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Last winter, Morgan Freeman and Matt Damon starred in the Clint Eastwood-directed Invictus, which tells the true story of the South African rugby team's surprise win at the 1995 Rugby World Cup. Freeman plays Nelson Mandela, the first president of South Africa elected after the end of apartheid, and Damon plays Francois Pienaar, the captain of the national rugby team. Some good physics happens during the play of rugby, and some cognitive science that teachers should be aware of in their classrooms. Invictus also provides an excellent opportunity for science teachers to team up with social studies or history teachers who are addressing the end of apartheid in South Africa.

The film opens with Mandela's 1990 release from prison and clips of his election as president in 1994. Apartheid's fall also ended the ban on South African teams' participation in international competition. South Africa was even selected to host the 1995 Rugby World Cup. Under apartheid, rugby was typically played by the white minority, while black South Africans played soccer and even rooted against the national rugby team, the Springboks.

In Invictus, President Mandela hopes a strong performance by the Springboks in the World Cup will help unite the country under the new national flag. Mandela invites Pienaar to tea, and they discuss leadership:

Mandela: How do you inspire your team to do their best?
Pienaar: By example. I've always thought to lead by example, sir. 
Mandela: Well, that is right. That is exactly right. But how to get them to be better than they think they can be? That is very difficult, I find.

Though they are talking about inspiring athletes and politicians, I see a lesson here for teachers about how our expectations can affect our students' performance.

In a scene from Invictus, Matt Damon is involved in a scrum.

The film's storybook ending would be unbelievable if we didn't know that it really happened. The South African team beat the odds to win the World Cup final over New Zealand in overtime. President Mandela presented the trophy to Pienaar before tens of thousands of fans.

Before I address the application of Newton's laws to rugby, I must explain a bit about rugby. When play stops due to a minor infraction, one way to restart the game is a "scrum." This is probably the one part of rugby most Americans are somewhat familiar with. Eight players from each side line up facing one another and loop their arms across one another's shoulders. The ball is placed on the ground in the middle, and each team tries to push the other back until a player is able to hook the ball with his feet and kick it back, out of the scrum. Though 16 large, strong players are pushing in each direction, the scrum often barely moves. How can that happen given the forces involved? Let's look at a scrum in the 1995 World Cup final between South Africa (the Springboks) and New Zealand (the All Blacks.)

A common misunderstanding of the situation is to argue that the scrum does not move because the force of the All Blacks on the Springboks is equal to the force of the Springboks on the All Blacks. Newton's third law says that statement is always true, no matter how the scrum is moving. One way of exploring Newton's third law is to see that it requires two objects to be involved in any interaction. If you cannot find two objects, no force is involved. So what determines the way the scrum moves? As strange as this may sound, the force the All Blacks exert on the ground compared to the force the Springboks exert on the ground is key here. Whoever can push hardest against the ground will be pushed forward by the ground, and will move the scrum. Imagine one team forgot their cleats and have to wear leather-soled shoes on the field. The slippery soles mean the team cannot push against the ground very effectively, while the other team wearing cleats can push very hard on the ground. Thus, the cleat-wearing team will win every scrum.

So which strategies help your team push harder on the ground than your opponent? Wearing cleats is an asset, since they dig into the ground and aid in traction. Getting lower than your opponent is important: If you can push up a little bit, that will tend to lift their feet off the ground, decreasing their traction. (This principle is used in American football as well, when linemen try to stay low to keep their footing.) Finally, the more massive your players, the larger the frictional force between the ground and their shoes will be. This is one reason the players in the scrum are usually the largest members of each team.

In the quote mentioned earlier, Mandela asked Pienaar about motivating people to perform beyond what they perceive as their limits. Both men agree leading by example is powerful, but to maximize potential, people must be inspired and feel confident. So teachers who communicate high expectations and inspire students to reach their full potential can get better results than teachers with low expectations. In addition, a large and growing body of literature in cognitive science and psychology indicates expectations affect human performance in academic subjects. One aspect of this is called "stereotype threat." If students are told before an exam that the test is particularly accurate at showing how the science abilities of male and female students differ, the women's scores will be lower than if no such statement is made. Women know our culture expects them to perform poorly in math and science; when reminded of this, their performance suffers. It seems distracting self-talk starts in the minds of people in this "threat condition," sapping cognitive resources needed for the exam.

Science teachers should consider teaming with a colleague in history or social studies to show Invictus to their students, then use the film to address Newton's third law and some of the psychology of human performance.

Note: Invictus is rated PG-13 for brief strong language.

Jacob Clark Blickenstaff is Assistant Professor of Physics and Assistant Director of the Center for Science and Mathematics Education at the University of Southern Mississippi. He can be reached at jacob.blickenstaff@usm.edu.

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