Question for the mathematics-challenged

[pavonis]

What's it like to find mathematics difficult or even impossible to understand?

 

I've been teaching university-level math and physics for the last two-and-half years and I continually find students who are stumped by basic algebra and trigonometry. Some of them claim to have never even encountered a radical before! The idea of a fractional exponent is staggering to them, apparently. I find it hard to believe that they never learned these things in primary school. They may have forgotten learning it, but to never have learned them is unlikely. But I have no idea what the curricula look like in primary schools nowadays.

 

I teach single-variable differential calculus to them, and when I tell them that calculus is old knowledge, foundation material for modern mathematics, their minds are blown away by the idea that more advanced mathematics exists beyond calculus! If they haven't mastered algebra, though, it's no wonder they can't do calculus.

 

I know it may sound like I'm complaining, but I do want them to do well, and I'm trying to see things their perspective, so that I can help them absorb and understand these concepts. But I learned algebra when I was 11, and calculus by the time I was a high school senior. I never found mathematics as challenging as these students apparently do. So I need some other perspectives. What is the perspective of the math-challenged posters here? What's life like for you?

[Pong Messiah]

Unless somebody has a genuine learning disability, I think the reason they are "stumped" by basic algebra is because it bores them and they're not willing to put the time in to grind it out.

 

Finding a way to make it apply in useful, day-to-day situations might help make it stick more than than being "interesting enough to get the minimal passing grade." But that's all I got, cause I don't believe it's a matter of "can't get it," so much as "It goes in one ear and out the other because I don't care about it and will never apply it outside the classroom."

[Driver]

I struggle with numbers, money, taxes, and higher maths. I understand them conceptually, but the process of making it work in my brain is extremely difficult. It fills me with anxiety and dread. I generally find complex make takes multiple tries to get a consistent answer.

 

I wish I could explain it, but I can't-- which just adds to the frustration.

[Odine]

I second Driver's. I have always been shit with maths and numbers, however it is getting slightly better as I get older.

 

But maths totally freaks me out. One, because it doesn't interest me at all, and two my mind simply can't process numbers and arrange them in my brain like it's supposed to. I guess it's a bit like dyslexia in that way, only with numbers. I remember being at junior high school and my mum going blue in the face trying to help me with maths, counting shit out on her fingers while I'm sat there looking stumped. I just don't get maths. But I was very good at other subjects.. English, history, art, music. Give me an instrument and I'll be able to make a tune come out of it. Give me some paper and a pencil and I'll draw something kick-ass.

 

Now, Pav you will no doubt find my strengths utterly useless in your mind but it's just how it is. Some brains ARE wired differently. I was never much of an academic, and maths has always been my Achilles heel. But anything creative and/or intuitive and I'm away.

 

Afterthought: funnily enough I remember at junior high, and high school that I used to be LESS terrible at algebra than regular maths problems. Probably because it was more symbolic I could get it. It's deffinately the number crunching that just leaves me stumped.

[Guest El Chalupacabra]

I was never that good with math, and my brain is wired in a way where it just isn't fun to do, either. I believe that most people of at least average intelligence can be taught almost anything, including math, given enough time and effort on their, and the instructor's part. When it comes to math, I did well enough to get through school, ranging between a B and C student in high school. When I went through college, I applied myself more and did better. I took a number of electronics courses which really were mathematics, GTA, calculus, and also a couple physics courses. I did reasonably well but I struggled with physics especially. I can understand the overall concepts, but there is a lot of attention to detail, and one can get lost in the process of it all.

 

I was one of those students that had trouble memorizing what formula to use in a given situation, or I would leave off a minus sign and it would mess up everything after, so thank goodness for partial credit! The ONLY thing that saved my ass with my physics courses was that I have an AWESOME teacher who had a very engaging personality, made things interesting, and actually tried to give us real-world problems where we could see practical applications. He even held study groups on his own personal off time, and I actually had fun learning kinematics and thermal dynamics (not that I could do any of that, now!).

 

To try to answer the original question, for many people, math is a very dry topic. I think teaching math, and holding a student's interest in math is an intrinsically up hill battle to begin with. When math, or any topic, isn't interesting, it becomes a chore, your eyes glaze over, and then you start to avoid it or tune it out. Also, it is often the case that math instructors, while often are very intelligent, suck at teaching because they don't have the personality for it, and just don't make math fun. Indeed, many math instructors can come off as boring as watching paint dry. Would you rather be taught math by a teacher with the personality of Ben Stein from Ferris Bueller's Day Off, or someone with a personality like Micheo Kaku?

 

In college, I also knew a couple math majors who went onto become high school math teachers that were just out and out arrogant and condescending, and just because they did well in math, they thought they were superior to others who didn't like or get math (not all that different from computer programmers/software developers...they are cut from the same cloth, really). That kind of personality is an instant turn off to a student, especially one who struggles with math, because it makes them feel stupid, and it frustrates them.

[Odine]

Totally agree. It's funny because some of the concepts of maths related subjects really interest me. Especially the bridge between philosophy (metaphysics) and maths. Quantum mechanics is super fascinating and I have no problem with the creative processes and creative leaps in thinking, but trying to back that up with nuts and bolts mathematics is impossible to me.

[Guest El Chalupacabra]

I am not an instructor, but I work in and around higher education. It does range from major, and is a case by case basis to be sure, but I think it is also a fair statement that some students don't put forth effort, and are used to instant gratification. The reasons can be debatable, but I don't want to get into that. However, I've seen cases where students just don't want to put time into their studies, and think that they complain their way to a better grade, either with the instructor, or the department chair. So, when they take a math course that requires more effort than they are used to, they end up getting the grade they earned. As a result, they find out the hard way, it really is just about the numbers.

[monkeygirl]

I have no real learning disability that I'm aware of and math has confounded me since I went to school. I don't even know what a radical IS.

My high school math teachers finally gave up and gave me a passing grade in it just so I could go on to college. In my first year of college,

my advisor was head of the math department and used me as an example in her class of how NOT to solve problems.

 

I don't know that I can say anything that can help you see things from their perspective or help them, though.

 

I'd like another go at learning math, knowing NOW that I have anxiety issues and learning how to control my reactions to that.

I know I'm not stupid and excelled in every other subject in school to the point they argued moving me up again so that I'd remain closer to

my age group-I was already bumped up one year early on and ended up in all AP classes in parochial school.

 

Math pisses me off-I know there's no way to rationalize, mitigate or use words or power of persuasion to arrive at the correct conclusion.

Worse yet for me, in all but basic math, the method one uses at which to arrive at the conclusion is important; many times I can come up

with the correct answer, but how I got there was haphazard (hence the 'example' in college).

 

Maths-to me-are a wibbly, wobbley ball of WHO THE **** CARES, WE NOW HAVE POCKET CALCULATORS.

[Tex]

I deal with numbers every day and I'm constantly surprised at how bad people are at math. Part of my job is producing financial reports that are so dumbed down that a monkey should be able to explain it to a client. But they can't . These people ask me the same basic math questions again, again, and then again. I just don't get it.

 

I'm of the belief that if you don't get math, you're not smart. You've either compensated by having people skills or you are reliant on someone/something else for income.

 

Math is logic, and if you don't get it you're probably not a logical person.

[Driver]

I'd argue with that.

 

SUPRISED!?

 

With all that is written about synthesesia I have no trouble believing that some people have a part of their brain that does not understand maths the same as others.

 

I've encountered the reverse of this when it comes to writing. In grad school the prospect of writing a 20 page paper within a week was not at all daunting or scary, while other people went into a full on panic over the prospect.

 

I don't think I'm stupid in the least-- but when people can't see the logical fallacy in saying Phantom Menace is a good movie, a movie that ignores all conventions of logical narrative structure and stroy-building, I'm pretty sure I think they are stupid too.

 

Point being-- when somebody can't see the simple logic of something I know like the back of my hand, I totally think they are morons. This holds true for politics too! There's times I wonder how conservatives manage to even get online, or operate things that use electricity.

[Odine]

Yeah, using one form of academia as a barometer for intelligence is totally flawed IMO.

 

It's like, some people think retrievers are smart dogs cause they know how to run and pick up your newspaper, or bring back a ball you throw. "How clever!". I'm more inclined to think the hound who won't bat an eyelid at a ball being thrown is the smarter animal. "Like, I'm not your dancing monkey. Pick your own ball and newspaper up". Hounds after all, were bread to sniff out the prey, flush it or kill it, and wait for the hunter to catch up. Not bring the goods back.

 

My point is your brain might be wired to excel in an area where others are weaker. Doesn't make anyone MORE or LESS intelligent. There are much more factors involved to gauge a persons smarts than their ability at mathematics.

[Pong Messiah]

Well, I'm still of the mind that if it were important/applicable/used regularly in day-to-day life (i.e. outside of a boring classroom lecture/activity) it wouldn't be so horrifying and alien to people.

 

I think aversion to mathematics creates a self-perpetuating cycle:

 

Math doesn't come easily to you and/or you don't see its worth

You don't force yourself to grind through it

You do poorly in a math course

 

Math doesn't come easily to you and/or you don't see its worth

You have another math course. Oh ****, last time was hella boring and it hurt my GPA

This one is even harder, because you're missing several foundational concepts

**** it, let's just do the minimum to pass and get through this Hell

You do poorly in math course

 

Math doesn't come easily to you and/or you don't see its worth

You have another math course. Jesus Christ, really? I suck at the maths. Gawwwwwwd!

You are borderline lost, because you're missing several foundational concepts

**** this ****. I'll bug the professor about my math inability until I find a way to get the minimum to pass through this Hell (but not buckle down and spend the necessary hours of catch up and study, ofc)

You do poorly in math course

 

Repeat and add +1 horror/intensity each time

 

I'm not saying everybody can get an A+ in their next calculus course, but I do think a HUGE part of people "sucking at math" is a matter of self-doubt from past bad experiences, then feeling utterly lost, due to lacking the basics.

 

Driver brings up writing, and I think there's a similar thing going on with people who say they "can't" write. No, the person who can't write will likely never be a novelist, but unless they have a genuine disability, they should be able to learn the basic mechanics and spit out a dry term paper before the deadline. Instead, they say they "can't write," and find ways of avoiding it, thus creating further stress, self doubt, and atrophy in their writing muscles.

[Tex]

My point is your brain might be wired to accel

Yeah.

 

Thing is you don't have to be smart to survive in this world. The whole thing is set up to allow people who have a strong personality to BS their way into wealth and prestige. All you have to do is be loud.

 

Just look at Donald Trump.

[Odine]

 

My point is your brain might be wired to accel

Yeah.

 

Thing is you don't have to be smart to survive in this world. The whole thing is set up to allow people who have a strong personality to BS their way into wealth and prestige. All you have to do is be loud.

 

Just look at Donald Trump.

I meant excel.

 

But yeah, I agree with you on that point.

 

And I agree with Pong largely too.

 

However, I still maintain that it has been my experience that mathematics and I are nemesis. No matter how hard I have tried, I have always struggled with it. And it is not for lack of intelligence. But until you experience a learning difficulty I guess it's hard to understand having one, or having difficulty with a particular subject.

[Tex]

Btw, what the fuck does writing have to do with anything? All writers do is plagiarize those that came before them because anything important has already been said.

[Pong Messiah]

Here is my new magnum opus. Never before seen!

 

7 * 8 = 56

 

Yeaaaaah!

[Driver]

Btw, what the **** does writing have to do with anything? All writers do is plagiarize those that came before them because anything important has already been said.

Whatever. Math was invented in greek times. Every math problem you do is plagiarism.

[The Kurgan]

I wonder if this doesn't have to do with a broader trend in society. I've noticed not so much that people struggle with math, but with basic language comprehension - written and verbal. I suppose such people would struggle with math since they appear to have a broader, more comprehensive problem with sensory processing in general. A certain percentage of the population simply cannot, or will not grasp the fact that 2 + 2 = 4, both literally or as a metaphor for understanding in general. And, as George Orwell once noted, allow a person to say (and understand) that 2 + 2 = 4, then all else will follow.

[DANA-kin Skywalker]

Math is basically logical reasoning, which is a skill. Learning is a skill. Some people are better at these skills than others. It's not supernatural. Professional athletes probably ask themselves why the average person can't throw a football like they can.

[Tex]

 

Btw, what the **** does writing have to do with anything? All writers do is plagiarize those that came before them because anything important has already been said.

 

Whatever. Math was invented in greek times. Every math problem you do is plagiarism.

Good lord. Read a book.

[Driver]

THAT'S ALL I DO IN MY FREE TIME THATS MY POINT

[Darth Ender]

I might be able to address why some students struggle with mathematics and why some do not. In developing mathematical fluency in children there are a few stages. The primary ones are concrete (touching an apple), representative (this picture is an apple), and abstract (this x is now the apple). Schools frequently rush children through these stages before they are developmentally ready. Because of this, students frequently are doing abstract equations, but do not understand why they are doing it. Most students can keep up to Algebra 2 or so of just memorizing equations, but quickly fall off after that. The use of manipulatives through the abstract and representative stages does well for both remediation and enrichment. Additionally, students that are involved in extended Piagetian programs also do well in advanced stages.

 

So yes, many students are exposed to the material, but due to how they were taught mathematics at an earlier age is likely to produce problems down the line.

[pavonis]

Wow, I'm pleased this topic is drawing some attention. I'm going to have to read it thoroughly again before responding further.

 

...my mind simply can't process numbers and arrange them in my brain like it's supposed to. I guess it's a bit like dyslexia in that way, only with numbers

Now, Pav you will no doubt find my strengths utterly useless in your mind but it's just how it is. Some brains ARE wired differently. I was never much of an academic, and maths has always been my Achilles heel. But anything creative and/or intuitive and I'm away.

There is an analogue of dyslexia with numbers - it's called dyscalculia.

 

I wouldn't say those strengths (English, history, art, etc) are useless. I'll admit to being a grammar snob - I correct the spelling and grammar of my students' lab reports as much as I nitpick their calculations, analyses, and conclusions. I took enough history courses to have had a minor (or one credit short) in history if I had desired one. I can appreciate art. I think educated humans need to be well-versed in humanities, the soft sciences (economics, psychology) as well as science and mathematics. Anyone not holding a basic understanding of the general fields of human knowledge shouldn't be considered educated.

 

Chalup, you raise good points about the approach to teaching math. I have tried to teach useful applications of mathematics, but that inevitably leads to word problems, and those scare students worse than the dry and boring mathematics problems! I have admitted to the students that they won't be solving problems in the exact manners that they are learning; I show them online resources like Google (which can plot functions and do most calculations) and Wolfram Alpha (which can do most of mathematics for free, and all of mathematics for a paid subscription) to help them learn the topics they're being exposed to. I also warn them not to treat these resources like magic boxes - garbage in, garbage out always applies, even with pocket calculators, MG.

 

Pong, your self-perpetuating cycle is dead-on. No one should move to the next level of mathematics without a complete mastery of the relevant topics. Calculus is predicated on a thorough understanding of algebra. Anyone who has trouble solving for x in an algebraic expression is not ready for calculus. Unfortunately, the people who teach algebra are passing students who either never were masters of the topic, or who let everything slide out of their brains once they think they're done with it ("Whew, I'll never need that again!"). Even topics that were only a year before are apparently not retained by these college students! I often wonder how they function at all when memories over a year old are apparently difficult for them to retain.

 

Regarding memorization - I have gotten many of my students to admit that they power through many of their classes with memorization. I tell them it won't work as a method for learning mathematics and physics. Memorization is the opposite of learning. I've probably offended more than one student by telling them I could train a parrot to memorize and recite equations, but that the parrot doesn't understand anything even though it sounds smart. I tell them to expect more of themselves than to just memorize stuff and regurgitate it on demand.

 

I appreciate the insights offered here. It's harder to ask the students these questions, as they don't often want to discuss these things or don't have the experience to articulate them. I do my best to excite them about mathematics and physics, and my evaluations tend to be strong. I just want to understand their point of view. I believe anyone can learn anything, given time, resources, and inclination to do so. For instance, I could learn to throw a perfect spiral again, if I practiced.

[Pong Messiah]

However, I still maintain that it has been my experience that mathematics and I are nemesis. No matter how hard I have tried, I have always struggled with it. And it is not for lack of intelligence. But until you experience a learning difficulty I guess it's hard to understand having one, or having difficulty with a particular subject.

But could you get a passing grade in a college mathematics course if your graduation depended on it? I bet you could, even though it would suck.

 

I recognize having difficulties and disabilities (already mentioned this in initial post), but I also think a lot of people confuse "difficulty" with "disability," either because they don't believe in themselves or because it's a "get-out-of-math-free" crutch.

 

And even if somebody has a disability, you still need (and can attain) a certain basic competency unless you are wiling to accept major impediments to your day-to-day life.

[Ms. Spam]

Math is logical thinking being taught at a young age. Don't look at it like solving equations but following a set of ideas to an end based on a "rule" of logic. Ender addressed pretty much some of the things I wanted to say but as to college kids not processing simple math like pavonis is talking about has a lot to do with upper level education, that is university and college, not being about further learning towards the betterment of yourself but about making money. I would say there are a lot of kids who attend college for the wrong reasons and do not belong in pavonis' classroom but for the sake of getting kids in debt for a higher education that will net them nothing but a piece of paper and living in their parents basement. In my school district we are measured based on how many kids go on to attend colleges or universities while I think it would be better to get them into trade schools where meaningful work can be had once they get their education. But pressure is on for parents and schools to get kids to attend university. You hear you can't get a good job without a degree from a University but I think that's not true. It's about marketing and upper level school is expensive on a certain level.

 

My ex sees this in his Art History classes he teaches at San Antonio Community College and Trinity. Trinity students can write a cohesive essay about the differences between Picasso and Matisse. My ex can say compare and contrast and the Trinity students get it. Those students will submit their papers with footnotes, annotations, pictures and present it in a Word document. When he teaches at San Antonio Community College the papers are often written on line paper and barely meet 500 words and make no sense. He also has to tell the students what compare and contrast means. SAC students are a facepalm. Trinity students can hold their own.

 

I know it's not math but my ex experiences the same frustrations in a way pavonis does. He wonders where I - a grammar school - teacher failed. I say we didn't for the most part we just construct a pandered school populace because we don't sort the kids out and realistically approach what they have ability to do. Parents want their kids to be successful but in reality the only one that is responsible for what they know is the student. I teach algebra and geometry in 4th and 5th grade and do lots of hands on and visual and work to push my students to learn more math and science at a younger age, but I can only provide the material and learning basis. If you want to go to college and be an engineer you do the work and prove yourself. I know. I'm doing my masters program and took a higher level math course and the math is a struggle for me because I haven't done calculus in quite a while. But I put effort in to reviewing before asking questions or going to my teacher.