Quadratics: Art and History in Mathematics??

Quadratics: Art and History in Mathematics?

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

Coolman, R. (2015). What are quadratic equations. Retrieved from https://www.livescience.com/50411-quadratic-equations.html

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.

Our topic is quadratic functions.  We selected this topic because it is a heavily used topic in secondary mathematics education.  It is one of the most important functions in mathematics and has countless applications and uses in the real world.  This topic is heavily focused on in Algebra curriculums and beyond.  Aside from being a core function family, quadratics also provide a foundation to understand more complex polynomials.  Professional fields in which quadratics are used include engineering, medicine, mathematics, business, science, physics, and manufacturing.  In searching for a text, we wanted to begin with an introductory approach to quadratics.  We wanted an article that was brief, concise, and informative.  I also wanted to be sure to find a text that touched on some real world applications, as well as concepts, in order to grow the interest and engagement of my students.  Because I teach 9^th grade Algebra 1, I wanted to look at this assignment through that lens, so all of my discussion will be based on that intended use.  In searching for a text, I did a few quick Internet searches and began to narrow my results.  We found this article and chose it due to the high level information included within it.  The web article is quite long, so we elected to adapt (shorten) it, in a way, to something more realistic to what would be used in a classroom setting.

During the first read, I was surprised about how much high quality information was packed into such a short reading.  Because of this, I had to take a second to digest each sentence and fully realize what information was just relayed to me.  I appreciate the fact that the author included life dates for all mentioned historical figures.  Not only did I read this article with increasing knowledge of the history of quadratics, but also I received an even better sense of time of the entire process of its development.  To look at specific portions of the article, I appreciate how the derivations of language were included.  For example, in the first paragraph, the meaning and establishment of the mathematical term “squaring” was included, as well as words like parabola and quadratic. I liked the fact that the article touched on introducing some of the higher-order vocabulary words, like quadratic focus and directrix. Finally, I liked the fact that it included both scientific and artistic histories and ended on the note of the impact quadratics had on the scientific revolution.

This could be great information for students to read to improve the common confusion of the meaning of math words.  The background the article provides on the creation of common content words, like squaring and parabola, will help clear confusing that students may have. I also noted that the article immediately jumps in to real word examples, like rocket ship landing, and water fountain trajectories to quickly capture attention of readers who may wonder, “when will we ever use this?”  When it comes to important concepts in the article, the most important take away for students would be a better working knowledge of quadratics, how they were created, and why they are used.  Students would need to have some background on functions, coordinate planes, as well as the ability to make inferences on word meanings from context clues.   This reading would be most effective in a quadratics introductory lesson immediately following the study of polynomials and factoring.  This would be the most important area to have knowledge of to make this reading more understandable and useful.  Common with most mathematical concept text, there is only one perspective, which is greatly objective and based on history and facts.  There is not much room for multiple levels of meaning, in my opinion, in mathematical texts like this, where the purpose of the text is to deliver facts, processes, or other indisputable information.  I would not say the text is in a chronological order, but dates and history are used to develop the concepts.  Like I mentioned, dates are included with any mention of a historical figure, which is definitely valuable information in developing a deeper understanding.  Although there are no specific citations, the article online does list additional resources for this topic at the end.  This is not something I included in my student version of this article, but could be explored further for other resources. All language is factual and clear.  There is no evidence of word play, or other figurative language.  The purpose of the article is to inform the audience.  It has mathematical, scientific, and historical significance and it does a good job at combining the three fields to provide rich, educational information.  The article has a good amount of rare words, though most of them can be mostly understood using context clues.  I feel like this text would be accessible, yet challenging for my 9^th graders.  I believe the text is meant for those types of high school students.  I think this mostly due to what I just mentioned about the word choice and language, but also the set up and the inclusion of plenty of background or introductory information for each topic.  This makes me think readers should be well practiced, but not as proficient as someone like a college student or professional.  The article was published on LiveScience.com, a modern news and analytical website that focuses on current science news and concepts.  I would say this reading is closest to the genre of a textbook or other informational piece.  The text is organized in short sections with headings and graphics.  Graphics have captions and there are also links embedded in the digital version of the text.  The accompanying graphics help to develop a sense of these more difficult words, especially useful for students in lower-level classes.  The cohesion of multiple subjects within this piece helps tie together other possible studies in science and history for students, making the use of this text an applicable, educational, and rich learning experience for students.

The strategy I used was semantic maps.  This involves beginning with a main idea, brainstorming subcategories, and filling each out with details (McLaughlin, 2015).  This strategy can be used to activate previous learning, develop new vocabulary, and organize new information in a graphic organizer format (McLaughlin 2015). When using this strategy, I began with my central idea as “quadratic functions.”  My sub-topics I thought of include real world applications, history, and quadratic graphs (parabolas).  I personally used this strategy as a post-reading, summary-building activity, and I think this would be the most appropriate use in a secondary classroom as well.  Students, I think, would have trouble coming up with ideas before reading, whereas after reading, students can get a better idea of different subcategories.  The fact that the article also was structured in a way that included sections and subtitles make it even easier and more manageable to summarize and put into a graphic organizer.  The organizer could even become a note-taking and study tool, which can be very useful during classes that follow where we build more information to this introductory text.  The strategy is very simple to understand, and I think students would enjoy completing this activity.  I think it would also be a great way to boost engagement, therefore comprehension, as this method provides a manageable and interesting way to ask students to summarize a text.  With this strategy, I believe students would be better equipped to understand, comprehend, and retain this information. 

References

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