# Remove Synthetic Division From Math III in NC

# Remove Synthetic Division From Math III in NC

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For too long, synthetic division has been confusing and bamboozling Math III students in the state of North Carolina. This is not because it is necessarily a difficult concept to master, though for some it definitely is. Synthetic division is not used in subsequent math classes in high school, such as Pre calculus, Calculus AB, BC, and Statistics. It is not useful in understanding any other later topics or solving any mathematical problems that long division cannot solve.

The topic that synthetic division covers is of polynomial division by a first degree binomial. This can be done using long division, which is taught. However, long division is much more versatile. It applies to any polynomial long division, not just one where the divisor is a first degree binomial. For the most part, when polynomial division needs to happen it will not be only by a linear equation. The very narrow window of synthetic division only makes it applicable in very few situations. However, it allows for a derivation of the remainder theorem, another part of the Math III . This same remainder theorem can be derived using long division, which eradicates the need to learn synthetic division to develop a full understanding of the remainder theorem. When the topic of polynomial division arises in later math classes, factoring or long division, predominantly the former, is used.

Secondly, most students who learn synthetic division do not properly comprehend it. I have talked with many students who have completed or are taking Math III, and those who I have talked to do not concretely understand why synthetic division works. While they may remember how to do it, these students did not understand why. This disconnect between understanding and execution is often what leads students to lose their comprehension and appreciation for mathematics, and while it cannot solely be blamed on synthetic division, teaching students the how without a why is not a good practice. One solution would be to spend more time on synthetic division to make sure students understand why this method works. However, not only is synthetic division not very applicable, as discussed in the previous paragraph, but with the already limited time that teachers have to convey information, wasting it on synthetic division seems like an insufficient use. There are much more difficult and practical things to use the time spent teaching synthetic division on, such as trigonometry. Most students I know would like to spend more time on these topics as opposed to juggling an additional, useless shortcut for division of polynomials by a first degree binomial.

Instead of teaching synthetic division as part of the Math III, it should be viewed as a shortcut that some students can learn, much the same way many other mathematical shortcuts are. For those who find it useful, the information can be readily available, but as a part of Math III, synthetic division has no place. It has a narrow window of things that it can be applied to, is not used in subsequent math classes, and is not taught in a way that furthers understanding or appreciation for math. For these reasons we as students in North Carolina implore the NC State Board of Education to drop synthetic division as part of the Math III.

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