Originally I had thought I was simply doing research and getting experience, in addition to generating a little bit of income flow, while I worked on the big project.
But now I find myself thinking that long after I finish writing Singapore Math Figured Out For Parents, I still want to keep tutoring math. It's simply one of the most rewarding activities I've ever found, I'm good at it, and I want to keep doing it. (I also want to keep writing and doing various other things, fans and friends; I promise not to become a mad tutoring-addicted hermit anytime soon).
So I began to figure out how to market myself as a math tutor, and a marketing campaign is like any other art form (and if your marketing people don't think marketing is an art form, fire them now. You really can't wait.) Something I learned to do in creativity classes which has served me in good stead for writing books and short stories, planning courses, designing for the stage, and yes, marketing campaigns, is to work up a longish personal statement about how I see the thing to be done, why I feel I am the one to do it, where the connections and the don't forgets and the traps and the opportunities are. Usually these stay in my desk, but as I looked at the now-almost-finished campaign plan, I thought that starting Personal Statement of Purpose was something I wouldn't mind having other people see. In fact, I thought it did a great job of explaining who I am and what I'm about, for this math tutoring gig.
So here it is, formatted for the blog, modified here and there. Sometimes it talks to parents of kids with math problems, sometimes to myself, sometimes to the sort of general social audience the blog has, and every now and then I guess just to the universe. It's a bit raw here and there, but crunchy, and some of you may find it tasty.
And if not, well, more math history soon. A couple think pieces about non math subjects, too.
All right, enough warnings, here we go:
The pitch as truthful as I can make it
Have you ever said anything like
this?
I know he's not lazy,
I know she's not dumb,
but my kid is having such a bad time with math...
I know he's not lazy,
I know she's not dumb,
but my kid is having such a bad time with math...
If you say that a lot, and you live
somewhere in the Denver metro area, I think I might be able to help.
About my approach to tutoring
- For kids with math problems that are neither lack of effort nor lack of intelligence, I identify the fundamental blocks to the kid's progress in math and teach them how to turn a wall into a bridge.
- In my experience, most math barriers are not cognitive and most kids struggling with math homework are not lazy; the problem is most often conceptual, a set of wrong, absent, or misleading ideas about math that a child acquired earlier. I offer a diagnosis that finds the conceptual problem, and exercises, experiences, and practice based on Singapore Math to correct the student's understanding, apply that better understanding to catching up with peers, and incorporate that correct view of mathematics into their approach permanently.
- My approach is family-centered; you will know the purpose of every exercise and assignment, how to help your kid master it, and how to extend what I teach to regular school homework and often to learning other subjects. Part of delivering the improvement in math skills is guiding the whole family to talking about math and homework more effectively (more smarts for less tears!)
- I think mathematics is one of the most powerful, profound, beautiful, and worthwhile achievements of our species and it is every kid's right to participate in it fully; I teach them how to claim their right.
For some of you, that might be
enough to pique your interest; if so, there's an email link over to the right.
Drop me a note, tell me about your kid, and let's see if I might be the person
you're looking for.
If you're still around but not sure
yet, here's more about what I believe, how I came into
this, and other things that might help you decide:
I want your kid for
the Math Path, and the Math Path for your kid
The Math Path is one of three
relationships to mathematics, or pathways through mathematics, that plays out
in ordinary Americans' lives. It's the good one of the three, and my aim is to
put as many kids on it as I can.
The kids who find the Math Path naturally
and on their own typically begin in the lower grades with math being a
"fun, easy subject." At some point after that they progress through
math as a "challenging, interesting" subject, and later on to
"this is hard, but I'll get it because I can and I want to," ending
up at "wow, that's actually kind of cool," (to quote one of my
tutoring students -- a third grader talking about commutativity and symmetry,
though he didn't know those words yet).
The Math Path is usually hard for part of the journey, and it is always
long, but though they may stumble and need to get up again, or get a little
ragged from fighting over the rough spots, eventually most of the Math Path
kids can travel as far as they want or need to. The difficulty is just part of
the trip; it doesn't throw them off forever, or destroy the pleasure they used
to take in the subject, or keep them from doing what they want to do.
For many people, the main reasons
for wanting their kid to be on the Math Path are security and money. Obviously,
kids who take the Math Path through their academic careers, and on into life,
can realistically consider claiming the STEM careers that the present and
foreseeable economy is so eager to offer to them.
But there are much more important
reasons to take the Math Path. If they do, their lives are more convenient,
better informed, and more comprehensible than those of their peers. The Math
Path is more convenient than the other
two pathways because they know and can use the correct math in everyday situations,
rather than guess at the answer and hope it works out. This is a power to
solve, quickly, easily, and accurately, rather than guess, and hope. Having
consulted for many small businesses and helped many friends with home projects,
I know how sadly common "guess and hope" is even though all the
information needed for the right answer
is right there. The kids on the Math
Path will have the proficiency and comfort for daily math, figuring out the
best strategy for buying gas; scaling recipes, drug dosages, and home repair
projects up or down; finding the length of a buried pipe without having to dig
it up; estimating the effect of a bad snowstorm, a supply price rise, or a
raised insurance premium on the business
they own or manage; deciding the balance between points, down, and minimum
payment on a mortgage or car loan.
The Math Path makes better-informed
citizens, who reliably recognize bogus numbers (or know how to find out if they
are bogus), whether it's crime statistics, pricing packages, health claims, or
thousands of other subjects we express in numbers. Math Path people confidently
grasp what differences in survival and complication rates for alternate
surgeries mean, whether the published statistics about a new government project
mean wise investment or screaming boondoggle, and how much of what kind of
benefits are likely to flow from a Social Security policy change. They're
harder to fool, which means harder to frighten or exploit.
Most of all, the ones who walk the
Math Path simply understand the world better. The patterns that organize the
real world are in mathematics; that so many people can't see them does not mean
they aren't there or relevant, only that they are unseen. The annual Darwin
Awards are full of people who could have saved themselves with five minutes of
arithmetic; people see supernatural mysteries and even the Hand of God in
situations explained by a simple equation that they can neither look up nor
interpret if they do find it; people repeat generations-old wrong explanations
that have more in common with associational or folk magic than with the science they could access in
five minutes if they knew a bit of algebra.
Also, the world needs your kid to
be on the Math Path
There's a grim parallel that
fascinates me, and maybe someday I'll get a book out of that as well: innumeracy
is what illiteracy would be like if it were ten times more common.
It's been thoroughly established
that the rate of functional illiteracy is much higher than anyone likes to
think about (and very hard to determinate because people are embarrassed).
Considerably more than 10% of adults can't fill out a simple form to apply for
a job, order a meal in an unfamiliar restaurant, follow written directions, vote,
take notes in a meeting, read an arresting officer's account and agree that it
does or doesn't represent what they saw accurately, and so forth.
But although there is far too much
functional illiteracy, functionally illiterate people are a smallish minority
in the adult population. Most adult functional illiterates have developed a set
of work-arounds and tricks for dealing with a literate world—copy and pasting
from the application a relative filled out for them, going only to restaurants
with pictures on the menu, finding a friend to ride with them and read signs
for them, and so on.
Now
consider functional innumerates. A functional innumerate is someone who can't
correctly figure out how much change he or she will get, reliably translate any
complicated numeric comparisons into what they're interested in (e.g. they
don't know offhand whether five for $6 or 3 for $4.50 is the better deal),
figure a tip or estimate sales tax, estimate how long it will take to drive a
distance they haven't driven before, double
a recipe, figure out how much a bond issue will raise his/her property tax, or
buy the right amount of bathroom tile or paint the first time. I would guess that the functional innumerate
population is several times the functional illiterate population; probably they
are distributed much further up the social scale (if the number of people who
proudly display "another day without needing algebra" on their
facebook walls is any indicator).
My
thought is that we're living in a world where con men and crooked politicians
expect to be able to use numbers to fool most of the people almost all of the
time; where people lose time, money, and every other precious resource because
they can't do the numbers; and where most of the scientific and technical news
for adults is dumbed down as if it were being reported to third graders. A world that has a massive innumeracy problem that we cannot easily recognize because innumeracy is so common.
In
the next generation, if we can put more kids on the Math Path, it will be a
brighter world for them, but it will be a far better world for all of us.
That's what's at stake.
The other two paths, from which I
hope to rescue them
I call the other two pathways Road
Closed and Refugee Trail from Eden:
•Road Closed is what
happens to those unlucky souls who just never get math at all. For them,
mathematics begins as an obscure ritual of no apparent point in kindergarten or
first grade, becomes more obscure every year, and eventually becomes something
to be faked if necessary and avoided if possible. If they are aware at all that
math could have opened doors to them, the Road Closed people experience it as something
like a magic spell they were never given. Some of them, of course, have severe
cognitive problems and genuinely can't do it; but I believe, based on what I've
seen as a tutor, and on the research coming out of East Asia, that many more of
the Road Closed population encountered a bad mis-match between teaching style
and learning style, or just weren't ready at the time the most basic ideas were
presented, or accidentally acquired bad copies of foundational ideas. These are
the severe cases; they can't do much of anything and they've given up.
•The Refugee Trail from Eden is the
busiest pathway of the three, and though it's a less severe problem, it is in
some ways sadder. These are the students for whom, when they are very young, math
is fun and interesting, and a source of confidence and success. But then one
day it's not, and it never becomes easy again. Rather, the kids go blithely
through the Garden of Easy Subject until they plow face-first into the Wall of I
Don't Get It, which their often seems not even to faze their peers on the Math
Path. wander haplessly in the wilderness for year or months, and finally end up
squatting down and muttering "But I used to be good at math," stuck by the side of the road.
What
I can do
Partly from a knack, partly from
dedicated study of Singapore Math (which I think is the best math instruction
method yet devised), partly because I've had my own struggles with math, I have
learned how to rescue kids from The Refugee Trail from Eden pretty reliably; it
takes months, but if kids will do some work, and the parents will support them
in it, there's a good chance of catching up with the peer group, with a secure
basis for continuing on at the peer group's pace, within a year or two. For the kids who are up against a genuine
Road Closed, there's a much longer diagnostic process, but I've had a number of
breakthroughs and seen some kids move from stuck to "just behind." Based
on that experience, I'm inclined strongly to think that true dyscalculia
(neurological/brain defects that make it impossible to do math) is probably
rare; much more often I see kids with basic conceptual problems, which can be
found (eventually) and addressed (with a certain amount of hard work).
My experience with Adult
Disadvantaged Learners (or ADLs, as we call them in the business) bears this
out. Using Singapore Math concepts, I can usually probe until I identify where
and when they hit the wall (even if the wall was in first grade), and gradually
build or rebuild their pathway around/through the place where they ran into
trouble, and about as soon as the fundamental wrong concept is fixed, they
start to make reasonably rapid progress. The big lesson is that although I
can't do much for people with severe cognitive problems, or unmodifiable laziness,
the great majority of people with math problems are neither.
Furthermore, with both child tutees
and ADLs, the experience of discovering that a conceptual error was at the root
of their problem seems to lead to not only a new confidence, but to a much
better approach to learning math; they stop focusing on remember what to write
in the format, and begin to seek genuine understanding. This puts them in much
better shape when the inevitable next rough spot hits. Conceptual correction, using the Singapore
Math methods, seems to make for much more resilient math students at any age.
Fixing the concepts and pointing the student in the right direction generally
seems to equip students to travel the Math Path on their own.
And fundamentally, I just hate the
idea of people walking around half dead and never hearing the music of the
spheres. Somehow my deep faith that math is beautiful and rightfully theirs
seems to be contagious over time.
It seems to me like we have a thousand times
saner view of music, art, sports, and so many other subjects than we do of
mathematics: sure, not everyone can play in MLB, dig Mahler, or live for the
next gallery opening, but we don't usually use that as a reason to deplore
church softball league players, One Direction fans, or Sunday afternoon
museum-walkers. Even if you're not going to go very far in math, as a human
being, you ought to have a chance to understand some of it mathematically and
to see what it's about. There is beauty and harmony even in the humble addition
table; even the student who can go no farther deserves to see that.
Who I hope to serve with this new
venture
The people who will need, want, and
buy my services are worried about their kids' being shut off from math, and not
just about his/her math grades. Especially, they are also worried about the
kid's emotional reaction to it; they are afraid their son or daughter may give
up, losing all the good things on the Math Path before s/he can understand what
that means for the rest of his/her life. They feel (accurately) that their kid
could be doing so much better, that the Math Path is one they should have the
chance to walk because it would reward them, not just financially but in terms
of life chances, yet somehow the kid seems to be slipping off the path before
even getting a fair start.
Working with ADLs I've seen how
deep and longlasting the traps can be.
I'm fascinated by how much and how well society is able to get along
without math that would make people's lives easier; astonishing numbers of
people would rather fail, or be cheated, or make a mess of their jobs, or miss
uncountable (by them) opportunities, rather than face the terror of
mathematics.
What I can bring to the aid of a
math student is a really clear model of the mathematical mind, how it works ,and
how it grows; a knack for questioning and observation that uncovers what the
kid is thinking instead of the math we want him to be able to think about; and
the knowledge and ability to use the rich and powerful Singapore Math toolbox
to help the wandering kid find the real path.
I've been along the Refugee Trail From Eden myself
I had to learn how to learn
mathematics very late. Oddly, I mostly
learned it from economists and political scientists. I flamed out of engineering school because I couldn't
do the math quickly and accurately. There were many other reasons, some of them
worthy ones, but the thing that tipped the balance was that math had stopped
making sense about a year and a half before.
So I changed my major to economics,
because a student with math abilities that are barely adequate in physics,
chemistry, or engineering will send economics professors into rapturous awe. I'm
not exaggerating; those guys gave out extra credit just for using calculus to
solve a problem marginal rates, which, in math terms, are plain old
differentials .
Looking back, I had ability -- my
SAT math score was 770 and a few years later my GRE math aptitude put me in the
95th percentile. It wasn't that I
couldn't do math. I just didn't learn how to learn math soon enough or know the
math well enough before I needed it, and that shut me out of the science I had loved
since childhood.
So, in my early twenties, having
discovered I still had ability but wasn't at all good at using it, I started
graduate school in political science in a very mathematically oriented
department, and resolved to just buckle down and learn the math I needed, no
matter how grim that might be in practice. Several surprisingly kind and
patient teachers (I was not what you'd call an ideal, or even a pleasant,
student) pushed me fairly hard in the right directions, and this time I was
ready for it.
The main thing they did for me was
to push me back to fundamentals -- in some cases fundamentals going back to
junior high school (middle school, for younger generations). Over and over, the rules and memorized
algorithms that had always been how I "learned" "math"
turned out to be idea-proof skins stretched over the real depths of what the
math actually meant. I had been going through my mathematical life cooking
numbers by recipes, like a robot; it was not till I was 23 or 24 that I began
to really hear the music, start to grasp the reality, or have any kind of
intuition or feel.
Life took me elsewhere than where I
thought I was going, but after I returned firmly to the Math Path, I kept
finding my way back to math-intensive fields, in the software industry, in
academic research, and half a dozen other ways.
There's still damage. I can still
feel the lacks and gaps induced by a background that was a mixture of
too-narrow-and-algorithmic applications and too broad-and-handwavy theory with
some huge outright holes, but still, math has been an enrichment and ultimately
a joy in my life, and my main regret is that I didn't learn more of it. (On the
other hand, I have a couple of decades left, and I still learn a few new things
every year).
So, my relationship to math is a
bit like that of St. Augustine or C.S. Lewis to Christianity: I started off
apparently well into it, lost it, and fought my way back in with far more effort than
I'd really have preferred. And like
those two preachers, I'd like to smooth the road for as many people after me as
I can. It can be a very rough road, but the rewards at the end of it are
immense: those better jobs are the very least and smallest part, compared to
the better understanding of the world around us, and that too fades compared to
the sheer beauty of the order that underlies everything. I wouldn't say that
math is my religion (I have one that I'm quite happy with) but if I ever need a
spare one, math would do just fine as a connection to the beauty, awe, order,
and reason that underlies reality.
Who I want to help, and what I want
to help them to
I'm trying to find kids whose lives
would be enriched and opened up by mathematics, who are unable to access the
math that can take them up into the perception, understanding, and beauty. And
after a rather surprising amount of experience, considering I didn't start out
to get it, I've been forced to realize I have a knack for guiding the lost
people out of the dark traps of confusion and up into the light of
comprehension.
It's a worthwhile job, and I like
it. Every kid I can break out of the
disappointing, frustrating trap that claimed a large part of my life is another
claim that I have done something worthwhile with my life.
Unfortunately, kids don't have much
money and would be curiously reluctant to spend it on math if they did.
Luckily, many of them have parents who do have money, want them to have full
access to the power of math, and notice when that isn't happening.
A mixed blessing in the whole stew
is that I'm fairly good at explaining the benefits and goals of developing real
math ability (as opposed to purely coaching math-test-passing skills). This
means not getting quite as many clients as I would like, since there are
commercial tutoring services out there that offer moneyback guarantees of
percentage increases or absolute scores. To be able to guarantee it, they sometimes
meet those goals by teaching math, but if necessary they'll concentrate on
test-taking skills, drilling short answers, and various other substitutes for
math. What I offer to do, and I'm blunt about this with parents, is to get
their kids through the present block, equip them to knock down future blocks
themselves, and most of all learn math, because math is a profoundly important
human activity in which every child has a right to participate. If you just
want twenty more points on a test score so you can brag about who's taking your
tuition checks, we probably won't work out. If you want your kid to know math,
and maybe have a chance to love it, get in touch.
Some of the situations that have
brought my successful tutees and students to me
This isn't so much a checklist of
symptoms or warning signs; it is a list of what parents (whose children went on
to succeed) experienced in the weeks or months before they brought a kid in for
me. If any of these seem to be true for
you, you might want to think about it.
- Kid identified as twice exceptional
- Teachers saying they don't know what to try next and nothing's working
- Kid has stopped doing math homework and won't try, or makes an attempt for show and then shuts down in tears of frustration
- Kid has been drilled heavily but can't remember math facts in a usable way; on homework or in class, if the kid is presented with exactly the same problem a few minutes apart, s/he does not recognize it and has to solve it all over again.
- Kid seems to start all problems at very basic level (counting on fingers, reciting rules out loud, etc.) and does not seem to be moving away from this.
- Kid applies rules arbitrarily (cross multiplies fractions regardless of the problem, chooses numbers apparently at random out of a story problem and does some simple operation on them).
- Executive function problems -- kid can do one step but can't break a problem into pieces and do the pieces in the correct order.
- Kid has and follows some inexplicable wrong rules all his/her own (for example, I dealt with one boy who had separate rules for adding and multiplying digits that formed closed loops -- that is, he had one set of rules for 1, 2,3, 5, 7 and another set for 6, 8, 9; and which way he tried to add or multiply 4 depended on whether it was written with an open or closed top).
- Kid appears to think that you or his teacher could just decide that his/her answers were correct, but you won't because you're mean.
If any of that sounds like you and
your kid, maybe I can help. I'm
confident that if it's a matter of finding a way over, around, or through the
conceptual barriers, there's almost always a tool in the Singapore Math
toolbox, and after my months of working with it, I know where those tools
are and how to use them. Those might be all the benefits you need, and certainly they are the ones I'm most comfortable claiming.
Other benefits might also flow from this, though they can't be guaranteed for all
cases. I generally give parents at least a quick oral summary at the end of
every session, and make sure you're well-equipped to help your kid with
homework (at the elementary school level; if your kid is having trouble in
calculus I won't make you learn it yourself!) Parents have reported that this
has made math coaching into much more pleasant family time, and much less of a
battle. Moreover, once your kid really knows what s/he does understand, and what s/he doesn't, anxiety tends to
decrease because the kid stops feeling like s/he has to fake it, and because in
their self-image, "I don't know it yet" replaces "I'm so
dumb." It has happened, now and
then, that math goes from terror and anxiety to a favorite subject, but of
course that's very individual and I can't promise it to everyone.
Finally, its about helping your
kids claim their human birthright to experience math as a bridge, not a
barrier. Just like reading and writing,
becoming good at math gives your kid a pathway, that Math Path again, to real
independence, whether it's academically (being able to pursue a subject for
love rather than because it's easy), perceptively (having the tools to see how
a snowflake, a sine wave, or a star are
the way they are), or economically.
Oh, yes, of course. No matter how
much I downplay it, a parent can hardly be unaware that math is the gateway to
science, and science is one gateway to medicine, engineering, and great jobs.
Almost a close:
So, if you've got a problem like
what I'm talking about, and you want your kid to walk the Math Path, drop me a
note at the email that appears in the menu to the right. Give me a way to
contact you and I'll be back to you ASAP.
