Exit Slip: Female Representation in Mathematics

October 21, 2021

    We spoke about the lack of representation of women in mathematics and science today, but I do want to acknowledge the progress that has been made for women in general over the years.  This might be small to some, but I feel really grateful and privileged that we, as a class of women and men, can discuss these ideas openly and respectfully with each other.  I also want to acknowledge that I'm speaking as a Southeast Asian Canadian woman and that my experiences and perspectives derive from the fact that I live in Canada and was born in a generation where women have been treated with more respect.  However, I do still feel the weight of being a woman everyday.  I don't always feel safe walking alone--day or night.  I don't always feel like my voice is heard when I'm speaking to a group of men.  I think this goes into the ideas discussed in class where women and men have been socialized in a certain way and to the point where society's discounted the abilities of half of the world's population.  I'm not entirely sure if there is a huge wage gap between women and men within math- and science- intensive fields, but these wage gaps do still exist in many other sectors like media and politics.  I wonder if this is why women are under-represented in mathematics and science.  

Inquiry Project: Topic, Concepts, & Motivations

My motivations and connections to this inquiry topic stem from my sister's experiences as a teacher.  She had a student whose parent is deaf, and when she learned about this, we both wanted to learn more about sign language.  American Sign Language was what her student's parent used to communicate to her child.  My sister and I had conversations about the different ways the deaf community could understand others.  For instance, reading lips is a method for deaf people to understand what is being said to them.  However, this kind of dialogue felt one-sided in the sense that only one person was "communicating".  They also communicated by writing on a piece of paper and passing the paper to one another, but again, that seemed to be the parent making the greater effort to communicate rather than the conversation being an equal effort.  Shortly after, my sister and I tried learning a little bit about American Sign Language so that she could communicate to the parent in a language they knew.  Very much like how my family and I enjoy hearing people speak to us in Filipino, there is a greater sense of community when people try to learn each other's primary language.  In our teacher education program, we've been learning about how to foster a more inclusive environment, and I have rarely heard about the deaf community and how they are supported in the school environment.  I think they are a community whose ideas and thoughts are not commonly recognized, so I want to bring light to their experiences and learn more about whether or not the deaf community is supported in the school environment.

Entrance Slip: On Marks, Grades, & Their Effects in Schooling

What are my "student bird" and "teacher bird" thoughts about assigning percentages or letter grades in the assessment of student work?  What do the grades indicate?  How are they arrived at?  Whose purposes do they serve?  What are positive and negative aspects to giving grades? To be assigned grades by an instructor?

The takeaway from John Sarte and Sherri Hughes' Refocusing our efforts: A shift from grading to an emphasis on learning is that "learning occurs without the use of grades".  My student bird reminded me of when I focused on attaining high grades because it felt good.  I'd feel accomplished and that all my hard work had paid off.  However, my teacher bird asks me if the marking schemes used to define my intelligence were even accurate?  Were my grades an actual reflection of my intelligence or were they a reflection of how well I managed to complete the work?  Jo Boaler highlights the idea that math competency is based on how student perform rather than what students really learned.  I have a strong belief in that grades and percentages aren't accurate feedback; they are superficial feedback and don't always give the student the entire story of what they actually learned.  I learned that many years ago, mark books would only be filled with words describing where a student glowed and where they needed to grow.   This approach of providing feedback seems more clear, more honest, and more thoughtful.  Raw marks or percentages are more convenient, but they can be misleading.  For example, what does half a mark even mean?  A student could have a high A while another student receives a low A, yet they both are A students.  

I think math and science teachers can offer so many opportunities of assessment that don't require a grade.  For example, listening to how students present their ideas to their peers is a method of assessing their comprehension of math or science ideas. As mentioned by Sarte, Hughes, and Boaler, grades get in the way of intrinsic motivation.  When students want to learn about something they then have the will to learn.

Exit Slip: Student Inquiry & Problems with Praise and Grades

    Both Jo Boaler and Alfie Kohn raised issues pertaining to education and the impact that traditional teaching has on students.  One quote that stood out to me was that "Math is popular... just not in education".  Math, in a way, is quite similar to those stereotypical, cool-kid, main characters in movies.  Math can be intriguing and admired by many people, but it may only be seen and understood on a superficial level.  If we want to take this metaphor further, math can be that popular but mean jock that terrorizes students, causing anxiety and stress.  However, usually when we're able to get to know this character a bit more, we begin to learn that he/she/or they have more dimensions to them, just like how mathematics is more than memorizing formulas and pencil-to-paper activities.  So, I wonder...how can we get to know mathematics better?  When we see how mathematics is used by other disciplines, like Physics, Chemistry, Engineering, etc., mathematics is elevating these subjects.  One would think a mathematics class is self-elevating, but the traditional ways that mathematics has been "taught" has diminished math's character.  The rumors about math being dull and uninviting have been deeply embedded in the school environment that math began to take on that persona.  

    It is quite scary to be defending something that has a lot of negative connotations.  Like what Rebecca said, it is scary that, as prospective teachers, we have a responsibility to undo the problematic methods of teaching that we once experienced and felt the repercussions of as students.  Having learned the traditional ways of teaching math as a student and then now learning our job as teachers is to unlearn a lot of these techniques is an overwhelming task.  However, I like to think of it as giving our students opportunities we weren't given when we were in their position, and hopefully, students do have a chance to get to know mathematics a bit better.  Even if I can build this bridge between students and mathematics, I should be aware that not all students will want to venture on to the other side; in other words, they might not want to pursue mathematics in the future despite my best efforts.  However, if my students can take something positive away from my class, whether that be a new passion for math or a lack of fear when approaching math, I'd feel like I've done math and math students justice!

Entrance Slip: How to Swing or Parkour the Grid of Schooling

    As I sit on my couch and look around my apartment, I see that my shelf follows a grid-like pattern, so do the keys on my keyboard.  Now I’m thinking beyond my apartment and how Vancouver city follows a grid-like pattern and how the windows on the building across from my apartment are in grid form, too.  I think about nature and search for a photo of a zoomed-in leaf and discover a beautiful system of grid-like designs.  

    So, I wonder why we see such a pattern in both spatial and conceptual structures.  As discussed in the article, grids exist all around us, and “we are a culture in love with the grid”.  This may be due to our natural gravitation towards feeling safe and perhaps wanting to combat overwhelming feelings and/or promote convenience.  The lines of a grid can act like supportive structures while also creating a restrictive presence; this is an idea that I’ve had concerns about when it comes to teaching.  The rigid boxes that I may need to fit into as a new teacher scare me, but the familiarity of timetables, organized curriculum, and a yearly calendar are comforting.  Having to find a balance and be able to ‘swing dance and parkour’ the grid is both an exciting and terrifying process; I worry that I need a lot of experience before I can do so effectively, but I also realize that the process could allow for exploration and creative discovery.  I feel that this is the thrill of teaching and what has really pushed me to take up the profession.  It’s like riding a rollercoaster; I may be terrified at times, but the ride is intended to be enjoyed.  What I wonder about now is how strongly will I be influenced by the established teachers I meet in the future.  How will I fare in a school with teachers and administration that strongly rely on the ‘grid’ or strongly detest it?  What do I do if during my practicum my potential school advisor is a diehard grid fan when I am not?   I also wonder how else we could combat an ‘indoor versus outdoor’ school culture.   

Exit Slip: Revisiting Our Spots & 'Geometrizing' Leaves

You never know who'll be there with you on your journey!  I met this little fella when we went back to 'our spots' and it made me think about how big the world is compared to this little slug.  Made me feel how big the world is compared to me.  

You can see another tiny slug near those chomped up clovers.  

During this activity, we were getting a better sense of the geometry behind leaves.  I tried to encase the segments of this leaf within a circle (I should've used a flatter surface to make those lines more defined) and then the entire leaf within a bigger circle to include the petiole.  Next time, I'd like to fill in the negative space with more circles of similar diameter and then possibly fill in the gaps in between these circles, and so on until very little, visible space is left.  Maybe I could use parts of the clover leaf to help me get an idea of what size circle can fill in the negative space.

 

Entrance Slip: Renert on Math and Climate Change

 A quote from Moshe Renert's Mathematics for life: Sustainable mathematics education article that really resonated with me was, "Since school is a social institution situated at the intersection between present society and the promise of what society may become, educators are more likely to succeed in their work with messages of hope and possibility."  Conversations about climate change can quickly lead to feelings of helplessness and despair--feelings in which many students struggling in math may experience.  There were many other parallels that Renert made when speaking on sustainability and mathematics education which I had never considered.  For example, sustainability itself, a term referring to the ability of living systems to endure over time, can relate to chaos theory, which is the mathematics of complex dynamic systems.  Both involve evolving systems--a commonality between mathematics and ecological sustainability that seem so obvious and yet is not immediately assumed.  To elaborate on this point, I want to mention Renert's claims about "humans' inability to feel large numbers".  I still find myself having a difficult time truly comprehending the magnitude of climate change.  Though I try to eat consciously, I might not always read the labels on products that I purchase to see if it contains palm oil (an ingredient in many products that is supplied by penny-pinching food companies that are supporting the mass deforestations in Borneo and Sumatra).  I think many people doubt their impact on the world--myself included.  I think if we, as prospective teachers, can have conversations with our students about mathematics and its relation to sustainability, like quantity sense and its implications on our ecosystem, then great strides can be made in nurturing a future generation of global citizens.