Semester Conclusion

Dear lovely, loyal readers: 

I have sad news. This is the last blog post of my MTH229 career. As such, this post will be a reflection on the course. 

First, I would like to thank all of my wonderful classmates. 

Shout-out to Leo for being perfect, too. 

Something that I feel often goes unnoticed in math classrooms is the importance of peer discussion. I am constantly amazed by the connections other people make. I  learned a lot just from listening to others share their thought process. In addition, everyone in the class was accepting and polite. Instead of trudging through the course with my head down, the classroom atmosphere fostered an environment in which I did feel like I could put myself out there, regardless of whether or not I was correct or incorrect. I think the best example of this is the Counting Circles. 

Speaking of Counting Circles, what started as a gut-wrenching activity turned into an enjoyable experience. When we did our first Counting Circle, I shuddered at the thought of saying the wrong number. I have a very difficult time with mental computations and I was rather embarrassed about it at the beginning of class. As we did more Counting Circles, I started to realize that many of my peers were the same way. It became less embarrassing to say the wrong number. In many ways, it was a very humbling experience. Even people considered to be good at math make mistakes, and that's okay. 

Education doesn't have to be individual despite most high school classrooms being taught that way. I am forever thankful for the experiences in class, especially the insights of my classmates (turned friends!), and I hope I can create the same environment in my future classroom. 

Next, I would like to thank my spectacular professor, John! 

As someone who easily becomes overly concerned with schedules and timelines, I learned a lot from my very chill professor. Some of the most interesting discussions had in class were unplanned. There were many times these discussions could have been cut short, but instead we were allowed to engage in these conversations very deeply. It's important to slow down sometimes and engage students in important, critical thinking discussions. Those conversations will help students far beyond the classroom. 

In addition, John gave many helpful resources. Even though the annotated reading log was tedious at times, I can honestly say I was connected with many useful activities and important ideas. Even though I was exposed to different ideas in the classroom, it was nice to read about other ideas at home. 

At the beginning of class, I generally opposed technology in the classroom. My experiences with it were that more time was spent trying to get the technology to work than actually learning about the material. However, John's consistent and meaningful use of technology changed my mind on this. Although I still prefer other forms of teaching and learning, I can definitely see myself being more open to the use of technology in the classroom. 

I could go on, but I think that's enough brown-nosing for this blog post. 

Similar to the Counting Circles, I think one of the most humbling experiences in the course was well, struggling with it. Often as collegiate math students, we assume we remember everything covered in high school. The truth is, I didn't remember a surprising amount. I spent a lot of time reviewing material so I could keep up with conversations in class. 

 How I feel after Googling high school math in college

I hope I don't forget how to relate to students in this regard. It can be very difficult learning a lot of this material the first time; it's even difficult to relearn it. I have a new-found appreciation for the effort students put into learning this material. 

The last thing I would like to mention is how much I learned about communicating with others. When I signed up for my first college semester as a senior in high school, I signed up for "Communicating in Mathematics" thinking it would be a class in which you work on your communication skills for teaching. 

SPOILER: IT WAS NOT THAT KIND OF CLASS.

The struggle was real. 

Fortunately, this class focused a lot on communicating ideas. I would say even though it's important to be able to do the math correctly, it's equally important to be able to explain how you did the math. I feel as though I am much better with multiple means of representation after taking this course. Math doesn't need to be cookie cutter. Math can be creative and taught in a number of different ways. 

Well, the time has come. Thank you everyone for reading my thoughts and sharing in this pretty cool experience with me. 

No need to be upset!

I'm sure I'll be back at some point! 

Constructivism, Observations, & General Thoughts

Hi, friends! Today we're going to be talking about a few different things, namely constructivism and observations. 

First, let's talk about constructivism. 

What is constructivism, you ask? According to Cherry D. Ward's article "Under Constructivism: On Becoming A Constructivist in View of the Standards" in Mathematics Teacher, 

"Simply stated, constructivism is a belief that all knowledge is necessarily a product of our own cognitive acts." 

Constructivism advocates for students to construct their ideas, not be directly instructed them. The reason this is advocated for is that it is believed students retain information better when they construct rather than when they are directly instructed information. I highly recommend reading her article and looking into constructivism, but today we're going to talk more about the practicality of it within the classroom. 

So, what does this mean for the classroom? Can we assimilate constructivism into our classrooms? 

Some people think constructivism is possible and practical in the classroom. 

Thanks, Giorgio.

We will discuss this first. Students have been shown to retain material better when they learn it through constructivism. They are directly involved in the process of learning and constructing, adding meaning to what they are doing. If we, as teachers, want to teach for long-term understanding, this seems like it is the way to go. 

In my time observing, most of class consisted of examples on the board. Unlike how many of my classrooms were run, students were directly involved in finding the answer. The teacher did not stand in front of the students, talking and writing everything they need to know on the board. The students clearly enjoyed class because they were involved and engaged. Special time was also taken out at one point for an activity to introduce the concept of reflections. Students worked with mirrors, reflecting points about a line. When discussing what they learned as the class, the students seemed to have a deep understanding for just having the concept introduced.This is a more direct example of constructivism. 

On the other hand, some people do not think it is practical and do not like the idea. 

There have only been a few days this semester in my education classes that time has not been brought up as an issue. With how much a teacher is expected to cover, it it becomes difficult to dedicate every day, most days, or even some days to discovery activities when sometimes it's more time efficient to instruct. Constructivism also does not necessarily ensure students will retain the material. In high school calculus, we derived the area of a circle. To this day, I mix up the equation. The constructive approach, although interesting, did not help me remember the material better. That poses the issue of whether or not the benefit will be worth the cost of time, considering the benefit is not certain. 

Almost every single day in my observation was covering a new topic. Most of the time, multiple topics were covered on one day. Although the students enjoyed the constructive activities more, lecturing and instruction clearly covered more material. 

Others are still unsure. 

And that's okay. 

In all, constructivism can be argued for and against. In my personal opinion, I feel as though constructivism is beneficial to the classroom and should be incorporated when time allows. Sometimes the best option is not always the most practical option in regards to time.  I think constructivism offers meaning to a classroom that is often cast aside. 

Leave a comment if you feel like sharing your thoughts. Either way, it is something to consider for future classrooms.