Math Blogging for Students

As a frequent blogger about education, I got to thinking about blogging for education. A blog is an ideal way for students to converse, share ideas, and provide each other with feedback. A class can share a blog, writing posts back and forth, or students can each be assigned to write their own throughout the year and to comment on each others’. Often, teachers tend to think of blogging as a medium for English or humanities classes to practice writing skills and critical thinking. But maybe students can benefit from math-focused blogs as well.

An article from the August 2010 issue of THE Journal recounts the story of a math teacher who suggested that one struggling student try asking for help from her peers through the school’s learning management system. Online, the girl, who had felt too embarrassed to participate in class, found it much easier to communicate and ask for clarification on algebra concepts. She even managed to build up her confidence in the classroom.

Why shouldn’t students be able to consult each other from home to share strategies and ideas for problem solving? In the humanities, students are regularly asked to critique each others’ work because collaboration is constructive. Since technology is such an engaging tool, students would probably relish the opportunity to consult with classmates online about challenging math concepts and problems. How have you integrated technology and web-based discussion into your math classroom?

http://www.flickr.com/photos/extraketchup/ / CC BY 2.0

School of One Program Promises a Truly Individualized Math Curriculum

The Atlantic reported that this September, New York City public schools plan to launch the largest prototype yet of the innovative School of One program for 1200 6th and 7th graders at three schools. The program envisions classrooms where students alternately learn in a variety of contexts: traditional teacher-led instruction, small group collaborative activities, online software-based instruction, online live instruction, independent learning, and one-on-one tutoring. Students will have the opportunity to learn at their own pace and in the manner that best caters to their learning style.

In launching School of One, New York has not eliminated its grade level standards or the sequence of content. However, it is allowing students to grasp content in their own way, thus hopefully reaching even the most reluctant and struggling students. Every student has different needs, and for some, the traditional classroom approach will never be effective.

Technology facilitates the simultaneous nature of the different learning modalities. At the end of each day, students complete short progress assessments that the program uses to generate tentative individualized lesson plans. Since some students can work with online tutors, instructional software, or in small group settings while others participate in teacher-led instruction, educators have more flexibility to tailor instruction to different students as needed.

The author of The Atlantic article, Ta-Nehisi Coates, speculates that having access to a more fun and personalized learning environment would have made school an exciting rather than a dreaded experience for him and could have deterred him from ultimately dropping out of college. Can technology be the key to sparking both the interest and understanding of underachieving students?

Photo Credit: http://schools.nyc.gov/community/innovation/SchoolofOne/default.htm

What can video games teach us about good learning environments?

This was the question posed by James Gee of Arizona State at the annual meeting of  the American Association for the Advancement of Science. ("First_Person Solvers: Learning Mathematics in a Video Game")

Stay with me; this not the usual old wine. Gee is basically inviting us to steal ideas that work, and points out that we can do this with or without technology.

Think about your basic video game environment. I mean really think about it, if you can bear it. (This part is hard for me.) What works? Break it down to its elements, and then picture how those might translate to the classroom. Gee highlights the following:

• Feedback is immediate, continuous and plentiful.

• Information is provided when it is needed, near to the point when it will be used (rather than all at once, as is often the case in the classroom).

• Game designers encourage "modding," and this invites meaningful engagement. ("Modding" is when players use the actual game software to modify or add to the game.)

• The environment is a big "problem-solving space" which Gee calls "pleasantly frustrating. The tasks are challenging but doable. That's a very motivating state for human beings," says Gee.

If you know your video games and what makes them tick, let us hear from you. What you might add to this list? A sense of accomplishment and progress? A game's multiple entry points? The ability to personalize an experience? Is it modding when your students write a story problem? (Do you like just using the word "modding"? I do.)

Most importantly of all, what do these things look like in the math classroom? What are you already doing that has a parallel in the world of video games? What features, small or big, could you see yourself adopting? It's an interesting thought experiment -- please do let us know if you make it a real experiment.

 

Brain on My Mind

My mind has been filled with thoughts about the brain even more than usual in the days leading up to Thanksgiving. On Saturday I spent time with an economist friend who has recently been asked to consult on the emerging field of neuro-economics. He agreed with me that education is a field ripe for this kind of approach to influencing behavior; sadly, he also didn't know anyone investigating this perspective. On Sunday I spoke at the Learning and the Brain conference at MIT where I focused on the intersection of technology and cognitive research. Then the following evening I participated in an idea-generating dinner among faculty and students from the TIE and MBE programs at the Harvard Graduate School of Education. Two big ideas in particular emerged for me over those few days.

First, we still have much to learn not just about the effects of technology on cognitive development, but also about what questions to ask. I heard a lot of assumptions about how the brains of the digital generation are wired differently, but I didn't see a lot of evidence of that different wiring. Do today's youth really have different brains? At what age did a child have to start using technology to get a different brain? What technology are we talking about anyway? Using a mouse? Hypertext? Playing video games? Watching TV? Talking on the phone? There have always been generational differences. What's different about this one? How do we separate the usual generational cycle from anything unique here? Good research requires specific questions that define and isolate variables. We have exciting and interesting work still to do here.

Second, we need to move beyond the either/or orientation that often accompanies hyperbolic talk about technology and cognitive development. In the good old days, we read books. Today's generation reads short passages on the web or even shorter pieces on Twitter. Back in the day we focused on tasks one at a time; today's hypertext, always-on, multi-tasked world leads to constant distraction. When I was a kid we played with other kids outside. Now children become avatars interacting with other imagined identities in giant virtual worlds. On and on it goes.

However, technology doesn't typically displace what we used to do. Children still read books, focus to the point of ignoring parental requests, and talk to one another in person. But they do these other things too. If we look at the technology as additive, we can start to ask questions about when and under what circumstances it might actually amplify what we already do (communicate) and when it might compete (watching TV instead of running around). Sometimes the amplification can be good, allowing us, for instance, to increase contact with family members. Sometimes it can be bad, such as allowing hate messages to spread more readily. It's a nuanced portrait that merits thoughtful examination. The better we understand it, the better we will be able to use it in constructive ways. That's part of what we're up to.

Photo credit: http://www.flickr.com/photos/dthai/ / CC BY-ND 2.0

Making stuff work

I’m Cathy. I’m invading the “Math Hub” with some thoughts of my own.

So, who am I? Officially, the sign on my cubicle says I’m the Producer of Formative Evaluation here at Tom Snyder Productions. When my parents ask me what my new job is, I tell them that I help make sure educational products do what they are meant to do and withhold the fancy, scary grown-up title. Ultimately, I’m just someone who likes to convince others how cool some things are. Through this blog, I hope to give you a glimpse of how educators and kids are helping us develop a math product and why that feedback loop between those folks and our developers is, well, cool.

I’ve long pondered about the research that goes into educational toys and products. I remember bouncing around a story idea about that near the holidays during my newspaper reporting days. Unfortunately, there was no big toy company in town, so not enough of a local angle to do such a story. But every time I drove to Los Angeles for figure skating practice, I’d pass by the Mattel headquarters, sit in traffic, and often wonder again. Maybe one of these days, I’ll just pop in and be like, “hey, can I learn about what research you do for your toys?”

Maybe. :)

In the meantime, I’m going to use this space to let you in on some stories about our product testing, subject you to some ramblings I’m sure, and hopefully stir some good conversations. Stay tuned and join in!

Back to School -- Time to Cherish Mistakes

It’s that time of year, and I’m feeling it from several perspectives -- as a parent, as a teacher, and as a developer chomping at the bit to test out some new ideas in real classrooms. Our only son is now a freshman at college. My wife and I have joined the ranks of empty-nesters, and my kid is enjoying a new found independence. I welcomed new students into the Technology, Innovation, and Education program at Harvard and started prepping for my first class on Friday. And we’ve been devising new programs at Tom Snyder Productions, testing out new ideas internally and getting ready to try them with actual middle school students and teachers. For me, a common theme running through these various perspectives is failure. I expect it, and I’m actually looking forward to it.

School is all too often associated with getting it right, but where’s the learning in that? We gain so much more from our mistakes. The original Deep Blue IBM chess computer that defeated chess champion Gary Kasporov was a monster machine. It had been programmed with all the possible moves for each situation on the chess board. Searching all those moves required incredible processing power, and technicians were nearby with fire extinguishers to handle the potential overload of the machine. Nowadays, software engineers build learning machines that don’t know all the answers ahead of time, as Deep Blue did. Instead, these new programs make mistakes, thousands of them every minute, and they learn from them. Researchers at IBM produced backgammon learning software that followed this approach, playing hundreds of thousands of simulated games to learn how to play. That program now plays at an expert level.

One nice thing about a computer playing games with itself is that the results are low stakes. Losing doesn’t matter. Learning does. Schools should be similar learning environments, a place where it’s safe to make mistakes…so long as we learn from them. So my message to my son and my students at the beginning of this new school year: take some chances, try out new ideas, and learn from the inevitable missteps. Getting everything right on the first try generally indicates a lack of challenge. Challenge leads to growth, and what better place to grow than a safe, supported place like school.

Blogs are for old people.

Here are I am trying to be technologically hip by thinking of something insightful and interesting to share with an unknown audience on a fairly regular (maybe not so regular; it’s been a while) basis, and I keep reading that blogging is dead. Okay, “dead” might be a little strong, but it’s certainly not hip or cutting-edge anymore. The latest nail in the coffin came from The Economist. The magazine noted that blogging has gone corporate. Every company has at least one, and they use their blogs as another way to reach and influence customers. I’m not blazing trails; I’m just one of the pack.

The early blog adopters have moved on to twittering and other emerging means of communicating. A similar migration is happening with Facebook. Once mom and dad join, the kids flee (my son recently unfriended me). Who can blame them (I’m not really in the 17-year old peer group)? As Walmart, Proctor & Gamble, and other staid corporate entities develop their Facebook presences, I may follow. The problem is, wherever the trailblazers go, mom and dad and the corporations will follow. You can’t really escape for long.

So what happens when new becomes old, when cutting edge turns into mundane, when the digital natives leave and the immigrants (like me) move in? Will enough people with sufficient energy stay in the neighborhoods to keep them vibrant? Which neighborhoods will survive and which will whither? It’s going to be very interesting to watch what happens. The speed with which new services arise, grow (or not), and disappear reminds me of biology experiments with fruit flies. Their lifespan is so short, the passing of generations so quick, that you can see the effects of evolution unfold in real time. Keep your eye on the web, but don’t blink. You might miss the life and death of a transformative service.

Digital nomads with their heads (and data) in the cloud

My son Jake, a rising high school senior, doesn’t have his “own” computer. Instead, he seems to have everyone’s. At school he moves from the computers in the computer lab to those in the student center to those in the film studio. He emails documents to himself or carries work on a flash drive. At home, well, at home no computer is safe. I’ll open my work laptop and find FirstClass open, my son’s Facebook page on the browser, and a couple of homework documents on the desktop. “Do you need any of this stuff?” I ask. “No, I got it.” My computer was handiest; he used it and pushed his work into the Internet cloud to be retrieved at the next available machine. When we travel Jake always manages to find someone or someplace with a computer, iPhone, or some other cloud-friendly device. He connects with friends, moves pictures to Facebook, and checks tennis scores. Welcome to the world of the digital nomad.

Don’t get me wrong, Jake wants his own laptop. He needs a base (we have an aging iMac at home that is “his” in general), but his ability to exist in the cloud frees him from that base (making anything “his” at any moment). And the shrinking size of computers and growing power of cell phones offer the promise that maybe the base can move with him as well. Or at least be available wherever he goes. For him, with the exception of a few specialized applications, school work has no boundaries. Any computer in our house, at school, at a public internet station, or anywhere will do.

As more and more work, student and teacher, exists in the cloud, the opportunity to do something really interesting with it grows because we can all access the cloud and what it contains. Despite my own experiences, direct and vicarious, with mash-ups and remixes, I’ve been slow to see the potential of the collaborative Web 2.0 promise. I’m finally beginning to see the light, but it’s fraught with questions and issues we still need to figure out.

Let me give a specific example: We are about to launch a new program, Timeliner XE. The original TimeLiner 1.0 in 1986 turned Apple IIs and early PC’s connected to dot matrix printers into simple systems for generating banner time lines with ease. Type in events in any order, and the software created a proportionally-spaced chronology that could be printed out sideways on the scrolled paper of those early printers. Simple and sweet. Over the years and releases, the program added the ability to print posters, save as html, create slide shows, and add graphics, links, and other media. This new version takes a huge leap forward. Timeliner XE, built with Adobe Flex and Air, contains a built in browser that enables users to gather, organize, and present information within the same application. In addition to time-related events, any sequential information -- like the life cycle, the steps in a research project, or the plot of a book -- can be managed in the program. It’s very cool.

So what happens to the time lines and sequences that students and teachers create? While having thousands of students create their family histories or story arcs for Tuck Everlasting each year is nice, can’t we take their efforts further by putting the work into the cloud? Imagine a Day-in-the-Life time line that students from around the world contribute to. Each contribution gets its own category and color code so that they can be distinguished and turned on and off. How about collaborative time lines highlighting the flow of information and technology around the world as it happens? What might it look like for users to stand on the shoulders of previous work rather than simply repeating what others have already done? We’re having fun imagining the possibilities.

We’re also straining to understand the implications. What student information is private? Is it okay to share a student’s day in the life in the cloud? Can other users change someone’s time line? What about ownership and attribution? How do we make sure that copyright is respected in what gets posted? It is exciting, but it’s also complicated.

Many of our students are already living in the cloud. It’s happening even as the rules are being created and understood. We’re working on it. I hope you’ll be part of the unfolding story.

A moment to brag...but not about myself

I recently finished evaluating student projects from the software design class I teach at the Harvard Grad School of Education. With all due respect to my past classes (which were all fabulous, each one better than the others), this year’s group really clicked, and the range of high quality projects was impressive. To complete the projects students work in small teams on a project of their choice. They gather evidence to define an educational problem they are tackling, review relevant research for clues about effective approaches, devise a plan, construct a prototype, and test and revise it. I learn an enormous amount; hopefully they do too.

I had a number of former, current, and prospective teachers in this year’s mix. They helped maintain a grounding in reality that sometimes gets lost when folks start playing with the possibilities technology offers. One group of students, who are in a mid-career teacher transition program, took on negative numbers. They wanted a program to help them with a problem they were encountering in their classrooms. Digging into the research gave them a depth of awareness about a core learning issue that few teachers have the luxury to plumb. They found no easy answers, but I suspect the knowledge and experience they did gain will serve them well down the line.

So too for the group that focused on teaching the physics of sound, the one that hoped to use a program on the Pilgrims to help elementary students see outside themselves to better understand history, and the one with fabulous activities to build reading comprehension skills. The physics group developed a pre-assessment on student conceptions of sound that was incredibly enlightening. The drawings and descriptions revealed a great deal about kids’ thinking and provided a powerful reminder about the importance of respecting the knowledge students bring with them to class. The Pilgrim project worked to push second and third graders developmentally, and the effort uncovered the edges of what young students can comprehend. The reading comprehension project simply radiated a graduate student’s passion about what she teaches in her high school English class in Florida. Her project introduced me to some very intriguing ideas about using comics and graphic novels to teach comprehension. More importantly, it allowed her to focus and deepen her thinking about some very powerful instructional lessons. Wouldn’t it be fantastic for all teachers to be able to take a semester to really grapple with some element of their teaching?

Three projects gave me hope that recently neglected parts of the curriculum may soon recover. One was a project that engaged students in using primary sources scaffolded reading and interpretation and helped turn what is too often a “read and remember” subject into one that is dynamic and alive. History is being made and interpreted everyday; we should teach it! When the “Culture Shock” team presented its project to the class, they started with a National Geographic geography online quiz. While the performance of my graduate students was pretty solid (this is Harvard, after all), the national results were pretty sorry. We are a geographically ignorant nation. That’s sad given how interconnected the world has become. The team’s simulation puts students in the role of manufacturers looking for the best resources and most responsible working conditions from around the globe. That’s real and relevant. Can’t we squeeze a little geography and culture back into the curriculum? The third project dealt with decision-making, civic responsibility, and conflict management. They developed a whole class prototype that had my students engaged in rich conversation and perspective-taking for two hours. Shouldn’t we devote a bit of school time to learning how to see and work with others?

Two groups of students gained experience by working with real clients. One team of international students partnered with a professor at the University of Athens in Greece. They aimed to design an online support environment for a course that’s part of a program training future teachers of English to native Greek speakers. The team that developed a technology-rich program for a media literacy unit in a local urban high school also had to revise and rethink based on the input from the teacher who would ultimately be using the materials. We all relearned the lesson that designing something cool might be different from designing something that will work somewhere real.

And speaking of contextual constraints, one group turned to cell phones as a delivery platform for teaching French to children and adult learners in Ghana. That team had to think through a whole new infrastructure that leverages a number of emerging technologies with solid, proven pedagogy. This mobile learning project, along with one working to incorporate some web 2.0 features into an online vocabulary-building environment, particularly highlighted the promise of new technologies. All of the projects had solid research foundations, but they each took creative paths to applying that research with the aid of technology to meet important educational needs.

I think I covered all the projects from this fall’s course. I hope I didn’t embarrass any of my students or leave anyone out. I just wanted to brag about their efforts a bit and tease out some of the general lessons that are easy to overlook in the details of each project. Nice work!

Board Games, Bowling and the Risks of Technology

I’ve always loved board games, and I’m happy to see new research demonstrating their educational value. The new study (Siegler & Ramani, 2007) looked specifically at the impact of playing a simple numerical (versus color-coded) board game on the number understanding of low-income children. Earlier studies (notably Case & Griffin, 1990) found that the number knowledge of low-income pre-schoolers significantly lagged that of their middle- and high-income peers. The difference most likely comes from the informal mathematical experiences kids receive at home. Just as exposure to books and vocabulary helps prepare a pre-school child for more formal reading instruction in school, so too do informal mathematical tasks like counting place settings, measuring ingredients, and playing board games get a child ready for learning math in the classroom.

From simple games like Chutes & Ladders to more complex ones like Monopoly, these fun activities contain lots of math lessons. Rolling dice reinforces sets and addition. Moving a playing piece along the ten squares on each side of a Monopoly board highlights number quantity relationships and a make-ten strategy (how many spaces to land on Free Parking?). The new research suggests that playing these games can significantly close the number knowledge gap among pre-schoolers. That’s a cheap (and fun) way to make a difference.

And then there’s all the social benefit that comes from playing board games. Children learn about turn-taking, following the rules, and self-handicapping (to keep things competitive among unevenly matched players). Players have to monitor each other for mistakes and cheating. Disagreements must be resolved and fairness maintained. That’s all really good stuff!

Sadly, technology can put many of these lessons at risk. Putting the games on the computer typically means robbing children of the opportunity to calculate the dice or count spaces on the playing board as the software does it for them. I felt robbed of these chances myself when I went bowling over the Thanksgiving holiday. I hadn’t been bowling (big ball, not candlepin for my New England friends) in over 20 years. I stunk, but that’s beside the point. Horrible low-tech graphics on LCD displays hung over each alley, and a computer counted the pins and did all the scoring automatically. The families with young children on either side of our “older” group missed out on some valuable educational moments. Sometimes technology can make things easier without making them better.