Methods of Solving Quadratics-Can You Chose the Best One?
Methods
of Solving Quadratics-Can You Chose the Best One?
An
analysis of textual readings for use in a 9th grade Algebra 1 class.
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.
One again, we elected to stay within the realm of quadratic
functions due to the increased importance in real life and in future low and
high-level mathematics courses following Algebra 1. This article focuses on another area we did
not discuss before, solving quadratics.
This article is a very useful guide with some additional information
about the common methods to solving quadratics.
This area is meant to be taught following comprehensive lessons of
factoring, as well as the introductory quadratics lessons, which cover
vocabulary, anatomy of quadratics, as well as graphing and analyzing the graphs. During the portion of the unit where this
reading would be used is really in the meat of quadratics for the Algebra 1
course. At least for my curriculum in my
current school, methods of solving are one of the last major topics in the
quadratic units. Compared to our fun and
highly engaging reading from last week, this article is really more composed of
hard math, completed with explanations and examples. This is a great resource document, and I
believe students will come to appreciate the content once they understand how
to use it and how to apply it to their work in class.
While reading for the first time, I liked how the text and
headings were organized. I noticed that
the four methods included in this article are listed in an almost progressive
order, getting to the more complex or difficult methods later. I think this is a great way to order the
content and organize it in a way that builds.
In subsequent methods, the article mentions things like “if the previous
method does not work, then try this,” which really helps the reader connect the
methods to the broad idea. The end result is a very clear, brief, and
densely packed article with valuable information, including worked examples, a
key element of a useful resource for students.
Reading as a teacher, I highly appreciate the inclusion of
worked examples. This makes a resource
or reading more “complete” in a sense that everything is right there that a
student needs to learn the topic. Not to
say that I would hand this paper to my students and expect them to learn it
alone, but this article becomes highly valuable in helping students answer
their own questions, or make an attempt to, before asking me. This helps in my efforts of creating more
self-sufficient students that know how and when to utilize a resource like this. Students would have to have a decent level of
background information, specifically concerning quadratics, to be successful in
comprehending this article. Like I
mentioned before, this would be appropriate to use towards the end of the unit,
after students have learned the basics.
Solving quadratics is one of the final pieces to this unit in Algebra 1,
therefore, students should have a decent working knowledge before learning this
concept. Otherwise, there is no other
concept in this article that would not have been recently covered in class,
making this article very useful. As
mentioned, this reading is highly brief and heavy on the pure math. This leaves no room for stylistic word choice
or any other figurative element. This
article is completely procedural and provides brief explanations of each
method. The purpose of this article is
primarily to inform, listing out methods and procedures. This article is designed for high-school
level students and I have no doubt that my 9th graders would be able
to comprehend this resource given their prior work in the unit and other given
comprehension strategies or activities.
This article was published by a South Carolina school district high
school teacher. The text is organized in
sections with headings and examples for each method. This breaks the article up in to clear
sections with each method as a clear heading.
The top of the article also includes some basic review information on
types of solutions and standard form, which is a good way to remind students of
previous topics that will be applied here so they can refresh their memory or
access previous notes in needed.
I used a strategy called paired summarizing. In this strategy, student’s work in pairs and
each select or are given a section of the reading to summarize (McLaughlin,
2015). Then, the students swap summaries
and create summaries of their partner’s summary (McLaughlin, 2015). I am already thinking of funny names to call
this activity in a classroom setting (AKA Summary-ception)… This method is great for getting student to
read and synthesize or further simplify information from a text. In this case with this reading, it would be
even doable to work in groups of four and each student gets to work on one of
the four methods, and then they rotate, then share their summaries with their
group. I think this is a great way for
students to practice understanding a reading, and then rewriting it in their
own words. I can definitely see how this
would extend and demand a higher level of comprehension. When I tried this method on my own, I
basically took the part of both partners, making a summary, and then a summary
of my own summary. This was another
interesting take on this activity, and I think this could also have some
interesting implications for a class setting if we altered it to an individual
activity to get students to further simplify and synthesize their own
thoughts. I also though of another way
to use this in a class with larger groups, where we could add another level of
“summary.” Following the second summary,
we could have students rotate a third time and create an even more brief
summary by creating bullet points or something else that is more simplified
than a paragraph. I think this would be
really helpful in getting students to recognize and isolate increasingly
important information. Extracting the
most important points from a text is a critical literacy skill, especially in
mathematics, and I think this strategy has the ability to further develop that
skill. This reading and strategy also
have some connections to building student critical literacy and information
literacy (McLaughlin, 2015). With
critical literacy, we are helping students to comprehend at a deeper level, and
understand more about information that is given to them (McLaughlin,
2015). This strategy definitely helps
students to develop this ability, as they continually summarize and synthesize
information. When it comes to
information literacy, this has more implications surrounding the skills of accessing
important information, and knowing how to effectively retrieve valuable
information (McLaughlin, 2015). This
level of literacy is developed through this strategy again, by having students
read and re-read to further extract or identify important pieces of information
from the previous part to use in the next part.
Overall, this strategy has a lot of potential, and there are many
alterations we could make to this strategy to make in more useful in different
ways depending on our goals.
References
McLaughlin, M. (2015). Content area reading:
Teaching and learning for college and career
readiness (2nd ed.). Pearson.
Caitlin, another great blog on reading comprehension strategy. It sounds like you would benefit from bundling this text with the other texts your group selected. I really like your adaptation of this strategy to complete this assignment. When I was reading your ideas to add another level to the strategy I thought you could start by having your groups work on a summary together for the first level then pass them to another group for paired summary. Great job.
ReplyDeleteJennifer
Caitlin, the summary you used was one I gave to Kim because I thought it was a great way for students to learn in a collaborative approach. Students are able to extend their thinking after reading and by sharing their summaries, they can discover new meanings that they didn’t think of or generate new questions (McLaughlin, 2015). You bring up a good point that this strategy can be used in bigger groups and I really like the idea of having students rotate their summaries. With this strategy, how would you be able to lower the threshold with students who find writing difficult? I provided a number of sentences I was looking for so students knew what was expected of them.
ReplyDeleteMcLaughlin, M., (2015). Content Area Reading: Teaching and Learning for College and Career Readiness. Boston: Pearson.