CCHs Online Catalog: Grammar Stage Math - Grades 1-6
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Copyright © 1997-2001
Option 1: Rays Arithmetic
Option 2: Math-U-See Arithmetic
Option 3: Professor Bs Mathematics
Option 4: Saxon Math
For 1st-6th, 7th, or 8th grades. Rays Arithmetic were the
texts used in 19th century America, before its jettison of the classical tradition in
education and the dumbing down of our schools. Over 120 million copies were sold in its
heyday. Rays teaches arithmetic in its logical progressive order of concrete -
mental - symbolic arithmetic, just as Harveys taught grammar in its logical
progressive order of letters (orthography) - words (etymology) - sentences (syntax). Most
early work is done with real objects--blocks, marbles, buttons, etc. Later the work shifts
to mental arithmetic with mental images of concrete objects. Then it proceeds to symbolic
arithmetic, gradually dropping the use of objects and images and proceeding to computation
quickly with digits. In this way the child is led carefully through the three progressive
stages in arithmetic: concrete (manipulative), mental, and symbolic. The Rays
Arithmetic Set includes all seven books listed below, plus the Parent-Teacher Guide for
Rays Arithmetic by Dr. Ruth Beechick. Again, the suggested grade levels are
just that--suggestions only. Once the material in each text is mastered, the child is
ready to go on to the next text. Children do not have to be held back to conform to
suggested grade level guidelines.
Test Examples in Arithmetic
Key to Primary, Intellectual, and Practical
Key to Higher Arithmetic
Parent-Teacher Guide for Rays Arithmetic
Rays Arithmetic Workbooks
The Math-U-See program utilizes systematic review over an extended period
of time, and manipulatives, to establish the link between seeing math and understanding
math in children. The program provides the interlocking, colorful blocks and fraction
overlays to teach math, along with the curriculum to provide the systematic practice and
reinforcement of concepts. The goal of Math-U-See instruction is not only to teach a
student how to do math, but to also simultaneously understand the concepts of math.
Because of its design, this program also provides teaching and practice in the grammatical
work of translation from one type of mathematical representation to another; i.e., 2
blocks and 7 blocks makes 9 blocks, and 2 + 7 = 9. One final note: the suggested grade
levels are just that--suggestions only. Once the material in each course is mastered, the
child is ready to go on to the next course. Children do not have to be held back to
conform to suggested grade level guidelines.
Professor Bs Mathematics
For beginning or remedial arithmetic students and up. Professor B
(Everard Barrett) takes the subject material of arithmetic, which in modern public and
private education is traditionally spread over seven to eight years of expensive
textbook/workbook materials and instruction, and presents that material in three texts,
three workbooks, and a charts book. The concepts are presented contextually, as a
developmental flow, like a continuing story. These developmental steps are like the rungs
of a ladder; mastery at previous rungs provides readiness for the next connection.
Arithmetic can be effectively taught as an upward, progressive climbing of the
ladder without gaps, rather than as a spiral review (the incremental approach).
Professor Bs texts, Mathematics Power Learning for Children, restructure the
traditionally disconnected, fragmented content of arithmetic and inform parents how to
consistently tell the truth simply in all the operations on the whole numbers,
fractions, and decimals, from basic to advanced levels of skill. This truth-telling
approach to arithmetic stimulates and activates a childs natural capacities for
mastery of mathematics, reduces mental tension related to math, teaches math as a
contextual story that makes sense, enables rapid and thorough understanding, eliminates
remediation and sole rote learning, and allows sustained mastery of skills.
Texts have 150 to 160 pages each, and are non-consumable; they can be used
for each child in the family as often as needed. The consumable workbooks contain the
students practice exercises, and each child should have their own workbook. The
workbooks have 131 to 144 pages each. The charts book -- a single non-consumable book
containing all the charts needed for the concepts introduced in Book One -- contains
detailed instructions for speed practice; counting to one hundred and beyond; doubling
numbers mentally; acquiring strong skills in column addition; and maintaining mastery of
the multiplication facts.
There are three levels in Professor B Mathematics. Your child may go on to
the next level when he has satisfactorially completed each level, regardless of grade.
Professor B Mathematics has been designed to allow children to proceed at their own pace,
whether slow or fast, it matters not. Level One includes the non-consumable text,
Mathematics Power Learning for Children Book One, the consumable Workbook Level One (one
per child), and the non-consumable Chart Book. Level Two includes the non-consumable text,
Mathematics for Power Learning for Children Book Two, and the consumable Workbook Level
Two (one per child). Level Three includes the non-consumable text, Mathematics for Power
Learning for Children Book Three, and the consumable Workbook Level Three (one per child).
Professor B has produced videos which correspond to each of the three levels. These videos
do not contain material that is left out of the texts, but they were produced to help
math-phobic parents learn to teach math to their children. They are not necessary, but
helpful for those that would like the security of a little extra hand-holding. When a
child has completed all three levels he may go on to Algebra, but if he is still in the
grammar stage, CCH recommends going on to Rays Higher
Arithmetic to learn business math, powers and roots, and all other higher arithmetic
practice, or Math-U-Sees
Advanced Mathematics (which does not include the business math), before beginning
Professor Bs is excellent for those children who have struggled with
traditional mathematics instruction (90% of the students in America), or are transferring
to homeschooling from public or private school, and are either behind in math, or have
been taught the wacky and confusing new-new math or some other such experimental and
damaging program, or who have already developed a failure mentality or phobia
about math. There is no such thing as a student who cant do math, just
as there is no such thing as a student who cannot read or write. There are just students
who have been poorly taught. The best instructional program in any subject is the one that
illuminates the subject and makes it clear for every human being. Professor Bs
Mathematics is such a program. I have found that it is also an excellent program for those
students in the dialectic stage who have done Saxon Math all through their career, who can
do arithmetical computations but who do not understand the *concepts* of arithmetic, which
in turn is keeping them from understanding algebraic concepts. It is not traditionally
structured and there are no grade levels, so an older grammar stage or even dialectic or
rhetoric stage child can begin in Level One (or Two, if math facts have been solidly
mastered) and work his way through the entire program in a summer, if he so desires,
before going on to Algebra. A parent who is terrified of the prospect of teaching her
children math because it was not her strong suit in school can go through the program
herself and finally learn arithmetic without the frustration. Professor Bs
Mathematics may not be for everybody, and it certainly is not a traditional grade 1-6
series, but as a remedial course or for those who have delayed mathematics instruction
until phonics, reading, and handwriting has been firmly established (and that is not a bad
idea, and something I would do if I could begin all over again with my children), it is an
excellent, excellent choice.
Saxon Math: An Incremental
For 3rd-6th grades. The Saxon philosophy of instruction is based
on the concept of incremental development: the introduction of topics in easily
understandable pieces (increments), permitting the assimilation of one facet of a concept
before the next facet is introduced. Both facets are then practiced together until another
is introduced. The incrementalization of topics is combined with continual review, wherein
all previously learned material is reviewed in every lesson for the entire year. Topics
are never dropped but are instead increased in complexity and practiced every day,
providing the time required for concepts to become totally familiar. Familiarization of
topics and skills with constant review allows students to internalize and automate
arithmetic operations, the goal of the grammar stage. A further benefit is that the books
are non-consumable texts: the child does his math by copying the problems out of the book
and solving them on notebook paper. The obvious advantage for families with more than one
child is clear - the materials need only be purchased once.
My personal opinion of pre-algebra is that it is a waste of a year of math instruction. Arithmetic is the proper preparation for algebra, and every algebra program worth its salt contains the instruction included in pre-algebra texts. If a 7th grader is not ready for algebra, he needs remedial arithmetic instruction, and not pre-algebra. Please see Professor Bs Mathematics for remedial arithmetic instruction.
Because of the style of presenting the material, through drill and review using concrete rather than analytical presentation methods, CCH does not recommended continuing the Saxon program into the dialectic stage, for Algebra and Geometry, unless the student is taking Algebra with Escondido Tutorial Service.
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