
All too often developing mathematics students view mathematics as a series of sometimes, but not often, interconnected procedures to be memorized and later reproduced in the form of answers on some form of formal assessment. They rarely see mathematics as a language that seeks to formally describe the processes of the natural world…because math just isn’t taught that way…to anyone.
Rather, mathematics courses typically follow this structure:
1. Introduce a topic through lecture or some form of media…this may include vocabulary, real world applications, etc.
2. Model as many possible examples of the mathematics being employed as possible. Typically, operations are taught followed by applications.
3. Assess the learning either formally or informally.
4. Repeat.
Our culture of large scale testing is part of the reason. The main culprit, however, is time and scope. Broad learning is valued more than deep learning. The result of such a culture is that students learn a little about a lot and a lot about a little. The consequences of which are as follows:
1. Students matriculate from grade to grade with cursory knowledge of everything they are supposed to learn in each grade level.
2. Once they get to high school/college they rarely posses the requisite skills needed to be successful in their courses.
Personally, I would prefer to see the middle grades structured differently to create deeper knowledge for mathematics students. 4th, 5th,and 6th grade students should focus solely on mastering the number system including exponents, the order of operations, fractions, decimals, percents, squares and square roots, rational and irrational numbers, sequences, and the various applications of these topics to the natural world.
7th and 8th grade students would focus on pre algebra skills including linearity, patterns, proportionality, solving equations, etc and their applications in the natural world.
Doing so would better prepare students for full courses in algebra and geometry in high school by ensuring that students have mastered the required skills to be successful in the later grades.
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