Final Blog Post

I came into this course not really knowing what inquiry was. I mean, I understand the word on a surface level, but I didn't really understand what it meant in an educational context. I've realized through this course that inquiry is just the verb-version of curiousity - something that I already intensely value in my life. That last statement really says everything I want to say, so I needn't say any more. 

I'm not sure it's necessary to change anything about the course content because the fact that I've arrived at the above conclusion means the course hopefully did its job. If I had to make a suggestion in the interest of being constructive, I'd say it's time to move off Blogger. The fact that I missed a blog post when I felt that I did my absolute best and was incredible diligent about reading all the posts and making sure I didn't miss any says that this format is difficult. If Blogger is truly the best platform, then perhaps a more detailed syllabus that lists all the assignments and their due dates could be a good middle-ground. 

Thanks for a great course!

Inquiry Project Update... again

 Turns out that the focus of my inquiry project changed AGAIN. Well, it's still on math anxiety but I've chosen to take it in a totally different direction. I'll summarize the whole process here. 

I initially chose math anxiety as a topic because it was something that I really had no idea about. It comes up in everyday conversation with self-proclaimed "non-math" people, it comes up in the classroom at our practicum schools, and it comes up in discussions in our classes as well. I initially thought it must have something to do with confidence. I figured that math anxiety is what happens when you just don't think you are good at math, or you think you can't be good at math. If students experiencing math anxiety could just boost their confidence and develop a growth mindset, then their problems would be solved. 

Well, it turns out it's a whole lot more complicated than that. Confidence is indeed one aspect, but there are a lot more moving parts. I went deep down the rabbit hole and read way more papers than were probably recommended for this project and ended up with a complex web of causes and correlations that help explain math anxiety. And yet none of them agreed with my own experience. I love math, I love high stakes testing, I love being put on a timer, having one right answer, and being competitive with myself. Oh, and I'm female which apparently is also positively correlated with math anxiety. So what is this topic just so darn complex, and why does none of it agree with my own experience? 

I found a paper that turned all of this on its head and provided a key to unlock some of the complexity and join my own experience with all the other literature on math anxiety. I won't spoil it before the presentation, but it's opened up a new, related, and now obvious topic for Inquiry 2. 

The process of inquiry this term was both frustrating (in a good way) and interesting. I quite enjoy going down a path not knowing where it will lead, and I enjoy being totally wrong even more. This process had both of those components. I don't have a neat little package to wrap up and present to the class tomorrow, and I think that's the best part. 

Here is the link to the presentation.

Here is the link to the updated annotated bibliography.

Inquiry Project Update + Annotated Bibliography

 As anticipated, the focus of my inquiry project has changed. I thought I was going to look at math anxiety at the student-level and how we, as educators, might help. However, when I went down the rabbit-hole, I learned that just looking at the nature and cause of math anxiety is a broad and complex topic in itself. For Inquiry 1, I'd like to therefore just focus on looking at the who, where, when, and why of math anxiety. Specifically, I'm looking at the following two questions:

• What causes math anxiety?
• What are the effects of math anxiety?

For Inquiry 2, I'd like to address:

• What can we do about it?

Here is a link to my annotated bibliography.

Exit Slip: Representation of Women

I'm lucky enough to grow up in the age of third-wave feminism, after the women (and other folx) of the first- and second-wave have paved the way for me (a white woman) to be here. When I attended my undergraduate at the end of the third wave, my class achieved approximate gender parity (assuming a binary). However, when I think about it, all my math professors were male. This was something I hadn't actually noticed. I did look up the current math faculty at UVic, and while I can't really tell what each person's gender identity is (due to either names I'm not familiar with or the fact that names and genders aren't necessarily related), the faculty appears to be roughly equal with a slight tendancy towards traditionally male names. However, the support staff are almost all people with traditionally female names.

What is more relevant today, and in line with the fourth wave of feminism, is the discussion of intersectionality (in the words of Kimberle Crenshaw). While we have come a long way in women's equality, we still have a lot of work to do to radically include trans women, non-binary folks, and people whose gender identities and gender expressions don't neatly fit into our socially constructed boxes. We also have to understand and acknowledge the ways that class, race, language, ability, and a host of other factors influence equality and equity, and how they intersect with gender and sex. Wealthy, white, English-speaking, able-bodied women aren't the only ones for which we need to fight oppression. We need to break that glass ceiling for all folx. 

Response to: Marks, grades and their effects in schooling

 I must be some kind of anomaly because I tend to be much more intrinsically motivated in school than extrinsically motivated. If I'm not interested in the subject material, I'm simply not going to learn it. No amount of threatening or rewarding with respect to grades (or otherwise) can typically get me to change my attitude. My student bird thoughts make it hard to relate to students who would be motivated by grades, nervous about tests, or competitive. My teacher bird, though, can definitely see evidence in the effects of grades on students. Indeed, they are as described in the reading! 

If we really need to have some sort of grading system, it needs to be reflective of how well a student has learned the course material, and how well they can demonstrate the required competencies. As we're learning in our Assessment (441) class, rarely do number-based grades (e.g., percentages) actually reflect this in an accurate way. Also, these types of grades come with the feeling of being final, that is, there is no way for the student to improve and no path forward. If they get high grades, they are "smart" and no longer need to continue trying. If they get low grades, they are "stupid" and might as well give up. Either way, students are not motivated to learn. 

The only positive (or perhaps just necessary at the moment, without a better system) aspects I can see of grading are:

• they might give the student's next teacher an idea of where they're coming from. In the new proficinency scale of the BC Curriculum, it might be useful to know if a student is coming from the previous grade with an extending level of understanding or an emerging level of understanding so you know how to best support them
• for universities and other competitive institutions, number-based grades are a cheap and simple way to rank applicants for entry if you really aren't interested in getting to know the students holistically
• for administrators to see, as a whole, how students are doing, how well the class/school/district is functioning, and if any interventions are needed

In both cases, the student needn't even be aware of their grade. They just need the qualitative feedback on what they know, what areas they could work on, and how to get to the next level. 

I'm all for ditching grading altogether; this reading is preaching to the choir! 

Inquiry Project

 For my inquiry project, I'd like to explore how to battle math phobia or math anxiety at the student-level, and also to explore how we, as educators, can help facilitate this. In particular, I want to look at how we can build resilience to math phobia in students through mindset and self-confidence. And finally, I'd like to link mindset and self-confidence back to the Core Competencies in the BC Curriculum. 

To be honest, I don't really know how this is going to play out, and it's really going to depend on what I find once I dig in to the lit review. There's a good chance the bolded statement above will change, but that's the rabbit hole I'd like to start down! 

And speaking of rabbit holes, he's an excerpt from Lewis Carroll's Alice in Wonderland that almost perfectly describes how I envision the start of my journey:

"...the rabbit actually took a watch out of its waistcoat-pocket, and looked at it, and then hurried on. Alice started to her feet, for it flashed across her mind that she had never before seen a rabbit with either a waistcoat-pocket, or a watch to take out of it, and burning with curiousity, she ran across the field after it, and fortunately was just in time to see it pop down a large rabbit-hole under the hedge. In another moment down went Alice after it, never once considering how in the world she was to get out again."

 

Exit Slip: Jo Boaler

 I resonated with a lot of the concepts in this video, partially because I already had some ideas about these things, and the video just helped to solidify and formalize them. I'll talk about three big ones here:

(1) The idea that only some students can be good at math vs. the research that says all students can excel at math

This one is both interesting and encouraging. 

I've often wondered about whether musical ability (or inability) is something that is genetic/inherent or whether it's something that's learned. There are people who have perfect absolute pitch (that is, they can identify a pitch accurately without a reference pitch) and that there have been no cases where an adult has learned to have perfect absolute pitch (that is, you seem to be born with it). On the opposite end of the spectrum, there are people who have musical amusia, which is commonly referred to as tone-deafness. This can be congenital or due to brain injury. Everyone else seems to lie somewhere in between with varying "natural" levels of musical ability which can be developed and honed depending on their opportunity, effort, and interest. 

I figured that math must be the same. If your parents are good at math, you might be good at math. You might be genetically pre-disposed to be good at math and, therefore, those on the other end of the spectrum would be not-so-good at math. However, this video says that the research points to this being false: all kids can excel at math. I don't know why or how, but I'm glad to hear it. 

(2) Growth Mindset vs. Fixed Mindset

This is something I've already explored in a previous blog, and something I've already written about ad nauseam so I won't repeat it here. What I didn't realize is that Carol Dweck actually wrote a paper specifically about math education. I haven't reviewed this yet, but it's on my list. 

(3) Humans vs. Computers in Math   

In the TED Talk Jo Boaler showed as part of her lecture, the speaker talked about the four stages of solving a real life math problem:

1. Pose the right question
2. Real world -> mathematical formulation
3. Computation
4. Mathematical formatulation -> real world

Humans can do 1, 2, and 4. Computation, 3, is done by a... you guessed it... computer. So why do we focus so much of our math classes on being computationally fluent? Yes, there are some benefits to being fluent, but it's definitely not worth focusing 80%+ of our attention on. 

I'm imagining a future classroom of mine where we spend more of the time on these multi-dimensional things like problem-solving, interpreting, formulation, communication, trail + failure, reasoning, and all those other things that humans do best and computer don't. In this model there would still be room for computational fluency, or the 1-D goals, but it's put it its rightful place as just one piece of the puzzle. 

Allow me to use a rock climbing analogy. In rock climbing, fitness and finger strength surely helps you become a better rock climber. Indeed, some of the best rock climbers in the world have really strong fingers. However, the best rock climbers in the world don't spend all their time hangboarding. They spend most of their time working on their climbing technique, honing their rope skills, training their mental capacity for stress, problem-solving the most efficient routes, and even a whole lot of time just climbing for fun! Hangboarding has its place, but it's just a tiny piece of their overall training. Their success as an athlete depends more on all the other stuff they do.

Computational fluency is the hangboarding of math - useful for some things, but needn't be the focus of the sport... or subject. In my future class, I might actually try framing it this way to the students. Let's call these worksheets "workouts" or "conditioning" so they too can see that it's just for mental fitness and is not the main event. 

Entrance Slip: Dancing Teachers Into Being...

 For whatever reason, this reading didn't resonate with me the way some of the others did. I'm not sure if it was my frame of mind going in, or what, but it's not firing off multiple areas of my brain. I'm not making connections, I suppose. 

I like the idea of getting "off the grid" (both literally and figuratively), and I like embracing the messy non-linear style of learning that comes with inquiry. I suppose in some ways, I'm already on board with basically everything this reading is saying. I like embodiment. I like questioning and rejecting the grid. I like learning through play. And I'm already comfortable with the syncopated rhythms of swing and jazz. I already see the cityscape as a play place (though not for parkour but for "buildering" = urban bouldering).

Perhaps I need to take this a step further and dig deeper to really fire up my brain. But I'm just not inspired to do so. And honestly? I think that's ok. 

Exit Slip: Leaf Geometry

I really enjoyed this activity. I once took a drafting course, and it reminded me of the joy I had participating in that course. It's this really nice middle-ground between art and problem-solving where you get to create your own artistic interpretation of the leaf, while still problem-solving how you are going to do so using only the compass and straight edge. 

I also quite like using these simple analog tools to explore geometry since you sometimes end up stumbling upon "proofs" of some geometry properties by exporing, say, why the methods of drawing a perpendicular or bisecting an angle actually work. 

Very cool activity, and it also correlates nicely with the mindfulness exercise of drawing or sit-spots since you have to study the leaf so carefully. I dig it!

 

Moshe Renert Response

This article blew my mind in a few ways! The first was the idea that, because of positive feedback loops and their relation to chaos theory, one small personal change that seems insignificant could actually change the world. Renert writes:

Consider the common belief that ecological problems are just too great for any one person to do anything about. This belief is founded on a linear argument that proceeds by quantitative comparison... Chaos can help change the way we think about power and influence. It teaches us that us that compex systems cannot be controlled, but can be accessed and perhaps influenced through the myriad of feedbackloops they contain.

The author goes on to explain how this type of thinking can actually help students take action if they are hopeful that they can actually make a difference. I find I'm often paralyzed by the idea that my tiny action couldn't possibly make a difference, so I really like this argument.

The other piece I enjoyed in this article was how the author framed how the modern world requires us to think and act in creative ways, rather than just be rigid rule- and algorithm-followers:

Most mathematical problem solving in today's classrooms relies on the unchallenged assumptions that each problem has one correct answer and that the teacher knows this answer. Students' creativity is tehrefore limited to replicating solutions that are already known by an adult. In contrast, the solutions to many problems of sustainability are not know a priori, and in some cases there is no certainty that solutions can be found at all. A different order of ingenuity is required to approach these problems, one that we may call radical creativity.

I used to be the kind of person that really enjoyed the cookie-cutter, black-and-white model of mathematics learning. Throughout my adult life thus far, I've learned to become much more loose, creative, and radical and I hope to inspire students to allow themselves to think in this way as well.

Exit Slip: Embodied Learning

 During the rope making, braiding, and poem-writing, I feel like it finally clicked for me what embodied learning actually means. Before, I was like "yeah cool, you use your body to learn." However, it actually took the contrast of what disembodied learning is for it to really hit home what we're trying to do here. Indeed, embodied learning is using your body to learn. But when you use your body to learn, you are also building these neurological pathways (presumably those that have to do with motor function) and associate it with the concepts or ideas.

This whole idea made me think of my own experience with playing music. I starting learning to play the piano when I was about 4 years old and guitar since I was about 7. I've taken periods away from practicing both of them, and sometimes have multi-year gaps between practice sessions. Interestingly, though, the "muscle memory" still remains and while my playing is not as polished as it once was, I can usually still remember how to play certain pieces with remarkable fluency. It's as though my fingers remember, but my brain doesn't! Now, I'm sure there's a psychological explanation to why my fingers appear to move on their own, but what's more interesting is how I can actually recall elements of music theory that I've long forgotten, simply by moving through the scales or chords with my hands. I can just let my hands play, then figure out what they did and work backwards from there. 

During class, Susan has elluded to embodying the shapes of graphs/functions by moving our hands through space in their shape. I'm really digging this idea: the students may forget what a cubic function looks like if they just draw it or view it, but what if they actually move their bodies? What if, later in life, they think "cubic" and then their body automatically traces the shape? Then suddenly everything is flooding back to them. 

I'm sure that triggering memories is just one tiny aspect of embodied learning. I'm beginning to see a lot of other benefits and am starting to make similar connections (though they aren't quite clear enough to express here yet). 

Entrance Slip: Building Change from the Ground Up

This first "stop" for me in reading this chapter was right in the very first paragraph. Kallis says,

"Participants can acknowledge where their skills are best suited to aid the community and where their own internal needs for creative fulfillment can be satisfied."

It's been a long-standing personal belief of mine that I'm "just not a creative person" or "I don't need a creative outlet". I have therefore focused on a lot more of my efforts on the former part of that quote (aid the community) than the latter (creative fulfillment). However, I've come to realize that many of my endeavours that I've previously just identified as problem solving are actually my version of a creative outlet. For example, my partner and I recently designed a carriage house (which is now under construction on our property) for us to live in. I considered this to be a strictly administrative and problem-solving task: where would the windows need to go to get the best winter sun? How does one move about the space, and can we organize it more efficiently? What are the geotechnical constraints and how do we work with them? It turns out, though, this act of design was actually a creative process veiled as problem-solving. Crafting could, similarly, be seen as simply a necessary and practical way to obtain the goods we need. And indeed it is! But it's also a way to express ourselves and explore our world creatively. 

I also enjoyed Kallis's discussion of backsourcing as a way to "re-[claim] what we outsourced when factories took over" for political/ideaological reasons, practical reasons, and individual reasons. 

And finally, I tried out the 7-strand braid by cutting up an old piece of climbing rope and rigging it up onto a coathanger. I found the process to be very meditative (once I got the hand of the method) and was actually a little disappointed when I got to the end of the rope because I wanted to keep going. The result is a beautiful (and huge!) flat braid.

Exit Slip: Human Sundials and Angles in Nature

 I have to say, I thoroughly enjoyed today's class. I definitely have a bias since I am already well acquainted with the outdoors and have devoted the last 7-8 years of my career in outdoor education. However, I have never really thought of the outdoors as not only a venue but a resource to teaching anything other than "outdoors skills". Indeed, in mathematics and sciences (among other subjects), we are learning the language that describes the natural world, and what better place to learn than surrounded by it. These types of hands-on lessons like measuring the angle of the sun with our bodies is also much more memorable than studying a diagram of the sun's trajectory in a textbook. It probably also would help a lot of youth stay engaged since they don't have to 'resist the urge to fidget', but rather participate in the lesson with their whole bodies. 

Exit Slip: Frank McCourt

Prompting questions: after watching these, what do you think 'teacher inquiry' meant to McCourt? What could you take from his sense of teacher inquiry for your own inquiry process?

After watching the videos and hearing some additional anecdotes about how he adapted his teaching based on his students, I think Frank saw his students as teachers for his own practice. He listened to them and got to know them, and his own teaching was inspired by their needs and interests. Had he come into the field thinking he knew everything, he may not have been able to be as flexible and adaptable as he was, and wouldn't have built the connections with the students in the same way. 

In my own inquiry process, I hope I never lose my voracious curiousity. I don't know what Frank's internal motivations were, but I hope we share the same path of always striving to be better than before. I hope that I'm always willing to be wrong, and to learn something along the way. 

Entrance Slip - On Becoming a Reflective Teacher

 "Becoming a reflective teacher is a continual process of growth."

This quote here is the one that stood out for me the most, probably because it connects with another similar concept that I already practice deeply: the Growth Mindset. I could go on and on about how adopting a Growth Mindset has absolutely changed my life, and how I've integrated it into all areas of my teaching life, but I'll spare you all the preaching. This discussion of being reflective, however, had a piece that I hadn't really thought too much about: wholeheartedness. In my own life, I try to focus my attention on the things I truly want to do wholeheartedly (by the colloquial meaning of the word). Doing things half-a$$ed or without intention can make them feel like empty and pointless pursuits. I like that the idea of being a reflective teacher brings in this idea. 

"There is no such thing as a neutral educational activity."

This quote definitely got me thinking about bias in math and math education. I mean, math is purely factual, right? Objective, even? We are teaching neutral content here, right? RIGHT?! Well, yes and no. We decide to focus on or omit certain topics in what this reading calls "value governed selections", even under a standardized curriculum. I wonder how we can teach our students to question what we teach in math education the same way we teach them to question teachings of, say, history. 

Hello World!

 This is my first blog post for 450B.

Here's a picture of a sunset swim in Squamish from a month or so ago. I've chosen this image becuase it was the first one that came up on my computer. LOL