The most politicallty incorrect,
innovative yet traditional,
rigorous, and effective math and reading
curricula on the market!
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Former public school teacher Charles Lewis was
ostracized for using methods proven to work, instead of
the "official" methods that had been proven not
to work.
...I finished that school year teaching my SAT Math
classes the best way I knew how, in spite of my administration's
exhortations to do otherwise. The next year in its welcoming
letter to parents, the school crowed about having received
an award as the city's most improved school on the SAT.
The letter mentioned that the most dramatic gains were
in math. The year in question, the school had had exactly
one teacher teaching its several Math SAT classes. That
teacher was not mentioned in that letter, nor was he ever
congratulated on his success; midway through the school
year in which the letter was mailed, in fact, he was fired. |
The "Math Troop Trilogy" (Sockcamp, Bootcamp,
and Deployment) was written over a period of many years by a
master math teacher who found that year after year
available textbooks got further away from addressing math comprehension
and competency needs of his students. The series has a history
of raising performance levels several grades in the initial
year.
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By insisting on absolute mastery of the deepest, subtlest
nuances of each succeeding concept (and by bolstering this
process with mountains of innovative association strategies)
- something which, at first, takes much longer than existing
courses that gloss over such niceties - we at mathandphonics.com
have found that our students develop an intuitive grasp
of math on a par with their instinctive understanding
of everyday mundane activities. Thus, in the long run, they
advance much faster than in conventional math courses and retain
much more of what they learn. |
Our "trilogy" combines unparalleled emphasis on the
fundamentals of math (especially arithmetic, which, tragically,
has been all but jettisoned from most American curricula, something
which, the "authorities" are
finally admitting has acted much to the detriment of American students)
with pervasive innovation that makes math natural
and automatic.
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Whereas typical contemporary courses offer "all-over-the-map" worksheets
with 10-15 or more disjointed concepts, most or all in word
problem format (another "mistake" the "authorities" are
now acknowledging - but, as with arithmetic, with no consequent
change in curricula), with perfunctory math content, at best:
- Our trilogy offers lessons which - in plain English,
with thorough verbal explanations before symbols
are presented - provide one basic concept, followed by
explorations of the consequent nuances, plus copious
examples,
- Then 20-50 or more math problems (none of them even distantly "spoon
fed") that probe ever deeper into these naunces, with
emphasis on the subtlest of them (which most books avoid),
which guarantee real comprehension of the given concepts,
- Word problems - meaningful ones, with meaningful math
content - presented, but only after the math concepts of
a given unit (example: fractions, with special emphasis
on mixed numbers) are thoroughly mastered, in all their
ramifications
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Arithmetic:
- American algebra teachers - for
more than a generation now - complain, not that their incoming
students don't know algebra (a ludicrous notion implicit is
current curricula), but that they have
no concept of arithmetic;
algebra teachers have to spend the vast majority of their time
teaching arithmetic, and thus can impart only a small fraction
of the algebra such a course should teach (leading to the shameful
advent of "algebra 1 part 1" and "algebra
1 part 2" courses)
- It is accurately estimated that only
about 10% of the arithmetic that used to be taught is presented
in most modern curricula. Without this arithmetic background,
it is impossible for students to understand or retain more
advanced coursework
- Before Mathandphonics.com
presents even the most basic algebra concepts (in Math
Deployment), assurance is guaranteed
that the student has mastered all the arithmetic possible
prior to algebra;
thus algebra involves only algebra, and comprises the most
rigorous algebra course on the market (more rigorous by
far than what passes for "algebra
2" or even "algebra 3" in the current anorexic
America math curriculum
- Topics that must be mastered range from
mutli-digit (and we do mean multi-digit) multiplication
and long division (with answers - including mixed number
answers - often required to be written out in words, to
prove comprehension) to all manner of operations and transformations
fractions and mixed fractions to decimals to per cents
to problems that combine the above to a treatment of signed
numbers that goes far beyond anything we've found that
even algebra 2 grads can handle ot powers and roots - up
to and including many-step, extremely diverse problems
involving conversion in and out of roots to and from negative
mixed fraction exponents (students exposed to our prerequisite
units can handle this!) to absolute value to average problems
up to and including ones involving mixed numbers and decimals
to ratios, proportions, a thorough exploration of scientific
notation to modular math, alternative bases, and yes, very
challenging word problems (and much more)
Sequence
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- Math is the one subject among all subjects where proper
sequence is absolutely imperative if the student is to
think for himself and understand and retain what he is
taught
- Such a treatment ingrains the appreciation that math
is true, that of all disciplines math is the one that
always means exactly what it says and can always be taken
literally
- Most current math curricula totally abandon this concept,
presenting pseudo-algebra, pseudo-geometry, pseudo-probability,
and pseudo statistics in the early elementary grades, long
before the requisite foundational skills and knowledge
have been introduced (if they ever are)
- This engenders the impression that math is arbitrary
or invented, that one must depend on authority (textbooks,
teachers, videos) for one "facts." Ultimately,
it undermines the student's confidence in the existence
of objective truth, an undermining that fits in quite nicely
with other elements of a post-modern curriculum.
- Sockcamp, Bootcamp, and Deployment, by contrast,
never present any new concept until all prerequisite
ones have been internalized. Thus it is always obvious
to the student that new concepts have to be true.
- We teach that math has to be automatic; that if it's
not, you're not getting it. It's all based on "mmm" (meaning,
meaning, meaning). Once the essentials have been established,
all we basically do is define new terms in terms of
familiar ones, and everything (with the requisite explication)
falls into place
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As for innovation,
we offer, among many other examples, the following:
Supply side
real world:
- Rather than teach 10% of the needed math, and retrofit
it into a spoon-fed, chaotic mix of "real world" word
problems, we do the reverse - taking everyday situations the
dynamics of which students have already long since internalized
and applying this intuition toward making the math as easy
as the tasks students already do instinctively
- We've found that most
students compartmentalize their math thinking, and don't apply
to math applicable and logically equivalent thought patterns
they already know intuitively and automatically apply to other
modes of thinking. We like to say that if students reasoned
out their daily activities the way they attempt to reason math,
they'd be tying their shoes together and putting their shirts
on inside out; the trilogy remedies this
- Because of this manner of presentation,
our system has a history of making students
- who have had success in other disciplines but who have had
a huge math phobia - just as proficient, if not more so, in
math as in their other
subjects
Analomonics
- Supply side real world works via constant anaolgy
to the "duh" real
world situations students "solve" regularly without
even having to think about them. We combine these anaolgies
with a system of carefully thought out mnemonic (word association)
references that help students call these analogies to mind
- Thus:
a combo of analogy and mnemonics: "analomonics"
No
rules, just mmm
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- Just for example, whereas no incoming student - even
with high grades in algebra 2 - has scored even 15 out
of 30 on our pre-algebra test on positive and negative
numbers (most have scored below 10 of 30), all of our pre-algebra
students have passed this test, including some perfect
30 for 30's. Other books present this topic via a bunch
of arbitrary rules that differ according to situation and
seem to tie just about all students in knots especially
when these situations are mixed on a test.
- The trilogy, by contrast, teaches positive and negatives
without a single rule; it just explains the meaning,
meaning, meaning ("mmm")
of the terms, and the "rules" write themselves. We
have never had any problems getting students to master
these concepts in this way. They are not trained seals,
but human beings perfectly capable of putting the pieces
of puzzles together, once they have mastered the prerequisites
and been armed with the meaning of what they're being asked
to do.
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SUPERPHONICS
Superphonics is
the flip side of our math troop trilogy strategy. Whereas the
latter decompartmentalizes math reasoning by approaching the
subject from a verbal perspective, the former applies the kind
of rigorous thinking generally relegated to math to the seemingly
hopelessly entangled, phonetic exception-laden American English
language. The result is amazingly accelerated
progress in reading.
 While Superphonics has numerous features and subsections (just
for example: a thorough treatment of punctuation, a common
bugaboo of young readers) to help students through various
pitfalls and dilemmas, our basic thrust is
to treat the whole English language as susceptible to phonetic
treatment. As unphonetic
as the language seems to be, there is never any need to "learn" a
word in isolation. Everything should, can, and must be analyzed
phonetically.
Surely, about half the words in a typical English sentence
violate basic phonics rules in one respect or another. But
even these words obey "sub-rules" or "sub-sub-rules," or
the like, and Superphonics facilitates greatly the learning
of these. Unlike with most phonics courses,
basic phonics is only a launching pad, a point of departure,
a necessary frame of reference for Superphonics.
For example, the simple words, "one" and "two" are
about as unphonetic - in terms of basic rules - as any two
words could possibly be. With Superphonics, a student who encounters
these words and finds them difficult is instructed first to read
them literally according to basic phonics (as in "own" and "twoe"),
to establish that frame of reference. Then he is directed to
easily find sections in the book with words that violate the
same rules in the same (or similar) ways.
In most cases, he will find quite a few such words. We find
that one to three visits to such lists "locks in" the
given new sub-rule. When the reader encounters the analogy
in later reading, the sub-rule tends to kick in automatically.
Unparalleled results:
Watch a just-turned-4-year-old sounding out the preamble to
the Constitution.
Watch see her lining up a 4-digit-minus-three-digit subtraction
problem (involving borrowing and other nuances) by herself
and getting the correct answer.
Here she writes out a 9-digit number in words, with perfect
spelling.
At age 5, she completes an 80-problem worksheet with just the
hardest addition, subtraction, multiplcation, and division "basic fact" problems
- all perfectly, and in three minutes, thirty seconds flat.
The average student taking a math course
from our sequence (including at charter schools - IDEA and World - where our
author, Charles Lewis, was math department chairman and principal)
has tested 4-5 grade levels higher at the
end of his first year than at the beginning. At these schools - where the books
have been used, along with other books in other classes - no
student using the trilogy has failed his end of course exam,
whereas no student using the conventional books has passed
these intentionally rigorous tests.
A student who had just turned 8 passed our
pre-algebra final with a score of 95%. We gave the same test
to a recent high school graduate who had finished pre-calculus
(generally 4 years more advanced than pre-algebra) with an A.
He scored only 36%. His parents signed him up that summer for our (Math
Bootcamp) pre-algebra course, knowing that (a) he knew very
little arithmetic, and that (b) knowing so little arithmetic,
he had understood and/or retained next to nothing from his
pre-calculus class, that A grade notwithstanding
We can provide testimonial after testimonial (including innumerable
home school reports) verfying the above and vouching for the
efficacy of Math Sockcamp, Math Bootcamp, Math Deployment,
and Superphonics. There is absolutely nothing like them on
the market.
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