Learning Activity 8-B-2: Reflections on Blogging

Overall, I enjoyed my blogging experience, although the initial stages of setting-up the blog were challenging.  As a novice blogger, everything was trial, error and experimentation for the first couple of weeks.  However, I eventually got the hang of the basics, and the process wasn’t as daunting.  In hindsight, the site is actually very user-friendly.  I learned a lot from reading my classmate’s blogs, and from the other math blogs I began to follow, after perusing the entire site.  I am grateful I was encouraged to explore the world of blogging; the experience was very beneficial as a student and a teacher.

If it weren’t a requirement, I would have never started a blog, and it is very unlikely that I will continue to post information any time soon.  However, I do plan to continue to follow others blogs, and use them as ancillary resources.  My primary reason for not continuing to post blogs is time.  For instance, this year my school district is mandating us to create websites, and post our grades, lesson plans and homework on-line.  Considering I am not very technologically savvy, I am still trying to adapt to the new requirements listed above.  Therefore, blogging, for me, would just be another item added to a very long list of “technological things to do.”  I do believe I can up-load my blog to my website, however.  If this is true, I am definitely inclined to up-load my current blog, although I don’t anticipate up-loading a new post.

As a result of my blogging experience, I learned that writing about math was more challenging than “doing math.”  For example, sometimes the writing process was time consuming, because I am not accustomed to articulating procedures in writing, and formulating my own definitions.  Since my mathematical education involved rote memorization, I was never asked to summarize my mathematical knowledge, and construct my own meanings; therefore, this was a new experience, and I never imagined it would take me as long as it did.

I entered this course confident I was adept at Middle School Math.  However, the blogging experience made the math more interesting, because it gave me the opportunity to explore, analyze and communicate in my own way.  For example,  whether I used blogging to explore Pascal’s Triangle, write a review about the Puma Site, or merely paraphrase vocabulary, the math became more interesting, because the requirements extended beyond merely “doing math.”  As a result, I am now inspired to allow my students to conduct more internet explorations, so they can discover something new and interesting that extends beyond the textbook and the classroom.

For example, one of the most interesting concepts I learned about in this course was fractals, and other non-linear patterns.  Although I’ve heard of fractals before, I never explored the concept to gain an understanding of what they really were.  However, once I conducted my own research, I was pleasantly surprised to see the plethora of fractals that can be found just about anywhere, including inside our own homes, as well as in nature.  So much time is spend trying to get students to understand linear patterns, tables and equations, that non-linear patterns become secondary.  Therefore, it was intriguing to see all the non-linear patterns we overlook, although we’re surrounded by them every day.

In the near future, I would love to incorporate blogging into my classroom.  My students are already required to journal bi-weekly; however, I would love to introduce blogging to provide them with a different alternative to writing in a marble notebook.  Since students love to work on the computer, although they loathe writing, I think blogging is a unique way to pique their interest, and increase their writing and participation.  It’s also a great way to have students share and exchange knowledge with their peers.  I wouldn’t be surprised if my students know more about blogging than I do; I am confident they will be eager and motivated to began the process.  Their motivation may actually inspire me to continue my own blog.

Learning Activity 8-B-1: Factoring Quadratics – In Your Own Words

Factoring Quadratic Equations: Paraphrased

Example: x2 + 6x + 8

Step 1: Locate the third term in the quadratic, and find all the factor pairs associated with that term.

Step 2: Identify the factor pairs that will give you a sum that’s equal to the number in the middle, or the second term.

Step 3: Factor the first term.  If the first term is X², both binomials will start with X.  For example, it would be (X  )(X  ) because X(X) = X².

Step 4:  Since the factor pair (2, 4) has a sum of six, two will be added in the first binomial, and four will be added in the second binomial.

For example, (X + 2)(X + 4).  Two and four are added because all of the terms in the original quadratic are positive.

By paraphrasing the steps, I was able to internalize the concepts more, because I had the opportunity to interpret and communicate the procedures in my own personal way.  Decoding language is an integral part of the learning process; thus, summarizing and paraphrasing allowed me to express my understanding in a unique way that made sense to me.  This type of lesson could be applied in class by having students paraphrase procedures that are difficult for them to understand; therefore, students will have the opportunity to “confront” difficult concepts and make sense out of them.  Since communication is essential to student’s understanding, if they are given the opportunity to paraphrase & construct meaning for themselves, the they will enhance their ability to learn and understand the math.  Even if students understand procedures without paraphrasing them, I would require them, for example, to explain the factoring process, so I could assess their understanding by having them answer questions similar to the ones below:

  • Why are both binomials X?
  • Why did you use the factor pair (2, 4)?
  • Where there other options besides (2, 4)?
  • How did you know that (2, 4) needed to be added?