker 2:I see where you're going with this. It's about becoming a more critical thinker, not just in the classroom, but in everyday life. Right?
Speaker 1:Exactly. And we're using a 9th grade teacher's guide from illustrative math as our springboard today.
Speaker 2:9th grade, So we're going back to school on this one.
Speaker 1:Back to the basics. But trust me, this is relevant for everyone no matter how long it's been since you've cracked open an algebra textbook.
Speaker 2:Okay. I'm intrigued. What are these 9th graders up to that we should be paying attention
Speaker 1:to? They're going way beyond just plotting points on a graph.
Speaker 2:Beyond the scatter plots. What else is there?
Speaker 1:Well, they've already tackled the whole how strong is this connection thing. This lesson takes it a step further. It's about figuring out if one thing actually causes another to change.
Speaker 2:Okay. Now we're getting to the good stuff. That's a whole different ball game. Just because two things are connected doesn't mean one is causing the other. Right.
Speaker 1:And that's a mistake even adults make all the time.
Speaker 2:All the time. So how does this guide help students wrap their heads around something so complex?
Speaker 1:Well, they ease them in with a really relatable example, used cars.
Speaker 2:Used cars. Okay. I'm listening.
Speaker 1:It's all about figuring out if a factor, like mileage, for example, has a strong or weak influence on something like the price of a used car and whether that relationship is positive or negative. More mileage usually means a lower price. Right?
Speaker 2:Makes sense. That's a strong negative relationship, high mileage, lower price.
Speaker 1:Exactly. But I bet there are some curve balls in there too. Right?
Speaker 2:Oh, I'm sure there are. Otherwise, it wouldn't be a very good lesson, would it?
Speaker 1:Well, they even throw in things like the number of cup holders a car has, you know, to get the students thinking critically about which factors actually matter when it comes to setting a price.
Speaker 2:Yeah. So it's about looking beyond those surface level connections and really digging into what's driving the patterns we see. Love it.
Speaker 1:Exactly. It's about learning how to separate the meaningful connections from the random noise.
Speaker 2:Which is a skill we could all use a little more of these days. But even if you find a strong connection, does that automatically mean one thing causes the other?
Speaker 1:That is the $1,000,000 question, isn't it?
Speaker 2:It is. And I'm willing to bet most people would get it wrong.
Speaker 1:And that's where things get really interesting because this guy does a fantastic job emphasizing that correlation does not equal causation.
Speaker 2:Music to my ears. It's a crucial point that, like you said, even adults sometimes forget. Just because two things happen at the same time or change together doesn't mean one is causing the other.
Speaker 1:And the used car example is a really clever way to illustrate that point. Just because a car has a lot of cup holders doesn't mean it's gonna be worth more. There are probably other factors at play.
Speaker 2:Right. Like, maybe people who buy bigger, more expensive cars just happen to like having a lot of cup holders. It's not the cup holders themselves driving up the price.
Speaker 1:Exactly. Alright. So we've established that just because two things are connected, like cup holders and car prices, doesn't mean one actually causes the other.
Speaker 2:Right. Correlation doesn't equal causation. It's a simple phrase, but it trips people up all the time.
Speaker 1:So how does the lesson plan build on that idea? Where do we go from here?
Speaker 2:Well, it brings back those scatter plots. Remember those?
Speaker 1:Oh, yeah. Good old scatter plots. Classic algebra.
Speaker 2:But this time, instead of just looking at how strong a connection is, the students have to put on their thinking caps.
Speaker 1:Thinking caps on what kind of thinking are we talking about?
Speaker 2:They have to explain why they see the patterns they see on the scatter plots.
Speaker 1:Yeah.
Speaker 2:It's not enough to just notice a connection anymore. They've gotta dig deeper.
Speaker 1:Okay. I'm liking this. Gets them using those critical thinking skills. So what kind of examples does the guide use? Give me the juicy details.
Speaker 2:Alright. So they start with something pretty straightforward, rain and the number of people wearing raincoats.
Speaker 1:Okay. Yeah. That one seems pretty straightforward. Rain comes out, people grab their raincoats, cause and effect.
Speaker 2:Exactly. But then they introduce something a little trickier, book length and reading time.
Speaker 1:Yeah. I can see where that one might get some people thinking. Obviously, a longer book takes longer to read, but what's the underlying cause there?
Speaker 2:Right. It's not just about the connection itself. It's about understanding the why. And to really get students thinking about the why, they introduce this concept of 3rd variables.
Speaker 1:3rd variables. Those always trip me up a bit even back in my algebra days.
Speaker 2:They're sneaky little things, aren't they?
Speaker 1:They really are. So for those of us who haven't thought about algebra in a while, remind us what a third variable is and why it matters.
Speaker 2:Okay. So a third variable is basically like a secret agent, a hidden factor that can make it seem like 2 things are directly related, you know, cause and effect, when in reality, they're both being influenced by something else entirely.
Speaker 1:Okay. I think I'm with you, but give me an example just to make sure I'm not getting tricked by a third variable someone. Okay. So think about this. Ice cream sales and crime rates, both tend
Speaker 2:to go up in the summer. Right? Yeah. That's true.
Speaker 1:But you're not saying that ice cream causes crime, are you?
Speaker 2:Exactly. There's a third variable lurking in the shadows. In this case, it's probably something like hot weather. People eat more ice cream when it's hot, and they're also more likely to be outside and, well, interacting in ways that could lead to more crime.
Speaker 1:Okay. Yeah. That makes a lot more sense. The heat is the real culprit, not the poor ice cream cone.
Speaker 2:Exactly. But it's easy to see how you might jump to the wrong conclusion if you're not careful. And that's what this lesson is all about, learning how to spot those sneaky third variables.
Speaker 1:So how do you do it? Yeah. How do you teach someone to be a third variable detective?
Speaker 2:Well, the lesson plan gives another really good example. This one involves height and test scores. You might see a connection there. Taller kids tend to score higher on tests or something like that, but is height really the cause?
Speaker 1:I'm gonna guess no. So what's the third variable playing tricks on us this time?
Speaker 2:Think about it. What else could be influencing both height and test scores?
Speaker 1:Well, maybe something like age. Bingo.
Speaker 2:Older kids are generally taller, and they've also had more schooling, so naturally they might do better on tests.
Speaker 1:It all makes sense now, those tricky third variables. But seriously, that's such a good example because it seems so obvious once you point it out. But without that critical thinking, it's easy to see how you might misinterpret the data.
Speaker 2:It is, and that's why this concept is so important, not just in math class, but in life. Being able to spot those 3rd variables can help you cut through so much misinformation. Whether you're reading news articles, scrolling through social media, or just trying to make sense of the world around you.
Speaker 1:Like a superpower. Yeah. The power of critical thinking.
Speaker 2:Exactly. And this lesson plan is like a crash course in how to develop that superpower.
Speaker 1:So we've talked about identifying those hidden factors, those third variables. What's next? How do students really solidify their understanding? What does the illustrative math guide suggest?
Speaker 2:Well, they take it a step further with a really cool activity called get this stronger and clearer each time.
Speaker 1:Stronger and clearer each time. I like the sound of that already. Tell me more.
Speaker 2:So instead of just relying on those preselected examples, you know, rain and raincoats, the students have to come up with their own examples of causal and non causal relationships.
Speaker 1:Oh, I love that. It's like they graduate from detective school, and now they get to go out into the world and solve their own mysteries.
Speaker 2:Exactly. And to help them really solidify their understanding, the guide provides this great example about snail shells.
Speaker 1:Snail shells. Okay. You're gonna have to explain this one.
Speaker 2:So, basically, a snail's weight actually causes its shell size to change. A heavier snail needs a bigger house. Right?
Speaker 1:That's actually really interesting, and it makes perfect sense. So even in something as seemingly random as snail shells, there can be a clear cause and effect relationship if you know what to look for.
Speaker 2:Precisely. And that's what this activity helps students learn how to do. It's about training your brain to think like a scientist, you know, to look beyond those initial assumptions and really analyze what's going on.
Speaker 1:To look for those third variables hiding in plain sight.
Speaker 2:You got it. And that's a skill that will serve these students well long after they've left algebra class.
Speaker 1:Okay. So we've gone from used cars to snail shells.
Speaker 2:Mhmm.
Speaker 1:And we've talked about those sneaky third variables. What's the big takeaway here? Why does all this matter? Why should we care about causation versus correlation?
Speaker 2:Well, the lesson wraps up by really highlighting why this is also important. It points out that recognizing the difference between correlation and causation, it's like having a superpower, especially in today's world. You know?
Speaker 1:Okay. I like where you're going with this superpower analogy. Yeah. So how does that play out in the real world? Give me an example.
Speaker 2:Alright. Well, the guide uses this really clever example about sugar and happiness. You've probably seen those studies. Right? The ones that say there's a connection.
Speaker 1:Oh, absolutely. Sugar makes you happy. Everyone knows that. Yeah. But I think we all know deep down that it's a little more complicated than that.
Speaker 2:Exactly. Just because you see a connection doesn't mean sugar is this magic key to happiness.
Speaker 1:Right. Like, maybe people eat cake at birthday parties, so they're happy about the party, not the sugar rush from the frosting.
Speaker 2:There you go. It's a classic example of correlation not equaling causation.
Speaker 1:So what I'm hearing is it's about taking a pause before we jump to conclusions. Just because two things happen at the same time or change together doesn't mean one is causing the other. There could be something else going on.
Speaker 2:100%. And what I love about this lesson is it doesn't just give the students the answers. Right? It gives them the tools to think critically about all the information that's thrown at them every day.
Speaker 1:That's what's so great about this lesson plan. It's like, yeah, we're talking about algebra, but it's really about so much more than that. It's about giving students the skills to be savvy consumers of information, not just number crunchers, but critical thinkers.
Speaker 2:Well said. And those critical thinking skills, they're more important now than ever.
Speaker 1:So true. So to wrap things up, it seems like this deep dive into causation versus correlation has revealed something pretty profound. It's not just about acing that next algebra test, but really about understanding the world around us. Right. And maybe making better sense of all the information out there.
Speaker 2:Clint have said it better myself. And a big thanks to the authors of Illustrative Math for creating such an insightful lesson plan. It's a great example of how powerful just a little bit of critical thinking can be.
Speaker 1:Absolutely. And all our listeners out there, next time you see one of those headlines, you know the ones, this one thing causes all your problems. Just remember what we talked about today. Think about those sneaky third variables, and don't be afraid to ask yourself, is there more to the story?
Speaker 2:Until next time.