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.

RYSK: Cobb, Zhao, & Visnovska's Learning From and Adapting the Theory of Realistic Mathematics Education (2008)

This is the 21st in a series describing "Research You Should Know" (RYSK).

It's Open Access Week (#OAweek) so I thought it would be fitting to use this "research you should know" post to highlight one of my favorite open access articles in mathematics education, Learning From and Adapting the Theory of Realistic Mathematics Education by Paul Cobb, Qing Zhao, and Jana Visnovska. Because the article is open access, I get to be less interested in summarizing it and more interested in giving you a reason to read it.

Realistic Mathematics Education (RME) is a theory for the design and development of mathematics curriculum. It is still deeply rooted in the Netherlands, where Hans Freudenthal greatly influenced mathematics instruction there with his belief that mathematics was a human activity, and that activity was characterized by mathematizing the real or readily imagined world. ("Realistic" comes from the Dutch phrase "zich realiseren," which in English means "to imagine.") This mathematization can be thought of in two ways, horizontal and vertical: "horizontal mathematization involves going from the world of life into the world of symbols, while vertical mathematization means moving within the world of symbols" (Freudenthal, 1991). Hans Freudenthal died in 1990 but his work continues, primarily at the Freudenthal Institute for Science and Mathematics Education at the University of Utrecht in the Netherlands.

There have been four primary avenues where RME has established itself in the United States. The first is with the middle school curriculum series Mathematics in Context, which grew from a partnership between mathematics education researchers at the University of Wisconsin (primarily Thomas Romberg) and researchers at the Freudenthal Institute. The second is the K-8-focused work of Mathematics in the City, which primarily brought together Cathy Fosnot from the City College of New York and Maarten Dolk of the Freudenthal Institute. The pair also wrote most of the Young Mathematicians at Work book series. The third place where RME is established in the U.S. is here at CU-Boulder, home of Freudenthal Institute US and its director, David Webb. David worked on the Mathematics in Context project at Wisconsin, and brought FI-US with him to CU-Boulder. The fourth place I recognize RME having a significant influence in the United States is in the work of Paul Cobb, particularly in his long research partnership with Koeno Gravemeijer, a researcher from the Freudenthal Institute. Cobb and Gravemeijer spent more than a decade working and publishing together, and that work did a lot to strengthen ties between RME as a design theory and theories in the learning sciences.

Like any idea or theory, RME has limitations. Over its 40+ years of existence it's proven to not be a static thing (van den Heuvel-Panhuizen, 2002), and this article by Cobb, Zhao, & Visnovska describes some of the important ways their work has both informed and been influenced by RME. They describe three adaptations: the first involves accounting for classroom activity and discourse in RME, the second acknowledges the mediating role of the teacher in making curriculum modifications and adaptations, and the third looks at how RME can focus on teacher learning, not just student learning. For details, I'll let you read the article for yourself at http://educationdidactique.revues.org/276. If you have any questions about the article or RME, leave a comment, find me on social media, or email me. We RME folks want to spread the word!

References

Freudenthal, H. (1991). Revisiting Mathematics Education: China Lectures. Dordrecht: Kluwer.

van den Heuvel-Panhuizen, M. (2002). Realistic Mathematics Education as work in progress. In F. L. Lin (Ed.), Common Sense in Mathematics Education: Proceedings of 2001 The Netherlands and Taiwan Conference on Mathematics Education (pp. 1–39). Taipei, Taiwan.

RME4: Webb's Opening Remarks

Opening Session - Friday, September 27, 2013

David Webb - Executive Director of Freudenthal Institute US and Associate Professor of Mathematics Education, University of Colorado Boulder

David Webb

David Webb welcomed us to the 4th International Realistic Mathematics Education Conference (#RME4) by addressing a shift in organizational structures. What used to be simply the Freudenthal Institute in the Netherlands is now the Freudenthal Institute for Science and Mathematics Education, and its American counterpart, Freudenthal Institute US, is now part of a larger CU-Boulder effort known as the Center for STEM Learning. These shifts reflect a desire to not just have cooperation between mathematics and science disciplines, but a perceived need to create innovative new STEM curricula along with the supporting frameworks, teacher education, and professional development to support it. Webb announced that earlier in the week that FISME and the Center for STEM Learning had formally agreed to collaborate, although we'll have to wait and see how this collaboration takes shape.

At its core, RME is a set of principles for curriculum design. It is sensible, then, to seek common ground in mathematics and the sciences for ideas upon which we can design curriculum. Some of that common ground is found in how we reason in math and science, and Webb offered these four activities:

• Recognition of patterns
• Making conjectures from observation
• Reasoning from evidence
• Generating new evidence

From these, we can think about how we consider the acts of modeling, problem solving, generalizing, and proving in both math and science. There are similarities and differences, and these things are meant as a starting point, not a definitive list. Perhaps the most fundamental RME principle is that of progressive formalization (see here for an example), so we must also think about how informal contexts can be used in both math and science, as well as the preformal models and representations that support more formal kinds of student thinking. Webb encouraged us to consider these RME traditions as we stretched ourselves beyond our usual disciplines, and with that the conference was underway.

NCTM Annual Meeting Fee Frustration (Updated 9-18)

I was recently informed by NCTM that my proposal to speak at the 2014 NCTM Annual Meeting was accepted. That's the good news. Unlike last year, when the conference was held in my backyard of Denver, I hesitated to accept NCTM's invitation to speak because of the costs involved. Registration fees, hotels, and transportation add up alarmingly quickly, especially for a graduate student getting by on a modest stipend and student loans.

Today I decided to accept the invitation and proceeded through NCTM's multi-step process. Step 1 was to accept, which was done with a quick login and a few clicks. Step 2 was to register for the conference. The registration fee for lead speakers is $281. Okay, but what are the fees for regular attendees? Here are the fees listed at http://www.nctm.org/researchconf/:

Fees at http://www.nctm.org/researchconf/, current as of 9/17/13.

Do you see what I see? If I were a regular NCTM member, the full, early-bird fee would be $345, which means the $281 speaker fee represents a $64 discount. That's a nice way to show your appreciation to speakers, isn't it? But what about student NCTM members? My full, early-bird fee is $172, which means the $281 speaker fee represents a $109 penalty.

Why is this? Does NCTM want to discourage students from presenting? I doubt it, but unless they get their fee structure sorted out that might be the result. I've emailed NCTM about this issue, and I hope they reply sensibly.

While I'm ranting, here's a selection of other things about this process that makes me mean:

• Silly me did Step 1 before Step 2, which mean I accepted before checking out the speaker fee. Even worse, NCTM warns you that accepting then cancelling puts you in the NCTM doghouse and decreases the chances that any future proposals get accepted.
• Too many policies at http://www.nctm.org/speak/neworleans/ disappoint me, such as:
  
• Remember that recording of Steven Leinwand's talk I posted from the last Annual Meeting? That apparently is (or will be) against NCTM's wishes, as they state: "Written permission to tape or record presentations must be obtained directly from the speaker involved at least thirty days before the NCTM Annual Meeting & Exposition. The request must contain a statement indicating the intended use of such a recording or videotape. The person making the request should also inform the NCTM Headquarters Office in writing at least two weeks prior to the NCTM Annual Meeting & Exposition." I had Leinwand's permission to post the recording, but didn't get that permission from him in advance.
• If you aren't a lead speaker, but a co-speaker, your registration rate is $344. Yes, a $1 discount compared to the regular, early-bird registration rate. That's like leaving your waitstaff a nickel tip. I'm assuming this higher fee applies to students, too.
• Speakers must submit a written request to use any art related to the Annual Meeting. I can't imagine there's any real risk to just letting registered speakers download that from the password-protected speaker's website.
• NCTM's idea of "going green" is to pick up your program book when you register so they don't have to mail it to you. This wouldn't have struck me as strange 10 years ago, but it sure does now. Why not try this, NCTM: Tell everyone that program books will be available electronically, and those wishing a paper copy can pay an extra $5 with their registration. That way you'll have an estimate of how many copies to print, and be "going green" 2014-style.

UPDATE! (Wednesday, September 18)

I received a reply this morning from Michael Barbagallo, Senior Manager of Member Services at NCTM. He said I can pay the student rate and not the speaker rate, but their system does not currently give me a way to register as a student until registration opens to everyone in November. For now I should confirm I will present (which I've done) and book my hotel room (uhh...can I just bring a tent and a sleeping bag to New Orleans?), then NCTM will sort things out in November when I register for the conference. It sounds like there's no automated way to do this and according to Mr. Barbagallo, "we have few students who speak." To that, I say to grad students: I know the culture of academia and research tells us that presenting at research conferences deserves higher priority than presenting at teacher conferences. Cultures can be changed and good things often come when they are challenged.