According to a recent study, people regret more what they did NOT do rather than what they did. In other words, sins of omission weigh more heavily on the mind than sins of commission.

The paper concluded: “In the short term, people regret their actions more than inactions. But in the long term, the inaction regrets stick around longer.”

I wanted to test the validity of this finding by querying my students. Granted, most of them are only in their mid-20's and are too young to lament what they have NOT done, since they have plenty of time to DO it, unlike most people in their 80's or 90's.

Still, I wanted to probe their mind to see if even at a relatively young age, the burden of inaction began to pile up and influenced their outlook on life.

This was the question I posed to them:*What is the one thing that you have NOT done in your life so far that you regret the most and that, if you could go back in time, you would definitely DO it?*

And this is what poured forth from most of them, that they should have traveled to other countries when the opportunity came and when they had the time, instead of opting to earn money through part-time jobs.

Brian’s response was typical: “I regret most not traveling overseas after high school when I had fewer responsibilities: France, Italy, China. But now I am too busy with all the stuff of life!”

Diana: “Wish I traveled. I wish I took a break just for me to have some fun, instead of working all the time.”

Karen: “Not going to Europe with my school friends when I had the opportunity. Now it’s too late! Already I have so much responsibilities!”

Leslie: Not traveling when I was younger. So many places, beautiful people, good food!

Kemala was born in Indonesia and studied in Germany before migrating to United States. Her plaintive regret is palpable: “I am really sad that I did not travel in the countries of Europe when I was in Germany. I always thought, ‘I can do it later,’ but now it seems too late. Caught up with too many things! I went back to Indonesia and now I am in the US and I don’t know when I can travel in Europe.”

Liz has the same remorse: “Not going backpacking with my sister last summer in Europe. She had such a great time and came back a new person! I was too busy working and making money. Bad mistake. The experience would have been so much better!”

Fred is a successful businessman but cannot shake off his regret: "I should have traveled to other countries when I was younger in my 20’s. Now I am older (37) and established and vested in my company. It’s harder to step away and take vacations. With age, we slow down physically. Now I am tired, something I was not when I was younger.”

Yvonne looks back with sorrow at the decision she made two years back: “I had an opportunity to teach English to children in Korea. I didn’t do it and now I am busy with life here. I wish I did what I really wanted to but didn’t. It would have made so much difference, more to me than to those children.”

Melanie also regrets not traveling: “The farthest I have been to are Lake Tahoe and Carmel. I am currently saving up money to travel to Mexico to see my grandparents.”

We have all met or read about people whose lives were transformed by travel. Take veteran actor Robert Redford, 82, whose latest movie,*The Old Man & the Gun*, has just been released to theaters around the country. In an interview (TIME, October 15, 2018), he disclosed how, while growing up in lower-working-class environment in Los Angeles, he hung out with his high-school crowd who often got into trouble. But a certain wanderlust always gnawed at him. “I wanted to be in Paris. I wanted to be in Spain. So when I was about 19, I saved up enough money to last me for a year.” Redford left the United States. “That experience is what really changed my life, because then I saw the outside world.” His time away changed his view of the world and of his home country. It saved him from a life that could have splintered into many useless fragments. “When I went to Europe, I understood more about politics and about human nature.” This new perspective is what he attributes to his activism.

I held up this example to my students and told them to seize the next opportunity that came along and just go!

While not traveling was their biggest regret (some are determined not to repeat that mistake), there were other regrets of inaction too.

Amanda regrets not opening her own business when she could, her own fashion store. “Nut maybe I can still make my dream come true.”

Gutierrez regrets not completing his Bachelor’s Degree right after high school. “I decided to focus more on money, so I dropped out of San Jose State University. It is difficult returning to school later in a life of career and child.”

Diaz regrets not taking more risks. “I always played it safe, do what others told me to do. I promise to listen more to my guts and do what I want to do, not what others tell me to do. It’s true: no risk, no gain!”

Cheryl regrets not completing her education and getting a career when she was 25. “By now I would have had my own house, called my own shots. Instead, I got married after high school. I promised I would return after a few months. Did not happen. By the time I returned to school, 7 long years have passed! I am now a mom with babies and both my husband and I work and there is no time or fun for anything, with babies around!”

Perhaps the most poignant response came from Jonathan. “Even though I am young, the one thing I haven’t done in my life is give my parents some stability, like buying them a house or helping them retire. My parents work extremely hard and growing up, I gave them a very hard time. I just want to be able to pay for their hard work and show them how much I care for them. They are older, and I don’t want anything to happen to them before I can help them.”

I was compelled to tell Jonathan: “You still can!”

But for the most surprising response, at once baffling and filled with bathos, this one beat all other entries. Clark wrote: “I should have dated more. I waited until I was 25 and the first person I dated, I ended up marrying her. Because of my lack of dating, I never learned to kiss properly and be romantic enough, because I had no practice. My wife dislikes that about me. I wish I had dated more!”

]]>The paper concluded: “In the short term, people regret their actions more than inactions. But in the long term, the inaction regrets stick around longer.”

I wanted to test the validity of this finding by querying my students. Granted, most of them are only in their mid-20's and are too young to lament what they have NOT done, since they have plenty of time to DO it, unlike most people in their 80's or 90's.

Still, I wanted to probe their mind to see if even at a relatively young age, the burden of inaction began to pile up and influenced their outlook on life.

This was the question I posed to them:

And this is what poured forth from most of them, that they should have traveled to other countries when the opportunity came and when they had the time, instead of opting to earn money through part-time jobs.

Brian’s response was typical: “I regret most not traveling overseas after high school when I had fewer responsibilities: France, Italy, China. But now I am too busy with all the stuff of life!”

Diana: “Wish I traveled. I wish I took a break just for me to have some fun, instead of working all the time.”

Karen: “Not going to Europe with my school friends when I had the opportunity. Now it’s too late! Already I have so much responsibilities!”

Leslie: Not traveling when I was younger. So many places, beautiful people, good food!

Kemala was born in Indonesia and studied in Germany before migrating to United States. Her plaintive regret is palpable: “I am really sad that I did not travel in the countries of Europe when I was in Germany. I always thought, ‘I can do it later,’ but now it seems too late. Caught up with too many things! I went back to Indonesia and now I am in the US and I don’t know when I can travel in Europe.”

Liz has the same remorse: “Not going backpacking with my sister last summer in Europe. She had such a great time and came back a new person! I was too busy working and making money. Bad mistake. The experience would have been so much better!”

Fred is a successful businessman but cannot shake off his regret: "I should have traveled to other countries when I was younger in my 20’s. Now I am older (37) and established and vested in my company. It’s harder to step away and take vacations. With age, we slow down physically. Now I am tired, something I was not when I was younger.”

Yvonne looks back with sorrow at the decision she made two years back: “I had an opportunity to teach English to children in Korea. I didn’t do it and now I am busy with life here. I wish I did what I really wanted to but didn’t. It would have made so much difference, more to me than to those children.”

Melanie also regrets not traveling: “The farthest I have been to are Lake Tahoe and Carmel. I am currently saving up money to travel to Mexico to see my grandparents.”

We have all met or read about people whose lives were transformed by travel. Take veteran actor Robert Redford, 82, whose latest movie,

I held up this example to my students and told them to seize the next opportunity that came along and just go!

While not traveling was their biggest regret (some are determined not to repeat that mistake), there were other regrets of inaction too.

Amanda regrets not opening her own business when she could, her own fashion store. “Nut maybe I can still make my dream come true.”

Gutierrez regrets not completing his Bachelor’s Degree right after high school. “I decided to focus more on money, so I dropped out of San Jose State University. It is difficult returning to school later in a life of career and child.”

Diaz regrets not taking more risks. “I always played it safe, do what others told me to do. I promise to listen more to my guts and do what I want to do, not what others tell me to do. It’s true: no risk, no gain!”

Cheryl regrets not completing her education and getting a career when she was 25. “By now I would have had my own house, called my own shots. Instead, I got married after high school. I promised I would return after a few months. Did not happen. By the time I returned to school, 7 long years have passed! I am now a mom with babies and both my husband and I work and there is no time or fun for anything, with babies around!”

Perhaps the most poignant response came from Jonathan. “Even though I am young, the one thing I haven’t done in my life is give my parents some stability, like buying them a house or helping them retire. My parents work extremely hard and growing up, I gave them a very hard time. I just want to be able to pay for their hard work and show them how much I care for them. They are older, and I don’t want anything to happen to them before I can help them.”

I was compelled to tell Jonathan: “You still can!”

But for the most surprising response, at once baffling and filled with bathos, this one beat all other entries. Clark wrote: “I should have dated more. I waited until I was 25 and the first person I dated, I ended up marrying her. Because of my lack of dating, I never learned to kiss properly and be romantic enough, because I had no practice. My wife dislikes that about me. I wish I had dated more!”

The dropout and failure-to-graduate rates in California’s 72-district, 114 community colleges serving over 2.1 million students are unacceptable. A study by the Institute for Higher Education Leadership at Cal State Sacramento found that 70 percent of community college students fail to graduate or transfer to a four-year institution. These students typically drop out without any degree but with considerable debt.

One strategy used to redress this grim reality was to pour resources into remedial math and English courses, populated disproportionately by African-American and Latino students. It failed abysmally. Only 18 percent of elementary algebra students completed transfer-level math to CSU and UC systems in three years, and only 6 percent of pre-algebra students.

Something radical had to be done. Enter Assembly Bill 705. Introduced by Jacqui Irwin, D-Thousand Oaks, it was signed into law by Gov. Jerry Brown on Jan. 1, giving community colleges a deadline for full implementation by the fall of 2019.

The two revolutionary aspects of the bill are: a) colleges must maximize the probability that a student enter and complete transfer-level coursework in math and English within one year and b) colleges must use high school coursework, high school grades or high school GPAs to place incoming students into transfer-level courses, providing concurrent support as needed.

To appreciate the radical nature of AB 705, consider what I have witnessed with heartbreaking regularity in my years of teaching math. Joe, a high-school graduate with a 3.0 GPA, enrolls in his local college as a springboard for admission to UC Davis to major in sustainable agriculture. He expects to spend at most 3 years to accumulate enough units to transfer. Without delving into his aspirations, however, the college gives him an impersonal placement test where he falters with fractions. He gets trapped into a three-semester sequence of non-transferable basic skills classes of pre-algebra, algebra 1 and 2. He manages to pass the first two but algebra 2, with complex conjugates, quadratic equations and such, proves insurmountable. Overcome by emotional and psychological problems, Joe drops out and accepts a low-wage job below his potential.

AB 705 recognizes that it is the structural problem of under-placement and long sequence of classes that prevent students like Joe from graduating. Under AB 705, Joe is placed in transferable statistics in his very first semester, with help in math provided as just-in-time or co-requisite remediation. Excited by the relevance of the predictive power of statistics to his major, Joe aces the course. In a year, he completes transfer-level math and English requirements for a four-year institution.

Pipe dream? No. Pilot projects at San Diego’s Cuyamaca College and San Bruno’s Skyline College among others have shown that placing students in transferable math and English courses based on high school GPA quadruples the completion rate.

AB 705 has its challenges and detractors. Some claim it is too draconian. Others, that it was forced down from above without adequate faculty consultation. These are legitimate concerns, but the overriding factor for embracing AB 705 is that through proper placement and emphasizing acceleration over remediation, it can lift students from failure to success.

The Golden State has the fifth largest economy in the world, after the United States, China, Japan, and Germany. Its demand for a skilled, innovative workforce is skyrocketing. California’s community colleges must play a significant role in nurturing and educating this workforce. Faculty, counselors and administrators must work together to help students reach the high bar set by AB 705. Knowingly or unknowingly, we have been guilty of the soft bigotry of low expectations, with minority students bearing the brunt of our casually cruel mindset. We wrongly focus on what our students don’t know rather than what they know. The pilot projects have shown that students rise to the challenge of higher expectations. By demanding more, we can not only help our students succeed academically but also guide them toward a life of meaning and purpose.

With Jupiter, Venus, Mars and Saturn gracing the night sky now, I decided to visit the observatory after a hiatus to renew my acquaintance with the storied planets.

About fifty of us gathered at the observatory recently to take in the beauty of the starry sky. The line was long at the domed building that housed the telescope focused on Saturn.

What I witnessed, however, was unexpected and, frankly, shocking.

Most of the “stargazers” spent more time taking selfies than looking at the planet. Parents held their babies close to the telescope and snapped photos as the unnatural light of their smartphones lit up the dark interior of the building. They photographed the telescope’s view of Saturn, experimenting until the image was to their satisfaction.

What I found incongruous was that everyone acted as if this was normal, that unless Saturn was captured in the circuitry of their hi-tech gadgets, the physical experience of observing the ringed planet through a telescope wasn’t worth much.

It was the same with Jupiter in the adjacent roll-off roof building. Jove and his moons took a backseat to the selfies, to the document-by-camera excitement that gripped so many of the visitors. A remark I overheard put the selfies in perspective. A man turned to his spouse and said, “It’s already on Facebook and Instagram.”

The standalone selfie was apparently not worth much by itself, unless authenticated by social media and “liked.”

I managed to see Saturn, its ring tilted at a steeper angle than when I saw it last, magical and awe-inspiring as always. But the flash and whirr of the cameras seemed so pervasive that afterwards, when I looked up with unaided eyes outside, I half-expected to see the image of a partially-eaten translucent silver apple dominating the night sky.

The selfie syndrome is everywhere, not just at public events and tourist spots but in parks, woods, shores, malls, stadiums, restaurants, museums, even at graveyards and funerals!

How is it that we have so casually surrendered substance to shadow, real to virtual? Why are we so in thrall to our devices 24×7?

One reason is that smart gadgets and social media allow us to unleash our very human instinct for self-expression to a degree unprecedented in history.

But pushed to extreme, self-expression can devolve into narcissism. In the presence of the sublime and the transcendent, however, self-expression through selfies, rather than engagement through the senses, can be absurd and short-sighted. It is like ignoring the eternal for the ephemeral.

How to subdue this abnormal selfie craving? One way would be to renew our acquaintance with nature.

“The world is too much with us,” lamented Wordsworth at the dawn of the 19th century when the poet felt that people had lost their connection to nature because of their growing attachment to materialism. “Getting and spending, we lay waste our powers:/Little we see in nature that is ours/…/For this, for everything, we are out of tune.”

Next time we go to the woods, the shore or the observatory, let’s leave behind the devices with the flickering screens so we can experience with our five senses the music of the songbirds, the wonder of tide pools, the lullaby of the surf, and the pageantry of the planets and the stars.

]]>About fifty of us gathered at the observatory recently to take in the beauty of the starry sky. The line was long at the domed building that housed the telescope focused on Saturn.

What I witnessed, however, was unexpected and, frankly, shocking.

Most of the “stargazers” spent more time taking selfies than looking at the planet. Parents held their babies close to the telescope and snapped photos as the unnatural light of their smartphones lit up the dark interior of the building. They photographed the telescope’s view of Saturn, experimenting until the image was to their satisfaction.

What I found incongruous was that everyone acted as if this was normal, that unless Saturn was captured in the circuitry of their hi-tech gadgets, the physical experience of observing the ringed planet through a telescope wasn’t worth much.

It was the same with Jupiter in the adjacent roll-off roof building. Jove and his moons took a backseat to the selfies, to the document-by-camera excitement that gripped so many of the visitors. A remark I overheard put the selfies in perspective. A man turned to his spouse and said, “It’s already on Facebook and Instagram.”

The standalone selfie was apparently not worth much by itself, unless authenticated by social media and “liked.”

I managed to see Saturn, its ring tilted at a steeper angle than when I saw it last, magical and awe-inspiring as always. But the flash and whirr of the cameras seemed so pervasive that afterwards, when I looked up with unaided eyes outside, I half-expected to see the image of a partially-eaten translucent silver apple dominating the night sky.

The selfie syndrome is everywhere, not just at public events and tourist spots but in parks, woods, shores, malls, stadiums, restaurants, museums, even at graveyards and funerals!

How is it that we have so casually surrendered substance to shadow, real to virtual? Why are we so in thrall to our devices 24×7?

One reason is that smart gadgets and social media allow us to unleash our very human instinct for self-expression to a degree unprecedented in history.

But pushed to extreme, self-expression can devolve into narcissism. In the presence of the sublime and the transcendent, however, self-expression through selfies, rather than engagement through the senses, can be absurd and short-sighted. It is like ignoring the eternal for the ephemeral.

How to subdue this abnormal selfie craving? One way would be to renew our acquaintance with nature.

“The world is too much with us,” lamented Wordsworth at the dawn of the 19th century when the poet felt that people had lost their connection to nature because of their growing attachment to materialism. “Getting and spending, we lay waste our powers:/Little we see in nature that is ours/…/For this, for everything, we are out of tune.”

Next time we go to the woods, the shore or the observatory, let’s leave behind the devices with the flickering screens so we can experience with our five senses the music of the songbirds, the wonder of tide pools, the lullaby of the surf, and the pageantry of the planets and the stars.

Comedian Woody Allen clarified the idea further for us: “Those who can’t do, teach. And those who can’t teach, teach gym.”

A snider version is available on the Internet (author unknown): “Those who can, do. Those who can’t, teach. Those who can’t teach, teach teachers.”

Is there any truth to these prickly sayings? Does the teaching profession attract only those who have failed at everything else?

Of course not. Teaching is a calling just like physics, literature, law, music or mathematics. In countries like Finland and South Korea, teachers are revered. They are considered the pillars of society. Their earnings reflect their standing and status.

It is a different story in the United States. Whether in income or status, teachers are, on the whole, at the bottom of the heap. Politicians pay lip service to the importance of teachers in shaping minds and then dutifully kowtow to the demands of Big Business and Wall Street honchos. Colleges and Universities are now run by CEOs who cut their teeth running corporations (often running them to the ground) and who, in cahoots with the textbook industry, see no distinction between an educational institution and a company selling, say, toothpaste. It’s all about market, free enterprise and academic capitalism, their argument goes. Besides, isn’t education a dream of a product to sell to stressed customers, that is, students, who, for them, are the perennial cash cows?

Compounding this problem is the rise in the number of part-time (adjunct) teachers. Currently, over 75% of college professors in the United States are adjunct. The dictionary defines ‘adjunct’ as ‘a thing added to something else as a supplementary rather than an essential part.’ And that’s exactly how adjuncts are treated: ‘things’ that earn minimum wage salary if you count all the hours they have to toil without pay (grading, counseling, and so on, without any office space) and of course, without any medical benefit or security. Yet they teach the bulk of the courses in our colleges and universities, saving untold millions that mostly go into building expensive gyms and cafeterias and hiring yet more administrators.

So why do teachers teach, even as adjuncts? Has this breed completely lost its sense of self-respect, its dignity?

The truth is more complicated. There are bad teachers, good teachers and a few great teachers, just like in any other profession. But whereas a middling cubicle-dweller at a high-flying startup can earn in his first year fifty times the salary of a teacher who has been toiling at his craft for over a decade, there is a crucial difference. A teacher, full-time or part-time, is the master of his domain, that is, of his class. She is the one who decides what will be taught, how it will be taught, and how her charges will be graded. Yes, there have been major shifts in pedagogy: the importance of student-centered learning, about teachers being “not sage on the stage but guide on the side,” about ‘it’s not what we teach, it’s what they learn.” Still, even if a teacher is not the sage on the stage, she still commands the most attention in her class as a guide. Whether she wants to or not, she is still her class’s focal point. Given her dismal financial status and her utter anonymity outside the classroom, this ‘looking up to’ feeling, this temporary sense of indispensability, when combined with the passion for shaping minds, can be priceless.

Yet this same feeling can undermine a teacher’s noble intentions. As Harvey Daniels and Marilyn Bazar point out in their book, Methods That Matter, “Teachers probably wouldn't have originally chosen their vocation if they didn't crave the spotlight on some deep psychological level. The hunger to 'really teach something' has probably derailed more student-centered innovations than administrative cowardice and textbook company co-option combined.”

Why do teachers teach? Other than a few academic superstars and Nobel laureates, teaching cannot surely be about money in America, since the pay is, relatively speaking, so little. Even with passion and nebulous talks about life’s calling, there are teachers who destroy the curiosity and the motivations of their students through mindless drill and uninspiring style. But there are also teachers who try to do their best by their students, day in and day out. There is something ineffable about their ways and methods, some x factor that cannot be reduced to algorithmic analysis. It is important for these teachers, however, to acknowledge the lure of the spotlight ‘at some deep psychological level.’ As long as they maintain the proper perspective about it and focus on what their students are learning, rather than what they are teaching, teaching will continue to be its own reward.

]]>Of course not. Teaching is a calling just like physics, literature, law, music or mathematics. In countries like Finland and South Korea, teachers are revered. They are considered the pillars of society. Their earnings reflect their standing and status.

It is a different story in the United States. Whether in income or status, teachers are, on the whole, at the bottom of the heap. Politicians pay lip service to the importance of teachers in shaping minds and then dutifully kowtow to the demands of Big Business and Wall Street honchos. Colleges and Universities are now run by CEOs who cut their teeth running corporations (often running them to the ground) and who, in cahoots with the textbook industry, see no distinction between an educational institution and a company selling, say, toothpaste. It’s all about market, free enterprise and academic capitalism, their argument goes. Besides, isn’t education a dream of a product to sell to stressed customers, that is, students, who, for them, are the perennial cash cows?

Compounding this problem is the rise in the number of part-time (adjunct) teachers. Currently, over 75% of college professors in the United States are adjunct. The dictionary defines ‘adjunct’ as ‘a thing added to something else as a supplementary rather than an essential part.’ And that’s exactly how adjuncts are treated: ‘things’ that earn minimum wage salary if you count all the hours they have to toil without pay (grading, counseling, and so on, without any office space) and of course, without any medical benefit or security. Yet they teach the bulk of the courses in our colleges and universities, saving untold millions that mostly go into building expensive gyms and cafeterias and hiring yet more administrators.

So why do teachers teach, even as adjuncts? Has this breed completely lost its sense of self-respect, its dignity?

The truth is more complicated. There are bad teachers, good teachers and a few great teachers, just like in any other profession. But whereas a middling cubicle-dweller at a high-flying startup can earn in his first year fifty times the salary of a teacher who has been toiling at his craft for over a decade, there is a crucial difference. A teacher, full-time or part-time, is the master of his domain, that is, of his class. She is the one who decides what will be taught, how it will be taught, and how her charges will be graded. Yes, there have been major shifts in pedagogy: the importance of student-centered learning, about teachers being “not sage on the stage but guide on the side,” about ‘it’s not what we teach, it’s what they learn.” Still, even if a teacher is not the sage on the stage, she still commands the most attention in her class as a guide. Whether she wants to or not, she is still her class’s focal point. Given her dismal financial status and her utter anonymity outside the classroom, this ‘looking up to’ feeling, this temporary sense of indispensability, when combined with the passion for shaping minds, can be priceless.

Yet this same feeling can undermine a teacher’s noble intentions. As Harvey Daniels and Marilyn Bazar point out in their book, Methods That Matter, “Teachers probably wouldn't have originally chosen their vocation if they didn't crave the spotlight on some deep psychological level. The hunger to 'really teach something' has probably derailed more student-centered innovations than administrative cowardice and textbook company co-option combined.”

Why do teachers teach? Other than a few academic superstars and Nobel laureates, teaching cannot surely be about money in America, since the pay is, relatively speaking, so little. Even with passion and nebulous talks about life’s calling, there are teachers who destroy the curiosity and the motivations of their students through mindless drill and uninspiring style. But there are also teachers who try to do their best by their students, day in and day out. There is something ineffable about their ways and methods, some x factor that cannot be reduced to algorithmic analysis. It is important for these teachers, however, to acknowledge the lure of the spotlight ‘at some deep psychological level.’ As long as they maintain the proper perspective about it and focus on what their students are learning, rather than what they are teaching, teaching will continue to be its own reward.

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.”

]]>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.”

Consider the following: Solve for x in the equation

x – 0.2x = 320

Students find it easy to solve:

0.8x = 320

Dividing both sides by 0.8, x = 400

Now consider the problem: After a 20% reduction, you purchase a camera for $320. What was the camera’s price before the reduction?

Suddenly this problem looks strange and difficult, even though it is the same as the one written in mathematical notation. There is that 20 percent reduction. There is that word ‘before.’ How exactly do they translate into mathematical notation?

Consider another problem: Solve for x and y.

x + y = 146

x = y + 12

Again, this appears to be an easy problem to solve.

Substitute the value of x from the second equation into the first:

y + 12 + y = 146

2y + 12 = 146

2y = 134

Dividing both sides by 2 give y = 67

Thus, x= y + 12 = 67 + 12 = 79

However, suppose the problem is presented like this:

In two consecutive games, the college basketball team scored a total of 146 points. The team scored 12 more points in the first game than in the second. How many points did the team score in each of the two games?

It is the same problem but writing down the two equations, in which x = points scored in the first game and y = points scored in the second game, pose a problem for many students.

Finally, consider this problem:

Solve for x and y:

x + y = 16000

0.06x + 0.08y = 1180

Students can substitute the value of x from the first equation into the second and solve for y and then solve for x.

0.06(16000-y) + 0.08y = 1180

Solving for y gives y = 11000. Hence, x = 5000.

However, suppose the problem is stated this way:

You invest part of $16,000 at 6% interest and the remainder at 8% interest. If the annual yearly interest from these investments is $1180, find the amount invested at each rate.

Again, creating a set of linear equations to answer the question seems as remote as the moon, visible but beyond reach.

It may be helpful for math and English teachers to compile a list of words and their meanings in everyday context and in the context of mathematics, as well as a list of mathematical phrases and their translation into mathematical notations. By working together, math and English faculty can help students overcome their fear of math word problems, enrich their vocabulary and enhance their critical reading and writing skills.

The larger goal is to help them see the connection between Math and English. It is through such interdisciplinary connections that students can discover new insights and make new connections of their own.

A partial list of words may include constant, variable, ratio, proportion, fraction, slope, factor, rational, irrational, commutative, percent, percentile, integer, decimal, compound, absolute, perimeter, area, volume, coefficient, term, monomial, binomial, trinomial, polynomial, simplify, evaluate, solve, equation, inequality, linear, non-linear, base, power, exponent, exponential, hypotenuse, numerical, numeracy, innumeracy, round-off, round-up, sequence, series, intersect, intercept, radical, elliptical, radius, circumference, circular, parabola, parabolic, ellipse, elliptical, quadratic, imaginary, complex, conjugate, matrix, unknown, vertex, model, prime, square, cubic, parallel, horizontal, vertical, grouping, precision, accuracy, dependent, independent, function, one-to-one, one-to-many, many-to-one, domain, range, average, mean, median, probability, hypothesis, regression, correlation, and so on.

Fragments may include at least one, at most 4, ratio of a to b, x split into k equal parts, golden rectangle, golden ratio, margin of error, confidence level, significance level, confidence interval …

Serendipity occurs at the intersection of disciplines. It is something that is missing in our schools. The time has come to address this urgent issue. A first step will be to create synergy between English and math teachers. There is plenty of data that show how student performance in solving math word problems increase when they are clear about the precise meaning of words as they are used in their everyday context and in mathematical context.

]]>x – 0.2x = 320

Students find it easy to solve:

0.8x = 320

Dividing both sides by 0.8, x = 400

Now consider the problem: After a 20% reduction, you purchase a camera for $320. What was the camera’s price before the reduction?

Suddenly this problem looks strange and difficult, even though it is the same as the one written in mathematical notation. There is that 20 percent reduction. There is that word ‘before.’ How exactly do they translate into mathematical notation?

Consider another problem: Solve for x and y.

x + y = 146

x = y + 12

Again, this appears to be an easy problem to solve.

Substitute the value of x from the second equation into the first:

y + 12 + y = 146

2y + 12 = 146

2y = 134

Dividing both sides by 2 give y = 67

Thus, x= y + 12 = 67 + 12 = 79

However, suppose the problem is presented like this:

In two consecutive games, the college basketball team scored a total of 146 points. The team scored 12 more points in the first game than in the second. How many points did the team score in each of the two games?

It is the same problem but writing down the two equations, in which x = points scored in the first game and y = points scored in the second game, pose a problem for many students.

Finally, consider this problem:

Solve for x and y:

x + y = 16000

0.06x + 0.08y = 1180

Students can substitute the value of x from the first equation into the second and solve for y and then solve for x.

0.06(16000-y) + 0.08y = 1180

Solving for y gives y = 11000. Hence, x = 5000.

However, suppose the problem is stated this way:

You invest part of $16,000 at 6% interest and the remainder at 8% interest. If the annual yearly interest from these investments is $1180, find the amount invested at each rate.

Again, creating a set of linear equations to answer the question seems as remote as the moon, visible but beyond reach.

It may be helpful for math and English teachers to compile a list of words and their meanings in everyday context and in the context of mathematics, as well as a list of mathematical phrases and their translation into mathematical notations. By working together, math and English faculty can help students overcome their fear of math word problems, enrich their vocabulary and enhance their critical reading and writing skills.

The larger goal is to help them see the connection between Math and English. It is through such interdisciplinary connections that students can discover new insights and make new connections of their own.

A partial list of words may include constant, variable, ratio, proportion, fraction, slope, factor, rational, irrational, commutative, percent, percentile, integer, decimal, compound, absolute, perimeter, area, volume, coefficient, term, monomial, binomial, trinomial, polynomial, simplify, evaluate, solve, equation, inequality, linear, non-linear, base, power, exponent, exponential, hypotenuse, numerical, numeracy, innumeracy, round-off, round-up, sequence, series, intersect, intercept, radical, elliptical, radius, circumference, circular, parabola, parabolic, ellipse, elliptical, quadratic, imaginary, complex, conjugate, matrix, unknown, vertex, model, prime, square, cubic, parallel, horizontal, vertical, grouping, precision, accuracy, dependent, independent, function, one-to-one, one-to-many, many-to-one, domain, range, average, mean, median, probability, hypothesis, regression, correlation, and so on.

Fragments may include at least one, at most 4, ratio of a to b, x split into k equal parts, golden rectangle, golden ratio, margin of error, confidence level, significance level, confidence interval …

Serendipity occurs at the intersection of disciplines. It is something that is missing in our schools. The time has come to address this urgent issue. A first step will be to create synergy between English and math teachers. There is plenty of data that show how student performance in solving math word problems increase when they are clear about the precise meaning of words as they are used in their everyday context and in mathematical context.

Feynman began his lecture with these words: “It is odd, but on the infrequent occasion when I have been called upon in a formal place to play the bongo drums, the introducer never seems to find it necessary to mention that I also do theoretical physics. I believe that is probably because we respect the arts more than the sciences.”

“Respect the arts more than the sciences!” The suggestion was perhaps hyperbole on Feynman’s part to set the stage for his inimitable presentation on the basic laws of physics and their role in defining how nature works. But even if it was true in the ‘60s that the arts received more respect than the sciences, the table has certainly turned in the decades since. Science, Technology, Engineering and Math (STEM) appear to have left the arts in the dust.

Is this development for the better?

Surely from an employment perspective, anyone savvy with programming or big data analysis stands a better chance of earning a livelihood than someone versed in the nuances of Shakespeare’s sonnets. After all, there are just so many positions available in English departments but those with proven ability to code or analyze data or conduct research on the mathematics of singularity or the strange properties of dark matter will be courted by numerous employers.

STEM has expanded to STEAM, (STEM + Art = STEAM) and garnered support from industry and academia but there is a general feeling that the ‘A’ in STEAM is an afterthought, a way to pacify those concerned about the decline of humanities from our curricula.

But it is true that a broad general education is a requirement for innovation and creativity, particularly because it leads to interdisciplinary research and cross-fertilization of ideas. If STEM fields are important, so is Art. Besides, as Nabokov observed, “There is no science without fancy and no art without fact.”

What do community college students think of the ascendency of STEM at the expense of the Arts?

Luis believes wholeheartedly in the importance of STEM in revitalizing education in the United States. He worked on a STEM project in a summer camp last year and was amazed by the enthusiasm of boys and girls, particularly girls from low-income families, in mastering STEM subjects. “In my experience, most girls don’t like to go for professions involving science and technology and math but these girls in my camp couldn’t wait for the next day’s activity to begin after a hard days of work. STEM is a way to lift students out of poverty and turn them into lifelong learners.”

Vanessa, on the other hand, believes that the emphasis on STEM is misguided. She finds the reach of technology disturbing. “Technology companies target even young children. I personally prefer for someone to be more artistic. Music and art of any kind help develop our brains. They allow us to actually think for ourselves. While STEM is important, art is equally important. I believe if we push more of the arts like painting and playing instruments, it will expand our minds and also improve our performance in reading, science and math.”

Cindy also believes that STEM education is limiting in many ways. “While it is good to be great test takers and have plenty of information sitting in our brain, STEM subjects by themselves don’t expand our horizon as much. By cutting classes like English, Art History, and any type of Humanities, you are taking away any chance to promote critical thinking. I think all subjects are equally important to learn. I have seen how dramatically Humanity classes have been cut from colleges. It's sad to see how everyone looks like robots taking the same courses!”

Garcia finds many benefits in STEM subjects but “there is also a downside to it as well. When I was in grade school, there was a push for math and science. I was terrible at it but with tutoring I was able to get through most of the classes. Students today are influenced by technology and the media. The focus on STEM doesn’t include what students learn working in a group or with other peers with different social skills. It removes the social interaction many children need. I do not believe STEM by itself will work because it does not address the issue of diversity in the learning styles of students.”

Madisyn believes in the importance of STEM subjects but feels that it has to be complemented by an equal emphasis on the arts and the humanities. It will be a mistake to set up the ‘two cultures’ as rivals. “Knowledge is synergistic. Who wants to hire a scientist who can’t write? Who wants to employ an engineer who isn’t a creative problem-solver? Doesn’t technological innovation require critical reasoning, ethical awareness and sensitivity to the diverse populations in which such advancements are actually put to use? The brain has two hemispheres. It will be a serious mistake to nourish only one half. In this day and age, promoting classes focused on technology and mathematics is much more of a surefire way to attain a career but I will argue that a CEO of a tech company must have a grasp on not just mathematics, but also of psychology and communication. Over-reliance on STEM education will be like putting all our ‘knowledge eggs’ in one basket. It may lead to short-term gain but will be bad in the long run.”

Jessica thinks that STEM or no STEM is a false dichotomy. She feels strongly in a balance between STEM and the Humanities. “If we cut funds from Humanities courses, thinking it will improve our math and science teaching, it will only handicap us and make us go backward. The probability of kids becoming more interested in the STEM subjects is not guaranteed. If there is anything Americans know about their youth today, it is that if they are forced to do something they are not interested in, they will rebel. Unfortunately, our youth have become lazy. They are more interested in celebrities and social media than in subjects that expand their minds. If you’re not studying subjects you are passionate about but join a job for the money where you won’t travel the world, experience new cultures and be stuck in a boring office working 9 to 5, you will be miserable. STEM should be encouraged. We should become more math savvy. We should be bilingual. And we should not ignore the Humanities.”

Erica understands that education system in America focuses on creativity but finds the obsession with STEM subjects alarming. She wants STEMS balanced with liberal arts and philosophy. “I attended a performing arts school all through elementary and high school. We had art, drama, ceramics, dance and many other art divisions. I was in the GATE program in elementary which stands for Gifted and Talented Education. I was good at math, science and history but I entered the program due to my metaphorical and critical thinking skills. I was really good at writing. I started losing interest in math because of my grumpy, uninspiring math instructor who would force us to go to the board and make fun of us when we didn't answer questions correctly. Our education system needs to focus on ways to help expand our creativity in mathematics. Perhaps taking ideas from other countries could help establish the right formula for our education system. Now that I am in college, I've grown to know myself and don't let anyone intimidate me. I've learned to value math and how much we deal with it on a consistent basis, something I never knew before but am grateful I do now.”

Jocelyn recognizes the importance of STEM but finds the overreliance on technology troubling. “STEM is important, but to improve our society, we need to also focus on social skills and creativity. Ever since Facebook and Instagram and smart phones have become insanely popular, people are obsessed with social media and gadgets. What people should be interested in is how they can improve society as a whole. I love science and I am pursuing it as a career; however, I also believe a society needs to thrive in different categories to be successful. For example, while mathematicians and scientists expand our knowledge, it is often the artists who change our society. We should emphasize both STEM and the Humanities.”

]]>Is this development for the better?

Surely from an employment perspective, anyone savvy with programming or big data analysis stands a better chance of earning a livelihood than someone versed in the nuances of Shakespeare’s sonnets. After all, there are just so many positions available in English departments but those with proven ability to code or analyze data or conduct research on the mathematics of singularity or the strange properties of dark matter will be courted by numerous employers.

STEM has expanded to STEAM, (STEM + Art = STEAM) and garnered support from industry and academia but there is a general feeling that the ‘A’ in STEAM is an afterthought, a way to pacify those concerned about the decline of humanities from our curricula.

But it is true that a broad general education is a requirement for innovation and creativity, particularly because it leads to interdisciplinary research and cross-fertilization of ideas. If STEM fields are important, so is Art. Besides, as Nabokov observed, “There is no science without fancy and no art without fact.”

What do community college students think of the ascendency of STEM at the expense of the Arts?

Luis believes wholeheartedly in the importance of STEM in revitalizing education in the United States. He worked on a STEM project in a summer camp last year and was amazed by the enthusiasm of boys and girls, particularly girls from low-income families, in mastering STEM subjects. “In my experience, most girls don’t like to go for professions involving science and technology and math but these girls in my camp couldn’t wait for the next day’s activity to begin after a hard days of work. STEM is a way to lift students out of poverty and turn them into lifelong learners.”

Vanessa, on the other hand, believes that the emphasis on STEM is misguided. She finds the reach of technology disturbing. “Technology companies target even young children. I personally prefer for someone to be more artistic. Music and art of any kind help develop our brains. They allow us to actually think for ourselves. While STEM is important, art is equally important. I believe if we push more of the arts like painting and playing instruments, it will expand our minds and also improve our performance in reading, science and math.”

Cindy also believes that STEM education is limiting in many ways. “While it is good to be great test takers and have plenty of information sitting in our brain, STEM subjects by themselves don’t expand our horizon as much. By cutting classes like English, Art History, and any type of Humanities, you are taking away any chance to promote critical thinking. I think all subjects are equally important to learn. I have seen how dramatically Humanity classes have been cut from colleges. It's sad to see how everyone looks like robots taking the same courses!”

Garcia finds many benefits in STEM subjects but “there is also a downside to it as well. When I was in grade school, there was a push for math and science. I was terrible at it but with tutoring I was able to get through most of the classes. Students today are influenced by technology and the media. The focus on STEM doesn’t include what students learn working in a group or with other peers with different social skills. It removes the social interaction many children need. I do not believe STEM by itself will work because it does not address the issue of diversity in the learning styles of students.”

Madisyn believes in the importance of STEM subjects but feels that it has to be complemented by an equal emphasis on the arts and the humanities. It will be a mistake to set up the ‘two cultures’ as rivals. “Knowledge is synergistic. Who wants to hire a scientist who can’t write? Who wants to employ an engineer who isn’t a creative problem-solver? Doesn’t technological innovation require critical reasoning, ethical awareness and sensitivity to the diverse populations in which such advancements are actually put to use? The brain has two hemispheres. It will be a serious mistake to nourish only one half. In this day and age, promoting classes focused on technology and mathematics is much more of a surefire way to attain a career but I will argue that a CEO of a tech company must have a grasp on not just mathematics, but also of psychology and communication. Over-reliance on STEM education will be like putting all our ‘knowledge eggs’ in one basket. It may lead to short-term gain but will be bad in the long run.”

Jessica thinks that STEM or no STEM is a false dichotomy. She feels strongly in a balance between STEM and the Humanities. “If we cut funds from Humanities courses, thinking it will improve our math and science teaching, it will only handicap us and make us go backward. The probability of kids becoming more interested in the STEM subjects is not guaranteed. If there is anything Americans know about their youth today, it is that if they are forced to do something they are not interested in, they will rebel. Unfortunately, our youth have become lazy. They are more interested in celebrities and social media than in subjects that expand their minds. If you’re not studying subjects you are passionate about but join a job for the money where you won’t travel the world, experience new cultures and be stuck in a boring office working 9 to 5, you will be miserable. STEM should be encouraged. We should become more math savvy. We should be bilingual. And we should not ignore the Humanities.”

Erica understands that education system in America focuses on creativity but finds the obsession with STEM subjects alarming. She wants STEMS balanced with liberal arts and philosophy. “I attended a performing arts school all through elementary and high school. We had art, drama, ceramics, dance and many other art divisions. I was in the GATE program in elementary which stands for Gifted and Talented Education. I was good at math, science and history but I entered the program due to my metaphorical and critical thinking skills. I was really good at writing. I started losing interest in math because of my grumpy, uninspiring math instructor who would force us to go to the board and make fun of us when we didn't answer questions correctly. Our education system needs to focus on ways to help expand our creativity in mathematics. Perhaps taking ideas from other countries could help establish the right formula for our education system. Now that I am in college, I've grown to know myself and don't let anyone intimidate me. I've learned to value math and how much we deal with it on a consistent basis, something I never knew before but am grateful I do now.”

Jocelyn recognizes the importance of STEM but finds the overreliance on technology troubling. “STEM is important, but to improve our society, we need to also focus on social skills and creativity. Ever since Facebook and Instagram and smart phones have become insanely popular, people are obsessed with social media and gadgets. What people should be interested in is how they can improve society as a whole. I love science and I am pursuing it as a career; however, I also believe a society needs to thrive in different categories to be successful. For example, while mathematicians and scientists expand our knowledge, it is often the artists who change our society. We should emphasize both STEM and the Humanities.”

What interests me here is showing how to calculate in your head the approximate monthly payment you will have to make on a car, given its price and the interest rate applied in financing it. (The assumption is that you are not paying full price at the time of buying. Most of us don’t have that much cash, true for maybe 99% of the population!)

Of course, the salesperson selling you the car will tell you what your monthly payment will be. Because most of us think that this calculation is beyond our ability, we meekly submit to whatever the salesperson says. It doesn’t have to be that way. There are some simple calculations you can make in your head that will tell you whether you got the best possible deal when buying the car of your choice.

Let’s say you are buying a car that costs $28,000. You put $3,000 down and finance the remaining $25,000 (principal) at an Annual Percentage Rate (APR) of 4% over 5 years (60 months), the term of the loan. What will be your approximate monthly payment?

To get an estimate of the lowest possible payment, that is, without any interest, simply divided 25,000 by 60 months. Six goes into 24 exactly 4 times, so for $24,000, it will be $400. To account for the remaining $1000, increase $400 to $420.

Now comes the correction for the APR, the interest you will have to pay on the loan. All such loans are compound interest loans, that is, you will have to pay interest on interest. To keep things simple, let’s assume it is simple interest in which the total amount you pay due to interest is fixed. (For compound interest, it is the APR that is fixed while the interest amount varies).

The total amount of simple interest in this case = 4% of 25000 for 5 years = (0.04 x 25000 x 5) = 5000. (Notice that 5 x 0.04 = 0.2, which is 1/5, and a fifth of 25000 is 5000.) So the total cost of the car over 5 years is $25000 + $5000 = $30,000. If you divide $30,000 by 60, (easy because 6 goes into 30 exactly 5 times), it comes to $500.

How much more does compound interest add to the monthly payment? If you were to do the formal calculation, it comes to about $510. So the ballpark figure of $500 comes pretty close! You can simply add $20 to $50 dollars to account for the compound interest. In other words, the minimum amount (no interest) is about $420 and the maximum is about $550.

By doing this type of approximate calculation in your head, you not only convince the salesperson that you are a savvy customer, you also become better at dealing with numbers. This can only help, sometimes in big ways when someone is trying to pull a fast one on you!

]]>Let’s say you are buying a car that costs $28,000. You put $3,000 down and finance the remaining $25,000 (principal) at an Annual Percentage Rate (APR) of 4% over 5 years (60 months), the term of the loan. What will be your approximate monthly payment?

To get an estimate of the lowest possible payment, that is, without any interest, simply divided 25,000 by 60 months. Six goes into 24 exactly 4 times, so for $24,000, it will be $400. To account for the remaining $1000, increase $400 to $420.

Now comes the correction for the APR, the interest you will have to pay on the loan. All such loans are compound interest loans, that is, you will have to pay interest on interest. To keep things simple, let’s assume it is simple interest in which the total amount you pay due to interest is fixed. (For compound interest, it is the APR that is fixed while the interest amount varies).

The total amount of simple interest in this case = 4% of 25000 for 5 years = (0.04 x 25000 x 5) = 5000. (Notice that 5 x 0.04 = 0.2, which is 1/5, and a fifth of 25000 is 5000.) So the total cost of the car over 5 years is $25000 + $5000 = $30,000. If you divide $30,000 by 60, (easy because 6 goes into 30 exactly 5 times), it comes to $500.

How much more does compound interest add to the monthly payment? If you were to do the formal calculation, it comes to about $510. So the ballpark figure of $500 comes pretty close! You can simply add $20 to $50 dollars to account for the compound interest. In other words, the minimum amount (no interest) is about $420 and the maximum is about $550.

By doing this type of approximate calculation in your head, you not only convince the salesperson that you are a savvy customer, you also become better at dealing with numbers. This can only help, sometimes in big ways when someone is trying to pull a fast one on you!

By itself, the sentence seems to convey the gravity of the situation. Yet the average reader is unable to gain a foothold with the numbers. What if more (or less) patients were studied, what would the number of mistakes be then? And how would you compare different studies over time to gauge whether the situation was improving or not?

What comes to the rescue is converting the numbers to a proportion or a percentage. If x out of n meets a certain criterion, then x/n is the proportion of those who met the criterion. If you multiply this proportion by 100, you convert it to a percentage. The power of percentage derives from the fact that it is out of 100. “Per Cent” simply means “Out of 100.” Once we reduce two numbers (one out of the other) to their equivalent percentage, we level the playing field because each number is calculated out of the same number, that is, 100.

The more important question is, can we calculate the percent to an approximation in our head?

Yes, we can.

Consider the two numbers above. Out of 651 patients, 309 were given the wrong medication in hospitals. If we approximate 651 to 600 and 309 to 300, we see that 300 is half of 600, which is 50%. In other words, we can say right away that approximately 50% were given the wrong medication, and half of them, that is, 25%, ran the risk of serious harm done to them.

When the numbers are reduced to percentages, it is easy to get a sense of what is going on, compared to absolute numbers. From there, it is a relatively straightforward matter to approximate whether the percentages have been under or overestimated. Because 651 was reduced to 600, and because it is doing the dividing, (remember, the larger the denominator, the smaller the proportion and the smaller the denominator, the larger the proportion) we overestimated the error. So instead of 50%, we may guess that the number is something like 45%. (Actual percentage of 309/600 comes to 47%).

When numbers are calculated out of 100, we have a way of comparing different numbers out of different totals, in addition to gaining a better understanding with the two numbers themselves. The mathematical playing field is leveled, because all comparisons are out of 100. What’s exciting is that you can calculate that percentage in your head to a good approximation.

When are proportions or percentages not a good idea? When the sample size (the number in the denominator n) is small, the variation in what you are looking to match (the numerator x) is larger, which distorts the comparison. But that should not keep us from appreciating the power of percentages to level the playing field in many instances.

]]>The more important question is, can we calculate the percent to an approximation in our head?

Yes, we can.

Consider the two numbers above. Out of 651 patients, 309 were given the wrong medication in hospitals. If we approximate 651 to 600 and 309 to 300, we see that 300 is half of 600, which is 50%. In other words, we can say right away that approximately 50% were given the wrong medication, and half of them, that is, 25%, ran the risk of serious harm done to them.

When the numbers are reduced to percentages, it is easy to get a sense of what is going on, compared to absolute numbers. From there, it is a relatively straightforward matter to approximate whether the percentages have been under or overestimated. Because 651 was reduced to 600, and because it is doing the dividing, (remember, the larger the denominator, the smaller the proportion and the smaller the denominator, the larger the proportion) we overestimated the error. So instead of 50%, we may guess that the number is something like 45%. (Actual percentage of 309/600 comes to 47%).

When numbers are calculated out of 100, we have a way of comparing different numbers out of different totals, in addition to gaining a better understanding with the two numbers themselves. The mathematical playing field is leveled, because all comparisons are out of 100. What’s exciting is that you can calculate that percentage in your head to a good approximation.

When are proportions or percentages not a good idea? When the sample size (the number in the denominator n) is small, the variation in what you are looking to match (the numerator x) is larger, which distorts the comparison. But that should not keep us from appreciating the power of percentages to level the playing field in many instances.