Miss Arguello's Classroom

What Makes a High School Teacher "Good"?  We have all had high school teachers that have made a significant impact on us. For one person I spoke with, her pre-calculus teacher was great because he encouraged students to ask questions and made every student feel as if they had a significant mathematical ability. Another woman’s favorite teacher was her high school English teacher, who had his students turn their desks into a circle and collaborate with one another, facilitating deep discussion and fostering a love of literature into his students. For another, her high school teacher stood out as being great because she helped her student to navigate some tough family issues in the midst of her depression, and allowed the student to seek solace from her, even though this went far beyond her role as a classroom educator. Besides personal testimony, various articles have also been written about the definition of a “good” teacher. One writer defined a good teacher by thei...

I have always struggled with any mathematics that is inherently visual, and so when I missed a class about Khwarizimi's visual representation of completing the square and had to look online to teach myself about it, I knew I was in for a challenge. However, as an education major interested in new ways to present difficult mathematical concepts, I was interested in this visual algebra and how such a tool could be utilized to teach completing the square to students. I was also interested in examining its similarities to the "box method" way of teaching factoring. So, the questions I wish to explore today are: How beneficial are these methods of factoring? How can we utilize visual tools such as these in teaching? What can mathematicians such as Khwarizimi teach future teachers about new ways of presenting concepts? Khwarizimi's Visual Representation of Completing the Square  I'm not sure about my other fellow educators, but, to me, both in the classroom and whe...

Note: If anyone is reading this who is also struggling with a mental illness, I have a couple introductory points to make-First of all, if you are struggling with any symptoms of anxiety or any mental illness in general, please talk to a doctor or a professional. They can help you and find a plan that works for you. Additionally, I want to emphasize that everyone has different experiences and if you have not experienced the same symptoms or events as I have, then that doesn't mean your experience is not valid. What works for me may not work for everyone else, and that is completely fine. YOU are the expert on your own mental illness, and I think it is important to emphasize that before beginning my own account. Thanks for reading.  I realized I had anxiety the summer after my freshman year of college. I had come home from college, happy with the new experiences I'd had and already missing my friends. I began working at the old retail job I had had in high school again, deter...

So, judging by the title of this blog, it's pretty easy to make the conjecture that I'm going into education. I knew that I wanted to be a teacher when I started college in the fall of 2014, but the step into the classroom was so far away at that point that I barely had any time to feel nervous for my role as Teacher Assistant. Now, I am a few short weeks away from the end of the semester, and after the holiday cheer wraps up, I'll be working with students and applying everything I have learned these past 8 semesters. At this point, I have gotten my acceptance letter to the College of Education in the mail, attended an orientation meeting, and have been reassured that I will likely receive my placement before Thanksgiving. While everything is exciting and definitely makes this whole math journey I've been on completely worth it, I'm also scared out of my wits. How will I apply what I've learned in math courses? Will my lack of knowledge about integral calculus...

"This, therefore, is mathematics; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes the oblivion and ignorance which are ours by birth. "-Proclus 

What is a Genius?  A "genius" is a difficult thing to define. I believe there are geniuses in many different facets of life: there are musical geniuses, there are literary geniuses, there are philosophical geniuses, and I would even argue that there are geniuses who have simply perfected how to make an awesome sandwich. I think everyone is a sort of "genius," since we all have the capacity to make life-changing discoveries and we are all able to make some sort of impact in some way. One person who I consider to be a mathematical "genius" is Archimedes. A brilliant mathematician, his influence is still felt today, since we use much of his area and volume conjectures (more on that later) and we even use some of his inventions, such as the Archimedean screw. In this case, he has definitely shown his capacity to change the world, and I am completely fascinated by him. I would like to take this time to share my (probably shallow) knowledge of this fantastic ...

Again, I find myself using this blog! Last time, I was an aspiring teacher, bright-eyed and ready for my junior year. Now I'm a senior, a semester away from BEING that aspiring teacher (how exciting!) and ready to finish learning about mathematics! So, in introduction to developing a relationship between every single mathematical concept I've covered in my four years at Grand Valley, I was asked: What is math? What is Math?  I would define math as using given information and prior knowledge to draw conclusions. Take the following logic question for example: Suppose there is a basket full of 14 apples and we take 3 apples from it. How many apple do we have? Of course, we have to use our assumptions and given information to determine the answer to this. We know that we definitely have at least 3 apples, but was the basket in our possession as well? In this case, we have at most 14 apples. So, the answer is that we have between 3 and 14 apples. In this way, we were able to draw...