Final Blog Post - Mathematics for Teaching Portfolio!

The following three subsections include a few of my favourite strategies, resources, and practices that I learned this year in the class! although I enjoyed everything we learned in the course, these are the three most important things that I think I will implement into my own classroom in the future!

Mathematical Activity #1: RUBRIC Writing (Week 3)

The reading for week 3 discussed RUBRIC writing and the steps that are involved.

This writing process could address any course or strand in any elementary, secondary, and post-secondary classroom. Although it should be introduced at a young age and practiced into the expert years, RUBRIC writing can be used by any mathematical learners, at any age, and in any level.

This activity brings out several mathematical ideas, including key terms, previous mathematical strategies, and reflecting on your work. The recommended words involved are CHECK, (Mason, Burton, & Stacey, 2010).

In my own classroom, I would have students post their work so that others can walk around and view it, just as Joyce had us do. Then I would have all of the students walk around and use the RUBRIC writing (explained previously) to reflect upon their classmates’ problem-solving methods with the same question. Finally, I would lead the students through a class-wide discussion on what worked and what didn’t, as well as how we could implement this method in the future and apply it to other, similar problems.

It was very insightful to listen to and observe my classmates’ reasoning behind their methods, and to explain my own techniques when solving the “Open Box Problem”. It was also useful to hear how my colleagues would plan and implement their own 3-part lesson using this problem. This not only supported my knowledge and understanding on the topic, but also provided me with a realistic way to apply this thinking into my professional practices. The small groups were also beneficial as they allowed every member to provide input into potential solutions and each one of us felt like a significant member. Our individual ideas and thoughts could be brought up to the group and considered in a collaborative effort with the others. Additionally, I found it especially interesting to see that every group thought of similar, but unique, solutions to the problem at hand. Not only did this allow us to see that there are multiple ways to figure out a solution, but also that every individual has different ways of thinking and learning. This is crucial knowledge for our careers, since we will encounter hundreds of students, no one having the same learning style. There are numerous different ways to solve mathematical problems, and there is no single “correct” strategy; so teachers must be weary of this and encourage diversity in the classroom by using differentiated instructional methods.

Mathematical Activity #2: Gallery Walk (Week 6)

            In week 6, Joyce explained the “Gallery Walk” strategy to us, and we had many opportunities to practice this throughout the course. This is a method of mathematical problem-solving in which the students complete their work, then they can either post their solutions or leave them on the desk for viewing. The name suggests the next part of this strategy, during which students walk around the “gallery” and view and reflect upon each other’s work.

This procedure could address any course or strand in any elementary, secondary, and post-secondary classroom. So long as there are motivated learners and a knowledgeable facilitator, the “Gallery Walk” strategy would work well. The content and process expectations that this strategy could address are also endless. In fact, this procedure could be used in any domain, not just mathematics. I could apply this to any subject in school that uses problem-solving processes, which is pretty much every subject.

Some of the mathematical processes that this activity imposes are independent problem-solving, mathematical communication skills, and reflecting on your own work, and that of others’. While the students initially solve the problem at-hand, they have the opportunity to practice their conjecturing and problem-solving skills on their own, or with little help from the teacher. Once the students have all had time to attempt the problem, they can then enhance their ability to communicate their mathematical thinking to peers, by both verbal and visual means. This involves elaborations that explain and justify mathematical ideas and strategies with enough detail. Once they have completed this communication process, they have time to reflect on their own work and review the work of others. They can also use their classmates’ feedback to learn how they can better solve similar problems in the future. Being able to implement colleagues’ feedback and use it to better your own understandings is critical in any subject matter, mathematics being no exception.

In my own classroom, I would have students post their work so that others can walk around and view it, just as Joyce had us do. I could also, if needed, arrange the students in small groups, so that they can collaboratively develop one solution to the lesson problem on chart paper. Then I would have all of the students walk around and use the RUBRIC writing (explained previously) to reflect upon their classmates’ problem-solving methods with the same question. Finally, I would lead the students through a class-wide discussion on what worked and what didn’t, as well as how we could implement this method in the future and apply it to other, similar problems. The purpose would be made clear to the students: to engage with a range of solutions through analysis and response. These solutions could also be recorded on computers, pieces of paper on tables, on the whiteboard, or posted on chart paper. I would likely schedule 10-20 minutes depending on the instructional purpose and depth of mathematical analysis expected.

For students, “Gallery Walk” is a chance to read different solutions and provide oral and written feedback to improve the clarity and precision of a solution (Unknown, 2019). On the other hand, for myself as their teacher, it is a chance to circulate around the classroom and gauge the students’ understanding of the topic. I could note students’ use of mathematical vocabulary and symbolic notation, as well as their mis-matched conceptions. From this, I would determine the range of mathematics evident in the different solutions and hear students’ responses to their classmate’s mathematical thinking. Such assessment for learning data can help – me teacher – to determine points of emphasis, elaboration, and clarification for the ensuing whole class discussion (Fosnot & Dolk, 2002). This would be a great way to apply assessment of learning and assessment as learning.

This activity influenced my own teaching journey by showing me that there is always more than one way to solve a mathematical problem. In other words, different students may have extremely different processes that they prefer, and may still come up with the same outcome. Every student in my class thought of similar, but unique, solutions to the problem we were given for that lesson. Not only did this allow me to see that there are multiple ways to figure out a solution, but also that every individual has different ways of thinking and learning. This is crucial knowledge for my career as an educator, since we will encounter hundreds of students, no one having the same learning style. There are numerous different ways to solve mathematical problems, and there is no single “correct” strategy; so, teachers must be weary of this and encourage diversity in the classroom by using differentiated instructional methods.

Mathematical Activity #3: Using Technology (Week 9)

Math can be fun! in week 9, we gained a plethora of resources, which can be accessed by going to the OAME website, the Math Resource Room, or other online websites. These are resources that we can implement in the classroom to make math more fun for students, or to create the lessons and content that we are teaching.

Technology could be easily used to address any course or strand in any elementary, secondary, and post-secondary classroom. It seems to have a great impact on student motivation, enjoyment, and success. The content and process expectations that this strategy could address are also endless. In the 21st century classroom, technology is a crucial tactic to get students more involved and interested in what it is that they are learning. this also reflects a flipped classroom model of instruction, since students can use technology to teach themselves certain concepts prior to discussing them in further detail in the classroom.

In my own classroom, I would have students select some of their own tech-based activities to investigate and complete, both individually and with each other. I could have students engage in the mathematical problem-solving processes and apply technology in their daily mathematical learning procedures. I could conclude these lessons by leading a a class-wide discussion on why technology is beneficial to use in mathematics and how it could be implemented differently in the future.

Overall, this course was a terrific learning experience! Upon entering this school year, I would have never imagined that I would be gaining all of the terrific resources that I have. Since Mathematics is my second teachable and I am not as confident teaching it as I am with Physical Education, I really appreciate all of the support that Joyce and my classmates have provided. I have really enjoyed this course as a whole, and it has been both insightful and delightful learning from Joyce and collaborating with my classmates. Throughout the year, I was fortunate to have been provided with various opportunities to practice and receive feedback on my mathematical teaching and instruction. I hope to continue to develop professionally and never stop learning about how to teach Mathematics in the I/S setting.

I am officially signing off of this blog, for now. Hope to see you all very soon!

via GIPHY

Resources

Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (Second Edition). Harlow, England: Pearson Higher Ed.

Fosnot, C., & Dolk, M. (2002). Young mathematicians at work: Constructing fractions, decimals, and percents. Portsmouth, NH: Heinemann.

Unknown (2019). Communication in the Mathematics Classroom. Capacity Building Series. Retrieved from http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_Communication_Mathematics.pdf

Online Class - Video and Webinar Reflections

            The videos and webinars that I watched for the online class this week were very interesting and stimulated a lot of thought for me as not only a future Mathematics teacher, but also as someone who genuinely enjoys math in general! I put a lot of thought and effort into choosing which videos I wanted to explore further; first, I specified the list to a few that look captivating to me, based on their name and topic. Then, I narrowed this selection down even more by reading the descriptions – if they were provided – for each of these videos in greater detail. Finally, I was able to select 4 videos/webinars to view, totaling about 100 minutes, collectively.

The first video that I watched, and the longest, was called Implementing Effective Mathematics Teaching Practices by Peg Smith, which she presented as the opening keynote at the 2015 CMP Users’ Conference. The University of Pittsburg professor uses “Connected Mathematics” as an example to describe the eight practices from the NCTM Principle to Actions and how they impact student learning. Primarily, Peg uses NCTM’s book as a framework for her discussion on how to effectively teach Mathematics. These practices explain to Mathematics teachers how they should work in the classroom, and how to anticipate and monitor the solutions being pondered by students. In this keynote lecture, Smith depicts the following practices (as taken from NCTM, 2014): establish mathematics goals to focus learning; implement tasks that promote reasoning and problem-solving; use and connect mathematical representations; facilitate meaningful mathematical discourse; pose purposeful questions; build procedural fluency from conceptual understanding; support productive struggle in learning mathematics; and elicit and use evidence of student thinking (NCTM, 2014). Peg opens by having the audience deconstruct and analyze a case study and transcript, then they discuss the practices, followed by a conclusion. She states that these practices are the vehicle that can essentially bring the math curriculum to life. Establishing goals is at the core of instruction, that ensures all students learn the expected outcomes. I have learned through my undergraduate years at Brock University the importance of starting with the curriculum, in any subject matter. Peg emphasizes the importance of this as the difference that causes students to learn. “Connected Mathematics” (CMP) is a strategy that I will use in my own future endeavors as a Mathematics teacher. CMP is a problem-centered curriculum approach promoting an inquiry-based teaching-learning classroom environment. Mathematical ideas are identified and embedded in a sequenced set of tasks and explored in depth to allow students to develop rich mathematical understandings and meaningful skills. This is a great way for me to help my students develop their mathematical knowledge, understanding, and skill along with an awareness of and appreciation for the rich connections among mathematical strands and between mathematics and other disciplines. I believe that all students should be able to reason and communicate proficiently in mathematics, and this approach will encourage the knowledge and skills necessary to do so. I found the video that Peg showed (Ms. Rossin’s class) to be especially helpful. The teacher in the video did not tell or show the students what to do; rather, she posed purposeful questions to get them focused and orchestrate productive discussion. As Peg engages the audience in CMP, guided by the eight principles listed, they can replicate students and act as learners in the activities presented. Professional development opportunities like this are ones that all teachers should be striving to attend, since our career entails frequent and ongoing professional growth in order to be the best that we can be.

The next video that I decided to watch was Dan Finkel’s Five Principles of Extraordinary Math Teaching TED Talk, via TEDxRainier in 2016. Finkel invites viewers to approach learning and teaching Mathematics with courage, curiosity, and enjoyment by focusing on the motivation, history, aesthetics, and deep structure of mathematics. He challenges the popular belief that math is dull, meaningless, and disengages students. As a young educator, I genuinely believe that making learning fun and enjoyable should be the main aim of every teacher. Learners are only fully engaged and motivated when they are interested in the topic and have a sense of enjoyment in it. The first principle “ask an authentic and compelling question” invites students to strive for a satisfying solution, since humans are inherently curious. The second principle, which acknowledges that we need time to struggle, helps us become “tenacious, courageous, and persevering”. Giving students time to think and grapple with real problems encourages them to interact, share perspectives, and deepen their ability to take risks and conjecture. The principle stating that the “teacher is not the answer key” addresses the fact that you, as the teacher, do not need to know everything. In this regard, teachers – and other adults – can teach children that learning is not failure, and encourages us to cooperate with the students to solve the question collectively. It also fosters cooperation between classmates via mathematical conversation and debate. The fourth principle is saying “yes” to students’ ideas, which I think can be difficult at times. Finkel says that there is a difference between correcting students when they’re wrong and saying “yes”. In other words, educators must accept children’s ideas and value them, and allow peers to show them why they may be wrong. The final principle explained is playing, which involves exploring, fighting, breaking things, etc. playing with math gives students ownership and gets their creative juices flowing. These 5 principles are crucial for me to implement in my future teaching practices, and I will ensure that I practice them each and every day in the classroom.

A third video that I found rather invigorating was How Professionals Use Mathematics to Solve Real-World Problems in the 21^st Century – a webinar by Keith Devlin. The speaker commences by presenting an article claiming that all the mathematics one learns becomes obsolete later in their lifetime. He continues to acknowledge that the way mathematics happened in the past is very different from how it is done now. He then addresses the question that stumps many humans today: Does having new mathematical tools mean we no longer need to teach calculation? Of course, he explains why the answer to this question is “no”. however, he claims that we no longer need to teach for accurate or fast execution. Instead, we must teach for understanding. As a teacher, I must understand that today’s users of mathematics require different skills. A creative analogy that he makes is that yesterday’s mathematics users had to learn to play many “instruments”; today’s mathematics users, however, have to be able to conduct an orchestra. Some of the things that we must teach our students, then, include number sense, deductive reasoning, creative problem-solving, and more. Therefore, we must teaching thinking! A heuristic is any approach to problem-solving, learning, or discovery that employs a practical method not guaranteed to be optimal or perfect, but sufficient for the immediate goals. In mathematics, educators need to develop their students’ post-rigorous thinking by practicing algorithms and procedures optimized for efficient performance. It is only through teaching for effective understanding in the 21^st century, then, that mathematics can be made meaningful for our students and allow them to develop their mathematical thinking skills.

The final clip that I wanted to reflect upon was another TED Talk (from TEDxNorrkoping) called The power of believing that you can improve by Carol Dweck. As soon as I read “growth mindset”, I knew this would be a video of grate interest and value to me. I have always seen myself as someone with a positive, optimistic viewpoint on life, and I try to facilitate this same perspective for others. The idea that we can grow our brain’s capacity to learn and solve problems fascinates me as not only a person, but also as an academic and future teacher. Dweck uses this talk to describe two ways to think about a problem that’s slightly too difficult for you to solve: either you believe you are not smart enough to solve it, or you just have not solved it yet. It is a major goal of mine to teach students to adopt the latter of these two mindsets. Having a positive self-conception is a critical life skill for humans to possess, which we can use to structure ourselves and guide our behaviour. I aspire to motivate students and enhance their self-regulation, and their impact on achievement and interpersonal processes. Instead of running from difficulty, cheating, and having a fixed mindset – like the students on the left side of Dweck’s opening example – I wish to raise children to think “yet” instead of thinking “now”. achievement is meaningless if we cannot better our efforts and become more knowledgeable and skillful. In contrast, if someone recognizes that they can be better and make every effort for this, the point at which they are starting is irrelevant, since they will eventually reach and exceed their goals for success. This is illustrated in the second example, where the Native kids outdid the Microsoft kids because the meaning of effort and difficulty was transformed so that the kids’ neurons made stronger connections, making them smarter. I believe that this should be a primary goal for all educators, since understanding that abilities are capable of growth is all one needs in life to succeed.

References

Devlin, K. (2018). How Professionals Use Mathematics to Solve Real-World Problems in the 21^st Century. Confent Video. Retrieved from: https://vimeo.com/292393546

Dweck, C. The power of believing that you can improve. TEDxNorrkoping. Retrieved from: https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve?language=en&utm_campaign=tedspread&utm_medium=referral&utm_source=tedcomshare

Finkel, D. (2016). Five Principles of Extraordinary Math Teaching. TEDxRainier. Retrieved from: https://www.youtube.com/watch?v=ytVneQUA5-c&feature=youtu.be

National Council of Teachers of Mathematics (NCTM). (2014). Principles to Actions: Ensuring Mathematical Success for All.

Smith, P. (2015). Implementing Effective Mathematics Teaching Practices. CMP Users’ Conference. Retrieved from: https://www.bigmarker.com/GlobalMathDept/Implementing-Effective-Mathematics-Teaching-Practices

My Weekly Report and Reflection 10 (Week 18)

Holy, it is hard to believe that this is my final blog of the year for this course! It has been ana amazing experience and I have loved every second of my time in the “Teaching Mathematics (Part 1)” course. This week, it was my turn to lead a learning activity. I really enjoyed the entire process: creating this activity and facilitating the students’ engagement in it!

This project provided me with several crucial insights as a future Mathematics teacher. I organized this activity based on there being three students per group. In a full class, I would put the students into three or full smaller groups. They would complete the main activity in a “Jigsaw” style. They would start by discussing the examples that they are given with their small-group members for about 10-15 minutes. Once all groups have finished considering their respective examples, each group member will be dispersed into a new group with one person from each other group. Here, they will represent their former, original group by speaking as an “expert member” and explaining their problems with their peers. Finally, the class will engage in a class wide discussion involving everyone, where we will converse some RUBRIC writing that we did throughout the process. This will include times when we were “STUCK”, special findings or “AHA!” moments, times when they reasoned or wrote “CHECK”, and other key ideas/moments/learning experiences as they “REFLECT”.

Kirsten said it could be good to add to each example by extending them so that they fit in more than one category. Thus, I began asking groups to turn these rather “black-and-white” examples into ones with multiple solutions by adding “grey” areas. For instance, in a question that involves a cigarette company asking 5 people in Niagara if they smoke obviously illustrates misleading statistics through small sample size. However, I could prompt the students to alter this question by adding, for example, that the cigarette company asked 5 people “Do you smoke cigarettes, even though they are disgusting and likely to kill you?” This would make the question not only a small sample size, but also faulty polling, since they are clearly persuading the respondents to answer that they do not smoke.

We also debated making this activity technological (done on computers), but concluded that we believe the hands-on format is more fun, engaging, and better suited for Grade 12 College level students. Although there is a time and place for technology to be implemented in learning, that place in not this particular context. High-achieving and Gifted students may benefit from answering the activity example questions online and independently. However, College level students prefer (for the most part) hands-on and visual-kinesthetic learning. Hence, I would leave this activity as is when teaching it in the future to a College or Applied level class.

Another thing that I started doing with the second group that worked really well was having them debate their answers to each example and try to get their group mates to side with them and change answers. This encourages the students to use higher-order thinking skills and consider other perspectives. It also enhances students’ verbal and communication abilities, which is a life skill necessary for all college-bound students. I find that this strategy worked especially well when the example actually did have more than one answer possible, since no students were “incorrect”. For example, the example that posed the student as the head of a marketing campaign that wants children to wear Champion brand clothing had more than one potential “correct” answer. The example went on to state that “you phone 8 of your friend’s kids, 7 of whom have admitted to wearing Champion”. After pondering this question, it is evident that it could have more than one possible solution: small sample size and selective bias. More open-ended questions like these encourage higher-order thinking skills and make the discussion was much livelier and more meaningful!

Overall, this curriculum assignment was a terrific learning experience! Not only was it a great opportunity to lead my peers through and activity and discussion, but it was also my first structured opportunity to teach a math lesson of any type in the classroom. Since Mathematics is my second teachable, I have never actually taught a structured classroom lesson in the subject, and this is something that I am somewhat anxious about doing in my future placemats. It is imperative, then, that I am provided with such opportunities to practice and receive feedback on my teaching and instruction. Experiences like this one are crucial starting points and allow me to exercise my “Teaching Intermediate/Senior Mathematics” pedagogies and practices in practical and applicable ways!

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!