expectation in mathematics in the modern world essay

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This article explores the importance of math in the modern world. It also offers guidelines for gauging the adequacy of your student's mathematics skills in relation to their grade level.

There is a great deal of pressure on high school students to do well in math. This is largely because college is looming on the horizon, even for ninth graders who are just beginning their high school careers. Experts recommend building a strong foundation in the principals of mathematics in order to reduce potential stress when college entrance exams and applications dominate the landscape. Strengthening your child's math skills can give them the confidence they need to excel in a high school environment that emphasizes the pressures of college applications, placement exams, standardized testing, in-class participation and, school competition. A strong foundation in mathematics prepares them for the challenges he or she will encounter both in the classroom and beyond.

To ensure that your child is receiving quality education in mathematics, monitor their progress and emphasize the important role the mathematics will come to play in life. Whether or not your child plans on pursuing a technical career, chances are they will have to work with numbers or with people who work with numbers in the future. According to the National Council of Teachers of Mathematics website, www.nctm.org , to maximize children's potential and to increase their odds of succeeding in a competitive and increasingly numerical world, children who are in (or about to be) high school should possess the following math skills:

• They should employ a high level of abstract, symbolic thinking.
• They should perceive relationships and be able to make translations among fractions, decimals, and percentages.
• They should deal easily with a wide array of equations, formulas and proofs.
• They should be able to explain and then illustrate mathematical concepts, rather than simply applying them.
• They should know how to plan and self-monitor during multi-step problem solving.
• They should feel comfortable using calculators and computers.

Making sure your child has clear comprehension and a strong mathematical foundation incorporating the list of key math skills provided above, will help to ensure your child's success throughout his or her academic and professional life.

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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

“Math is a valuable tool and function of the world.”

As a musician, math is intrinsically related to my passion. As a sailor, math is intertwined with the workings of my boat. As a human, math is the building block for all that functions. When I was a child, I could very much relate to wanting a reason behind math. I soon learned that math IS the reason behind all of the world’s workings. Besides the benefits that math provides to one’s intellect, it becomes obvious later in life that math is a valuable tool and function of the world. In music for example, “adolescent mathematics” are used to portray functions of audio engineering. For example, phase shifting a sine wave to better project sound or understanding waves emitted by electricity and how they affect audio signals. To better understand music, math is a recurring pattern of intervals between generating pitches that are all mathematically related. The frets on a guitar are measured precisely to provide intervals based on a tuning system surrounding 440Hz, which is the mathematically calculated middle of the pitches humans can perceive and a string can effectively generate. The difference between intervals in making a chord are not all uniform, so guitar frets are placed in a way where all chords can sound equally consonant and not favor any chord. The power of mathematics! I am fascinated by the way that math creeps its way into all that I do, despite my plentiful efforts to keep it at a safe distance …

— Renan, Miami Country Day School

“Math isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life.”

I believe learning mathematics is both crucial to the learning and development of 21st century students and yet also not to be imposed upon learners too heavily. Aside from the rise in career opportunity in fields centered around mathematics, the skills gained while learning math are able to be translated to many facets of life after a student’s education. Learning mathematics develops problem solving skills which combine logic and reasoning in students as they grow. The average calculus student may complain of learning how to take derivatives, arguing that they will never have to use this after high school, and in that, they may be right. Many students in these math classes will become writers, musicians, or historians and may never take a derivative in their life after high school, and thus deem the skill to do so useless. However, learning mathematics isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life. A student who excels at calculus may never use it again, but with the skills of creativity and rational thinking presented by this course, learning mathematics will have had a profound effect on their life.

— Cam, Glenbard West

“Just stop and consider your hobbies and pastimes … all of it needs math.”

Math is timing, it’s logic, it’s precision, it’s structure, and it’s the way most of the physical world works. I love math — especially algebra and geometry — as it all follows a formula, and if you set it up just right, you can create almost anything you want in at least two different ways. Just stop and consider your hobbies and pastimes. You could be into skateboarding, basketball, or skiing. You could be like me, and sit at home for hours on end grinding out solves on a Rubik’s cube. Or you could be into sketching. Did you know that a proper drawing of the human face places the eyes exactly halfway down from the top of the head? All of it needs math. Author Alec Wilkinson, when sharing his high school doubting view on mathematics, laments “If I had understood how deeply mathematics is embedded in the world …” You can’t draw a face without proportions. You can’t stop with your skis at just any angle. You can’t get three points without shooting at least 22 feet away from the basket, and get this: you can’t even ride a skateboard if you can’t create four congruent wheels to put on it.

— Marshall, Union High School, Vancouver, WA

“Math gives us a different perspective on everyday activities.”

Even though the question “why do we even do math?” is asked all the time, there is a deeper meaning to the values it shares. Math gives us a different perspective on everyday activities, even if those activities in our routine have absolutely nothing to do with mathematical concepts itself. Geometry, for instance, allows us to think on a different level than simply achieving accuracy maintains. It trains our mind to look at something from various viewpoints as well as teaching us to think before acting and organizing chaotic thoughts. The build up of learning math can allow someone to mature beyond the point where if they didn’t learn math and thought through everything. It paves a way where we develop certain characteristics and traits that are favorable when assisting someone with difficult tasks in the future.

— Linden, Harvard-Westlake High School, CA

“Math teaches us how to think.”

As explained in the article, math is all around us. Shapes, numbers, statistics, you can find math in almost anything and everything. But is it important for all students to learn? I would say so. Math in elementary school years is very important because it teaches how to do simple calculations that can be used in your everyday life; however middle and high school math isn’t used as directly. Math teaches us how to think. It’s far different from any other subject in school, and truly understanding it can be very rewarding. There are also many career paths that are based around math, such as engineering, statistics, or computer programming, for example. These careers are all crucial for society to function, and many pay well. Without a solid background in math, these careers wouldn’t be possible. While math is a very important subject, I also feel it should become optional at some point, perhaps part way through high school. Upper level math classes often lose their educational value if the student isn’t genuinely interested in learning it. I would encourage all students to learn math, but not require it.

— Grey, Cary High School

“Math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful.”

Although I loved math as a kid, as I got older it felt more like a chore; all the kids would say “when am I ever going to use this in real life?” and even I, who had loved math, couldn’t figure out how it benefits me either. This was until I started asking my dad for help with my homework. He would go on and on about how he used the math I was learning everyday at work and even started giving me examples of when and where I could use it, which changed my perspective completely. Ultimately, I believe that math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful and where they can use it outside of class.

— Lilly, Union High School

“At the roots of math, it teaches people how to follow a process.”

I do believe that the math outside of arithmetic, percentages, and fractions are the only math skills truly needed for everyone, with all other concepts being only used for certain careers. However, at the same time, I can’t help but want to still learn it. I believe that at the roots of math, it teaches people how to follow a process. All mathematics is about following a formula and then getting the result of it as accurately as possible. It teaches us that in order to get the results needed, all the work must be put and no shortcuts or guesses can be made. Every equation, number, and symbol in math all interconnect with each other, to create formulas that if followed correctly gives us the answer needed. Everything is essential to getting the results needed, and skipping a step will lead to a wrong answer. Although I do understand why many would see no reason to learn math outside of arithmetic, I also see lessons of work ethics and understanding the process that can be applied to many real world scenarios.

— Takuma, Irvine High School

“I see now that math not only works through logic but also creativity.”

A story that will never finish resembling the universe constantly expanding, this is what math is. I detest math, but I love a never-ending tale of mystery and suspense. If we were to see math as an adventure it would make it more enjoyable. I have often had a closed mindset on math, however, viewing it from this perspective, I find it much more appealing. Teachers urge students to try on math and though it seems daunting and useless, once you get to higher math it is still important. I see now that math not only works through logic but also creativity and as the author emphasizes, it is “a fundamental part of the world’s design.” This view on math will help students succeed and have a more open mindset toward math. How is this never-ending story of suspense going to affect YOU?

— Audrey, Vancouver, WA union high school

“In some word problems, I encounter problems that thoroughly interest me.”

I believe math is a crucial thing to learn as you grow up. Math is easily my favorite subject and I wish more people would share my enthusiasm. As Alec Wilkinson writes, “Mathematics, I now see, is important because it expands the world.” I have always enjoyed math, but until the past year, I have not seen a point in higher-level math. In some of the word problems I deal with in these classes, I encounter problems that thoroughly interest me. The problems that I am working on in math involve the speed of a plane being affected by wind. I know this is not riveting to everyone, but I thoroughly wonder about things like this on a daily basis. The type of math used in the plane problems is similar to what Alec is learning — trigonometry. It may not serve the most use to me now, but I believe a thorough understanding of the world is a big part of living a meaningful life.

— Rehan, Cary High School

“Without high school classes, fewer people get that spark of wonder about math.”

I think that math should be required through high school because math is a use-it-or-lose-it subject. If we stop teaching math in high school and just teach it up to middle school, not only will many people lose their ability to do basic math, but we will have fewer and fewer people get that spark of wonder about math that the author had when taking math for a second time; after having that spark myself, I realized that people start getting the spark once they are in harder math classes. At first, I thought that if math stopped being required in high school, and was offered as an elective, then only people with the spark would continue with it, and everything would be okay. After thinking about the consequences of the idea, I realized that technology requires knowing the seemingly unneeded math. There is already a shortage of IT professionals, and stopping math earlier will only worsen that shortage. Math is tricky. If you try your best to understand it, it isn’t too hard. However, the problem is people had bad math teachers when they were younger, which made them hate math. I have learned that the key to learning math is to have an open mind.

— Andrew, Cary High School

“I think math is a waste of my time because I don’t think I will ever get it.”

In the article Mr. Wilkinson writes, “When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life.” His experience as a boy resonates with my experience now. I feel like math is extremely difficult at some points and it is not my strongest subject. Whenever I am having a hard time with something I get a little upset with myself because I feel like I need to get everything perfect. So therefore, I think it is a waste of my time because I don’t think I will ever get it. At the age of 65 Mr. Wilkinson decided to see if he could learn more/relearn algebra, geometry and calculus and I can’t imagine myself doing this but I can see myself understanding even more how important it is and appreciating it more as I get older. When my dad was young he hated history but, as he got older he learned to appreciate it and see how we can learn from our past mistakes and he now loves learning new things about history.

— Kate, Cary High School

“Not all children need to learn higher level math.”

The higher levels of math like calculus, algebra, and geometry have shaped the world we live in today. Just designing a house relates to math. To be in many professions you have to know algebra, geometry, and calculus such as being an economist, engineer, and architect. Although higher-level math isn’t useful to some people. If you want to do something that pertains to math, you should be able to do so and learn those high levels of math. Many things children learn in math they will never use again, so learning those skills isn’t very helpful … Children went through so much stress and anxiety to learn these skills that they will never see again in their lives. In school, children are using their time learning calculus when they could be learning something more meaningful that can prepare them for life.

— Julyssa, Hanover Horton High School

“Once you understand the basics, more math classes should be a choice.”

I believe that once you get to the point where you have a great understanding of the basics of math, you should be able to take more useful classes that will prepare you for the future better, rather than memorizing equations after equations about weird shapes that will be irrelevant to anything in my future. Yes, all math levels can be useful to others’ futures depending on what career path they choose, but for the ones like me who know they are not planning on encountering extremely high level math equations on the daily, we should not have to take math after a certain point.

— Tessa, Glenbard West High School

“Math could shape the world if it were taught differently.”

If we learned how to balance checkbooks and learn about actual life situations, math could be more helpful. Instead of learning about rare situations that probably won’t come up in our lives, we should be learning how to live on a budget and succeed money-wise. Since it is a required class, learning this would save more people from going into debt and overspending. In schools today, we have to take a specific class that doesn’t sound appealing to the average teenager to learn how to save and spend money responsibly. If it was required in math to learn about that instead of how far Sally has to walk then we would be a more successful nation as a whole. Math could shape the world differently but the way it is taught in schools does not have much impact on everyday life.

— Becca, Bentonville West High School

“To be honest, I don’t see the point in learning all of the complicated math.”

In a realistic point of view, I need to know how to cut a cake or a piece of pie or know how to divide 25,000 dollars into 10 paychecks. On the other hand, I don’t need to know the arc and angle. I need to throw a piece of paper into a trash can. I say this because, in all reality and I know a lot of people say this but it’s true, when are we actually going to need this in our real world lives? Learning complicated math is a waste of precious learning time unless you desire to have a career that requires these studies like becoming an engineer, or a math professor. I think that the fact that schools are still requiring us to learn these types of mathematics is just ignorance from the past generations. I believe that if we have the technology to complete these problems in a few seconds then we should use this technology, but the past generations are salty because they didn’t have these resources so they want to do the same thing they did when they were learning math. So to be honest, I don’t see the point in learning all of the complicated math but I do think it’s necessary to know the basic math.

— Shai, Julia R Masterman, Philadelphia, PA

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Looking through the New World of Mathematics: Experiences of College Students in Mathematics in the Modern World Course

2022, International Journal of Research Publications

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Davao Research Journal

Jhonnel Villegas , Arrel Jay Velez

Understanding mathematical concepts involve developing an intuitive grasp of the underlying ideas and principles that govern mathematical operations and relationships. The primary purpose of this study is to investigate the difficulties and coping strategies in understanding mathematical concepts. This study used an explanatory sequential research design through the collection and analysis of quantitative data followed by a qualitative inquiry. To collect data, the researchers developed questionnaires for the quantitative and qualitative inquiries, which were validated by external experts. The sample of the study for the quantitative part included conveniently selected 297 students from a private Higher Education Institution (HEI) in Tagum City, Davao del Norte, Philippines, in the academic year 2017-2018. In addition, seven (7) individuals participated in the Key Informant Interviews (KIIs). One session of Focus Group Discussion (FGD) was also organized with seven firstyear students enrolled during the second semester of S.Y. 2017-2018. Five skills areas were examined: number fact, arithmetic, language, informational, and visual. Based on the results, students find difficulties in understanding mathematical concepts, specifically in visualizing mathematical concepts and manipulating geometrical shapes and spaces meaningfully. The students also demonstrated difficulties in analyzing the problem, understanding the concept, identifying the correct solution, establishing the equation, and simplifying the expression. In addition, the students cope with the difficulties through selfperseverance, expert consultation, reading and studying, constant practice, and confidence building. Mathematics teachers are recommended to design need-based teaching strategies to optimize student learning.

enzo ivan tilandoca

The main purpose of the study reported in this paper was to determine Filipino college students' (n=336) positive and negative beliefs about mathematics and mathematical problem solving by administering the 36-item (six scales) self-report questionnaire through stratified random sampling. The study was also aimed at analysing possible significant differences in mathematics-related beliefs related to gender, year level, and field of specialization. Using correlations, t tests and multiple analysis of variance, results showed positive beliefs that Filipino students valued effort in increasing one's mathematical ability and considered mathematics as useful in their daily lives. On the contrary, Filipino students believed that all word problems can be solved by simple step by step procedure and word problems are not important. Statistical tests revealed that gender difference in positive beliefs that effort can increase mathematical ability and in the usefulness of mathematics is significant. This gender difference in the beliefs mentioned reflected also in all year levels and in various field of specializations.

jaycel penaflor

The study aimed to identify the factors that affect the achievements of students in Mathematics and to determine the relationship between the students' achievements and individual, instructional, classroom management and evaluation factors. The 239 Bachelor of Elementary Education (BEEd) students were the subjects of the study. The descriptive-correlational design was used. Data were subjected to statistical analyses using t-test, Pearson r and multiple regression. Findings reveal that 1) achievements of students in Math Courses (Fundamental Mathematics and Contemporary Mathematics) is poor; 2)students perform low in both subjects; 3) mathematics achievements are highly correlated to individual and instructional factors and moderately correlated to classroom management and evaluation factors; 4) individual factor and instructional factor greatly affect achievements in fundamental math; 6) instructional factor is the number one predictor of achievement in contemporary math; 7) instructional factor is the factor that affects most the achievements of students in Mathematics.

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Mathematics is important for a person to live a better life. It has a special position in the educational curriculum. However, it is well known that most students find mathematics challenging. This study examined the high school student's struggles and challenges in learning Mathematics. The Interpretative Phenomenological Analysis (IPA) anchored from the Modified Van Kaam Approach popularized by Moustakas was utilized in this study to come up with meaningful data on the struggles and challenges of the high school students in learning Mathematics. The subject of this research was chosen using a purposive sampling technique and the participants are all qualified according to the study's inclusion criteria. 10 high school students of Bartolome and Manuela Pañares Memorial National High School participated in the interview. Analyzing the causes is crucial before taking additional steps to enhance students' Math learning. Through an open-ended survey questionnaire, students were questioned about potential causes of their learning challenges. The researchers generated four themes from the gathered data, and these are the following: The Crux of the Matter, Stumbling Block, Get to Grips With, and Significantly Essential Matter. These themes were formulated based on the students' shared experiences in learning Mathematics. The study included cognitive, affective, and contextual factors that determine the struggles and challenges in learning Mathematics. The challenges that students have in learning mathematics include having trouble recalling information from previous classes, forgetting information easily, and having trouble understanding mathematical ideas. It has been observed that students who find mathematics to be extremely difficult tend to give up more easily than those who find the subject simple. The results also showed that teachers must understand the value of making classroom mathematics engaging so that the students will put effort in learning the subject. The result is presented in the context of the students' perspectives and learning methods.

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The group 2 of grade XI section A is the one who conducted the research about “Factors Affecting Students’ Performance in Mathematics at Parañaque National High School - Baclaran.” Most of the students found difficulty in understanding the Mathematics lesson and in tackling Mathematics. Why do students’ struggles in Mathematics, because as a researcher or being as students, the researchers also experience the struggles in Mathematics. When students don't understand the lesson, students ask question to their classmates rather than consulting to their teachers. Students feel also confused with many different formulas. Sometimes students do not know what is the best formula that they are going to apply in the problems, that's why students have lower grades or have low achievement in Mathematics? These, are one of the evidences that the researchers have observed that’s how they came up with the thought that most of the students are struggling in Mathematics. Our ultimate goal in this study is, for the students to gain an understanding of this concept can greatly perceives the world around them. Therefore, new enlightenment may come about with this understanding. In this approach problems are a means by which students learn new mathematical concepts and synthesize mathematical knowledge.

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This study examined the correlation between mathematics performance and academic achievement of junior high school learners in a government-run laboratory high school institution in Leyte and compared the mathematics performance and academic achievement of male and female learners. The study employed the quantitative method using correlational and comparative research designs to analyze the secondary data. It encompassed the records of 1,500 learners obtained through the convenience sampling technique. Pearson's correlation coefficient and the Ttest for two independent samples were utilized in analyzing the gathered data. Findings revealed a positive and highly significant correlation between the learners' mathematics performance and academic achievement, indicating that high school learners who are adept in mathematics tend to succeed and perform better in their academic courses. Whereas low performance in mathematics correspondingly connotes low achievement in overall intellectual abilities. No significant difference was found between male and female learners, suggesting that both genders of learners can succeed academically. The study concludes that mathematics performance and academic achievement go hand in hand, while gender does not affect the learners' ability to excel in mathematics. Effectively, secondary learning institutions must provide mathematics learners with learning opportunities during Mathematics classes and classroom activities regardless of gender. Teachers must help learners understand how to solve problems and think critically, expose them to real-world applications, and build their confidence and motivation to excel academically.

Necdet Guner

The aim of this study is to identify whether high school students encounter any difficulties in mathematics and reveal the reasons for such difficulties. The participants of the study, which was a descriptive case study based on qualitative understanding, were a total of 164 students, including 85 students from Anatolian High Schools and 79 students from Science High Schools. Approximately 11% of the participants said they had no difficulties in math, whereas 99% of the students from Anatolian High Schools and 78% of the students from Science High Schools said they had difficulties in mathematic. Their thoughts about the reasons for such difficulties were analyzed by content analysis method considering the type of high school they attended. The findings obtained revealed that the difficulties encountered by the participants in mathematics were teacher-, contentand studentbased. Anatolian High School students stated that they intensely faced teacher-based difficulties, whereas Scienc...

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The Architecture of Modern Mathematics: Essays in History and Philosophy

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This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.

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MATHEMATICS IN THE MODERN WORLD

Contributors.

• Purelyn Umpay

Description

This course deals with the nature of mathematics, appreciation of its practical, intellectual, and aesthetic dimensions, and application of mathematical tools in daily life.

The course begins with an introduction to the nature of mathematics as an exploration of patterns (in nature and the environment) and as an application of inductive and deductive reasoning. By exploring these topics, students are encouraged to go beyond the typical understanding of mathematics as merely a set of formulas but as a source of aesthetics in patterns of nature, for example, and a rich language in itself (and of science) governed by logic and reasoning. The course then proceeds to survey ways in which mathematics provides a tool for understanding and dealing with various aspects of present-day living, such as managing personal finances, making social choices, appreciating geometric designs, understanding codes, used in data transmission and security, and dividing limited resources fairly. These aspects will provide opportunities for actually doing mathematics in a broad range of exercises that bring out the various dimensions of mathematics as a way of knowing, and testing the students’ understanding and capacity.

• Course Syllabus

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