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.