patterns and rules

This past week, I learned how pattern recognition can help students find a rule and develop algebraic thinking. In honesty, while I've certainly detected patterns to solve problems before, using patterns to define rules is not something I've spent much time doing. Growing up, rules were given to you. You memorized them. It did not matter why or how they worked. Using inquiry methods to derive a mathematical rule from a perceived pattern - and expressing that rule algebraically - isn't something I ever remember doing in school. While I developed a real appreciation for inquiry methods in last quarter's math methods class, for some reason last week's activity "Crossing the River" (in which we determined how many trips, subject to certain rules, it would take to ferry a given number of adults and children across a river) really reinforced their value.

One question I have about using patterns to develop algebraic concepts is how to differentiate instruction for varying ability levels. For example, some students may not be able to detect a pattern when solving a problem like "Crossing the River" and members of their learning group may not be able to successfully explain it. Perhaps there is another entry point for this exercise, but I am not sure what it would be.

In the classroom, while we may choose to do an exercise such as "Crossing the River" and be resolved to allow as much time as is needed for every student to achieve comprehension, the reality is that we may not be able to. Running out of time seems to be a common occurrence, in my classroom experience thus far. On the other hand, if we're able to successfully differentiate an exercise like "Crossing the River," small group or math station work lends itself to differentiation quite nicely. This strategy might better enable every student to succeed.

moo-ing

I just wrapped up my web 2.0 reflection on my tech portfolio website, and it got me reminiscing about the ancient future of internet facilitated discourse, the MOO. A MOO is an multi-user, object oriented virtual space. I actually built an educational MOO as my senior project in college, called MOO-tropolis. I interned with an intellectual historian who was certain that electronically mediated communication would enable us to remake our very identity.

People connected from around the word to interact in these text-based environments. Many MOOs existed purely for entertainment, but others had higher aims, such as facilitating intellectual discourse (Postmodern Culture MOO) or revolutionizing the way we thought of classrooms (Diversity University). What's most intriguing about these environments nowadays is that a) no one has ever heard of them, and b) the way we approach education is mostly not revolutionized by their once-upon-a-time prevalence. This makes me think twice when I hear something claim it's going to change everything.


PMC MOO screenshot

I use, like, and benefit from modern technology, the internet, and "web 2.0" technologies, but I like to maintain proper perspective, too.