My Weekly Report and Reflection 9 (Week 16)

The content for this week was very stimulating and it sparked a lot of engagement for the entire class! Functions is one of my favourite strands of mathematics. I love everything about this topic, from solving equations using algebraic methods to putting these equations on paper or graphing their them on technological software. This is also an important and applicable skill to develop, since it can be used in the real world in different ways. For example, equations of functions can be plotted with each other to show their relationship with each other and their point of intersection. One of Catherine’s questions, for instance, had us compare the prices to buy a pizza for two restaurants. The point of intersection of each function (based on the starting price, and the price of each topping) is something that people could use weekly, whenever ordering pizza! There are numerous other reasons that Functions is a crucial mathematical topic that is used by professionals worldwide to create things for the public to use.

I really enjoyed taking part, as a student, in the lessons that my peers taught. I thought it was rather insightful to learn about different and new strategies that I can use in my own teaching in the future. I found it very creative that each of my classmates incorporated a different method of teaching and learning for each of their lessons. Catherine had us play “Battleships” using different functions and equations, which made her lesson both fun and educational! This is a great way to motivate students to learn, especially the many students who find mathematics tedious and complex to begin with. Applying a game-design to education makes it much more interesting and, therefore, benefits student learning of the topic. Another station that was taught used a geometric approach to complete the square. I believe that most people prefer a hands-on and visual approach to learning, and this activity allows for a more visual and interactive way to complete the square. This is especially beneficial for children and adolescents, since it gives them another perspective on the technique of completing the square based on how it may have originally been invented. When problem-solving, using your hands and doing things in real-life makes it much more enjoyable and easier to visualize. Children tend to learn through play, so it makes sense to incorporate hands-on learning in the classroom. Geometrically putting together a square and a rectangle, then trying to add another thing to it, allows us to make a perfect square in a way that is more authentic than just solving an equation on a piece of paper. Lastly, Maxim introduced me to an online program that allows teachers to present slides to their students virtually. This resource is called Desmos, and it is something that I will certainly use in my future teaching! I had heard of Desmos before, but have never actually explored it at all. I was very surprised to see just how useful and engaging Desmos was from the student’s perspective. For anyone who has not tried Desmos before, I highly advise that you do so!

I am excited for the weeks to come. Specifically, I cannot wait to participate in more lesson stations as a student to my classmates. I am also looking forward to teaching my own lesson for a Grade 12 Data Management College level class!

My Weekly Report and Reflection 8 (Week 15)

Class 15 was another great one! We worked on factoring which was a great refresher since I haven’t done this type of mathematics in a while. We also gained some resources as future mathematics teachers, which we can use in our classroom in our careers! In fact, I was proud to be the first student in the class who completed the "pop-up" card! Check out the picture below to see my staircase! One thing that I wanted to focus this blog on was the TED Talk that we watched at the beginning of the class.

I love watching TED Talks, and the video we watched this week lived up to my expectations! The beginning of the TED Talk was about how mathematics has to do with patterns, as the speaker defines mathematics as being “about finding patterns (connections, structure, etc.), then representing these patterns with mathematical language.” He also states that math is about doing cool stuff. I found this definition to be useful because it is so true, and it expresses mathematics in a way that makes it seem doable and enjoyable. I feel like many individuals find math to be a challenging and discouraging domain, which they will never truly grasp. Many students feel like they have been defeated in the subject of mathematics, which is a stigma that educators must work to diminish in the classroom.

The speaker’s main claim in the TED Talk is that changing one’s perspective is is a critical skill to have when solving mathematical problems. He explains that every equation has multiple perspectives, and everyone’s point of view when looking at an equation may be different than someone else’s. this is an interesting point because it proves that there is no single best solution when approaching mathematical problems. The examples that the speaker uses are extremely beneficial and the way he discusses these illustrations are conducive to the viewer’s understanding of the topic. This is a concept that our class has been exploring all year, and it is something that could encourage students when struggling trying to solve a problem. In other words, if an individual is “STUCK” and having trouble in their mathematical processing, they can be motivated again once they realize that reframing the question may lead them to the correct answer. Of course, if they still cannot solve the equation, they simply need to look at the question from a new perspective, and keep doing this until they can finally solve the problem in front of them. Often times, understanding is only possible when the problem-solver takes a step back and looks at the bigger picture. The speaker acknowledges the fact that this is true for every subject matter, not just mathematics and science. The essence of understanding, then, is being able to change one’s perspective and adjust our point of view in order to learn more and more about something. He calls this ability to change perspective “empathy”, claiming that this competence is crucial when trying to understand something. It makes your mind more flexible and, subsequently, allows you to understand more about the world. He also explains how metaphors and analogies are an essential strategy to include in teaching and learning. I agree with this because I think that people learn better when a field that they are not so comfortable with (in this case, mathematics) is related to everyday life. These comparisons can serve as symbols with which the learner(s) can relate to ideas that they are much more comfortable with. Therefore, it is imperative that educators in any domain – especially mathematics – encourage their students to always change their perspective when looking at a problem, since there is never one single process to come up with a solution. It is only once students and teachers realize the importance of changing their perspective that they can truly understand how to solve mathematical problems and enable this understanding for others.

Bringing different experiences to the learning environment is necessary for individuals to gain more knowledge and enhance their learning. This is something that I think all educators must be aware of, in any classroom. It is the teacher’s responsibility, then, to connect their own experiences, and the experiences of their pupils, into their instruction.

My Weekly Report and Reflection 7 (Week 14)

The content for Week 12 was very interesting and provoked some great discussion! We started the session with each group presenting one of our Digital Math Word problems to each other. This was a good presentation for two reasons. Firstly, it was beneficial for us to explain our own problem and justify our problem solving to the rest of the class.

The first activity was a “4 corners” type of activity that had students choose which corner of the classroom to stand in based on our resolution the selected problem. In this case, Joyce asked us what cylinder could be created by folding paper in order to maximize volume: a hamburger-type shape or a taller, hotdog-type shape? At first, the entire class went to the hamburger corner because we are all university mathematics students who are highly proficient at measurement and geometry. Then, Joyce asked us to think like a student would, and we dispersed into separate corners. It was advantageous for us, as future educators, to consider what students might be thinking. Teachers have the responsibility of considering their students perspectives and educating them on why they may be correct, or where they may have gone wrong. This “4 corners” activity is one that I can, and will, use in my own classroom in the future. Not only does it force students to take multiple perspectives and brainstorm different solutions and justifications, but it also creates small groups where all students are encouraged to discuss their thinking. Small groups are much more inclusive and more efficient than larger groups or the entire class. I think that using popcorn for the activity would be especially useful because it motivates children to complete the problem at-hand so they can eat it after.

Measurement and geometry is a mathematical unit that I have not done in a school environment in quite some time. I find that University courses are very advanced and comprise of mathematical strands such as Calculus, Statistics, Algebra, etc. More hands-on mathematical problems, therefore, usually do not occur in University due to an emphasis on solving equations and algorithms mentally or using technology/software. However, solving problems by manipulating diagrams/shapes, measuring, rearranging pieces, or other hands-on strategies, is still a huge part of mathematics at the school-age level and in many practical instances in real-life. Thus, it is nice to have classes like this one that focus on more rudimentary mathematical processes, which are both useful in real life and are what we will be teaching in our future careers.

Joyce divided us into three groups and lead each group through three separate stations, one at a time. She created handouts for us that could be given to Intermediate/Senior Mathematics classes in public school. These activities provided us with a hands-on, interactive way to solve measurement and geometry problems, including parameters such as area, perimeter, and volume. We had to manipulate the objects that we were given to create certain shapes, which extended our knowledge on how shapes translate to another form, either having the same parameters or different ones. I was proud to be part of the only group that solved all eight squares that could be made on the geoboard (see geoboard photo below). These activities could also be adjusted and implemented in any I/S grades and for any level of students’ abilities! 

I look forward to the weeks ahead and am especially excited for the “Teaching a Learning Activity” assignment in which I must teach my classmates a lesson designed for Grade 12 College level students in the unit of Data Management and Probability. I have never been part of a College level class, nor have I observed any lessons in such a class, so this will be a very interesting and education experience for myself as a future Mathematics Teacher!

My Weekly Report and Reflection 6 (Week 13)

For Week 13, the main purpose of the lesson was to reflect on our placements. Since physical education is my major, I sometimes have anxiety when thinking about teaching mathematics. Although I am extremely confident in my mathematical ability and have tutored many students in math in the past, I sometimes feel as though I will not have enough experience as a math educator once my career begins. In relative terms, I feel like I will be less prepared than my classmates because they have placements in Mathematics, whereas my current placement is in Health and Physical Education subjects. I will not have experience actually teaching math – as a professional – until I am in my final teaching block. This makes me apprehensive about whether or not I will have the experience necessary to be a professional Mathematics teacher in a secondary school setting. Physical education is a far different domain than mathematics, so I am nervous about having to teach both, when I have only focused mainly on the former domain.

One advantage to teaching both Mathematics and Health and Physical Education is that I think it will help be integrate both curriculums. Teaching an integrated curriculum is a major task in 21^st century education and is extremely beneficial for learners today. Math and physical activity may seem to be very distinct from each other, but I see many similarities between the two subject matters. For instance, pathways and directions (special awareness) in the gymnasium relates to coordinates and shapes in math. Furthermore, sport and physical activity rely heavily upon statistics, which is a mathematical course. Keeping records and quantifying physical achievements is how athletes progress in sport, which is dependent on math and statistics. Therefore, I can see statistics – among other math courses – being incorporated in physical education courses, and vice-versa.

It was really satisfying to be able to interview Alyssa and have her do the same for me. Talking about my placement was much needed, and I really enjoyed discussing it with Alyssa and the rest of the class. My placement did not go as well as I had anticipated, and my associate teacher had much more negative feedback than I expected. Instead of criticizing me during the teaching block and allowing me to work on my areas that need improvement each day, she gave me all the feedback at the end on the final day. She presented me with the feedback sheet, which had one line of what I did well – my lessons and activities. The rest of the page was entirely things that I need to improve on, and my associate teacher even wrote sideways to fit it all on the page. This was very surprising, and even somewhat overwhelming, to me since she had not discussed any of it with me beforehand. This not only made me feel overwhelmed with advice, but also was a bit of a shot to my confidence in my teaching abilities. Mainly, the teacher said that I need to work on my classroom management skills. I found her critique to be a bit redundant and unnecessary, as I think classroom management is something that I need to work on and believe it will come with experience. Therefore, I think my associate teacher could have just reminded me to work on my classroom management skills, rather than drowning me in negative comments about how poorly I am doing at the moment. I think it would have been much more beneficial if she had been a little more positive in her review, given the fact that it is only my first placement.

Nonetheless, the rest of my classmates and Joyce were extremely helpful and supporting. They reassured me that some teachers can be enormously nit-picky and expect perfection. Joyce also mentioned that if the problem escalated to the point that I could not withstand it, I could request a transfer. I am not considering this at the moment, but it is good to know for the future, in the case that I change my mind. Mainly, it is really great to know that I have an amazing group of colleagues and a terrific, caring professor in my mathematics class that I know I can count on to make me feel better! I hope to encounter teaching partners like this in the future as a mathematical educator!