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Students today often classify themselves as being either math and science enthusiasts or liberal arts and humanities aficionados. Of course, there may be a small group of people who express an interest in all areas, but a person’s academic focus is typically binary. From my various experiences teaching math to high school juniors and seniors, students either adore the technical computations and challenges math brings while utterly despising the writing assignments in their English classes, or they love to write and dislike their math courses. Math and English are practically treated as opposites in my community, and perhaps in several others as well, but when I teach math, I tend to ignore this so-called opposition and integrate writing into my lessons at every opportunity.
Recently, there has been serious discussion about the notion of Americans favoring STEM courses over a broad liberal arts education, with the conversation revolving around emphasizing technical instruction rather than providing a general education that incorporates STEM fields with others, such as literature. Without a doubt, the liberal arts play a tremendous role in developing critical thinking and imagination in adolescents and deserve to be equally incorporated into their education. Math class, where computations and analytic writing supplement each other, is a great place to do that.
When most students think about math, numbers and calculations are the first things that pop into their minds. They expect to spend time solving countless pages of problems by using the meticulous techniques and algorithms they were taught in class. Using these techniques over and over again will help them remember everything, but it leaves little to no room for interpretation and critical thinking. Sure, students may follow these problem-solving processes precisely and obtain the correct answer, and this probably gives the teacher the impression that the student knows what they are doing and is ready to move on to the next topic. But did the student get the problem right because they understand the question well, or because they know to do the process — to use equation X or formula Y? Change the question slightly, and most students might attempt to use the same process exactly the same way, only to stumble while finding the new solution. Following an algorithm by showing lines of work helps students focus on the numerical computations, but usually doesn’t help them understand the mathematical theory or why and what they’re really doing.
Writing assists with addressing this drawback. When teaching calculus, I have my students write a few sentences explaining their steps, the question’s ideology, and any given figures in addition to their numerical work. If they use a certain formula or technique, I ask them to write why they used that specific method or what conditions the question satisfied that compelled them to use it. Usually, once they start writing, they can’t stop. What first starts as a thought and sentence causes a chain reaction that ends in responses that are beautifully reasoned and detailed.
In these response papers, it’s amazing to see the different interpretations and approaches that students use. Perhaps one approach requires less work, while another uses a different operation. Writing helps students analyze and clearly lay out their ideas while serving as a great communication tool between them and me. My students’ responses allow me to assess how they view and approach a certain question or topic. By writing, students provide me with much more information than what their numerical work initially shows.
Writing also helps develop communication between students and their peers. Individual interpretations are so unique that students always learn from each other during any peer-to-peer discussions. Collaborating through writing serves as great practice for communication and teamwork skills, which students will use when interacting with their future school and work colleagues.
Good communication skills are essential when trying to share your ideas with others. It’s extremely difficult, sometimes impossible, to understand what math another person is thinking or doing just by looking at numbers. Today, the educational math technologies available to us have features to allow us to do just that: write.
Wolfram’s Mathematica, for example, isn’t just a computer algebra system (CAS) that facilitates computations, but also a tool that allows users to create notebooks where they insert text and annotations near mathematical expressions or plots. Certain sections of the notebooks, including individual equations and formulas, can be displayed or hidden with the press of an arrow. Interactive mathematical typesetting can be incredibly useful when giving a lesson or presentation. Users can display the annotations for certain objects at appropriate times and hide them afterwards, all while maintaining visual aesthetic.
The first time I wrote for math class was during senior year of high school in my multivariate calculus course. My teacher told us to write a short paper about a triangle and include a picture of it as well.
We students immediately had questions. Was the triangle in 3D space? Did it have to be equilateral? Did we have to find its area? My teacher refused to say anything else. We accepted the assignment and, after the holiday, turned in our papers. If I remember correctly, someone wrote about a triangular slice of pizza. Another student wrote about the front view of an ice cream cone. Someone even wrote about his triangular nose!
I don’t know for sure why the teacher gave that assignment, but I did find some purpose in it. Writing in math brings out the creativity and imagination in students, and these qualities are extremely important when the adolescent mind is still developing. Writing in math gives students the chance to think critically and focus on details and theory rather than just crunch the numbers. It allows educators to see what and how students are thinking, which helps to set the pace for the class. It assures professionals that these students, whom they’ll be hiring in the near future, have had adequate writing experience to collaborate and perform well in their workforces.
The benefits of writing are endless and do not stop in math class. Both students and educators should practice applying at least some form of writing to their math courses. The advantages don’t stop at understanding the material and getting a good grade, but rather continue for years to come.