Playing Sports: Subconscious Quadratics?

Playing Sports: Subconscious Quadratics?

An analysis of textual readings for use in a 9^th grade Algebra 1 class.

Ferguson, T. (2016). The sport of solving quadratic equations. Retrieved from https://www.sagu.edu/thoughthub/the-sport-of-solving-quadratic-equations

Common Core Math Standard: CCSS.MATH.CONTENT.HSF.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

We chose to stick with our topic of quadratic functions.  As mentioned last week, this function family has countless applications in the real world, including science, physics, engineering, and business.  One application that we did not mention specifically last week is the application in sports, branching off from the concept of projectile motion.  Following our broader introduction last week, we wanted to go into a little bit more detail and really build an engaging connection for younger high school students.  I actually used this concept in teaching this topic recently and my 9^th graders were absolutely stunned and amazed by this connection that most of them had all along without even knowing it.  Selecting an engaging, interesting, yet educational article like this can be crucial in a successful reading lesson in mathematics.

As I read for the first time, the article flowed very well and I have no doubts that my freshman would be able to fully read and comprehend this.  The accompanying graphics really help to build connections and substantiate understanding.  The information is organized in a way that is clear, simple, and brief.  There is not an overwhelming amount of complex phrases or concepts, yet the article conveys some higher-order ideas in this content area.  The article began with a catchy introduction, informing readers that they calculate and solve quadratics, sometimes for hours, without even realizing it, by watching sports on TV.  Then, the article goes into subsequent sections that describe the quadratic implications in each sport, including football, basketball, and baseball.  The way this was broken down really helped to connect existing knowledge and ideas about how these sports worked with the new mathematical concepts behind them, introduced in the reading. Overall, it was very clear and interesting to read.

As a teacher, there are many things to analyze about this reading that pertain to classroom use.  The key concept here is the application of quadratic function in different sports.  This is a very useful connection to use to build student engagement, interest, and buy-in during this lesson.  Although the article does describe each sport briefly to the point where unfamiliar individuals would understand, I believe having some background knowledge of these sports will be crucial in building deeper connections.  This is something to consider when selecting this reading.  To be most effective, this reading should be selected when the teacher knows student interests and sports applications apply to them.  When it comes to figurative language, voice, and other stylistic features, the text is very straightforward and informational.  The information is presented clearly and in a simplistic manner.  The purpose of this article is primarily to inform, with areas of interpretation and analysis.  It feels like this text is designed for mid-range high school students.  I think this due to the fairly simplistic nature of the text.  It is very brief, direct, and clear in explanations, and sentence structure seems mostly straightforward without any confusing phrasing or wording. The article is published by a university website. The text is organized in the format of sections with headings.  This breaks the text up into manageable parts with a clear purpose in each section.  There is one image included in the web version of the article, accompanied by a video that narrates the article along with some animations.  In the process of adapting this into a handout format for classroom use, I also took some screen grabs from the video and placed them with the appropriate text section to add more graphic support.  If possible, this reading could be administered online if students have access to a device.  This way, students can use the video to listen while they follow the text, or they can watch the animations to improve understanding. 

The strategy I used was called photographs of the mind.  This strategy is based around the idea of having students stop at designated points in the reading to sketch their visualizations of the text (McLaughlin, 2015).  I feel as though this could be a great way for students to really think about the shapes and scenarios the article describes.  I tried this strategy when I read the article online, with just the very basic image of a quadratic, not with any sports embedded.  I stopped to draw visualizations for each of the three sports the article mentioned.  Having to read, and then create a picture from the text that was given forced me to really re-read and understand the details given in the text so I could draw the image properly.  When I went back and viewed the video to realize there were animations of each sport with the mathematical models, I compared these to my pictures and they were very similar.  I think this would be a highly beneficial strategy for this specific article due to the graphical nature of this concept.  Understanding how the text and formulas relate to the image produced is a fundamental concept of quadratics, and I think this strategy develops that.  Thinking to what an actual class would look like, I think it would be a great experience for students to actually read this article without the sports graphics I included from the video.  I think I would have my students read just the text with just the first image, and then during each “pause” to sketch, I could incrementally show the video animation for that section so students can compare the model with their visualization and clear up any understanding issues.  This would also help to create a really blended learning experience of reading, drawing, and watching an animation, where the reading can be broken down into manageable chunks.  The more I practiced with this strategy, the more cool ideas and alterations I thought of to make this a really neat and involved activity for students.  I think this strategy with this particular text has the capability of creating an excellent learning environment by getting students to really dive deep into this reading to engage and comprehend at a higher level.  This article and strategy also have some deeper connections with the basis of constructivism, which is the theory that meaningful learning occurs when students make connections with prior knowledge and personal experiences (McMillan, 2015).  The fact that this application could be so closely connected to something students see and do in their daily lives can make the reading and the concept as a whole so much more meaningful, to which they will be more interested and more likely to engage with the content.  Especially in mathematics, building these types of connections to sometimes seemingly distant content is so important in creating an environment for successful learning.

References

McLaughlin, M. (2015). Content area reading: Teaching and learning for college and career readiness (2nd ed.). Pearson.