The Complexity of Algebra

The Complexity of Algebra

Video Link:

The Complexity of Algebra

In the TED video “Why IS Algebra So Hard? The Answer Is Surprisingly Simple,” Emmanuel Schanzer delves into the broad applications of algebra and why it is complicated to understand algebra. Schanzer avers that algebra is a vital gateway to STEM (science, technology, engineering, and mathematics) (Schanzer, 2019). Besides, algebra is highly applicable in standardized testing. Standardized testing applies to making economic comparisons between countries, among other applications (Schanzer, 2019). Given the broad application of algebra, those who specialize in it tend to make relatively more income.

One of the reasons why algebra is complicated to most people is because of its difference in arithmetic functions. Whereas the rest of math is a process that involves solving arithmetic problems, algebra is significantly different. Algebra includes dealing with abstract functions that do not necessarily require process solving (Schanzer, 2019). For instance, in simple math, problems may include additions like 1+2=3. On the other hand, algebraic functions are expressed differently and do not involve the traditional mathematical process taught early in school, like f(x)=2+X.

Another reason why it is difficult to understand algebra is due to the failure of programming languages to address the algorithmic demands of algebra. Whereas a compiler in a program captures the notation programmers may use to compile algebraic functions, the problem domain often evolves and may not be supported by the compiler of the program (Baldwin et al., 2013). Subsequently, a programmer is forced to use old and often inappropriate programming languages that fail to yield expected results. In the same breath, conventional programming languages do not support abstraction, which is central to algebraic functions (Baldwin et al., 2013). As a result, a compiler meant to make programming simple has to adjust to the abstract nature of algebraic functions. Ultimately, the compiler overburdens programming activity, leading to reduced productivity in algebraic problem-solving.

Reflection

Schanzer’s video shows that computer science plays a significant role in mathematics and algebra. However, there is a shortage of computer science teachers, which partly contributes to reduced math and algebra comprehension. There is a need to train more computer science teachers and certify them to practice in schools. However, another problem arises while contemplating increasing the number of computer science teachers in the mainstream syllabus. The syllabus is quite overcrowded, and there is no room to reduce time allocation to other subjects. Already, enough time has been cut off from subjects like music and art; hence, there is no opportunity to cut off any more time. Therefore, the most viable solution is to incorporate computer science into math so that it forms part of mathematics lessons.

Moreover, I learned that students tend to disengage from math due to the frustrations presented by algebra. Since success in algebra is critical to students’ entry into STEM, high school success, and potential successful careers, it is important to focus on enhancing its adoption. Notably, integrating algebra and computing fosters students’ success in both subjects (Bråting et al., 2020). Besides, it helps schools struggling with personnel and staffing issues since a computing teacher can still teach algebra. Such a paradigm shift will eliminate the glaring inequalities that students looking forward to studying STEM face. Sometimes, low income and insufficient resources prevent children from low-income backgrounds and schools in poor neighbourhoods from pursuing STEM courses. Also, integrating the two subjects will speed up the adoption of programming languages that support the abstract nature of algebra.

References

Baldwin, D., Walker, H. M., & Henderson, P. B. (2013). The roles of mathematics in computer science. ACM Inroads, 4(4), 74–80. https://doi.org/10.1145/2537753.2537777

Bråting, K., Kilhamn, C., & Rolandsson, L. (2020). Integrating programming in Swedish school mathematics: description of a research project. In MADIF12: the twelfth research seminar of the Swedish Society for Research in Mathematics Education, 14-15 Jan 2020, Linnaeus University, Växjö, Sweden (pp. 101-110).

Schanzer, E. (2019). Why is algebra so hard? The answer is surprisingly simple [Video]. TED Talks. https://www.ted.com/talks/

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Directions for Ted Talk Project

The goal of this project is to learn something about mathematics that you did not know before. TED Talks: Ideas worth spreading are a way to learn about the applications of mathematics, mathematics education, and pure mathematics from leaders in those fields who have the ability to reach audiences of all levels with powerful presentations.

The Complexity of Algebra

For this project, you will go to TED.com on your web browser. Using the TED search engine (magnifying glass in the upper right corner), do a search for “math”. There are thousands of math-related talks on TED.com. Please don’t choose the first one that pops up; search for a topic that sounds interesting to you. If you are interested in applications of math and art or math and music or math and computers or math and …, you can also search for those specific topics.

Once you find a topic of interest, watch the video on that topic and write two pages or more about (1) what you learned in the video, and (2) your reaction to the content of the video. You may want or need to do a little more research outside of TED.com for words/topics with which you are unfamiliar or for which you want to dig a little deeper.

Personalize your paper, that is, relate what you learned to yourself: what did you learn? What do you think about it? What is your reaction to the content of the video?

Your paper should be submitted as a PDF file in the designated D2L folder. Keep these requirements in mind when typing up your paper:

The paper must be two or more typed pages long.
Type your paper on a standard letter-sized (8 ½ x 11-inch) page
It should be double-spaced using a 12-point font.
One-inch page margins. This includes top, bottom, and side margins.
Your paper must include a title page with your name (this does not count as one of the two pages).
Include the link for your video on the title page.
Proofread and spell-check your paper carefully before submitting it. If possible, have a tutor at the Writing Center go over the paper with you.
Submit your paper as a PDF file. (Word documents are “converted” for viewing in D2L and that can affect the formatting of your document.) From Word, you can just “save as” and find “PDF” under “file type.”