Blog Post #2: We're SPECIAL, not GENERAL!

Welcome back everyone!

Now I don't know if you guessed what I'm going to be reflecting on today from the title of this blog, but maybe you did! Well, if you still don't know, today I am going to be talking about the two fundamental processes of mathematics - specialization and generalization! These two processes will help anyone find their bearings for different mathematical problems in order to move closer to a resolution. Essentially, these two mathematical processes move students towards improved mathematical thinking. 

I have really reflected on this week's reading as well as throughout lecture and I have consolidated some thoughts on these mathematical processes. I have designed a graphic organizer to debrief my key takeaways from the reading this week (Thinking Mathematically - Chapter 1) that I'll show you all.

This reading really made me think about how I approach different mathematical problems.  I would consider myself to be a visual learner, so patterns are always a go-to strategy in problem solving for me. I like to analyze the problem at hand to see if I can detect any sort of repetition or underlying pattern first (generalization). After doing so, I test out my pattern observations in random examples to see if I am any closer to a resolution (specialization). Prior to this reading, I did not realize that I was actively engaging in these two processes when I approached mathematical problems. I definitely think that these two processes are crucial in the improvement of one's mathematical thinking because it allows the student to unpack the problem instead of seeing it in a close-minded way. 

BUT WAIT... That wasn't the only thing I reflected on this week! Have you guys ever heard about this method of note-taking called RUBRIC notes? I had no idea what RUBRIC note taking was before this reading so don't worry. Basically, RUBRIC is a way to write yourself notes while problem solving to mark your train of thought and monitor your progress throughout the solution. You can use words like "stuck", "aha!", "check", and "reflect" to ensure you fully comprehend the resolution that you arrive at. 

Personally, I wasn't a fan of RUBRIC because I felt like I got too caught up in the words that I would lose track of my thought process within the actual problem. I love the reflection component of RUBRIC though because I think it is really important to go back to your completed problems and reflect on each step that you took to ensure you understand and engage in the logic behind the resolution. But hey.. if RUBRIC note-taking works well to organize the problem solving process for some students, I am all for it! I am an organization freak after all. 

As a teacher candidate, I think it is really important to motivate and encourage our students to engage in these fundamental mathematical processes because they will help improve their mathematical thinking. Therefore, as a future teacher, I will strive to minimize the math anxiety within students so that they can begin to develop a growth mindset. A growth mindset is really important for students to have; they need to believe that they can learn anything! Providing students with the opportunities to engage in mathematical problems that promote this growth mindset is our job as their teacher. 

Overall, I believe that it is our responsibility, as teachers, to foster our students' mathematical thinking. I intend to remind students of the importance of making mistakes and trying again as this is how we learn! I want to teach my students not to be afraid of mistakes so that they can engage in the mathematical processes with confidence when approaching a problem. 

Anyways, thanks for stopping by and listening to my reflections on the topic of mathematical thinking this week! This weeks topic really opened my eyes to how I want to be as a teacher in my future mathematics classroom. I hope I either taught you something new or opened your eyes in some way about teaching or problem solving. I love coming on here and sharing my thoughts with you guys. Feel free to let me in on any thoughts or reflections that you may have had on this topic! 

See you guys next week!

Signing off, 

    

        Ms. Blackwell

Blog Post #1: Exploring the Growth Mindset!

Hello everyone and welcome back to my blog!

This week we discussed many aspect about the benefits of a positive attitude when engaging in mathematics. I was very surprised by a lot of the science behind the importance of having a positive attitude when approaching mathematics. In this blog post, I will be sharing with you my reflections on this lecture and why I value the knowledge that I have gained. 

This positive approach to mathematics has been referred to as the growth mindset and is discussed in great detail by Jo Boaler in her Ted Talk (https://www.youtube.com/watch?v=3icoSeGqQtY&vl=en). Often times, especially in mathematics, students become very discouraged when they have made a mistake or arrive at an incorrect answer. However, Jo Boaler discusses the neurological advantages to making mistakes. When an individual makes a mistake, synapses in our brain are fired triggering more in depth thought to the solution of the problem. When an individual gets the answer correct, however, less synapses are fired because the brain does not need to dive deeper into the context of the problem. This reinforces that mistakes are beneficial to make and thus, we need to teach students the additional knowledge that is gained when mistakes are made. It is important that students learn not to be afraid of mistakes and instead, embrace them. 

With all that said, the growth mindset allows individuals to truly believe that they can learn anything. This mindset makes them more capable of success than the latter of having a negative mindset. However, as teachers, we need to ensure we are providing students with the opportunity to develop a growth mindset. We can do this by providing students with mathematical scenarios that do not just have one correct answer. This will allow students to explore their mathematical abilities and produce one of many correct answers/possibilities. By providing students with short and closed questions that only have one right answer, we are hindering their ability to develop a growth mindset. 

As a teacher candidate studying to become a mathematics teacher, I think that it is crucial that we learn how to effectively communicate like mathematics educators and not like mathematicians. In the reading for this week, Mathematics for Teaching, by Deborah Lowenberg Ball and Hyman Bass (2003), the importance of unpacking one's knowledge was discussed. To unpack one's knowledge means to decompress the knowledge you have in order to effectively teach students and push them through their zone of proximal development. By unpacking our knowledge, we can scaffold their learning in a way that resonates best with the student. If we can successfully do this, we are teaching like a mathematics educator and not like a mathematician. This was really eye-opening for me because I have had a person experience in my grade 11 mathematics class in which my teacher spoke like a mathematician instead of a mathematics educator. He took every short cut and did not explain the logic behind the mathematics he was doing. As a result, he compromised the quality of learning for his students. 

Overall, I found a lot of value in this weeks topic of the growth mindset and how we, as teachers, can help students reach this positive attitude. Some key reflections of mine throughout this week include:

• Minimizing short and closed math questions that have only one correct answer and instead, providing students with the opportunities to explore open questions with multiple possibilities. I believe that this will avoid the development of math anxiety in many students. 

• As teachers, we need to believe in ourselves to unlock our own unlimited potential. Therefore, we need to ensure we can scaffold our students' learning to allow them to believe in themselves as well. 

• As frustrated as I get when I mistakes in my own mathematics classes, I now know that these mistakes have helped further my knowledge to get me to where I am today. 

• We need to be the future of teachers that changes the message that students are receiving in their math classes. We need to create a more positive and open learning environment in order for students' to believe in themselves and gain the confidence to develop a growth mindset. 

I hope that you all enjoyed my reflective thinking on the topic of this week in EDBE 8F83! Let me know if we had any similar reflections or if you were inspired by anything I said in this post. I'd love to hear some of your thoughts and reflections too! 

Thanks for stopping by and I hope to see you soon!

Signing off, 

            Ms. Blackwell

Welcome, I'm Ms. Blackwell!

Well, it appears that you've found my secret... I'm a math nerd! 

Hello everyone! My name is Ms. Blackwell and I am in my fifth year of Concurrent Education at Brock University. I have just started my first year of teacher's college during this weird time of COVID-19. My first teachable is mathematics and my second teachable is geography. Despite the challenges everyone is facing during this pandemic, I am excited to utilize technology to communicate and get to know all of you through both our lectures and blogs!

As a teacher candidate, I am excited to extend my knowledge on how to approach teaching mathematics in the classroom throughout EDBE 8F83. My goal as I move through this course is to improve the quality of my lesson plans while also incorporating fun and engaging activities within them. I will use this blog as a platform to express my knowledge gained as well as insights that I may have towards teaching mathematics in an intermediate/senior classroom. This blog will be centred around mathematics, my reflective thinking, my overall learning, and how technology is playing a role in my education as a teacher candidate. 

This blog will express how I have processed what I have learned in order to adjust my framework of teaching and how I envision my future classroom to be. I hope to express my overall philosophy of mathematics education and how I hope to approach math education in my future classroom. 

As a future mathematics educator, I believe that it is crucial to avoid the development of math anxiety as best as possible by meeting students' learning needs and creating opportunities for equitable and continuous learning for all students in the classroom. I will use this blog to dive into ways I hope to do this in my own classroom in the future. Math is like a fun puzzle! Sometimes it takes a little bit longer to find that next piece, but if you strategize and explore different options, you will be one step closer to the full picture! 

Thanks for stopping by and giving my blog a read! You're welcome back anytime. 

See you soon!

Signing off, 

        Ms. Blackwell