Wasn't Once Enough?

I am not a math person. Let me be clear.

Mental math makes me nervous. In high school, algebra made me sulk. I survived pre-calculus 15 years ago largely because college was in sight. To me, college was defined as a leafy oasis where no one is required to use formulas.

I eventually became an education reporter, a nice job where I could continue forgetting about systems and functions. But lately, a lot of my writing has centered around -- guess what? -- math.

Algebra has been creeping into middle schools and elementary schools at an alarming rate. And advanced algebra is required increasingly for all students, not just the nerdy ones. A national testing obsession is causing everyone to pay closer attention to pesky math scores. And chief executives and politicians are trying to drum up workers for a changing technology-based economy that they maintain is built upon an invisible mountain of equations.


Michael Alison Chandler, right, with Arzoo Hassan during algebra class at Fairfax High School. (By Dayna Smith -- For The Washington Post)


Bottom line: Math is in. (Again.)

But has anyone told the teenagers? Changing policy is one thing. But countering the stubborn “math stinks!” refrain heard in so many classrooms is going to be much tougher.



And parents? Do they know? Are they ready to pitch in with an encouraging "You'll appreciate this later" or an explanation wihen their daughters or sons are stuck on Question 11 late Tuesday night?

What is algebra anyway? If we are going to agree that it’s important, let’s agree on what it is and get a better idea of what people actually do with those x’s and y’s after school.

Finally, is algebra any different than it was 15 years ago? Sure, schools have traded in crumbling chalk and yellowing overheads for higher-tech toys. But is there a new way to teach the subject that will get students to head for the nearest engineering program?

Given all the fuss, I figured I should probably give math another go myself.

With some difficulty, and a little tutoring from some top math department officials in Fairfax County schools, I managed to place into an Algebra II class at Fairfax High School. (Social promotion may have played a role in this, given that I would have tanked a standardized Algebra I test. But a Washington Post reporter in a class increasingly populated by seventh graders? That would be embarrassing!)

Now I report to school every other day at 7:20 a.m. There, for 80 minutes each session, I join 27 other Fairfax Rebels in a windowless room, under the laminated gaze of Albert Einstein. Together, in somnolent camaraderie, we practice solving linear equations and graphing inequalities and take turns at the Smartboard. These days, I carry a three-ring binder full of graph paper in my canvas work bag, along with a TI-84 graphing calculator, a handful of mechanical pencils, and a purple, rubber eraser that smells like grapes. I am 32 years old.

I have homework to complain about and studying to procrastinate, and last Saturday, I spent the better part of an afternoon holed up in a D.C. public library finishing a take-home test. I am not yet exactly sure what I am going to do with this algebra (or why I am doing this). This blog is part of my attempt to figure that out.

x=why? is a place where I aim to bridge the cultural divide between math people and the rest of us, to make the abstractions of algebra a little more lifelike. Visitors will find scenes from math classrooms, profiles of people who use math at work, research about math education, debates about how best to teach math, and--why not?-- an occasional pop quiz, for which I invite you to submit your best, or your worst, word problems.

I welcome math experts and math novices, math teachers and math students, math lovers and math loathers, to chime in with ideas and experiences about why so many Americans struggle with math, and how that can change.


By Michael Alison Chandler  |  September 30, 2008; 6:00 AM ET  | Category:  Class Time
Next: Room A-142

Comments



Math class at 7:20 am? You've got to be kidding. Fairfax County Public Schools have, for years, ignored parents' please to begin the school day at a reasonable hour for learning. Other school systems in our area (Falls Church City, Loudoun County) have adopted start times as late as 9am for high-schoolers, to the relief of sleep-deprived students and their equally sleep-deprived family members who must push them out the door to bus stops at 6am or earlier, in pitch black darkness, on empty stomachs (who can eat at 5:45am?). Coincidentally, schools that switched to later start times experienced an immediate uptick in students' GPA, including Math. Why does Fairfax County perpetuate a schedule that clearly disadvantages its own students, year after year?

Posted by: acampbell1 | September 30, 2008 7:16 AM | Report abuse

To say that "Other school systems in our area (Falls Church City, Loudoun County) have adopted start times as late as 9am for high-schoolers" is an incorrect statement. You make it sound as though LCPS recently made this change and that is not the case. As a former farm area the county is on this school schedule because the need for the kids to help out on the farm before going to school.

Posted by: blue78 | September 30, 2008 8:36 AM | Report abuse

Michael, math is challenging and the reason is because I believe it doesn't directly relate to something we can apply it to. If teachers can show how this knowledge will apply and where we will use it, I believe math (algebra specifically) will become more appealing to the students. I am starting to mentor/tutor students in DC so I will be brushing up on my math skills. I am also in the process of networking with as many people possible who would be interested in making an impact in the lives of students in DC. Would you be open for a conversation about that?

Posted by: inspired2b | September 30, 2008 8:37 AM | Report abuse

What bothers me is not that the students are taught algebra at younger and younger ages or the time that class begins (Though this can be a problem). I feel that my failure at learning algebra can be attributed to the Graphing Calculator that Ms. Chandler mentions fleetingly. These devices become a crutch for students who don't have the time to learn the math.

When I arrived to college, 5 years after Algebra 1 in the 8th grade, I knew how to use a calculator but not how to do math. At UMBC, where I now go to school, the calculator's are left outside of the classroom door, much to the chagrin of many students. With no calculators in the classroom, students are forced to LEARN the algebra or calculous, not to input them into a calculator. Math education in secondary school must be reevaluated and returned to the basics. The calculator should stay out of the classroom.

Posted by: tal1 | September 30, 2008 9:42 AM | Report abuse

I'll admit to being a "math person". I always like math in school. I majored in math in college. Even the decades ago that I was in public school, I took algebra in junior high. It really wasn't a big deal.

What I've found disappointing in all of that time is the way our society condones and encourages the notion that math is just too hard for some people and that it's ok to not have a basic, minimal understanding of concepts like solving for an unknown variable. I have coworkers who can't figure out how to compute percentages and rather than learn will just ask me to do it because I'm the "math person."

I think that it must be incredibly difficult to convince young people that subjects like algebra are important when the adults in their lives are so blasé about their own ignorance.

Posted by: gnatselbow | September 30, 2008 9:47 AM | Report abuse

I am very interested in the impressions you will have of your algebra study. As a former grad student in a math department I have taught math to undergraduates and now have an 8 year old daughter that says she hates math and questions its utility. My sense is that math differs from other subjects (particularly in middle and high school) in a number of ways.

1) It builds sequentially so difficulty in understanding an earlier concept will arise again and again in studying later ideas. This can reinforce frustration so that progression becomes nearly impossible.

2) It is hard to be rewarded for partial understanding -- one either 'gets it' or feels varying degrees of discomfort about not fully understanding.

3) Traditionally, problems are presented with increasing difficulty essentially asking one to think a little harder or beyond the initial idea. Again this puts students in an uncomfortable situation for those who do not enjoy resolving puzzling problems (the vast majority)

4) I've come to believe a certain analytic approach to problems is indispensable -- and that not everyone may be aware of or interested in it. As an example, when stumped I often ask myself the seemingly stupid questions: What is it, exactly, I don't understand? What, exactly, is being asked? What do I know? etc... Breaking down a problem into manageable components is a necessary but not universal skill in problem solving.

5) Ego becomes involved when one gets stuck -- one thinks 'am I stupid?'. The discomfort associated with this can really impede learning and lead to distraction, procrastination, and unproductive effort.

6) Not all minds work alike (duh!). Yesterday, I asked my wife how she remembers 8x7 = 56. She told me she imagines 8 and 7 dancing and together they make 56. Further, as numbers go, 4s are not very smart and 8s are surprisingly intolerant. I have no idea how she perceives and works with numbers but she is a respected consultant in her field.

Not all of these points are specific to math but they seem to come up more often for this subject. I look forward to reading more about your back-to-school experience.

Posted by: fedbert | September 30, 2008 9:49 AM | Report abuse

First off, let me say that I think fedbert has some extremely good insight.

But in addition to that: I believe the central problem is HOW math is taught. Fedbert is right that "problems are presented with increasing difficulty essentially asking one to think a little harder or beyond the initial idea." Particularly when you are being given a bunch of ugly variables, "thinking a little harder" about something like limits given a messy trig identity function becomes a gargantuan task.

The central issue is that like it or not, some people are naturally good at math, and some are not. Those who are good at it tend to pursue it (and teach it). To them, however, the "logic" behind the problems is so crystal clear that they honestly do not understand that non-math-people do not see the math problems in the same crystal clear way - we are not wired the same way. Yet instead of "coming down" to the level of non-math-people, they simply stomp their foot and declare that non-math-people need to work harder and are just being lazy.

We are all just wired differently. Until the establishment starts to realize that and design courses that cater to the majority of us who are NOT math-people, the frustration on both sides is going to continue to mount. As a non-math-person, I have excelled in college-level coursework that has been taught by people willing to tone it down a notch (or 10) and work with us as much as needed so we understand the concepts - and I haven't done so well with the majority of the stomp-your-foot variety, which sadly is the majority of teachers.

Posted by: Pantoufle | September 30, 2008 11:04 AM | Report abuse

To those for whom math seems irrelevant -
1) Probably everyone is bombarded with ads (especially in DC) touting studies that show such-and-such percentage of experts believe in x. Do you know when you are being taken for a ride?
2) There are many offers out there for installment loans, saying the monthly payment is x dollars over y months. Can you calculate the interest rate and determine whether this is really a good deal? The wrong answer can cost you a lot.

Posted by: JeffRandom | September 30, 2008 11:35 AM | Report abuse

I don't know about algebra but your parents need to retake high school English. Your name is spelled like a man's.

Posted by: carrierj1@yahoo.com | September 30, 2008 11:56 AM | Report abuse

Our education system already caters to Pantoufle's request to lower math courses'levels to the non-math interested. Our current financial crisis is one example of the results. Math skill reflects one's ability to think logically. Unless math training begins at an early age, brain circuits to perform additions and subtractions, let alone interest costs, will not be present at a later age. We need to raise the bar for students of all ages so they can survive in adulthood.

Posted by: michaelcise | September 30, 2008 12:28 PM | Report abuse

One ingenious tool I found for teaching the "boring" subjects so they are more interesting is something called Thinkwell Lectures at this website right here:

http://www.thinkwell.com/marketing/demos/

Posted by: James_H1 | September 30, 2008 1:15 PM | Report abuse

carrierj1:

Michael is a girl's name. Not an uncommon one, but one nonetheless. As I'm sure Ms. Chandler will tell you (and has been telling people most of her life). As would some of my female family members. Stale joke for those of us girls with "male" names (not Michael for me, but generally "male").

As for this blog:

Much like tal1, I found the throw-away comment about having the graphing calculator telling. I'm not that many years older than Ms. Chandler, but when I went to FCPS, these were contraband items, at least in a class level as low as Algebra II. Because this was the time when you were supposed to be learning how to make the graphs yourself, not understand how to input them into the calculator.

At higher levels (like Calculus, which I actually took at TJHSST, the math-geek nirvana), they were allowed to a certain extent, but not all the time (and certainly not during quizzes and exams). So I, too, see these as something of barrier to learning the basics. Much like learning to tie your shoelaces before progressing to velcro on your shoes, or having a digital watch without first learning how to read a traditional analog version.

What I'm most curious to see from this blog, though, is how teachers motivate students, and make them understand that math does have a place in your daily life.

For example, if the kids like Mythbusters, has anyone pointed out that the guys constantly use math in the show for their scale experiments and general construction? Sometimes with calculators and computers, granted, but it's there and a part of the day to day life of having a cool job like Mythbusting and doing movie special effects.

Or on a more simple level, if they want to do things like build web sites or learn how to create video games, basic math skills are a basic part of your skill set. Because you need to understand the parameters of your screen "canvas", and how to calculate how much of that space you can use down to the last pixel. If your average viewer has a screen resolution width of 1042 pixels, you have to understand how to build a virtual world that fits inside that. Or how to build a world that scales up and down to fit screens of different sizes.

If you give kids fun and practical examples of *why*, then it's the sugar that makes the medicine go down. Word problems and prepping for SOL tests simply aren't as motivating as showing them that math is important to their career goal.

Posted by: Chasmosaur1 | September 30, 2008 1:23 PM | Report abuse

I've read the post and its many responses with great interest. I am a math professor at a university and I've had the privilege of graduating high school in India and college (and beyond) in the US. I would humbly make a few observations gathered from 14 years of teaching at various levels.

(i) I like the college mathematics education system in the US (of course I have my complaints, but who doesn't). However, the biggest problem is not, in my opinion, calculators or teaching philosophy or that "math is hard" (it is), but the singular lack of preparation in high school. Most of my students (and I've taught math in several universities in different states) come in with little or no understanding of fractions, equations or even the notion of "size".

(ii) The school system in India was mind numbing but it did do one thing well: we had to work very hard with endless homeworks and drills on the basic notions. The alternative was failing the class which meant being left behind and therefore not graduating high school. Which in India (back in the eighties) meant that you were aiming to live under a bridge. It seems callous but teachers were much tougher and while I think they could be more helpful, it did put things in perspective.

(iii) 9 out of 10 students tell me that there was little or no expectation from their math teachers in high school, i.e., very little homework and virtually no chance they would be held back for not working. Let me add that I really don't mean to put down high school teachers (my sister is one herself) and I have great respect for the tough job they do; I think the problem is cultural where we (in the US) do not allow kids to fail until they reach college.

I'm not certain what is the correct remedy, but one could start in middle school or high school with more homework and less tolerance for failure. I am very interested in math education so I am more than happy to listen to alternative ideas.

Posted by: shankar2 | September 30, 2008 1:26 PM | Report abuse

Fedbert, very well said!!! To accompany your observations, I ask the parents/guardians of the KIDS that ask "what does it have to do with real life?" , what happened to the answer "Do it because you are directed to do it!" I (and my parents) made the children drill the basics as they were taught, do their homework, I checked their homework, and if needed, WE corrected it! (a whiteboard became invaluable!!) If this doesn't start at the outset (2nd or 3rd grade), that student is going to have a rough hill to climb! BTW, My children and I handled HS and College level math classes with no issues! :)

Posted by: TC12 | September 30, 2008 1:28 PM | Report abuse

First, as fedbert mentions, math education generally builds on the foundation established in previous years. This is problematic when so many elementary school teachers do not like math themselves, or do not have a strong foundation in it, but are expected and relied upon to teach important concepts like fractions.

Second, I find it fascinating (and a bit infuriating) that many people ask why they need to know math, but other subjects do not get the same scrutiny. One could just as well ask why students need to read Shakespeare. Math ultimately can explain so much of the world around you, from how a driver instinctively times the deceleration to a stoplight, to the workings of the stoplight itself. You don't *need* to know that information to get by in the world. Math, and the idea of learning for the pure sake of gaining knowledge, needs a better PR rep.

Posted by: skh619 | September 30, 2008 2:11 PM | Report abuse

I often wonder where our country went wrong in educating our kids in mathematics. At some point, educators decided more "creative" methods were necessary to communicate math topics. Yet these very educators learned themselves using more traditional methods like working lots of problems and spending time in deep thought about these concepts.

I don't think the human mind has changed over the years. I think the same methods will work today that worked 200 years ago.

The following is what I think has changed...There are more distractions than there used to be. With internet, video games, sports, tv, movies, there's so much for kids to do that homework gets pushed further down the list. This stuff was available when we were kids, but not to the convenience it is today, and it was new to our parents and they wouldn't allow it to occupy our lives. Homework still came first.

Also, educators see technology as a way to get through to the kids. I see it as a shortcut to more traditional learning tools. To some extent, visualization tools can be helpful in geometry and calculus. But they should be used sparingly. There's no substitution for deep though and problem solving.

I will end with an observation. I notice educators get tied down with what they think kids "need" to learn. Just because you may use a computer in your job doesn't mean we have to sacrifice fundamentals to have kids using them in school regularly. If we educate our kids properly, they will be able to learn on their own how things work and figure out what's important for their lives. Teach our kids to learn. Don't hand it to them on a platter.

Posted by: HOKIE1525 | September 30, 2008 2:46 PM | Report abuse

I agree with skh619's comments:

*************
I find it fascinating (and a bit
infuriating) that many people ask why they need to know math, but other subjects do not get the same scrutiny. One could just as well ask why students need to read Shakespeare.
************

Why is math (and math alone) so often singled out as "good/necessary because it's useful"? It's like we've defined "math" as the cod liver oil of the high school curriculum: "Take it because it's good for you" we tell students over and over, but saying that does NOT make the subject any more palatible. And all the while we ignore the true nature and beauty of one of the oldest (and once most respected) of the original liberal arts.

The best essay I've *ever* read about what is wrong with both how and what we teach in high school mathematics is "A Mathematician’s Lament" by Paul Lockhart (available on the MAA web site at: http://www.maa.org/devlin/LockhartsLament.pdf )

Robin

Posted by: robinsuesanders | September 30, 2008 2:57 PM | Report abuse

There have been several (negative) comments about the use of calculators.

I've been teaching college level mathematics for almost 30 years including my graduate teaching assistant days at UIUC. Yes, some students rely too much on calculators, but it is way too simplistic to blame studens' lack of mathematical competence on their use of graphing calculators. A calculator should be treated as a tool---much the same way that slide rules were tools back in the 50's and 60's.

A much bigger problem in my opinion is that students come to my caculus classes *expecting* and *wanting* all the problems to be solved in less than a minute or two using a special Four Step process:

1) Identify the specific type of problem and find a worked example.

2) Copy the relevant formula from the example-preferably without the need to think whether it's really relevant.

3) Change the numbers in the formula to those in the problem and compute with as little thinking as possible until the answer magically appears.

4) Compare to the answer in the back of the book and celebrate (if it looks like your answer) or sink into "I guess I'm just not a math person" self-pity(if the book's answer is different than yours.)

What's missing on the students' part?

Plain old fashioned curiosity and a desire to do some original thinking about problems that don't look exactly like the worked examples in the text come to mind.

Robin

Posted by: robinsuesanders | September 30, 2008 3:01 PM | Report abuse

I went through high school with nothing but C's, D's and F's in every math class I ever took. I went to college, took Math 101, got a D in it, and never took another math class - which is just fine for an English degree. (And I consider it a major source of joy that I will never have to take another math class as long as I am alive on this Earth.)

Despite all the problem solving involved in math classes, the one question I never got the answer to is 'why?'. For example, why does the denominator go on the bottom? Or, why do you have to change the sign when you subtract negative and positive integers? Without being able to answer why, math problems were just a set of arbitrary steps, and it was impossible to use intuition to figure out the next step.

Today I am doing just fine in my career field of choice. I feel that the time I spent working so hard on learning, and failing, math could probably have been used more wisely. More classes on things like how to deal with a tough boss would have gone a lot further than Algebra I for me. I guess math has a place in the curriculum. However I think it's a mistake to give it so much weight in your school career, because it's definitely possible to be successful and happy in life if you bomb math.

Posted by: john65001 | September 30, 2008 3:26 PM | Report abuse

What do you mean, math is challenging? It's easy as pi. I discovered math at the age of four; my Mom says I was playing with toy bricks and discovered that one and one made two and that two and two made four. By the time I started first grade, I could do long division.
When I was in my senior year of high school, I had just returned to school after surgery and was in my home room when another guy told me to get down to the cafeteria right away for the math contest. So I did, and I placed first in the state of Connecticut!
Math is an exact science. You can't argue about mathematical formulae, the way you can about history or politics. When I get bored, I work out math problems in my head. I love math!

Posted by: dergans76 | September 30, 2008 3:28 PM | Report abuse

Regarding comment on slide rule vs calculators: A slide rule is a tool that, when a student learns how to operate it, that student has a more intimate knowledge of the number system. That's because in order to operate a slide rule properly, you have to understand decimals and fractions.

A calculator is different. Students learning to punch numbers into a calculator don't have to learn much more than the numbers and the operations. Then they fall into the trap of relying on the calculator.

Keep in mind that no business is going to hire someone to punch numbers into a calculator. You get hired to solve problems. And educators may decide you need to learn how to use tools because you will need them in your business, but the problem is most businesses have their own tools. Since graduating college, I have been exposed to no less than 30 different pieces of engineering software that I have needed at one time or other. I rely only on my fundamental mathematics and problem solving education to figure out how they work. Nothing I learned about calculators or computers in high school have been helpful to me here.

Posted by: HOKIE1525 | September 30, 2008 3:28 PM | Report abuse

john65001 writes:

********************
Despite all the problem solving involved in math classes, the one question I never got the answer to is 'why?'. For example, why does the denominator go on the bottom? Or, why do you have to change the sign when you subtract negative and positive integers? Without being able to answer why, math problems were just a set of arbitrary steps, and it was impossible to use intuition to figure out the next step.
*******************

This is, I believe, the heart of the issue. In all your classes, the "why" was never addressed. It's no wonder that you never saw math as logical and intuitive. And I'm willing to bet that you also did not see "math" and "thinking" as being connected in any significant way.

If you'd been encouraged to ask your "why" questions and gotten some thoughtful answers (as opposed to "learn the formula" explanations), would that have made the time in a mathematics classroom less painful?

If you'd been encouraged to *play* with mathematical ideas rather than simply being taught to solve problems by doing "a set of arbitrary steps" would that have made mathematics more interesting?

Robin


Posted by: robinsuesanders | September 30, 2008 3:51 PM | Report abuse

Interesting idea looking forward to the reports.

As far as the argument for not using algebra and higher math on a daily basis I could say the same about history, science, and almost any other subject area.

Most white collar professionals sit around writing reports staring at spreadsheets or messing with powerpoint most of the day. Most of the skills needed for that aren't even taught in schools.

Posted by: novamiddleman | September 30, 2008 3:55 PM | Report abuse

If you want to embarrass a high school student, ask him/her how many inches are in a foot, or in a yard. If you want to get real mean, ask them at what temperature water boils on either scale.
Remember, five out of six adult folks in the U. S. can not calculate the perimeter and area of a simple rectangle.
PS: "Rectangle" is not a naughty word.

Posted by: jhurley1 | September 30, 2008 3:59 PM | Report abuse

"Algebra has been creeping into middle schools and elementary schools at an alarming rate."

You phrase it like algebra is some kind of disease or plague. Algebra is the very basic language of math and science. If you can't understand algebra, then you effectively close yourself off from understanding how our increasingly high-tech world works. It applies to everything in the world, and not even so-called "hard sciences." If you don't understand algebra, then you'll find it impossible to really understand engineering, weather, economics, commerce, psychology, biology, etc.

We drill children on arithmetic at an early age when we should be introducing algebraic concepts along with the arithmetic concepts and showing how they relate. Unfortunately our educational establishment emphasizes "how to teach" much more than it does mastery of individual subjects such as mathematics. We have many educators teaching math who have a shaky understanding of what algebra is and who share Michael's aversion to math. Is it any wonder that our children later struggle with basic mathematical concepts?

Posted by: granite78 | September 30, 2008 4:18 PM | Report abuse

"Algebra has been creeping into middle schools and elementary schools at an alarming rate."

You phrase it like algebra is some kind of disease or plague. Algebra is the very basic language of math and science. If you can't understand algebra, then you effectively close yourself off from understanding how our increasingly high-tech world works. It applies to everything in the world, and not even so-called "hard sciences." If you don't understand algebra, then you'll find it impossible to really understand engineering, weather, economics, commerce, psychology, biology, etc.

We drill children on arithmetic at an early age when we should be introducing algebraic concepts along with the arithmetic concepts and showing how they relate. Unfortunately our educational establishment emphasizes "how to teach" much more than it does mastery of individual subjects such as mathematics. We have many educators teaching math who have a shaky understanding of what algebra is and who share Michael's aversion to math. Is it any wonder that our children later struggle with basic mathematical concepts?

Posted by: granite78 | September 30, 2008 4:23 PM | Report abuse

May of your questions were answered in John Allen Paulos' books "Innumeracy" and "A Mathematician reads the Newspaper". He explains how pre-college math is poorly taught and uninteresting and gives pretty easy suggestions for fixing it.

Posted by: bdc9977 | September 30, 2008 4:27 PM | Report abuse

I am impressed with many fine comments among these postings. I could only echo some but will add a few in addition to those about calculators, the assumption that everything is useful, etc.

For one, even if there is a use for a certain concept, it is unlikely that an algebra student will understand it. And to a mathematician, a theorem that leads to proving another theorem might be seen as useful. I am not sure this is what kids mean by applications. But the saddest part of the question is they have no imagination. I suggest instead that the teachers respond to such a question but telling the students to look up an application for any topic (surprisingly, this can be done on the internet). It will have two effects. They will find out that most of these things ARE used in something and eventually they will quit asking and get back to just learning.

I also agree that while people may be more or less inclined to any discipline, there are very few people who cannot learn math. Let me change the subject. Many people will the same about a language. After graduating from high school, college, and getting two master’s degrees, I have never learned a foreign language. But I do not pretend I could not learn one. I admit that I did not work hard enough to do so. Nobody is at fault but me. I have no doubt that if you dumped me in another country where nobody spoke English, I would learn their language. I dare say that is true for all students who are told they cannot learn a language. Most of our ancestors came to this country and did just fine learning a language. I do not think math is any different. There is nothing taught at the high school level that an average person (and even a below average person) can not learn. Will it be easier for some than others? Of course. So is driving a car which I find far more complex, but even people diagnosed with learning disabilities get drivers’ licenses.

Back in an earlier post, someone mentioned the sequential nature (interestingly, the same is true for languages). This can be a problem. Some subjects depend a lot on memory. But math does not. If a young person succeeds in a memory course, it is natural to attempt that same technique for everything. We spend much time speaking about the individual students learning style, but do we tell these same students that each discipline also has its own learning style? It is obvious by my age, but I am not at all sure it is obvious to a youngster. I have found math has very little memory involved with it. We have the stereotypical absent minded math professor for a reason. One can do math just because it makes sense without having to have too good of a memory (although I have met mathematicians with phenomenal memories). So the student who sits down to read his or her math book the same was as a novel is in for a shock. You work your way through it.

In an English class, one might have to write an original paper and so the student might be punished for taking something directly from a book. But nobody is ever accused of plagiarism in math. Go see if you can find this problem or a similar one. Nobody will ever even dream that a high school kid is doing original math. Nor will anyone require you to footnote the fact that you solved an equation using the quadratic formula. It will be obvious and the teacher will not think you are claiming that you were the first to think of it.

The professor from India had a good point. Am I the only one to have noticed that people come from all over the world to study at our graduate schools but that our high schools (and elementary schools) fall way below those of other countries. And if we do notice, why do we not ask what the differences are and how we could learn from those professors who teach grad students? What is different? One thing is the freedom of the professors to enhance the course with his or her research. Two college courses with the same title will be quite different and reflect the background of the professor. They may both be English 543 or Affine Geometry and you will learn the very basics of these fields, but there is a world of difference between one professor and another. Unfortunately the schools want conformity. In some big cities they want such lockstep compliance to a course description that they even dictate what examples to teach. This is not teaching. This is work for robots.

I was blessed with teachers who thought for themselves. They adapted on the spot to our needs independent of what might be in a lesson plan. But most importantly, they let us do things our way. I have heard horror stories of people learning math in such a manner that everything had to be done the teacher’s way. We were encouraged to do things in our head (for which I am still most grateful). When learning arithmetic, if we came up with another way and it worked, we were congratulated, not told to conform. To this day, I still add columns of numbers by looking for pairs that add up to 10 rather than just go up or down in order. I see children have less freedom in this today. But even worse, when all the teachers must teach the course the same way, we end up with the least common denominator. The teacher who can do much more and enrich the class and open the students to alternative processes and (heaven forbid) challenge them more finds that he or she cannot do this because another teacher lacks these skills and all must be on the same page. Of course that other teacher may also have unique skills that will be lost because nobody else has them.

Why? Partly because the schools (both public and private) kowtow to the parents either through political influence in the former or financial pressure in the latter. Instead of doing what is best for students, we do what the parents think is best for the student and I believe the parent is too close. I know my mother was not objective when she viewed me. And this is good. A child needs to experience unconditional love. But just as they should not referee their children’s games, I do not think they should try to be the arbitrator of the kid’s education.

For example, someone has written about the time the students spend at homework. Now, I believe that extracurricular activities are good for young folks. However, it is carried too far. There are teens who play for their school team, a travelling team in the same sport, and maybe an AAU team too boot. Independent of the toll that this takes on the body [the NHL and most HS leagues do not allow games on three consecutive days and yet kids In these various leagues, sometimes play three in one DAY!], when does the child have time to do homework. Math requires leisure to just think and contemplate what is happening (as do other courses). Now when I say the parents cannot be trusted to make the best choice for their children, I need only point out that one needs parental approval to play on each of these teams. Physical or sexual abuse are not the only forms of cruelty to ones children. Will anyone take a stand on these? I doubt it. People really think that their little darling has a chance of becoming a professional athlete. But if you look at the numbers of people who do make it compared to the numbers who play the game, there is but one conclusion – learn your algebra!

Posted by: TomfromNJ1 | September 30, 2008 4:36 PM | Report abuse

Seeing as I am one of the "kids today" that we keep discussing, I figured I'd throw in my two cents. I'm a 16-year-old junior at Blair (I'm not in the math-science-comp. sci magnet, but I did take algebra in 7th grade and have always done well in math, even if it's never been my favorite subject).

A few points:
I agree with that there is an over-reliance on calculators. I'm embarrassed to admit this, but without my calculator I'd be completely lost. The basics of math were not drilled into my head the way they probably should have been when I was younger, and now that I have a calculator to do the work for me, there's no immediate need for me to learn them (yes, it would be beneficial, but I simply don't have the time to do things not absolutely required of me, especially in math). My friends who are in the magnet often were quizzed outside of school and had math forced upon them at a very young age by their parents. Their parents enforced the "math is good" mantra that many of our parents who themselves struggled with math never really embraced.

Another thing that could be contributing to a lack of math skills is students' study habits. I'll be the first to admit that cramming is my study style of choice. Where that may work in the short term, concepts don't get plugged into my long term memory, which is a problem in math where concepts are built upon previously taught concepts (as opposed to in English, where you are tested on one book and then move on the next one).

Finally, there's the point that many of us won't use math in our daily lives. Someone pointed out that few of us use Shakespeare, yet schools are really adamant about students studying his work (even if the students are always enthusiastic. But that's a different topic...) But knowing Shakespeare is (almost) a cultural requirement. Math is not. Which is kind of the problem.

Posted by: maddyr | September 30, 2008 5:14 PM | Report abuse

Thanks for the great topic and many fine posts. I've wondered about this for a long, long time - wondering why so many struggle with math and others fly through it, at times with ease. Several years ago I even wrote Keith Devlin at Stanford (and an NPR contributor), to ask my questions: could math instruction be structured differently? and are we not understanding how the mind perceives these things? I've always thought the missing link in all of math instruction is an overarching demonstration of what math is all about. For those of who understand things in "big pictures", math is hopeless. We are taught the little pieces and it's hoped someday we will 'get it', that is we will cross over into a land of understanding. Which leads to my second questions: is math and music perceived understood by our minds in similar ways? I recall learning to read music (uggh, piano lessons)- staffs, cleffs, measures, rests, half notes and quarter notes, etc. while my best friend picked up his new saxaphone and began playing. Like those who learn to read music and those "gifted" souls who intuitively know "how to play music, even jazz without knowing how to read music", is there some fundamental difference in our minds that allows some to have an 'intuitive understanding' - can they 'see something' those of us more literal don't 'see'. If this is valid, could this distinction be explored in order to find keys that would help those of us who struggle with the small bits and pieces to know the joy of understanding the larger picture. Of course, I'm told by some of those those who can play music intuitively that they would really like to know 'how to read music'. Interesting.

Posted by: ljines1 | September 30, 2008 5:44 PM | Report abuse

Hi Michael Alison. I must say that I really admire what you are doing – putting yourself in the trenches of a high school classroom to understand it from a student’s perspective. In my 40+ years as an educator, I have always advocated for beginning to teach math concepts at an early age so children can begin to build the mathematical foundation needed for middle or high school algebra. I think a big struggle is that, as adults, many of us are afraid of and dislike math, and our children pick up on that. Every time we say things like, “I hated math in school,” we are giving our kids permission to do the same. Instead, we need to be proactive by promoting math and showing them how often we use it in our daily lives.

For the rest of my thoughts, here is a link to my blog entry: http://www.drrickblog.com/post/2008/09/24/Preparing-Students-for-Algebra-Early.aspx.

- Dr. Rick

Posted by: DrRick08 | September 30, 2008 5:54 PM | Report abuse

When you're getting to the "profiles of people who use math at work," don't forget the fun! Now that 97% of American youth play videogames (according to the Pew Internet & American Life Project), a lot of kids are interested in this subject. It turns out that making games requires a substantial amount math -- and not just for the programmers. Game artists need to understand a bit about 3D math, and designers need to work with formulas for game mechanics. Definitely check it out.

Posted by: Malkyne | September 30, 2008 5:57 PM | Report abuse

Febert is "spot on". I lived it as a young man and still have significant math phobia. In fact I noticed this trend in my 5th grade daughter and have spent thousands of dollars at Huntington Learning Ctr to address her deficiency. She just got a B+ a year later and has grown tremendously in confidence! You cannot delink emotions and intellectual abilities.

I salute Michael for retaking math on...go Girl!

Posted by: allensford | February 12, 2009 5:29 PM | Report abuse

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