Resources Week of January 10th

 

Wrigley, W. J., & Emmerson, S. B. (2013). The experience of the flow state in live music performance. Psychology of Music, 41(3), 292-305.

The authors of this article investigated the state of flow when in regards to the performance of music. As I believe that the performance of math is very much similar in sense of practice and reproduction in a creative way, I wanted to investigate the initiation of flow in other performance areas in order to find applicability to the math classroom.

 

Keller, J., & Bless, H. (2008). Flow and regulatory compatibility: An experimental approach to the flow model of intrinsic motivation. Personality and social psychology bulletin, 34(2), 196-209.

In this article, the authors experimentally investigate the level of performance when one is the state of perceived flow. I wanted to see that while the ultimate form of engagement is the state of flow, there must be a real benefit involved in entering the state of flow. I want to see if there was a performance benefit when fully engaged in a task and is this benefit a measurable benefit of merely just to have students be engaged in the task.

Final Course Reflection

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Reflection:

I feel that it has been an eye opening experience this term in Educ 450. I really liked how the class was not structured like a typical math classroom. We went outside, we looked at embodying math in the arts and in the world around us and it was just refreshing to see that math can be taught differently than the stand and lecture style that I'm so used to. There something to say about bringing in hands on activities and emotions into the math classroom that is so human in it's nature and so engaging. While I myself and not really a fan of being outdoors, I can see the benefit of the practice of the outdoor classroom and I might try taking my students outside when the topic allows. I feel that doing something like this together builds a sense of community in the classroom which benefits learning as a whole. I feel that in the future, we do even more hands on activities that embody math that would give even more incorporation of other fields into the math classroom, maybe something along the lines of using technology in the math classroom.

Final Project: Motivation into Flow

https://docs.google.com/presentation/d/1kq3ZR4OBiHR5Vlq71VYsZkU3RS7uRM6wdYdXN2h0JQE/edit?usp=sharing

Reflection:

I really enjoyed working on this project that allowed me to pursue an area that I was really interested in, in terms of my math career. While I was always interested in math, i noticed the mast majority of people around me where not interested in math. Using my work previously in a school and my observations in the classroom, I noticed that one theme dominated the math classroom. "How can we increase engagement, what is the ultimate form of engagement and how do we as teachers accomplish this?" In my research, experience and conversations with teachers and students, I learned that motivation and engagement is key to gaining the optimal learning outcome. While some students will always perform regardless anything we do as teachers in the classroom, all students benefit from increasing motivation and engagement. I think that in my inquiry 2 project I would like to continue diving more deeply into getting students to be motivated and more deeply into the state of flow. It's truly a fascinating idea of how someone can be so engaged that there is only one goal in mind losing track of all ease. By having students in this state, they can achieve optimal engagement and learning. Things have mostly turned out the way as I expected as it was my experience previously in the classroom, but one idea I had not realized is that this idea of engagement is beneficial for teachers as well. I had not realized how important it was to for students to be engaged for the wellbeing and comfort of the teacher as well as the student. I think I will continue to explore the ideas of engagement and flow and how I can create an involved, engaging classroom that promotes this idea of the state of flow.

Exit Slip Dec 2.

What a wonderfully engaging class. At first when I considered bell ringing in the cathedrals and churches, I never thought that there was so much math behind it. I assumed that someone just went up there and rang the bells however they see fit. I did not know how much organization and structure there actually was to something that sounded very much chaotic at the moment. The idea that the bell ringers could play for hours in order to complete a specific pattern is truly amazing. When it was broken down to combinatorics, that's when it became truly intriguing. The idea that using something so physical and ancient as ringing bells could bring about such advance math concepts and embody them in such a hands on way really fascinated me. I really enjoy music and using a structured pattern in math to connect with the physical act of making music is a great experience that any math student can enjoy. 

Annotated Bibliogrpahy

Annotated Bibliography

Connecting with teachers and students in regards to our inquiry project

 When I was on my short practicum, I had already had in mind to talk to various teachers in regards to my inquiry project. I have visited many different classrooms and was able to talk to and witness different teachers and their approaches in regards to engagement in the classroom. 

I however, did not talk to any students about this topic and plan on talking to a few students which I have built some rapport with in my previous visits and ask them about how they feel about engagement flow and their experiences in that regard in my next follow up visit.

Pro D Day Reflection

 After attending the math pro-d virtual conference. I have come to realize the innovation that teachers have strived for in the teaching of math. While I have attended plenty of Pro-D sessions working in a school for the past 5 years. I have never attended the math conference as I was more focused on conferences that involved work with students with learning differences as working with these students was my main role in my school. The conference was vey engaging and lead to some useful information that I actually used in my short practicum experience. The most impactful was the use of desmos in the math classroom. Previously I worked in a more affluent neighborhood and the students were afforded with the luxury to speed $100+ on a Texas instruments graphing calculator and since this was required for their courses, this was the norm for them. It was "no big deal" when they lost or damaged their calculators, they simply asked their parents to buy them a new one. So as I was aware of the Desmos as a program you could use online, much of my work was focused on students using the graphing calculators. When I went to my practicum school however, it was in a far less wealthy school where parents did not have extra income to spend on an expensive graphing calculator. My SA therefore did not require the use of a graphing calculator in his classes. Instead, he would demonstrate and explore graphing using desmos. The students all had phones which they could access desmos from and explore graphing in a completely new and much more powerful way. Using desmos, students could do much much more than just using a regular graphing calculator and the accessibility and ease of use I feel really enhanced their learning. The user interface was quite intuitive and important information such as intercepts, intersection points and such were automatically shown to them. The workshop on desmos showed me how to engage with the students using the program and how to let the students explore on their own in order to come to conclusions about graphing and solving equations that is much more effective than just telling the students about the properties of those functions.

Another take away from the conference was the idea of engaging with students in a low risk environment. In order to take a much more involved and personal approach, creating an environment where risk taking is encouraged and both curricular and non curricular problem solving and exploration can really help to increase engagement to for students. I witnessed this first hand in my practicum experience. The first was when I conducted a group problem solving activity using Susan's locker problem in class as an activity that taught students to recognize patterns. The students were so engaged that many of them wanted to stay after class in order to solve the problem when in most cases these same students would be rushing to pack up and leave 5 minutes before the bell. The second was when my SA changed that way he assessed the students. He told them to bring in a game of their choice and consider that probabilities involved in those games. The students then worked in small groups to play those games. At the end of the "lesson" My SA asked each student to describe their game and based on what they learned about probability explain to the class how their game related to probability. He took notes on how each student responded and gauged their understanding based on their answers. I found this a very interesting way to make the class fun (with students engaged in games) but at the same time turned it into a way to formatively assess his students' understanding.

Welcoming in the math field

 

In my career as a math student from secondary to post-secondary, my math teachers have always been men. I have never really thought much about this as the majority of my teachers as a whole have been women. I just assumed that this was matter of coincidence. It was not until this class that I have reflected on this and it does seem women are underrepresented in the field of math. All of the “great minds” of the past were always men due to the structure of society in the past and it seems at least to some degree this has changed today. Just having a look at our math classes in the Bed program, there seems to be a relatively even distribution of men and women. I see that while the math field may not seem to be especially welcoming to women (and I would argue to most people in general), there has at least been some positive change in this regard. Math seems (to me at least) a more challenging and academic field that still carries the stigma of being old fashioned, traditional and more strictly academic than most fields and is rather unwelcoming as a whole. This might or might not be correct but that is how a lot a people seem to feel when I tell them I have a degree in math.

I find that in order to build a classroom and society that is welcoming for all, it is important to value respect and understanding above all. In order to be inclusive to all in our classrooms we have to at least be aware of different ethnicity, socioeconomic backgrounds, identification of gender etc. in our classrooms and in society as a whole. We need to be understanding and be respectful to all in order for individuals to feel welcomed and included. We need to aware of the language we use, the materials we teach and out interactions and do our best to be inclusive and build relationships with our colleagues and students. This allows for everyone to feel safe and valued in the learning environment. When people feel safe, they are free to explore and learn to the best of their ability.

Final Inquiry Ideas

 

 Search Topic: Investigating methods in improving student engagement of mathematics in the classroom.

Analyse your Topics into Concepts:

A: Building a math environment that encourages students to make mistakes and explore ideas.

B: Using comedy, visuals (animations) and stories/events to engage students in mathematics.

C: Using interactive problems and hands-on experimentation to engage students in applying mathematics

Do Grades Matter?

 

Do Grades matter?

From my “student bird” perspective, I personally have found comfort in grades and percentages I did not think much about what they actually meant, but more of something to try to achieve. Maybe I had always done well in standardized test and in school in general so grades were relatively attainable and I did not feel the stress that other students felt. I tried to keep my marks to myself and so comparison or competition did not really cross my mind. The only time that stress began to creep in was in Grade 12, where there was competition to enter university. I might be dating myself a little but my grade 12 year was the last year of grade 13 in the east coast so there were significantly more students trying to enter university at a time when grades were all that mattered for university entrance. So, I do see the validity of the argument that grades can cause stress and competition among students. As a teacher, I see grades as basically a tool for accountability in teaching. It is merely an easy way to demonstrate that a teacher has done some work in order to evaluate students. It is far from effective was a gauging a student learning but many teacher clings to the percentages as a way of standardizing their work and providing some level of accountability in their teaching.

There are some key side effects from using percentages and grades in schools is that they foster a need for competition, an atmosphere of anxiety and an imbalance of power in the classroom. I feel although unavoidable, grade put a teacher at a position of power and this makes it difficult for students to truly feel safe in the classroom. There will always be students who pander what they think the teacher might like or want, but not actually pursue their own learning. They simply seek a meaningless number of letter on a piece of paper in order to feel successful. And this too is unavoidable. There is always pressures to enter university, pressures from home and pressure from peers for a student success. I feel that while the school system is established to help students learn, it might not help students learn to the best of their ability. Students are merely forced to learn by a system that puts too much value on a letter or a number that might not even truly reflect a student’s learning.

I believe that it is definitely possible teach math and science without the emphasis on grades. As “math people” we take comfort in the numbers, the quantifiable and the structured, and it seems not very structured to teach to a student’s learning rather than a specific percentage or grade. There just seems to not be enough accountability. But, I argue that as the BC Curriculum has moved to standards-based assessment, we as math teachers too can move from the rigid box of percentages and grades to teach towards a student’s understanding, giving them multiple opportunities to demonstrate proficiency in their learning and move away from the punishment of grades and percentages.

Exit Slip October 15, 2021

 

Both of videos were very interesting. There seems to be some common ideas such as student engagement. In the first video Jo Boaler described the idea that the world today has a much greater need for mathematics than in the past, I had not really thought much about this but it is a great point to bring up. In our more technological world, math truly has grown in importance and become a more essential part of our lives. It was also concerning that the speaker brought up that there is a decrease in math fluency in the world at the same time as the importance of math increasing. I can honestly agree with this video about the idea the numeracy is important in our lives and to not understand numbers is much like being blind in our colorful sight-oriented world. A lot of people see mathematics as something to be studied in a classroom with little value in real life, but, I see math as so much more. With a more inquiry-based approach to learning students can come to realize the manner facets math that extend well beyond academics, reaching out to touch every aspect of a student’s life. The second video did not mention the idea of inquiry but I feel that it linked up nicely with the first video emphasizing the need for student engagement in order to have the best outcomes for our students. I feel strongly that grades should not be the main driving force behind a student’s learning in the classroom and that our goal as educators should be to prioritize a student’s learning goals in our classrooms. Thus, the move towards standards-based assessment can be beneficial not only in reducing stress for our students, but also create a more wholistic learning environment for our students.

 

Dancing Teachers

 

The article was really interesting. Being a person who does not really like being outdoors. I find comfort in structure and safety of the classroom environment. To this extent, I had not realized how Eurocentric ideas can be expressed and be influential even in the structure of building themselves. I see buildings as mainly “a place that keeps me from being too hot or too cold” and not as a social construct that influences us on a deep intellectual level. Although like the structure and order of the classroom, my preferred organizational method is order in chaos. It might look messy to you, but I know exactly where I left everything. In my teaching, I hope to foster the idea that there are different forms of learning and understanding and one is not necessarily better than another. One key aspect of being in the outdoor classroom is that we would no longer be bound by constructs of a classroom and therefore have the freedom to explore other ways of knowing and coming to different levels and types of understanding than we would in the classroom. As the article states, the garden classroom allows students to be more reflective and learn from more senses than the mostly visual delivery of the regular classroom setting. One metaphor that resonated with was the ideas of classroom as parkour or like swing music. As teachers we often need to go with the flow and within the structures of school, teach in a way that suits the needs of ourselves and our students. I’m not sure if there is anything I really disagree with the article though I don’t know if I would put such importance into the structure of school governing the mindset of the people that work within them. Perhaps I’m not as progressive as some but I take comfort in tradition and structure and although I am willing to try new approaches to teaching as it might be best to support my students.

"sit spot" and Geometry of leaves lesson reflection

 

 "I like to rise with the sun she rises........."

This class always surprises me on what a math classroom can look like. Being out in nature and our surroundings as a guide for teaching is a wonderful tool to keep students engaged. I personally don’t really like being outside. I enjoy the structure of the classroom and being shielded from the elements. I have, however, come to realize and appreciate the value of the outdoor classroom and its use as a teaching tool for mathematics. The “sit spot” activity is one that causes a lot of reflection on not only the environment around us, but of our own bodies and thoughts. It’s somewhat peaceful and calming to simply be in one place and to concentrate on one’s own senses. It allows us to slow down and reflect on what is happening all around us; to see what we normally miss in the hectic nature (teacher education….) of our daily lives. It’s a great activity for students to ground themselves and prepare for the learning that is about to happen. The next activity, using geometry to approximate nature was also one that was somewhat calming but at the same time educational. We use our more rigid systems geometry to approximate the seeming chaos and yet somehow ordered and symmetrical properties of nature into a piece of math art that can at the same time teach us about mathematical theorems. These two activities were great ways of keeping the students engaged and to be able to teach the students mathematical concepts in a new way was rather eye opening.

"and ramble in the new morn hay......"

Sustainable Mathematics

 

There are couple of points from the article that really resonated with me. Mathematics as a subject is often seen as a purely academic discourse with little relevance to the real world. Often, students who are “good” are math are “good” at calculations but not necessarily “good” at the greater scope of mathematics. As I have slowly learned this year, Mathematics can been experienced in many forms such is in art, geometric, nature, music, daily life and in the sciences. While this idea was in the back of my mind throughout my academic career, I really had not given it much thought. With the movement towards the (not so) new curriculum there has been a greater emphasis the on not so much pure mathematics as with numeracy and being able to actually apply mathematics to daily life. This brings me to the first point in the article that resonated with me. The author mentions that integrating the environment into the discourse of the mathematics classroom creates a more genuine mathematics education speaks to the idea that be allowing student to relate mathematics to something more tangible to them such as the environment makes math more meaningful to them and will have a greater impact. Another point the resonated with me is the ideas that emotions play a crucial role in decision-making and human action and that we need “feel” the numbers or the effect on us would be diminished. I feel that in order to “do math” effectively we need to be able have a feel for numbers. It is an important skill for students to be able to give a number context, without context numbers are meaningless. You are simply shuffling things around to get a result. With a feel for a number, you are able to better understand a problem and to be able to determine if there is merit to the answer you obtain after calculations. I feel that mathematics is much more than just meaningless calculations, it is a living language that allows us to come to deeper understanding of the world around us.

Exit Slip September 23, 2021 (Updated)

 

This was a wonderfully engaging lesson. There was something magical about working with your own hands to make something that is seemingly simple but at the same time so intricate and beautifully symmetrical such is the case with rope making. My first rope was a very simple twisted rope and after I mastered that I wanted to try something a little more advanced. At first I started with a simple all one color 7 layer braid that took a few tries to get going and to understand how the braiding actually worked. It was not difficult but you have to make sure to keep track of the procedure of it is very easy to get lost and braid the wrong strand in the wrong order. Once I was confident, I endeavored to create something a little more interesting. I used several colors to create the seven layer braid and that’s when the fun really began for me. I started to notice a pattern emerge in the raid as a braided more and more of the rope. It really made me think of how I can create new shapes and patterns simply by using the strands of ribbon. The structure of something so simple created such detailed and beautiful patterns. I really enjoyed the exercise and when used a classroom setting can really keep students engaged in a math lesson.

Entrance Slip September 23

 There were a few things that made me stop and think when reading the Kallis article and watching the videos.  The ideas of backsourcing, creating fulfillment in our lives and that rope making can be a form of technology really caused me to think more deeply about my lifestyle and my place in society.  I am completely new to the ideas of backsourcing  and un-venting ancestral knowledge and lost skills. I have never even considered that we could be growing useful crops for ourselves and become less reliant on industry. I have always thought of food as just something you buy at the store. While I know that it comes from farmers and such, growing my own food was not something I considered doing or attainable. I really like the idea of the self esteem gained from one’s own creation and that this movement is equally about becoming less reliant on industry as it is about creating fulfillment emotionally, physically and spiritually. I have never considered this until reading this article and it has really changed the way I view consumerism. This being said, I not sure if I’m ready to give up on buying things just yet at the moment. I love my modern conveniences and technology and it was eye opening when I watched the rope making video that rope making is a form of technology. I had really not considered this as when I think about technology, I think mostly of modern technology. But as the video points out, technology is cumulative and even our most modern devices can have roots in the technologies of the past.

Outdoor class reflection

 

I was truly surprised by the structure and content of the class. It was truly eye-opening that a “Math” class could be taught in such a way that was so lively and engaging. I did not realize that seemingly unrelated activities such as sketching items in nature and singing a song can be integrated into the “classroom” in such a meaningful way. I’ve always pictured math class, especially in the university setting, as a place where you sit and learn from a lecturer who is often not really interested in teaching and engaging his/her students. Even the sharing of watermelon in class I feel is an invaluable activity of community building where students and instructors can interact freely and enjoy themselves in a more informal manner. The free-flow structure of having an outdoor classroom and having students move around and become a part of the lesson itself seemed quite foreign to me at first but after experiencing it first hand, it has really resonated with me as a something I could try in my own practice.

On Becoming a Reflective Teacher

 

Grant and Zeichner’s article “On Becoming a Reflective Teacher” resonated quite strongly with me and there are a few points that really intrigued me. I was struck by the article mentioning the amount a choice a teacher faces. From the choice of style, institutional values and views, to which content to stress as being important, to how we teach to specific groups of children and even our very mindset as to how we go about teaching. I was unaware of the level of influence that a teacher has on a child goes beyond just the classroom and has a huge impact on the student in the future. In the school I worked at previously, the administration stressed that how a teacher conducts him/herself as a person both inside and outside a classroom is equally as important as the actual act of teaching itself; that as a teacher, we are held at a higher standard than the regular person. This completely resonated with me after reading this article where the point was raised that because of relationship between school and society, the consequences of school lay beyond just the classroom and we must be responsible for ourselves and our students understanding the consequences of our teaching.  The article mentions that as a teacher candidate and the as a future teacher, that I must be critical of the information and training provided to me by the institution and at my practicum as there are often inherent biases, viewpoints and knowledge that are all distinct from one another and that I must make my own decisions on what is important to me and how I will approach teaching as a whole. Being reflective in this point will allow me become a better educator and help to further the field of education.

On Becoming a Teacherman

 

What I took away from class was the idea of inquiry can stem from many places. In the video we watched about Frank McCourt, I was inspired by the fact that McCourt truly accomplished the American Dream. He grew up from basically nothing, and through his need for knowledge and education to becoming successful and accomplishing his dreams. It really struck me as the difference of past times to where we are now is that McCourt without any sense of formal education was able to attend a University and become a teacher. That seems like it would be pretty much impossible today. It truly demonstrated that because he was curious and driven by inquiry, he was able to succeed. There was little requirement aside from the pursuit for knowledge itself that is the driving force to success and that this inquiry based approach to learning can be applied at any level especially for ourselves and our future students. The video inspired me to wonder about what education actually means and is the simple pursuit of knowledge enough as the basis of our learning? It caused me to wonder if institutional learning should be the only source of education or is there other forms Education that would work equally as well for different individuals.

Hello World.

 Hello World! Looking forward to the rest of year!