RYSK: Boaler's The Development of Disciplinary Relationships: Knowledge, Practice and Identity in Mathematics Classrooms (2002)

This is the 22nd in a series describing "Research You Should Know" (RYSK)

Today Geoff Krall (@emergentmath) posed this on Twitter:

It's a cycle I've seen before, and you probably have, too. Students struggle on complex tasks (or, far worse, we just assume they'll struggle without giving them the opportunity) so we opt for the "back to basics" approach and change our mathematical practices to include a lot of repetition on lower-level, procedural tasks. We convince ourselves that this is the right thing until either the students tune out, or underperform, or both, and then we bark about "raising the bar" and the cycle begins anew.

Geoff's cycle reflects knowledge and practice, but I wanted to dig a little deeper into the idea of "student resistance." Jo Boaler (@joboaler) found herself in a similar position after she'd done some studies that linked reform-oriented practices to a more flexible and robust form of mathematical knowledge, but felt there were some stronger links to make between knowledge and a student's mathematical identity, or the way they see themselves as and becoming knowers and do-ers of mathematics.

Boaler described this process in an article titled The Development of Disciplinary Relationships: Knowledge, Practice and Identity in Mathematics Classrooms, published in 2002 in the journal For the Learning of Mathematics. You can find a preprint of the article on Boaler's faculty website, but I took the time tonight to add a summary of the article to the MathEd.net Wiki:


My takeaway from reading this particular Boaler article is that while both traditional and reform approaches can result in student learning, the attention to student identity and affect in the reform approach shapes student learning in a way that makes the knowledge more useful in more situations, or, in the relative absence of knowledge, gives students both the disposition and a set of practices to make mathematical progress. When students get caught in Geoff's "Cycle of Low Performance," it's not that they aren't learning. Instead, they just don't see their knowledge as particularly valuable, nor do they see themselves as active users of that knowledge. As teachers, we need to design our classrooms and activities in ways that give students opportunities to have some authority over their mathematical ideas if we expect them to use their knowledge productively.

The MathEd.net Wiki

Today I'm announcing a project over a year in the making, the MathEd.net Wiki.

The project has its roots in my own attempts as a graduate student to connect the literature I engage in. Tools like Zotero and Mendeley helped me organize PDFs and references, but I really wanted something that could help connect literature and citations together. Several times I tried setting up a wiki to do this, but each time it felt disorganized and overwhelming. As I prepared for my comprehensive exams in the fall of 2012, I finally found an organizational system for the wiki I thought I could sustain. I've been quietly contributing to it as a private side project ever since, and now feel it's reached the critical mass it needed for me to stay committed to it — and to make it public.

One of the things that drove me to graduate school was a desire to engage in the academic scholarship of my profession. Unfortunately, that's not easy to do as a teacher — either the literature is behind paywalls or inaccessible without a way to get the background knowledge needed to understand it. Usually both. When I started the "Research You Should Know" series on this blog, I hoped I could make some small dent in that problem. But blog posts still didn't let me make all the connections between the literature that I wanted to make. I wanted something that was less linear, and I think this wiki could be that thing.

Having read about similar specialized wikis, I know most fail to meet the expectations of their creators. I'm keeping my expectations modest. It's still a side project. (I have to finish my PhD program sometime, right?) It's a work in progress, and always will be. I don't expect dozens of contributors, although I'd really enjoy having at least a few. I don't expect the simple act of having access to more research to revolutionize anyone's practices. You deserve access to it, but alone it won't solve all our problems. I'll keep contributing to it, and I encourage you to visit the wiki, read the welcome message, and browse around a bit. I would love to get feedback, so either leave a comment or send me an email with your ideas!

Why I Blog

In preparation for her featured NCTM presentation next April, +Kate Nowak is asking why we blog. I also have an NCTM presentation about teachers and social media use, so everybody helping Kate is helping me, too. (That's part of why we blog.)

I think I had my first website in 1996, and I joined Blogger (back in the pre-Google Pyra Labs days) in 2001. I didn't have an education-specific blog until 2009, but any nervousness about self-publishing content to the web had long passed by then. So to answer Kate's questions...

Q1: What hooked you on reading the blogs?
A1: I was the sole full-time math teacher at a small rural school when I attended the 2008 NCTM Annual Meeting in Salt Lake City. Suddenly I found myself talking to members of the National Math Panel, math education professors, and teachers from all over. I'd forgotten what it was like to be part of the larger mathematics education community, so after I got home I tried reaching out to that community in support of my own teaching. I subscribed to Mathematics Teacher and the Journal for Research in Mathematics Education, and while the articles in JRME looked interesting, I quickly got the feeling they weren't written for me. When I searched the internet for information on mathematics education, I found most scholarly articles behind paywalls — another sign that what was out there wasn't meant for me. All those academics that made me feel welcome in Salt Lake City now made me feel shut out of my own profession.

But where journals failed me, blogs succeeded. +Shelly Blake-Plock's "TeachPaperless" blog was very interesting to me, and I was very impressed by Stacy V on Twitter, as she tirelessly searched for and replied to students who expressed their math frustrations via tweet. It was around that time I started following +Dan Meyer and +Cassandra Turner, and when I started graduate school in the Fall of 2009 I had decided that I wanted to use my blog to bridge the research world and the practice world.

Q2: What keeps you coming back?
A2: In many ways, the blogs are my bridge back into the practice world, which, if you allow it, can feel as distant from the research world as the distance feels to teachers looking across the gap from the other direction. I admit that I find myself less interested in the content of any one blog or post, and more interested in the general nature of the conversation and how that represents math teaching as a profession. (If you're wondering how my talk will likely be different from the other math-teacher-blogger sessions at NCTM, this is it.)

Q3: If you write, why do you write?
A3: I'm in a very privileged position; I have access to great people and great literature and I get to think about mathematics education as my full-time job. I feel a responsibility to share. I benefit personally from greater social capital, as now people introduce themselves to me at conferences and tell me they've read my blog. But as a student who is funded by Colorado taxpayers, tuition-paying students, and the National Science Foundation, I hope those funders would be pleased to see me writing and sharing online.

Q4: If you chose to enter a room where I was going to talk about blogging for an hour, what would you hope to be hearing from me?
A4: Like it or not, Kate, you're in a position to steer conversations beyond your own. I think there's a low bar to be a blogging teacher, but a rather high bar to be a really good one. For example, some teachers blog to reflect on their own practice. But are those reflections just casual, or more serious, in a Zeichner-Liston reflective teaching sort of way? Some teachers share resources. Do they try to describe the qualities of those resources? What measures/attributes do they use? So, Kate, if you're going to talk about teacher blogging, make sure you go beyond blog/noblog. Frame participation along a spectrum from novice towards expertise, and steps you'd suggest good bloggers take to get even better.

Trained in First Aid

I was at a conference recently and, much to my embarrassment, I got a rather bad paper cut. As luck would have it, the woman sitting to my right said she was an ER nurse and she offered to help. But then a young woman on my left said she had just finished an intensive five-week course to become Trained in First Aid. With a mixture of innocence and confidence, she asked me, "Could I test out my new skills?"

I appreciated the young woman's eagerness so I accepted her offer. She set about mending my finger with a few first aid supplies she kept in her bag.

As she mended my finger she described the process: "Apply pressure with sterile gauze to stop the bleeding, clean the wound, apply an antibiotic, then bandage neatly and securely to ward off potential infection." Her process looked like what I pictured other healthcare professionals doing in that situation, so I was happy.

"Is that how they taught you in the first aid class?" I asked.

"Yes, we practiced how to stop bleeding and fix cuts many times. I learned how to fix all kinds of things," she replied confidently.

I looked to the nurse for her approval. "Is that how you learned to fix paper cuts?" I asked, hoping my tone didn't come across as too condescending. Her reply began with a "Yes" but continued in detail about the benefits and potential problems with different kinds of antibiotics, how to determine when cuts need stitches, and then she started using some medical terms I didn't know. My mind wandered in the jargon, thinking she misunderstood my reference to a simple paper cut. I asked again, "But my paper cut...what this nice girl did should fix it, right? Can I consider myself healthy?"

That unfortunately struck a nerve with the nurse: "Being healthy is not a matter of 'fixing' things. I didn't spend four years getting a nursing degree and many more hours in professional training to learn how to 'fix' things. The notion of being 'healthy' is a very big idea, and there's no such thing as 'perfect health.' I'm just one part in large system dedicated to people's health care needs, and helping patients help themselves is more important than anything I could pretend to 'fix'."

The nurse's tone made me uncomfortable so I turned back to the eager young woman, now neatly putting away her first aid kit. "How do you see yourself as a healthcare worker?"

"I guess I haven't thought about it that much. I just want to help people when they're sick or hurt," she sweetly replied.

"Have you thought about being a nurse or doctor someday? I really liked your bedside manner," I said.

"No, not really. I just took the first aid class so I could work at a summer camp for disadvantaged kids. I've always liked working with kids, and the experience will look good on my resume when I apply to graduate school."

"Medical school?" I pressed.

"Probably not," she said. "My dad is a doctor, but I'm really hoping to pursue business or law."

What a shame, I thought to myself. We'd be better off as a society if eager young people trained in first aid were always there to help, especially for those people without much access to health care. For many people, I thought, a young man or woman like this could help with many things we typically leave up to nurses and doctors who require longer and more expensive training.

The session ended and we filed towards the exit of the conference center. Just as we approached the doors I heard a loud explosion from across the street. I was stunned and confused and saw both the nurse and the young woman running outside to help. Through the smoke and debris on the street, I saw a few dozen injured people making their way out of a restaurant. The young woman rushed to one of the first ones out, a man with a cut on his arm. First aid kit in hand, she began the same practiced procedure she used with me to clean and cover the injured man's wound.

I looked for the nurse, but she hadn't stopped at the first few people she saw. Instead, she was busy putting people in groups: she directed people with cuts to gather together in the street, while those too injured to walk were carried down the sidewalk to relative safety. There was a small group of people nearby who appeared to have suffered burns, and the nurse was attending most closely to three people who were having trouble breathing. She spotted a man carrying a first aid kit and I heard her yell, "Take that over there," pointing to the group with cuts. "Get some people to help you apply pressure to the wounds." I joined the man in helping people tend to their lacerations, following the same steps the young woman had just used minutes before when helping me with my paper cut.

Sirens from multiple directions got louder and as the EMTs arrived both the young woman and the nurse described the situation. I heard the young woman talk about people who were bleeding while EMTs pressed her for more detailed information. The nurse, on the other hand, was able to give very short, specific directions to the EMTs using medical terminology I didn't understand. When she had used that jargon with me I had been unimpressed, but in this context it took on urgently needed usefulness and carried a mark of professionalism.

As the injured were treated and rushed away to a nearby hospital, I thought about the eager young woman Trained in First Aid. I don't think I had misjudged her — she did what she had been trained to do and provided valuable help. With more training and experience, I saw no reason she wouldn't be able to triage victims and respond with the level of professionalism I'd seen from the ER nurse. What I had misjudged, however, were the demands of people needing help. Had I been in that restaurant, I probably would have suffered far worse than a paper cut.

Accidents can happen anywhere. People need quality health care everywhere. For the eager young woman to be part of a long-term solution, she'd need to commit to far more than five weeks of first aid training and a summer at camp. But that wasn't her plan. To me, that means she and others like her are unlikely to be part of a solution. That doesn't mean she's part of the problem, but there is a problem when we fail to believe and invest in well-trained, experienced nurses and doctors. The ER nurse was right: health care needs come both big and small, and it's not about providing a 'fix.' Health is a process, and health care needs to be a system to support that process. Needs run deeper than paper cuts, and we can't expect to meet them all with eager young people Trained in First Aid.