Year: 2013 (page 3 of 15)

As I was travelling to St. Ives, I met a man who’d lived seven lives,
In each life he’d learned seven lessons,
Within each lesson he’d had seven chances,
With each chance he’d made seven mistakes,
With each mistake he’d found seven connections,
How many connections, mistakes, chances, and lessons are missed by those who fear to live?

I grew up in a household that read all the time, talked about the world as we thought it exists and imagined possible worlds, and had conversations all the time about anything that interested us. I had my first computer at age 8, and had the freedom to use it as I pleased, which turns out involved programming it. My world was rich with numbers. My toys were mostly things that I could build things with. My house had a hallway full of many thousands of books, and so I never ran out of something to read.

When you say that I’m smart, I beg to differ; I come from privilege. Or if you insist on wanting to continue using the word smart, we should redefine it not to mean an inherent fixed trait that someone has and possibly inherited from their parents, and think of it as a trait that is developed by immersion in rich experiences. 

The objective of this workshop is to talk about different ways of making abstract ideas in mathematics more real for students. Sometimes this involves using various technologies, and other times it does not. I also want to create a set of slides for my workshop so that I can respond to the potential needs of the participants who come to the workshop. In general, the idea is pedagogy first, and then asking the question, what tools (technological or other wise) can we use to address the pedagogy?

Huge hat tip to Dan Meyer for making some resources that are particularly useful in addressing some of the pedagogical ideas I’m trying to explore with participants.

Any suggestions?

I may be presenting on social media use in education for a group of administrators in month or so, and a discussion I had on Twitter prompted me to think about why I use social media. An important aspect of any presentation on any tool is addressing the question; why should I use this?

Educators are right to be skeptical of social media use. It is commonly protrayed in the media as frivolous or inane. It can be time consuming. It is certainly the case that many people use social media as a distraction from the world around them. It is hard to convince educators that social media is worth the investment in time.

Given that there are obvious drawbacks to the use of social media, it is reasonable to ask, do the benefits outweigh these drawbacks?

I use social media to collaborate with people from around the world. I curated a presentation on different formative assessment strategies which has been viewed thousands of times. I did not create this presentation myself. I seeded it with 20 strategies for formative assessment, shared a public link tso that people could add to the presentation, and then made sure to keep the formating in place as people added their ideas to the presentation. Once the ideas stopped coming in, I closed off the document for editing, and refined the formating of the document.

I use social media to find out about things in education that are outside of my immediate world. I have heard people say that social media acts as a bit of an echo chamber, where ideas are bounced around and rarely challenged. This may be true to some extent, but if social media is an echo chamber, the typical faculty room is a linen closet by comparison. It is not that there aren’t great ideas that come out of discussions, there absolutely are, it is that the frequency of these ideas is a lot less, and they become stale more quickly.

I use social media to connect with people from around the world, share my project ideas with them, and get feedback on my work. I also get feedback from my colleagues at work on what I do, but educators are busy people. If I share something with my network, not only am I helping contribute to a growing pool of shared knowledge, a few people may help me find the bugs in my work, or even tell me that I’m completely crazy.

I use social media to discover that there are completely different ways of teaching. Teaching is a cultural activity, and to some extent we have a shared cultural knowledge of teaching, but it is also the case that there is a lot of variation within cultures, and between cultures. Cross-pollinating between different cultural understandings of teaching is a bit like preventing in-breeding by marrying someone from a different village.

I use social media to share my personal narrative with my colleagues around the world, and seek advice on how to change the ending.  I try not to forget that at the other end of each of the blogs I read, the tweets I see, and pictures that are shared, are people. These people have their hopes and dreams just the same that I do, and social media can act as a way for people to share their dreams, find other people who have the same dreams, and commiserate over our failures. While I do get lots of emotional support from my family and friends, I often have ideas that I want to discuss that are completely outside of their interest (actually, this is surprisingly common).

I use social media to transcend some of the social hierarchies of our educational society. Through social media, I discuss ideas with mathematics education researchers, professors of education, administrators, authors, and many, many teachers like me. Without social media, it is highly unlikely that any of these conversations would happen. In social media, it is more about your ideas (although not exclusively) than about who you are, what you look like, and where you work.

I use social media to learn when I have time, wherever I have Internet access, and whatever it is I feel like I need to learn. I am self-directed in my learning, and I am not restricted in what I learn to a small number of professional development days per year. Learning new things becomes something I do daily rather than monthly. Instead of having to spend my available time searching for or creating resources, resources come to me (although not always exactly when I need them).

Do these sound like compelling reasons to use social media? Can you offer suggestions for other reasons to use social media?

When my wife and I moved our family to NYC from Vancouver, we knew that we would have to get used to many changes, we just did not know how large some of those those changes would be.

We started our planning in January because we knew that finding an affordable place to live and a school for our son was going to be challenging. We created a map to overlay the information about schools we were gathering with information about rental prices. Very quickly we noticed a few trends.

Rental prices in New York appear to be at least partially influenced by whether or not the local zoned school is considered good by the community. We found ourselves, over and over again, finding a school that appeared from the outside to be good, only to find that the cost of rent in the community surrounding the school was out of our price range.

We also noticed something else disturbing when we started searching for schools. Every school review website we looked at included the same type of statistics at the top of their review; what percentage of kids were eligible for the school lunch, what the average number kids being successful on the state math and reading tests, and what the racial distribution of the school was. 

We found the sharing of these statistics to be kind of bizarre in a city whose education system claims to support reducing inequity in education. If you wanted to greatly increase racial segregation in schools, I think of no better way than to loudly announce which schools "those black and latino kids go to." If you wanted to create the misconception that schooling is primarily about getting high test scores, a great way to start would be to highlight those test scores as much as possible for each school.

We even looked into some private schools but either found them to be completely unaffordable or making dubious claims. One Montessori school my wife visited told her over the phone that "they stop using the Montessori materials after kindergarten." When she visited the school, she found their classrooms were filled with wall to wall workbooks and the desks were carefully arranged in rows. We were reminded of the saying "Buyer beware!"

We were also really surprised by the lack of options for alternative types of elementary schools in the NYC public system. For a system that advertises itself as a "school system of choice" we were shocked to find out that there were no Montessori, no Waldorf, no International Baccalaureate, no Reggio Emilio, and no Democratic schools in the public system, notably all of which exist as public schools in British Columbia (there is one Montessori charter school in the Bronx that opened recently). There is not even, as far as we know, a way to search for NYC public schools by educational philosophy. We did find a few progressive schools but they were either open by lottery or located in some of the most expensive areas of NYC. Choice in NYC, it seems, is limited to the rich.

We eventually settled on our local community public school, because they advertise that they are exempt from the mandated city-wide curriculum because of good performance, they have a strong arts and music program, and it is conveniently located two blocks away from a house owned by my wife’s family.

We moved to NYC at the end of June, rented a suite in the family owned house, and spent the summer anxiously waiting to see if we had made the right decision.

About a week before school began, my wife went down to the school to register our son for school. Actually, she went down three times, each time being told that school registration wasn’t open yet, and that she should come back tomorrow. On the third day, she finally found someone to help her fill out the paperwork required to register my son, which included a report card from my son’s previous school that would end up never being forwarded to his teacher, despite assurances to the contrary.

The first day of school was a bit disorienting for us. The sidewalks outside the school were jam packed with kids and their parents, and there were various adults trying to shepherd the crowd around and keep them off the street. There was no inspiring first day of school speeches, no friendly faces welcoming our son into the school, just loud voices telling us to "stay off the street and to leave as soon as our child is safely inside the school." We waited until our son was safely inside the school, and then we left, slightly bewildered by the experience.

"This is the no fun school," my son told my wife a week later, "I don’t like it." He told us he had done nothing but worksheets by the end of the first week of school.

I took the morning off from work, and my wife and I went together to the school’s Meet the Teacher event. Before we met with my son’s teacher, the Principal of his School talked about the school year. "We don’t have any classroom aides this year, unfortunately," she started, "We had to let them go because we couldn’t afford them anymore." During her speech, the challenges with the school budget came up a couple of times, and the need to prepare students for the 3rd grade tests came up three times. It is probably worth noting that the group of parents she was talking to all have children in the school in 2nd grade. After our time spent with our son’s classroom teacher, we both left with a lot more questions about the school.

There is no morning recess. There is a lunch recess but the kids were not allowed outside for the first two weeks of the year because there were no aides available to supervise them. The kids aren’t allowed to run outside during lunch recess because the courtyard is too crowded. My son only has gym once a week (and apparently some children do not get gym at all) during which all he has done so far is walk around the gym. The dance teacher was sick for the first two weeks of school but fortunately they were in this past week. He only has science and social studies for two short periods each a week; the rest of his time is spend on reading, writing, and arithmetic.

My son has homework for the first time, lots of it. He is supposed to read for at least 15 minutes a day, which is never a problem for him, and write down 5 sentences based on some spelling words he needs to know, and do a math worksheet. He typically finishes the math worksheet in a minute, but he has been struggling with the writing, which is easily ten times as much writing per day than what he was expected to do last year.

We met with the teacher recently to voice some of our concerns. I won’t share exactly what was said in this meeting, except to say that my wife and I both left feeling like my son’s teacher is a caring and thoughtful person who is deeply committed to her students, and feels greatly constrained by the mandates she is given by her school district.

A couple of years ago, a friend of mine told me that my concern about what type of school I wanted my son to attend was overblown. He told me, "The most important factor in determining how well your kids do well in school is if you have books on your shelves at home. Do you have books? Well, then your kids will do fine no matter what school they go to."

While I understand my friend’s argument, I think he and I have different goals for our children’s schools. I’m not so concerned that my son does well at school, which is largely a function of how well he does compared to other children (and I’m not really interested in that kind of comparison), I’m concerned that he will learn messages about what it means to learn and to be human that are very different than what I believe. What messages about the value of learning will he learn in a school that keeps talking about the tests the kids will have to take? Is my son learning to be an autonomous learner? What about the value of living a healthy and balanced life?

A couple of days ago my son told my wife, "It’s okay mommy. I’m getting used to this kind of school." 

I know son, and that is what scares me. 

Update: The server this blog is on had its hard drive crash recently, which means that 12 comments on this post have vanished forever. I’m sorry about that. Thank you for everyone’s support!

Based on this image created by Matt Henderson, I decided to write something for myself that would explore other possible random walks, although mine are generated in a slightly different way than what Matt did.

• Pi
• Phi
• e
• Root 2
• Root 3
• One seventh

Each of these images (which will only appear in Chrome, Safari or Firefox, sorry people still using Internet Explorer) is a visual representation of the first 100, 000 digits of the number where each digit of the number corresponds to a different rotation. They may take a while to calculate, depending on the speed of your computer.

Note that for the last "random walk", I increased the scale significantly over the other random walks so that it made the pattern more obvious.

In the fall of 1994, after several months of watching tapes, the project staff met to present some preliminary impressions and interpretations. We invited distinguished researchers and educators from Germany, Japan, and the United States to attend, and we listened intently to what they had to say. We were ready for a fresh perspective. It came late on the last day of the meeting. One of the participants, a professor of mathematics education, had been relatively silent throughout the day. We asked him if he had any observations he would like to share.

"Actually," he began, "I believe I can summarize the main differences among the teaching styles of the three countries." Everyone perked up at this, and here is what he had to say: "In Japanese lessons, there is the mathematics on one hand, and the students on the other. The students engage with the mathematics, and the teacher mediates the relationship between the two. In Germany, there is the mathematics as well, but the teacher owns the mathematics and parcels it out to students as he sees fit, giving facts and explanations at just the right time. In U.S. lessons, there are the students and there is the teacher. I have trouble finding the mathematics. I just see interactions between students and teachers." (James Stigler and James Hiebert, The Teaching Gap, 1999, p25-26)

The Teaching Gap is a synthesis of the research done during the TIMSS video study. This study was an effort to randomly sample classrooms from Japan, Germany, and the United States, and videotape randomly selected lessons from those classrooms. From those lessons, another randomly subset of lessons was chosen, and carefully analyzed and coded by researchers. The objective of the study was to attempt to determine if there are cultural differences in how mathematics is taught in different countries.

The conclusion of the researchers is that although the classrooms look very similar in many ways, there are vast cultural differences in how mathematics is taught, on average, in the different countries. They also concluded that these differences far outshadow the relatively-minor-by-comparison differences between individual teachers in each of the countries. In other words, the difference in teaching methods between a typical Japanese teacher and a typical U.S. teacher are greater than the average differences in teaching between randomly selected U.S. teachers.

The quote above does not quite accurately capture the U.S. classrooms. The researchers concluded that there is mathematics being taught in U.S. classrooms, but that the mathematics content of a typical U.S. classroom is less than that of the other two countries.

A couple of pages later in the book, there is a table comparing typical lessons for German, U.S., and Japanese classrooms. One footnote was particularly interesting to me. In the U.S. classroom, it is "[t]ypical for teacher to intervene at first sign of confusion or struggle," and in the Japanese classroom, it is "[t]ypical for students to struggle with task [sic] before teacher intervenes." (The Teaching Gap, 1999, p30).

Japan currently ranks 5th in the world in an international comparison of mathematics achievement worldwide. The U.S. currently ranks 9th in the world using the same comparison.

Is this data (from nearly 20 years ago) still relevant? If it is, should U.S. teachers adopt the style of Japanese lesson plans? How much do other factors in culture from outside the classroom influence these findings?