Wednesday, April 11, 2012

Why did integrated math fail?

Most high schools around the US teach mathematics as single topics like Algebra, Geometry, Advanced Algebra/Trigonometry, Probability/Statistics, Pre-Calculus, and Calculus.  Elementary and middle schools teach mathematics as a combination of some the mentioned topics.  Hence the name, integrated math.  For example, fractions are taught with an algebraic sense and geometric sense with symbolic and pictorial representations.  At the high school level, Algebra and Geometry are like islands despite the strong connections between the two.  In most Algebra 1 classes, students learn about linear, quadratic, polynomial, exponential expressions, equations, and inequalities.  Geometry obviously focuses on shapes and lines but students explore and prove properties.  In most cases, Geometry is the first math class to introduce proofs.  This is disappointing since students can make conjectures about the functions they learn about in Algebra 1 and attempt to prove them.  On the other had, there is very little Algebra in the typical proofs explored in Geometry classes.  There are some very rich proofs about areas of polygons that involve some great algebraic techniques.  There are also connections with Probability/Statistics and Geometry.  For example, examining the probability of getting a certain score with a limited amount of darts when playing a game of darts.  I just don't understand the need to separate these topics of Mathematics at the high school level when there are so many connections that can strengthen students' learning.

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