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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.)
Hey, everyone, and welcome back. Today, we're doing a deep dive into a lesson plan from illustrative math.
Speaker 2:Sounds good.
Speaker 1:And Yeah. It's all about bringing technology into teaching algebra.
Speaker 2:Mhmm.
Speaker 1:And I'm really excited about this one because I think it's something that a lot of teachers are gonna find really useful.
Speaker 2:Definitely.
Speaker 1:So the lesson is called technological graphing, and it's lesson 9 from illustrative math.
Speaker 2:Okay. Have you
Speaker 1:had a chance to take a look? I
Speaker 2:have. Yeah. I actually just looked at it this morning, and I gotta say I'm really impressed. Yeah? It's really well put together, and I think it's gonna be a game changer for a lot of teachers and their students.
Speaker 1:I think so too. Yeah. And you know what I really like about it?
Speaker 2:What's that?
Speaker 1:It's not just about teaching kids how to use technology
Speaker 2:Right.
Speaker 1:Which is important, of course.
Speaker 2:Of course.
Speaker 1:But it's really about using technology to help them understand the math more deeply.
Speaker 2:Exactly. That's what's so exciting about this lesson, I think. It's not just about using computers for the sake of using computers. It's about leveraging the power of technology to make these abstract algebraic concepts more concrete and visual for students.
Speaker 1:And I think that's so important because especially, we were talking about things like data analysis and statistics.
Speaker 2:Totally. I mean, think about it. Our students today, they're growing up in a world that's just inundated with data.
Speaker 1:It's true.
Speaker 2:And we need to equip them with the skills to not just consume that data Yeah. But to actually analyze it, understand it, and use it to make informed decisions.
Speaker 1:I completely agree. And I think this lesson does a really good job of laying the groundwork for those skills.
Speaker 2:Absolutely.
Speaker 1:So the lesson focuses on using technology, specifically Jo Bobra, for graphing and analyzing data.
Speaker 2:Oh, I like Joobra.
Speaker 1:Yeah. It's a great tool, and it's free for educators.
Speaker 2:Google's always a plus.
Speaker 1:Which is awesome. Right. And it covers sections 9.1 through 9.4 of the illustrative math curriculum.
Speaker 2:Okay. Great. And what are some of the key concepts that the lesson covers?
Speaker 1:So it starts off by having students enter data into a spreadsheet Okay. Which seems pretty basic.
Speaker 2:Right? But you know what? Yeah. Even that can be a little tricky for students who haven't had a lot of experience with spreadsheets.
Speaker 1:Oh, absolutely. Yeah. I remember when I first started using spreadsheets, I was so lost. Right. Like, where do I even begin?
Speaker 2:I know. And it's easy to forget that what seems intuitive to us
Speaker 1:Totally.
Speaker 2:Might not be so obvious to our students.
Speaker 1:Especially those who are encountering this kind of technology for the very first time.
Speaker 2:Exactly. And that's why I appreciate that the lesson takes the time to really walk students through the basics Okay. Like how to navigate the grid, how to select cells, how to enter data, all of that.
Speaker 1:Yeah. Yeah. Those little things make a big difference.
Speaker 2:They really do. And it even goes into detail about the coordinate system of the spreadsheet.
Speaker 1:Oh, like cells a 1, a 5, that kind of thing.
Speaker 2:Exactly.
Speaker 1:That's smart. Yeah. I think sometimes we assume that students just inherently understand that, but it's not always the case.
Speaker 2:No. It's not. Yeah. And it's such a fundamental concept for understanding how spreadsheets work.
Speaker 1:Absolutely. It's like the foundation upon which everything else is built. Right? So it's really important to make sure that students have a solid grasp of that before moving on to more complex concepts.
Speaker 2:Definitely. And I'm curious. How does the lesson build upon that foundation once students have a handle on the basics of spreadsheet navigation and data entry?
Speaker 1:So once they've got that down Okay. The lesson introduces them to the power of formulas Oh. Like, how to use formulas to calculate things like sums, averages, and other statistical measures.
Speaker 2:Now that's where things start to get really interesting.
Speaker 1:Right. And this is where JOBRIS' capabilities really shine, I think.
Speaker 2:Totally. And it's not just about the formulas themselves. Right? It's about understanding the why behind them.
Speaker 1:Exactly. Like, what do these calculations actually tell us about the data?
Speaker 2:Right. And I think that's something that's often overlooked in traditional math instruction. Yeah. We get so caught up in the how to that we forget to emphasize the why.
Speaker 1:Totally. And I think that's one of the things that makes this lesson so valuable.
Speaker 2:Me too. It's about making those connections between the abstract and the concrete, the numbers and their real world significance. Absolutely.
Speaker 1:And I bet George Rebbe makes it even more engaging for students to explore those connections visually.
Speaker 2:It really does. Yeah. It has all these amazing graphing features that allow students to see the data in different ways. Like, they can create histograms and block plots and dot plots.
Speaker 1:Wow. So they get to experiment with different visual representations of the same dataset.
Speaker 2:Exactly. And I think that's so powerful because it helps them to Yeah. Understand how different visualizations can reveal different aspects of the data.
Speaker 1:It's like giving them a toolkit
Speaker 2:Yes.
Speaker 1:And teaching them how to choose the right tool for the job.
Speaker 2:And that's a really important skill for them to develop.
Speaker 1:Absolutely. It's about being able to critically analyze data and choose the most effective way to present it.
Speaker 2:I completely agree. So, yeah, I'm really excited about this lesson.
Speaker 1:Me too. Yeah. It sounds like a really comprehensive and engaging way to introduce students to the power of technology for data analysis.
Speaker 2:It really is. And I it's a great example of how we can use technology to make math more meaningful and relevant for our students. Couldn't have said it better myself.
Speaker 1:And the best part is it's not just about plugging in numbers and hoping for the best. Right.
Speaker 2:Like, we don't want them to become little robots just blindly following formula. Exactly. We want them to really understand blindly following formula. Exactly.
Speaker 1:We want them to really understand what those numbers represent, what those graphs are telling us. Absolutely. It's all about interpretation. Right? Mhmm.
Speaker 1:Making sense of
Speaker 2:those patterns and trends. And that's where the
Speaker 1:lesson really digs
Speaker 2:deep into those
Speaker 1:key statistical concepts like mean, median, interchordal range.
Speaker 2:Yes. Those are the building blocks of data analysis.
Speaker 1:They really are. And I I think it's brilliant how the lesson incorporates these concepts into the technology activities.
Speaker 2:Oh, absolutely. It's one thing to memorize definitions
Speaker 1:Right.
Speaker 2:But it's another thing entirely to actually apply them to real data to see those concepts come to life.
Speaker 1:And that's where GeoGebra can be such a powerful tool because it allows students to visualize those concepts in a way that just isn't possible with traditional pencil and paper methods.
Speaker 2:Totally. I mean, think about histograms, for example. Yeah. They can be tough for some students to grasp when you're just drawing them on the board.
Speaker 1:That's true.
Speaker 2:But with Jadobra, they can actually see the data being grouped into those bars. They can experiment with different bin sizes.
Speaker 1:And they can see how those changes affect the shape of the histogram.
Speaker 2:Exactly. And that kind of dynamic exploration, that's where the real learning happens.
Speaker 1:I totally agree. And it's not just histograms either.
Speaker 2:Right.
Speaker 1:The lesson also covers box plots, which are amazing for visualizing things like spread and outliers.
Speaker 2:Oh, yeah. Box plots are so useful for identifying those extreme values that can really skew our understanding of the data.
Speaker 1:They really are. And again, Jadabro makes it so easy for students to create and manipulate those box plots to see how the data is distributed.
Speaker 2:And don't forget about dot plots.
Speaker 1:Oh, yes. Dot plots are great too.
Speaker 2:They're so simple Yeah. Yet so powerful for showing the distribution of data, especially with smaller data sets.
Speaker 1:And they're really easy for students to understand, which is always a plus.
Speaker 2:Absolutely. So we've got histograms, box plots, dot plots. It's like a data visualization buffet.
Speaker 1:I love it. And I think that's one of the things that makes this lesson so engaging for students.
Speaker 2:Oh, for sure. It's not just about crunching numbers anymore.
Speaker 1:Right.
Speaker 2:It's about exploring data, visually experimenting with different representations.
Speaker 1:And really digging into the story that the data is telling us.
Speaker 2:Exactly. And I love that the lesson doesn't just stop at creating the
Speaker 1:graphs.
Speaker 2:It goes a step further and has students analyze and interpret those graphs, asking those higher order thinking questions.
Speaker 1:Like, what does the shape of this histogram tell us about the distribution of the data?
Speaker 2:Exactly. Or what can we infer about the relationship between these two variables based on this scatterplot?
Speaker 1:Those are the kinds of questions that really get students thinking critically about the data.
Speaker 2:Absolutely. And it helps them to see that data analysis is more than just a set of procedures.
Speaker 1:Right.
Speaker 2:It's a way of thinking, a way of understanding the world around us.
Speaker 1:I love that, and I think this lesson does a fantastic job of conveying that message.
Speaker 2:I agree. It's a great example of how we can use technology not just to teach math, but to really empower students to become critical thinkers and problem solvers.
Speaker 1:Absolutely. So if you're looking for a way to spice up your algebra lessons and give your students the tools they need to thrive in our data driven world.
Speaker 2:This lesson is definitely worth checking out.
Speaker 1:I completely agree. And it's not just about the fancy graphs and calculations. Right?
Speaker 2:Right.
Speaker 1:There's a real emphasis on making sure students can actually explain their thinking, which is so crucial.
Speaker 2:Oh, absolutely. It's one thing to get the right answer, but it's another thing entirely to be able to articulate why that answer makes sense in context.
Speaker 1:Exactly. And I noticed the lesson emphasizes this analyze it routine, encouraging students to justify their reasoning.
Speaker 2:Yeah. That's a really powerful strategy because it forces them to slow down to really think about the why behind the what.
Speaker 1:It's like that old saying, the best way to learn something is to teach it.
Speaker 2:Right. When you have to explain something to someone else, it really crystallizes your own understanding.
Speaker 1:Exactly. And I think that's especially true when we're talking about data analysis because it's not always intuitive.
Speaker 2:No. It's not. It takes practice, and it takes being able to articulate your thought process.
Speaker 1:And I like that the lesson provides opportunities for students to do that both in writing and through discussion.
Speaker 2:Yeah. That's so important because not everyone learns the same way.
Speaker 1:Right. Some students might be better at expressing themselves in writing.
Speaker 2:Exactly. While others might thrive in a more collaborative setting where they can bounce ideas off of their peers.
Speaker 1:And I think that's one of the things that makes this lesson so adaptable.
Speaker 2:Oh, absolutely. You can easily differentiate the activities to meet the needs of your students.
Speaker 1:Exactly. And you can even extend the activities by having students create their own datasets or research real world examples.
Speaker 2:Oh, I love that idea because that's when it really becomes relevant for them. Right.
Speaker 1:When they can see the connections between the math they're learning in the classroom and the world around them.
Speaker 2:Exactly. And speaking of real world connections, I was really intrigued by the lessons focused on outliers.
Speaker 1:Oh, yeah. That was interesting. It even encourages teachers to create some what if scenarios with students to explore how outliers can impact the data.
Speaker 2:Right. Like, what happens if we add a really extreme value to this dataset? Does that change our conclusions?
Speaker 1:Exactly. And it gets them thinking critically about the data collection process itself.
Speaker 2:Right. Because sometimes outliers are just errors.
Speaker 1:Right.
Speaker 2:But sometimes they're actually the most interesting and important data points.
Speaker 1:It's true. They can be the key to unlocking new insights or challenging our assumptions.
Speaker 2:Absolutely. So it's important for students to understand how to identify and interpret outliers.
Speaker 1:I completely agree, and I think this lesson does a great job of introducing those concepts in a really accessible and engaging way.
Speaker 2:Yeah. I was really impressed with how the lesson was seamlessly integrated technology, real world applications, and those core statistical concepts.
Speaker 1:Me too. It's a really well rounded approach to teaching data analysis.
Speaker 2:It really is. And I think it's a great reminder that technology isn't just a tool for computation.
Speaker 1:Right.
Speaker 2:It can also be a powerful tool for exploration and discovery.
Speaker 1:Absolutely. Well, I think we've covered a lot of ground today.
Speaker 2:We have. This has been a really insightful deep dive.
Speaker 1:It really has. And I hope our listeners are feeling inspired and equipped to bring these ideas into their own classrooms.
Speaker 2:Me too. And remember, you don't have to be a tech expert to make this work.
Speaker 1:Exactly. Just start small, experiment, and have fun with it.
Speaker 2:That's what it's all about.
Speaker 1:Well said. So to all of you listening, thank you for joining us on this deep dive into the world of technological graphing with illustrative math.
Speaker 2:It's been a pleasure.
Speaker 1:Until next time. Happy teaching.