In a previous article, I suggested that making a connection between the vocabulary of Math and English can help students overcome their fear of math word problems while increasing their appreciation of English texts. Is that true? Does it really work? Here are some student responses to the hypothesis, as they experienced it themselves.
Amanda believes that when one understands the meaning of certain words both in their everyday context and in their mathematical context, it can make both subjects flow more seamlessly. “Creating a table of words that show their everyday meanings and their mathematical meanings right next to each other made me think more about how the words correlate in both subjects. It gave me a new tool to study when presented with word problems. Rather than avoiding math word problems at all costs and only studying exactly what I need to before an exam, maybe I need to spend more time studying the linguistics of the words so I have a better comprehension of what the words are presenting. By doing this, I hope to achieve the skill of being able to decode the problems and understand how to get the algebraic equations.”
For Brian, the synergy between English and Math has obvious benefits: “I enjoy learning new words every day. For both Linda and Axel, “learning to increase our vocabulary in Math class is important because it helps us understand word problems. It sure makes math more understandable.” Athena is equally emphatic: “Vocabulary is very important to express ourselves. One of my favorite books is the thesaurus.” Desarae finds the connection “good, almost necessary. It helps you better understand what we are learning. Knowing the vocab makes the concepts less scary!” Lizeth goes so far as to say that “a weekly vocal quiz in our math class would be a great idea!” It is an opinion shared by Kathy, who finds that “sometimes a word has a different meaning in the context of algebra than in regular usage, and you need to know the difference to solve word problems.” Leslie says flat out that “if you don’t understand the words, you don’t understand algebra!” As Dana sees it, “it is important to know what the words mean in math. If I didn’t know the meaning of function or factoring, I wouldn’t know how to solve the problems!” Alexander has a different angle: “Knowing these words can honestly impress girls!” Alma finds that “math is useful everywhere, in school, job, shopping etc. Knowing what the words mean and increasing vocabulary can only help.” Nico feels that “learning new words and using them properly can actually make you smarter.” But Eduardo will have none of it. “This is a math class, not an English class!”
For Hess, the issue is more nuanced. “I am one of those people who have a hard time with word problems. It’s not that I don’t understand what the terms mean, because I get when it says a number increased by 6 is x+6, but somehow when it comes to writing the equation I suddenly have short-term memory loss or something. Maybe it is PTSD, Post Traumatic Solving Disorder! Whatever, I need to find a way to overcome it. One way is to understand math words like “rational” and “radical” in both their regular usage and in their math context. I think a lot of students understand the terms. It is not the language barrier but more of a sentence structure issue. Also, like when you learn Spanish, you may know all the terms but put the adjective before the noun like you would in English, and the sentence becomes grammatically incorrect in Spanish. It is the same thing in math: If you put the equation in the wrong order, you may end up with the wrong answer.”
Alyssa knows from personal experience that when there is an equation in front of her, she knows where to begin “but as soon as it is surrounded by words I’m completely lost. The ironic part is that English happens to be my strongest subject and Math my weakest. I do like the idea of having a better understanding of terms and phrases and how they relate to in Math and English. Looking at math and English phrases in depth will certainly help me overcome my fear of math word problem. I think the two questions in a word problem are always: ‘Where do I start’ and ‘How do I know what the equation is asking?’ Word problems are tricky, because they ask a question at the end but there are a lot more steps before you can solve it. Breaking them down to certain key phrases is already helping me solve them with more confidence.
Ashley learns best “when I can learn something from two or three different angles. Making the link between “reducing” or “reduce” at work to fractions is really helpful. If I can see a fraction in my head when I hear that word, I can learn to practice the mathematical term “reducing” more and become better at it. I also think some of the words in math are rather beautiful and if I could use them in everyday language, I would sound more educated. ‘Exceeds’ is one of those words. I use ‘difference’ a lot but not really thinking of math directly, unless I am working on a word problem. Using words in daily language that can be applied to math is turning out to be a very useful concept for me.”
Brandon finds that a clear understanding of words in their math and regular usage context “helps me understand word problems and math itself a lot more. It definitely helps with learning everyday language. Not only are you learning more about the word itself but you are also learning how you can use it towards math and real life. For example, the word ‘rational’ is used in life to explain reason. When it comes to math, it means a ratio, either of numbers or polynomials. It is really amazing to me how math can be so connected to the English language in such a weird but helpful way. It helps me understand algebra a lot more and at the same time helps me learn the English language even better. I never realized how important it was to connect English and math together!”
Yannick agrees that “understanding meanings of words contributing to everyday and math context will increase math skills, but I disagree it will help with English skills. In every math textbook, there should a handful of word problems. But if you open up an English textbook, there might be a few math problems, but not as detailed or as skilled as the problems in the math textbooks. However, it may not apply to somebody whose first language is not English. I feel this way because in math, there are sections and chapters in the book, with each one building its way up to more skilled formulas and methods, challenging individuals as they go through the book. When one has to solve a problem from an English textbook, that person is already used to the language and reading a simple sentence or a paragraph will not be an issue, unless it is asking the person to apply the problem with numbers and formulas. We are too used to speaking English every day. That’s why English texts are meant for English and Math textbooks for Math. In my opinion, the only reason people hate to solve word problems is not because the way it is worded, but rather the way it is printed on the paper, which is much longer than the equation problems.”
For Tyler, “learning the meanings of the words that have context in both English and Math would greatly improve the skills in both subjects. In Math, to know how to form a problem would help in a few situations in the real world, say, trying to figure out how much yarn you need to make a sweater. If you don’t know how to structure the equation, then the problem becomes impossible to solve. However, in English, one should constantly attempt to learn new, more complex words and various meanings so that in the future you could describe a complex sentence or in this instance, a mathematical problem. In my own accounts I use mathematical vocabulary to figure out pay in my job to make sure I get the right pay. As a referee I am paid different amounts depending on the games refereed. For example, I am paid $20 for a regular 45 min game, but I am paid one-and-a-half time more for a high school or junior high game. So if I work 20 regular games and 8 High school games then the expression should be: 20x + (20 x 1.5) y which becomes 20(20)+(20x1.5)(8). Since 1.5 times 20 is 30, so the equation ends up being 400+240=640. This is not my actual pay, but I wish it was! To form this equation requires the knowledge of a mathematical equation structure, as well as knowledge of how to form a proper English sentence with mathematical terms. Thus I can honestly say that the knowledge of Mathematical vocabulary will help students learn how to solve word problems far easier than they would before they knew what the words structuring the sentence mean!”
As an ESL student, Pariya is convinced that knowing and understanding English is critical to understanding Math word problems. “My first language is Farsi. During the first days of class, understanding word problems becomes very hard for me. I try to learn the words that are the most useful in math as I came to appreciate the connection between English and math. It helped me a lot and now I have less difficulty with math word problems. Understanding such words also helped me to speak English more fluently at work that I could before. An Architectural interior designer and I deal with numbers and math problems most of the time at work, for example, for calculating the occupancy of a building. Also, knowing and understanding these words have helped me to think more logically.”
Jessica believes that “having command of the English language is absolutely crucial to understanding any type of math. Even though I have a strong understanding of the English language, as I’ve been speaking it my entire life, I find that I still struggle with understanding math word problems. Not being able to solve word problems is a huge issue in the real world. Outside of the classroom, real life issues aren’t presented in nicely laid-out equations for you to solve. In real-life situations you’re presented with a number of variables that you are tasked to put together to solve a problem. Though equations and formulas are helpful to know, students should be able to solve real situations with real numbers. For instance, when an anesthesiologist is tasked with administering anesthesia a patient, they must take into account a number of different variables in order to make sure that the patient is receiving the correct amount of medication. In the classroom it is important to practice the concepts of math and understand how to correctly solve problems but it is also critical that students understand how to solve problems that aren’t completely spelled out for them.”
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Hasan Z Rahim
Hasan Z. Rahim is a professor of mathematics and statistics at San Jose City College,
located in the heart of Silicon Valley, California.