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Starting from: observing, discussing, comparing, and analyzing then conclude.
In the classrooms, building up solid foundation of mathematical ideas: What are the possibilities?
One of the possibilities which the students learned with the different types of manipulative is how to find out different ways to solve the same given problem, also how to look at patterns and analyze them.
Prof. Arthur Powell said that it is very important to get the sutdents involved in looking for justifications. Why? Because in the heart of mathematics we can look at patterns and relationships and try to understand the underline reasons why those patterns and relationships exist.
How students think about problems or to solve problems? How do they think about that particular problem. The why and how asked questions would justify to develop an inner criteria for knowing when they're right or wrong.
Pascal's Triangle and High School Algebra
we identify the What is the connection between elemantary school and high school algebra? In pascal's triangle summitry line: when a pattern starts must reach its highetst point, then goes back to its original starting point. The symmitry line in pascal's triangle, as it is shown on the picture above, expresses the number of possibilities. the symmetry line in pascal's triangle represent the idea of going back to the starting point with the opposite.
In Jeana's classroom the students were experiencing the combination between pascal's triangle and binomials. The first row where the exponent is 1 with 2 terms, the second row the exponent is 2 with 3 terms and so on.
By 11th grade, the students gain skills that help them think mathematically and in higher level.