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Showing posts with label middle school. Show all posts
Showing posts with label middle school. Show all posts

Sunday, February 21, 2010

On Shoulders of Giants: Historical Math Cubes

One of my favorite topics in math is actually HISTORY.

All too often we treat MATHEMATICS like some monolithic and pure subject, devoid of the quirks of human nature.

But as Spock (Star Trek) so clearly stated, "We are essentially irrational beings." And mathematics is a part of it all.

Each year I have my 7th graders do a mini research project I call "On the Shoulders of Giants" (a quote attributed to Isaac Newton). They are asked to research an important historical figure in mathematics and present this information on a 5 inch cube. I do not tell them how to construct this cube so that they have to muddle through the measurements and design. When all the cubes are completed we stack them up in class. It is a fun way to present information.

This year I had my university students do this project. Here are some samples:


















They brought their cubes to class and without following a real script, each present the info to the group. It was interesting to hear how much they had found out and been impressed by their historical figure. The feedback I received was that the project was quite a bit harder than they had anticipated. In particular, it was challenging to create a sturdy 5 inch cube and then condense the information to the 6 faces in meaningful ways. One student found herself trying to layout the required information in a logical manner on the faces, which gave her a new way to think about what she had learned and wanted to present.

Overall, a successful project.

Thursday, September 24, 2009

5 Core Concerns

I read this from the Psychology Today web site and got thinking: this is very applicable to middle school students and their teachers as well.

Five core concerns shape our perceptions and actions.

Every day we face decisions that help determine what tomorrow will look like -- for ourselves and for others as well.

The decisions we make are powerfully influenced by five core concerns. These concerns revolve around issues of vulnerability, injustice, distrust, superiority, and helplessness. Their impact is felt almost everywhere.

These five concerns shape our perceptions and actions by serving as persuasive yet imperfect guides to the world around us. In our pursuit of positive personal and social change, they can both illuminate the path forward and lead us far astray. Sadly, too often we fail to recognize the difference. Let's briefly consider each in turn.

Vulnerability

Concerns about safety are central to the way we evaluate our circumstances. This isn't surprising. Survival is an obvious first priority -- without it nothing else would be possible. So efforts to protect ourselves and the people and groups we care about are a primary focus of our attention.

Nevertheless, we're not particularly good at making judgments about risk. As a result, we routinely discover too late that valuable time and resources were wasted on unnecessary precautions, and promising opportunities were cast aside as we built defenses against phantom threats. Of course, such lessons are hard to apply because we've also learned that the failure to exercise due caution can have devastating effects. Indeed, "better safe than sorry" is a philosophy that has saved innumerable lives.

Injustice

We are strongly affected by perceptions of injustice, both in our personal lives and in our group attachments. Most of us react to perceived mistreatment with anger and resentment, as well as an urge to right wrongs and punish those we deem responsible.

But again, our judgments are fallible, in both directions. In some cases, our perceptions of wrongdoing are misguided -- such as when we confuse what's unfair with what's merely unfortunate, or when we blame the wrong people for the adversity we face. And then at other times we're much too slow in recognizing the legitimacy of another's grievances, or in holding accountable those whose unjust acts have caused great suffering.

Distrust

We tend to divide the world into people we consider worthy of our trust and those we view with doubt and suspicion. In so doing we hope to choose our allies wisely, while avoiding harm from those who have hostile intentions or are simply undependable.

Yet here too, errors are commonplace. Acting on the basis of information that's often incomplete and unreliable, we regularly mistake potential friends for foes and as a result fail to pursue important avenues for collaboration. But at the same time, we're all too familiar with the painful consequences that can result when we gullibly place our faith in people who abuse our trust for their own selfish purposes.

Superiority

We are quick to compare ourselves to other individuals and groups. In many cases, we hope to confirm or demonstrate that we're better in some important way -- perhaps in our accomplishments, our values, or our destiny. And to reinforce this positive self-image, at times we choose to focus on what we consider worst about others.

But these judgments can prove problematic. Perceiving others as inferior often leads to destructive conflict. At the same time, excessive pride and overconfidence tend to encourage dangerous overreaching that can produce personally disastrous outcomes.

Helplessness

We strive to avoid the experience of helplessness by doing our best to control the important events in our lives. But when we believe our efforts are futile, despair and resignation can quickly overwhelm our commitment and motivation to pursue change.

Our perceptions can lead us astray. In some situations, repeated setbacks cause us to abandon our goals prematurely. We lose sight of the progress already made and discount the likelihood of future advances. On the other hand, there are times when we greatly overestimate our capabilities. As a result, we may stubbornly persevere with unproductive strategies when we'd be much better off pursuing alternative routes.