Exit Slip - Geometry of longsword locks

 I wasn't able to participate in the dance and the associated activities, as I had to excuse myself from being in class due to sickness. However, seeing the photos of the models my colleagues made and observing their engagement is rewarding.

The idea of making shapes through dance is fascinating. It raises my curiosity regarding the participation of my classmates and friends in this fun activity. To me, watching the films, drawing the shapes, and making the shapes with the stir sticks sounds like a step-by-step scientific process where we watch and observe, then draw using the ideas, techniques, and strategies observed. The drawing is then followed by applying the ideas we watched and tried on paper.

Moreover, it is worth noticing that drawing the shapes after watching the films allows room for exploration and emergence of new ideas that can be tested and implemented in addition to applying the techniques showed in the films.

It also me reminds me of the common topic we have talked about in this program, i.e. Passive Consumers vs. Active Producers. Making the shapes with the stir sticks allows us to transition from being passive consumers to active producers.

Also, the issue of varying learning styles are implicitly addressed where visual and auditory learners benefit from watching the films and drawing the shapes, and kinesthetic learning is maximized via making the shapes with the stir sticks where dancing is another interesting layer of learning that can be a motivation factor for some students.

I absolutely look forward to including hands-on activities in my lesson plans to allow students to test and implement what they learn in addition to having students watch films to open doors for creativity and student-centered learning. I would want the students to see the gaps in what they learn and prove it if they can in contrast to absorbing the knowledge with the notion that the teacher is always right.

Inquiry Presentation - Math & Music by Iqra, Pacus & Sid

Here is the link to the presentation:

https://docs.google.com/presentation/d/1nGAjc6jO6Z6uzi04mjFjnOZpC2knl3A3rJFi3aY2Ur8/edit#slide=id.g74c1212f0_0_85

Enjoy!

Annotated Bibliography

Research Question: Can music and poetry help make Math fun, relevant, and accessible? What are the common grounds shared by these domains?

1. Major, A. (2014). Barbers and big ideas: paradox in math and poetry. Journal of Mathematics and the Arts, 8, 54-58. doi:10.1080/17513472.2014.943999

This article is one of the unique instances that is accessible by both mathematicians and artists. It relates the common  paradox between Math and poetry, and illustrates the resonating forms of expressions between Math and poetry via five beautifully constructed poems. 

2. Burgin, J.S., Pearson, L.C., & Szirony, G.M., (2008). Hemispheric Laterality in music and math. Learning Inquiry, 2, 169-180

The article mainly deals with the hemispheric laterality, i.e. the common perception that left hemisphere is for logic and reasoning, whereas the right hemisphere is for emotions, etc. While this article does not serve as the primary source for our research question, it will be useful in integrating this perception into the inquiry project and draw extensions. 

3. Edelson, R.J., & Johnson, G. (2003). Music Makes Math Meaningful. Childhood Education, 80, 65-70. doi:10.1080/00094056.2004.10521259

This is one of the articles that we, as a group, will focus on for concluding our inquiry project, i.e. implementation. One of the things we, as educators, want to learn and bring forth is how to make Math fun and accessible, this articles does exactly that. It presents ways, activities, and ideas that we, as Math  teachers, can use to add rhythm and fun in the form of music to teaching and learning Mathematics. 

4. Daniel, T., Margaret, C.M., & Song, A. (2013). Elementary Teachers Integrate Music Activities into Regular Mathematics Lessons: Effects on Students' Mathematical Abilities. Journal for Learning through the Arts, 9, 1-21

This article will be one of our primary sources, as it examines the results and outcomes of integrating musical activities into teaching Elementary Math. A study including two classes of first grade and third grade students are observed to have positive effects on multiple mathematical ability areas after having covered a variety of music-math interdisciplinary lessons.

5.  Jan, L., & Kathy, D. (2004). Reading & Writing Poetry in Math. Reading Horizons, 45, 1-53. Retrieved from http://scholarworks.wmich.edu/reading_horizons/vol45/iss1/3

This article deals with the curiosity we had when we first discovered our inquiry project, i.e. parallels between Math and poetry. Although poetry and Math may seem to be unrelated, there is an overlap that specifically addresses rhythmic language and language skills. This article features an annotated list of mathematical poetry books and a variety of writing ideas for math poetry. We want to see what it means to have students write poetry about math and whether it will encourage them to find a deeper meaning of math concepts as they develop their poetic voices.

6. Vaughn, K. (2000). Music and Mathematics: Modest Support for the Oft-Claimed Relationship. The Journal of Aesthetic Education, 43, 149-166.

Retrieved from http://www.jstor.org/stable/3333641

It is one of the many articles that discovers and inquires into relating Math and Music. Additionally, it addresses the need to learn Math specifically ratios (2/4, 3/4, etc) and repeating patterns for deeper understanding of Music. 

7. Davidson, D., & Keller, R. (2001). The Math Poem: Incorporating Mathematical Terms In Poetry. The Mathematics Teacher, 94, 342-347.

Retrieved From http://www.jstor.org/stable/20870705

This article is another effort in making Math relevant and accessible, i.e. it incorporates Mathematical terms into writing a poem. This can also be extended to including Mathematical ideas.

8. Emmons, C. (2013). How to Cook Up a Math Poem in n Easy Steps. Journal of Humanistic Mathematics, 3, 108-114. doi:10.5642/jhummath.201301.09

This article digs deeper than most other articles in incorporating and integrating Math and Poetry. It uses mathematical concepts and present them in a literally and visually compelling way. It also personalizes the process of composing such poetry.

 

Inquiry Project - Primary Sources

1. Edelson, R.J., & Johnson, G. (2003). Music Makes Math Meaningful. Childhood Education, 80, 65-70. doi:10.1080/00094056.2004.10521259

This is one of the articles that we, as a group, will focus on for concluding our inquiry project, i.e. implementation. One of the things we, as educators, want to learn and bring forth is how to make Math fun and accessible, this articles does exactly that. It presents ways, activities, and ideas that we, as Math  teachers, can use to add rhythm and fun in the form of music to teaching and learning Mathematics. 

2. Daniel, T., Margaret, C.M., & Song, A. (2013). Elementary Teachers Integrate Music Activities into Regular Mathematics Lessons: Effects on Students' Mathematical Abilities. Journal for Learning through the Arts, 9, 1-21 

This article will be another primary source, as it examines the results and outcomes of integrating musical activities into teaching Elementary Math. A study including two classes of first grade and third grade students are observed to have positive effects on multiple mathematical ability areas after having covered a variety of music-math interdisciplinary lessons.

 

3. Burgin, J.S., Pearson, L.C., & Szirony, G.M., (2008). Hemispheric Laterality in music and math. Learning Inquiry, 2, 169-180

The article mainly deals with the hemispheric laterality, i.e. the common perception that left hemisphere is for logic and reasoning, whereas the right hemisphere is for emotions, etc. While this article does not serve as the primary source for our research question, it will be useful in exploring the concept of Musical Mathematics and drawing extensions.

 

 

 

Response to Inquiry into Assessment and Evaluation of Learning

After the discussion we had in class, my mind is focussed on the following two questions:

1. Are marks accurate?
2. Are marks effective?

For both questions above, I found myself to be in the middle of yes/no. This is mainly because it's not easy to give a definite yes/no answer to such questions as they can easily lead to never-ending discussions. For instance, accuracy of marks/grades can be multifaceted depending on many factors including personal experiences, the way marks are computed, teachers, subjects, etc. Speaking of personal experience, marks were more/less accurate for me especially during Secondary education. For me, marks were an excellent indication of the areas I needed to wrok on. Moreover, I almost always knew the marks I would get based on my comfort level, confidence, and effort I would put into mastering the test/exam/course content. This is different from my understanding of my classmates' experiecnes.

Furthermore, depending on how marks are computed, whether or not teachers modify marks once they are calculated, and the models used to do that, grading may/not be effective. The effects of grading is highly dependent on the personality of studernts and their perceived notion of grades. For example, grading was definitley effective for me as a student that is not willing to accept anything less than A or A+. Low grades or grades not meeting my personal expectations and standards became a great motivation for me to improve, do better, excel, and enhance my leanring/studying.

Databases Search Plan

Ideas for Inquiry Project

I'm considering the following to focus on for the inquiry project:

- Integration of Culture into Mathematics (and/or the implications)
I wonder if we can interview Susan...
- Math & Poetry
- Embodied View of Mathematics

Note to self: Make connections with the real world!

I've finally decided my inquiry project!

Math & Poetry/Dance it is with Sid and Pacus.

Ancestral Genres of Mathematical Graphs

This articles draws inspiring connections between Math and the world around us. I found this piece to be a great motivating factor for changing the attitude of general public toward Mathematics. It allows us to see Math above and beyond numbers, and calculations.

While reading this article, I stopped at a few places including the following:

“Mathematics is a system of human interpretation of the world and has human qualities inextricably woven into its very nature.” (p. 14). I found this perspective unique, as Math is usually thought of as something that’s abstract, dry, and boring. The terms ‘human qualities’ caught my attention and I found myself asking questions like:

Can Math be flexible? Can it help reform the society?

Similarly, the description of graphs in the Cartesian plane as having their bases in “fundamental human metaphors of up and down, horizontality and verticality that come from embodied experiences of the world” is intriguing (p. 15). I found the metaphors familiar, as they are seen as the standards the society sets and maintains, yet I paused and said to myself ‘No, I disagree with the societal definition of what’s “up” and what’s “down”’. For instance, “rational is up and emotional is down” is no surprise, as that’s the way the society has been. However, I want to take this opportunity and challenge the notion that emotions are bad. Emotions that are bad are bad, e.g. hatred. Being emotional is ‘down’ only when emotions are not balanced or left unguided. To me, emotions are amongst the most beautiful aspects of human life. They are what make us human. For example, love and hate are the strongest human emotions, yet they both have the tendency and potential to turn impossible possible.

Lastly, the table displaying equivalences/connections between human bodies, houses, cosmos, and graphs is absolutely new to me. These connections are convincing, and remind me of the definition of Math as ‘human thought’ and interpretation mentioned in the beginning of the article. The culture we grow up in is usually integrated in us, and make us who we are, just like our bodies define us. Thinking of Math as ‘human interpretation of the world’, culture, physical human body, and cosmo being in acquaintance with graphing is rational.

Previous Learning Experiences

Speaking from the student’s perspective, learning and schooling has been both fascinating and uncomfortable. During my Elementary and Secondary school years, I had always focused on marks/ranks than the learning itself. This, as a result, affected many aspects of my life. I would always worry about getting best marks, best grade, etc that I lost track of my social life, my friends, my relatives, etc. This was mainly becasue my family wanted me to attend Meidical school. Although, they never forced me, I always obliged to consider their expectations. 

Based on the stories we shared as group, we found frustration was a common emotion we had felt while experiencing what we experienced.

In addition, one of the ways to deal with negativity is positivity, i.e. we don’t make others feel what we felt.

 

Entrace Slip - Pedagogical Sensitivity

"Jeff learns that it is not good to seem smart among his peers, and Siri seems to feel special and yet also seems to feel embarrassed for feeling special." (p. 4). I find the above quote intriguing, as it is an indicative of the notion that teenagers' percepton is most dominantly influenced by their peers' perception of them. There is no sense of the outer world or reglistic/practical life as of yet, their innocent minds seem to be dominated by their constant desire to fit in and seek their peers' approval. This poses a challenge for teachers/educators and requires additional tools in the teachers' toolkit. In other words, teaching is above and beyond knowing the subject matter, teachers are expected to be "pedagogically sensitive". Pedagogical sensitivity requires that teachers are not only aware of the class atmosphere, relationship between students, and their impulsive feelings, behaviors, and attitudes, but also take them into consideration as they teach. For example, asking one self what needs to be done or can be done in order to promote peer-peer encouragement as needed in the above case. 

In order to incorporate the above which Van Manen refers to as "pedagogical sensitivity" into the tact of teaching, we need to become reflective of our actions and plans, as Manen describes: "[Reflection] converts action that is merely appetitive, blind, and impulsive into intelligent action." (p. 6). Reflection is not limited to official documentation, but getting comfortable with the uncomfortable, expecting unwanted/unexpected situations, and being ready for almost everything is all part of the reflection process. In addition to being self-reflective, teachers are to be open-minded, flexible, adaptable, understanding, and most importantly selfless, as least for the time they spend in classroom settings. Selflessness allows one to be calm, open and less-reactive in situations where anger and frustration can easily take over.  

The above tact of teaching is what Manen views as 'practical wisdom'. It is one of the mandatory skills for teachers that can't be taught in the Teacher Education program, instead they are acquired and learned by being in classroom settings via experiments and experiences, as Manen agrees:

"Tact can neither be reduced to some kind of knowledge base nor to some set of skills that mediates between theooy and practice. Rather, a third option is offered in the realization that tact possesses its own epistemological structure that manifests itself first of all as a certain kind of acting: an active intentional consciousness of thoughtful human interaction." (p. 15).

Exit Slip - 'Problems with Praise' & 'Beautiful Maths'

One of the things that caught my attention was Kohn's perception on the effects of praise on children. I've always thought that praise is a good motivating factor for children to work harder, but Alfi has clearly challenged that perception. I want to explore more on this particular issue. Furthermore, the notion of static/fixed mindset vs. dynamic/growth mindset needs to get more popularity and public support. In other words, I want to incorporate the concept of growth mindset into my teaching and learning.

Lastly, I really liked the short video clip where the teacher stopped students before they solved the problem and they solved it together as class. It is a great illustration of ESA (Engage, Study & Activate) phenomenon. The students studied by actively engaging themselves in the problem. It is also a great example of making learning especially Math fun. I look forward to making my teaching and learning fun and engaging!

EDUC 450B - Entrace Slip for "On Becoming a Refective Teacher"

It’s really interesting to observe this article speaking to the teachers of today even though it was written in a different time and place. For instance, the concept of open-mindedness which I’m sure is new to many citizens even today was alive back then. This concept openly challenges traditional ways of teaching where the teacher is thought to be the one that has knowledge of everything. I found it relevant, I see teacher as a facilitator and guide, rather than authoritative figure. 

Furthermore, the discussion on responsibility and consequences of our actions as teachers (or educators) makes me regard this profession even more. However, it puts so much responsibility on the educator to be mindful of almost everything we do, we say, we promote, etc. It’s touching to notice that the educators can have long term effects on students’ lives. 

Lastly, considering the discussion on self-reflection, I see teaching as a life-long learning process, where learning happens in a variety of formats. In other words, I, as a future educator, can’t imagine myself improving without actively reflecting and/or critically thinking of my teaching philosophies, approaches and styles.