Grant and Zeichner’s Article Sept. 14

Grant and Zeichner’s article “On Becoming a Reflective Teacher” made me think a lot about the teaching profession and there are a few points that really intrigued me. I was interested by the article mentioning the amount a choice a teacher faces on a day to day basis and over the course of their careers. From the choice of teaching style, instructional values and views, to which content to stress as being critical, to how we teach to specific groups of children and even our attitude as to how we go about teaching. Futhermore, what this article discusses is relevant to modern teaching as well. Teachers have a lot of impact on the lives of their students. The theme of the impact that teachers have on their students resonated with me becuase I am a math tutor and have seen this impact firsthand. “Reflective action” was the vocabulary in the article that stood out to me the most. I don't believe that there is one approach that solves teaching and learning, however, there are best practices in each style, pedagogy, etc. that can be used to make the classroom the best, more inclusive learning space it can possibly be.

Final Reflection on EDUC 450

I learned a lot about different styles of education especially embodied, multi/cross-disciplinary, and outdoor learning. I had never experienced many of these styles of education before so it was an informative and enlightening experience. One of my favourite aspects of this course was the learning about multi/cross-disciplinary pedagogies. For instance, in one class we learned about rope making, weaving, and braiding. I tried a traditional form of bag weaving which was a really interesting experience because it was a indigenous form of weaving from another part of the world and it was challenging! Figuring out how it was meant to be done and what the pattern might be took me a good portion of the class, but by the end of the class I had settled on a pattern and was able to make substantial progress on a bag. This was an interesting activity because there elements of math (the pattern) but also Indigenous ways of knowing, critical thinking, and problem solving involved; so much of which is involved in mathematics in general. I also really enjoyed the inquiry project aspect of the course as it satisfied my desire for autonomy, choice and relatedness. I think my main suggestion for improving this course would be to focus more on the inquiry project side of things and allow students more exploration in an area of their choosing. This was the strongest part of the course for me, I enjoyed the research, the collaboration with other students, and coming up with ideas about my subject area.

Final Project Slides and Reflection

 https://docs.google.com/presentation/d/1qLdufvO58D6oKedjwJ7fSl9MCZEUAqd50kt-JeygpmM/edit?usp=sharing

Reflection

During this inquiry project I learned a lot about my own position on what makes math interesting through reflection and consideration of my own math journey, while also simultaneously learning about the educational systems of highly successful countries Finland and Singapore and their techniques to achieve such success. Did they care about student interest in the subject? Or was their goal only to get high scores on PISA testing? It turns out that interest in mathematics is a foundational principal in their education systems and I learned how they define 'interest' and the purpose it serves in their system. There are so many interesting aspects of this project that I discovered along the journey. If I were to consider what to take forward into future inquiry, I would want to investigate more into how our education system is fundamentally structured to support student interest, how higher mathematics could be integrated into the high school curriculum, and I would possibly want to dive deeper into the education system of Finland. This project lead me in many interesting directions, many of which I did not expect. For example, I did not expect to feel so strongly about integrating higher mathematics into the high school classroom, but when I thought about it over an extended period of time, the more it seemed to make sense. If we want students to be interested in math, then we need to make math relevant to them and give them the most interesting problems mathematics has to offer. Many of the concepts in calculus, abstract algebra, geometry, etc. can be broken down, simplified and made approachable for unseasoned mathematicians. Many of the concepts in these topics already connect to the fundamentals our curriculum is based on. From this point in my inquiry, I am very interested in pursuing inquiry into the technological revolution of education and what that means for the framework of our school systems.

Dec. 2 Exit Slip

 I enjoyed learning about the change ringing practices and how it relates to combinatorics. It's a very practical problem that we could give to students and ask them to figure out how a team of people ringing bells could simply move through the various combinations. The answer of course is the end switch, middle switch algorithm which enables easy navigation of combinations. I think this would make an excellent activity to explore combinatorics but also learn about mathematics in everyday life and how intertwined mathematics is in seemingly simple activities like ringing bells. Furthermore, this could be a great way to introduce braiding and weaving patterns in general which you could connect to Indigenous education which I think essentially is our job as educators, to facilitate students making connects and expanding their intellectual horizons.

Annotated Bibliography

1.  Paksuniemi, M., Keskitalo, P., & Brill Online Books. (2019). Introduction to the Finnish educational system. Brill Sense.

       This source provides detailed information on the Finish education system which is a point of interest for my inquiry project. It gives the history, modern formulation, and even includes aspects of their system with relation to Indigenous education. I will be looking at the foundational ideals behind the Finnish education system this book discusses and relating them to how they help create better mathematics learners and genuine interest in those learners.

2. Yarborough, C. B., & Fedesco, H. N. (2020). Motivating students. Vanderbilt University Center for Teaching. Retrieved Nov. 24 2021 from https://cft.vanderbilt.edu//cft/guides-sub-pages/motivating-students/.

    This article is about motivating students and specific tools that can be used to increase intrinsic motivation. Interest and motivation are linked concepts and it is one aspect of my project that I will be exploring. Specifically, I will be using their expectancy-value-cost framework as an example and their insights on self-determination theory to provide concrete ideas for how teachers can create interest in students.

3. Stemhagen, K., Henney, C., & Taylor & Francis eBooks A-Z. (2021). Democracy and mathematics education: Rethinking school math for our troubled times. Routledge.

Democracy and mathematics education is about a modern approach to mathematics education that is founded in student inquiry and relates math to society and democratic practices. Figuring out what makes math interesting involves finding educational practices that motivate students and enable them to find interests in previously boring or uninspiring subjects. I will be using their tenets of democratic mathematics to argue for a more social and collaborative approach to math education.

4. Danesi, M., SpringerLink (Online service), & SpringerLINK ebooks - Education. (2016). Learning and teaching mathematics in the global village: Math education in the digital age (1st 2016. ed.). Springer International Publishing. https://doi.org/10.1007/978-3-319-32280-3

This source also discusses modern mathematics education and how innovations in technology have transformed pedagogical practices. If students are to be interested in technical and sometimes challenging subjects we must modernize our teaching practices to remove barriers to education. I am personally an advocate for more technology use in the classroom, bringing the classroom outside of the school, giving students more autonomy and moving away from strict student teacher dynamics. This article provides insight and support for many of those ideas.

5. Tan, O., Low, E. L., Tay, E. G., & Yan, Y. K. (2021). Singapore math and science education innovation: Beyond PISA. Springer Singapore Pte. Limited.

Singapore is another country (along with Finland) that has received international attention for their success on global testing standards and their educational practices. I will be looking at their educational systems to see how they impact student interest and achievement. Specifically, I will be looking at their foundational curricular principals and inquiring about whether these help students to have genuine interest in what they are learning.

6. Elias, M. J. (2016, January 14). How and why Intrinsic Motivation Works. Edutopia. Retrieved December 2, 2021, from https://www.edutopia.org/blog/how-and-why-intrinsic-motivation-works-maurice-elias.

This article provides more insight into intrinsic motivation and how it can be harnessed in the classroom. If students are to be interested in a subject, they must be motivated to do it! My inquiry project will incorporate their suggestions of controlling versus supportive instruction and giving constructive feedback.

7. Rubach, C., & Bonanati, S. (2021). The impact of parents' home‐ and school‐based involvement on adolescents' intrinsic motivation and anxiety in math. Psychology in the Schools, https://doi.org/10.1002/pits.22577

This article looks at intrinsic motivation from a different perspective, specifically home/parent involvement in student education. Often student interests come from influential people in their lives such as parents, so it is important to consider the role this might play in my inquiry. If we our goal as educators is to foster genuine interest in students, we must use all options and resources available to us and the parent involvement this article advocates for is one of those resources.

8. Besser, L. (2020, January 31). Why Finland's schools outperform most others ... - youtube. Retrieved December 2, 2021, from https://www.youtube.com/watch?v=7xCe2m0kiSg.

This video is an interesting news piece done by ABC news in Australia that looks at differences in the finish education system and provides much more visual and intuitive reasons for why their system is so effective. I will be using this source as an audio-visual aid during my presentation to illustrate the Finnish education system for my peers because it gives the perspective of students, parents, teachers, and administration.

Nov. 18 Exit Slip

I think for my inquiry project and connecting it to the real world, I will be having informal conversations with my SAs and even some of the students during my Tuesday visits. The information I will be able to gather from students will be limited because it often takes time to build rapport and have genuine conversations with anyone. Furthermore, I will be talking to future CFE placement options (I know them personally) about their thoughts on math pedagogy and what it means in their areas.

I have focused my project topic to thinking about personal interest and how curriculum and exploration can play a role in building genuine personal interest. So essentially, I am looking at genuine personal interest and how that can be used to the advantage of the math classroom.

Exit Slip Oct. 21

I enjoyed our discussion in this class about gender and diversity in mathematics, it was so interesting. It is an important discussion to have as we try to create a space that is welcoming for anyone who is interested, passionate or curious about math. The videos that we watched in class were great introductions to diverse people who have been highly successful in the math world and can act as models for those who feel they may not have been represented in math up until recently. Although there was some debate about the video with the woman mathematician, I liked the video because I thought it (much like the video about the mathematician of Indian descent) portrayed her as a normal person not some kind of cave dweller with no friends. This is an important thing to do because there are negative stereotypes about people that like math and the type of person you need to be to do or appreciate math.

Inquiry Project Topic Sheet Oct. 21

 I chose this subject area because I have always been very interested in the curriculum, what makes some people "math people" and other not, and how we can use the tools at our disposal to create more engagement and personal interest in math. I have broken my topic down into three concepts accordingly. Exploration and creativity because I think students should have more free reign over what they are learning in their high school classrooms and the math curriculum can be a bit boring at times. Personal interests because I want to see what creates any sort of personal interest in academic subjects. And finally, making advanced math topics more accessible because I think that the BC curriculum is pretty limited in the scope of mathematics that it teaches and especially for young, eager students, I think there should be opportunities for exposure to more advanced topics. 

Response to Grading Practices, Entrance Slip Oct. 21

 Grading is a really tricky issue especially in math and the sciences where it is traditionally assume that there are correct answer and incorrect answers. Assigning grades to students can be a very subjective practice and when students are only given percentages or letter grades and no feedback or direction, the grade is of limited value in my opinion. I think it is good to give students grades to inform them about their learning, where do they stand? How much of the content do they understand? but those grades also need to come with direction for the student, where do you go from here? How can you improve in your weak areas?

Some of the limitations of grading become apparent because grades are a very binary 'right and wrong' type of assessment. They can give students the wrong impression about education and learning by discouraging students who perceive their situation to be hopeless or not worth improving. There is also a perception around what grades make which students successful or smart and they can also deter students from taking classes where they won't excel. A good education is a well-rounded one and a student that doesn't take an upper-level math class because it will destroy their GPA despite being interest, well that's a sad situation to say the least.

The new grading system being implemented in the secondary system by the ministry is a really interesting take on how grades are changing and how their role is transforming. I can imagine teaching a class and using something like that to grade my students. I think it is a much more effective way of guiding students on their learning journey.

Sept. 16 Make-Up Assignment Part 2

Two kinds of sundials

1. Horizontal sundial: The horizontal sundial is one of the simplest sundials and has been in use since at least the ancient Egyptian and Babylonian times. Obelisks in Egypt are thought to have once been used as sundials. The construction of such sundials is done according to the latitude of the location where the style height of the gnomon (the angle the gnomon makes with the perpendicular) is equal to the latitude and the angle separation of the hour lines can be done according to a formula.

2. Vertical sundial: Similar to the horizontal sundial, the vertical sundial is also constructed according the latitude of its location. This time the style height of the gnomon is also calculated according to a trigonometric formula as is are the separation of the hours lines. Depending on the location and orientation of the sundial, it will be restricted in the amount of daylight hours it can be used. For instance, a direct north-facing vertical sundial in the Southern Hemisphere will only be usable during the hours of 6AM to 6PM. Examples of a vertical sundial can be seen in Ireland in the 7th century.

Exit Slip: Oct. 14th

 I really likes the ideas presented in the videos we watched in class today. In particular the idea that math should not be associated with speed really stuck out to me because I am a slower learner and often a slow problem solver, I really like to think about the problems that I am tackling so that means I don't do well on tests where there is a significant time constraint. I also really liked the idea of grades not being a motivating factor for students. I think it's very true that students will pander to what the teacher wants to hear or pick the easiest route because it means they will get a decent grade or pass the course or whatever goal they are trying to achieve by being in a class. Some students learn just as much even with grades, so there is a diverse range of students and needs, but I think we need to think more about how grades are implemented into our classes and what they really mean for students. Another idea that I really liked from the videos is the idea of the growth mindset. It is very damaging to children and their education when they are engaged with a fixed mindset, ie. "I can't do math.". As teachers, I think it is our job to engage students in a growth based mindset and to ask the questions and provide the guidance that can get them to fully embrace a growth mindset. 

Entrance Slip Oct. 14

One of my main concerns as I am in the process of becoming a teacher is that I will lean too heavily on the methods and experiences that I have from my time as a high school student. When I went to high school, everything took place in a very traditional classroom with very traditional assignments; there was homework assigned from the textbook and we did a test every few weeks or so. This article talks about how there is so much more to education than the traditional "grid" based systems imported from western nation over hundreds of years. There has been a heavy focus on organization and homogenization of the education system and we are doing a disservice to our students by perpetuating the negative aspects of those systems. I don't think that we can completely reject the "grid" because there are useful aspects to it, however, I think the key is realizing that there is more beyond the "grid" that can be used to greatly enhance our teaching.

I agree with the  idea of an alter-global approach to education. I think this is a very powerful idea that can help students to veer away from the harsh hierarchies that are dominant in our social structure thus allowing them to think and learn differently. We need to seek a different kind of connection with our peers, our community and our global neighbours so this idea really resonates with me. I think that this connects with the swing dancing and parkour ideas presented in this article as well because they styles of movement are very different from traditional way of movement and therefore could be used as a metaphor for how we must approach global issues like climate change and how those issues can be integrated into the classroom. We must approach these issues differently and we must teach differently if we are to make progress in our education systems.

Reflection on Rope Making and Weaving: Sept. 23rd

I really enjoyed this exercise of making rope as it demonstrated to me how we can utilize an Indigenous way of knowing and integrate that into our mathematic education. This activity was also a really interesting activity because of how easy it would be to do this with a class and to link it to mathematical concepts. Encouraging kids to think about Indigenous ways of being and learning from the land is very important to me as our society is taking steps towards reconciliation so this is a way of educating ourselves and our students on such an important issue. I chose to also engage in the bag weaving project which provided a challenge to work out how the bag was constructed and to create a feasible method of creating a bag for myself. The progress I made on the bag is pictures.

Leaf Geometry Exercise Oct. 7

 Doing this activity helped me this about the patterns and elements of chaos present in nature and specifically how I could represent some of those aspects using simple geometric tools. My method was to to draw circles inside and around the leaf to see what patterns I could discern while also allowing for space to incorporate the jagged edges of the leaf that would require additional iterations to include in the construction.

Sustainable Mathematics Education: Oct. 7

"Issues of sustainability call for an interdisciplinary conversation. Mathematics educators can bring important perspectives to bear on this conversation, due to their familiarity with the vast network of metaphors, exemplars, applications, and algorithms that underlie proportional reasoning." pg. 21

This quote speaks to me because I personally love the interdisciplinary nature of math and I love seeing the way that math can be applied in novel ways in other fields. One of my own favourite topics of study is mathematical biology which also has a strong environmental/sustainability aspect which makes this quote even more relevant to me and makes me eager to share this kind of learning with my students.

"Sustainable mathematics education is about seeing the world anew through renewed mathematics. It is concerned not only with feeling large numbers, but also with feeling the global situation. It trades linear metaphors of certainty and separation for complexity metaphors of possibility and connection. It helps us relinquish our desire for deterministic predictability and embrace the contingency and stochastic probabilities of each living moment. It turns mathematics from a collection of objects, or a series of competencies, into an open-ended state of observing the world. It aims towards a more complete and appropriate mathematics, and from this position it calls on us to engage in ethical action for healing the world." pg. 25

I really like this quote because it describes mathematics in quite a beautiful way. It moves away from describing math as something rigid and cold to something that is highly applicable to the real world and applications that really matter. It is the language by which we can communicate ideas regarding all disciplines and create solutions for issues regarding the environment and sustainability. 

I will address the climate crisis with my students by discussing the mathematics of climate models, recommending books and other literature for them to read, and providing real applications of how math is used and specifically how the math they are learning can be used and will lead to even more interesting applications. Gearing projects and assignments towards this issue would also be a valuable way for students to put their minds towards this pressing issue and get them thinking and interested in the various fields that are involved.

Entrance Slip Sept. 23rd

 One of the striking questions for me asked by Kallis is "what if we started to make some of the things we need for ourselves a social and cultural norm?". I think this is an incredibly powerful concept from an environmental perspective because it shifts us away from consumerism and into a mindset of recycling, upcycling, making use of what we have, and being thoughtful about what we need. Furthermore, I think this concept connects deeply with learning because it challenges us to produce things for ourselves and in doing so, solve the problems that might otherwise be fixed by someone else's product because it is convenient. This concept of producing what we need for ourselves helps us to become lifelong learners as well because to make a thing often requires some skill or other that we might not have developed otherwise. While we are making a conscious effort to help the environment, we are also learning and building upon are knowledge base to become more self-sustaining. This also provides an opportunity to connect with Indigenous ways of knowing and being in a more meaningful way by participating in those practices.

Of the three videos, I am very interested to try the Turkish string bag technique because it creates a very interesting geometrical 'web' pattern and I am wondering how that design could be altered. What other kinds of designs or patters could you imprint into the bag as you weave it? The 7-string braid video was also interesting because the pattern reminded me of Celtic designs I have seen before.

Sept. 16 Make-Up Assignment Part. 1

Reflection: Learning by Drawing in Stem

The "constructive use" idea of using drawing as a means of inventing a novel form of visualization is a really good idea for a math classroom because of the way it allows students to connect with the topic they are learning, but also possibly find understanding for themselves and a way of visualization that could benefit their classmates as well. Further to this point is the "interactive use" of drawing that the authors explore. Drawings can be used to exchange ideas, construct arguments or even tell stories, all of which are tools that could be used in a math classroom to enhance learning and create a sense of ownership among students of the knowledge they are exploring.

I would use drawing in my math classroom as a means of creating visualizations (novel or not) so that students can discover more about the topic and have a better understanding of it. Drawings take time, especially drawings that are meant to be mathematical in nature. If you are trying to be accurate to a pattern, function, or set of data, care must be taken to ensure correctness. This helps students by giving them time to process what they learning and also to help each other to figure out this different kind of "problem".

Natural and Unnatural Drawings

Drawing Reflection

Drawing natural objects and comparing them to natural objects is an interesting process because of the differences in structure, form and purpose. Straight lines and right angles typify these characteristics in human made objects because it makes manufacturing easier, they are built for one purpose, and it is easier to arrange or organize objects of a regular and confined shape. For instance, a box or rectangular container is built to hold things, the construction of such a box can be done by machine because a rectangular prism is a relatively simple object, and the arrangement of multiple boxes is easy because they can be conveniently placed next to each other or stacked. Right angles and straight lines also exist in nature in places like certain rock formations, the path that light travels is always a straight line, certain plants grow in very straight lines (bamboo) and will sometimes have branches that occur at right angles by chance because of optimization towards resources. 

Fractal geometry: a pattern that can be defined by some process or mathematical relation which identify subsequent iterations of the pattern.

Exit Slip Sept. 9

I like what Dr. Mccourt said about not fighting with students and instead using what they disagreed with or were fighting against as a way of engaging with them. He had to learn the American culture and specifically the teenage culture of the time which probably worked to his advantage because it would have offered him a better insight into their worlds. His success seems to be largely based on his adaptability and ability to work with students, not against them creating a more enjoyable and engaging learning environment. Dr. Mccourt had a long and very successful career so he must have also developed effective assessment methods. What would such celebrated teacher say his most effective tool was? Being an English teacher, I would also like to ask him about his take on mathematics education: how would someone like Dr. Mccourt lesson plan, teach, and assess mathematics from the perspective of an English teacher? Dr. Mccourt's way of teaching informs my own because I also strive to work with students in a way that engages their energies, so his methods of teaching are particularly interesting to me.

Hello world

 First test blog post