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.