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Union Teachers Sold On 'Saxon' Approach To Learnina Math
BY SUSAN USHER
Remember grade school math?
Chances are you learned math by
one of two approaches:
A: The traditional textbook ap
proach, in which a new math skill is
introduced in every chapter, in isola
tion. Students typically never see the
material again once the class moves
on. Either you "get" it or you don't
B: The applications approach, in
which students grapple with a prob
lem, and are then introduced to con
cepts that help solve it
But what aUkut C? Union Ele
mentary School teachers believe
they have found a way to teach math
that makes more sense than A or B
above, a method that works for more
students. It doesn't skip from topic
to topic, doesn't change language in
mid-stream, doesn't use application
or frustration as a starting point for
learning.
It does build on what students
have already learned and provides
plenty of opportunity for mastery
and recall. It emphasizes skills first
then abstract theory.
The approach is called incremen
tal development, in which a concept
introduced at one point keeps reap
pearing. and being practiced,
throughout the year.
Advocates call it "Saxon" math
after its renegade publisher, former
U.S. Army omcer and junior college
algebra instructor John Saxon of
Norman, Okla.
This year kindergarten and first
grade students at Union use Saxon;
next year third grade will too.
Union's performance-based ac
countability plan requests a waiver
to use state textbook funds to buy
the materials. The waiver is needed
because Saxon isn't on the state list
of approved math IWOWCM, even
though the approach is getting good
reviews iron far Keel teacners wno
use iL
Veteran Union first-grade teacher
Amy Watkins read about Saxon's
approach ic math is a profession*!
magazine, then followed up. "We
were so upset with the math we
were using." she recalled. "1 sent for
a sample of the materials and a list
of iCaCucis iniug ii iii Nuiih Caro
lina."
She got on the telephone and
came away convinced Saxon should
be tried. After eight months of use,
she's more certain than ever.
"In 18 years of teaching I've nev
er wen anything like it" she says.
"I'm impressed"
What's got her and other teachers
so enthused that teachers from other
county schools are coming to Union
to see what's goisg on? A complete
turnaround from the fragmented ap
proach found in most texts; a consis
tent scholar's vocabulary; a fresh
way of looking at math conceptual
ly, practical applications that rely on
everday situations such as counting
money, ratting time, forecasting the
weather and making a calendar; and
a heavy emphasis on reading skills,
uae of manipulative* such as blocks
and ruler*, and practical applica
tions.
Teachers don't need special train
ing to use the Saxon approach. The
packct comes with detailed instruc
tions on everything from how to set
up the eta?room to scripted Inma.
Watkins follows the scripts carefully
when introducing new material; she
wants to make sure nothing impor
tant is skipped.
With 130 lessons provided for a
180-day school year, the program
provides plenty of time for teachers
HH
to incorporate lessons on topics of
their own choosing, like calculators,
the one subject on the state first
grade math curriculum not covered
by Saxon.
Using Saxon, kindergarten stu
dents work frequently with cubes
and pattern blocks, two types of
"manipulatives." Lessons are at
tuned to a young child's short atten
tion span, shovt, moving quickly
from one activity to another.
At all grade levels, new material
is introduced in hits aivl niens inte
grated into what students are already
doing. Work sheets include prob
lems based on new information and
previous lessons.
Basic math concepts and vocabu
lary once considered out of first
graders' range are common. During
a recent visit to Watkius' class, stu
dents eagerly drew examples of
oolvgnns on ?hf board, carefully lev
ing off each line segment with a
ruler.
Corey FormyDuval has also used
his ruler to measure the height of his
bean plants. The first time he mea
sured, one plant was three inches
tall, the other six inches tall. When
he measured again, the tallest was
nine inches. He was impressed.
Before writing their name at the
top of a paper, students first draw a
line segment. But they don't just
draw a line, they draw a line of a
specific length ? 4 inches, 2 inches,
8 centimeters ? with endpoints. And
learn to adjust their signature to fit.
As part of their classwork during
one recent visit, watkins' students
were writing math sentences for
problems. To illustrate 6 + 4 = 10,
Heidi Bas wrote. There were 6 pigs
in a pen, 4 more came in."
Qock skills build on students' un
dCTw?ridifi? Of f aaCiiOii5, USiug !C> iiu
such as "half past 10"
The approach appears to encour
age students to reason, to begin see
ing relationships, asking questions
and drawing conclusions.
"Because of this math some of
my kids have thought about multi pi
rat ion who wouldn't have other
wise," Wstkins said. They begin to
see it when we work with 2 + 2 + 2
? 6 and you ask 'How many times 2
ts ft? Three times 2 is 6."
Watkins asks a special question
every day that requires students to
draw on tlieir growing logic and crit
ical thinking skills. One recent ex
ample: How could you divide a pack
of 8 sticks of gum with four friends
(plus yourself, of course)?
"Wc couldn't ask those kinds of
questions before because our stu
dents couldn't think that way," inter
jects Reading Recovery teacher
Nancy Wemyss, who formerly
taught a self-contained class.
"We have always done the calen
dar every day," said Phelps, who has
taught kindergarten students TA of
her nine years in education. "The
one thing we have noticed is that
now that we have added counting by
10's and the clock, they arc picking
up skills like telling time. You don't
have to teach a specific lesson; they
just pick up on it naturally."
"I've always used a lot of hands
on activities, but this program ties it
all together."
Like Watkins, she's impressed
with the incremental learning Kmilt
into every activity. When working
with the calendar kindergarten stu
dents are first cxnected to create
ABAB (like red/blue/red/blue) or
ABCABC (red/bliie/greea) se
quences with their pattern blocks,
she said, and "now they're being
asked to do A/B/B/C patterns. ''
Calendar time is also a standard
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M* IMM fciuwv, ? ?!? % VI IIM> IVlMrUUK
Place." With the Saxon approach the
period is used to subtly work on a
larger range of skills than in the
past.
This day it is Ryan Bennett's turn
to "teach" in Watkins' class. He
guides classmates through a routine
that includes reviewing the date, day
of the year, month, season, time of
day, day in the school term and the
remaining days of school.
Ifi a tap bcai iocy uuul aiuud,
"It's fun. it's fun. I can count bv 10
and I'll sun with 1. 10. 20, 30 j"
On "The Meeting Place" board
students track the weather for each
day of the week, creating a graph.
Studying the graph, the Student of
the Day gets to predict the next
day's weather.
In Mary Dawson's class, a shy
Melanie Evans takes classmates
through a similar routine. Today's
MMpc m s trapezoid, she uc*
fore leading the class in counting by
S's to ISO.
It's the 154th day of the school
year (only 26 days until summer va
cation, the kids point out).
Translated into money. Drew
Winters calculated, that would make
$1.54. He begins pulling out real
money ? a do!!ar bill phis two quar
ters and four pennies or five dimes
and four pennies.
The dass has only recently begun
working with quartets, but hasn't
forgotten dimes. "When we count
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DREW WINTERS converts the day in the school year (No. 154)
into cash, using real money.
with dimes, we count by 10's,"
Hau/cnn reminds the clsss.
Teachers haven't had any problem
adapting use of the Saxon-made ma
terials to their own anrviurh in In.
mm
son planning or instruction. During a
recent thematic unit built around
plants, instead of comparing blocks,
kindergarteners compared carrots as
they explored the concepts of
"longer" and "shorter," said Phelps.
"in kindergarten we've always
come up with our own things and
we do grade-level planning," said
Phelps. The teachers find that Saxon
covers more skills than the state cur
riculum for kindergarten and fits in
well with what they are trying to
teach.
According to one Teacher Maga
zine article, some of the educators
who object to Saxon view him as a
"drill and -practice fanatic" whose
app?u?ui conflicts with the Stan
dards of the National Council of
Teachers of Math ? the basis for
form.
Saxon's reply to people who
question the need for practice: "Ask
your favorite athletic coach for his
opinion on the necessity of practic
ing fundamental skills."
Supposes* of Saxon's use of
"gentle repetition" and frequent, cu
mulative assessment say they don't
see major differences in Saxon's and
the Council's objectives. They be
lieve differences between the two
are more a conflict of personalities
and egos. What they object to is the
fragmented way traditional textbook
publishers treat math.
They cite years of research that
indicate properly spaced review and
repetition may not only increase the
quantity of what is learned, but also
the quality. Learners are more likely
to recall conceptual principles. With
frequent testing of all material ? not
just that covered since the last test ?
researchers have noted higher levels
of achievement
At Union, both first-grade and
kindergarten teachers have seen en
couraging results using the material
with students of varying ability and
don't see any basis for the criticism
of Saxon's approach coming from
some math reformers. They've seen
entire classrooms of children
brought farther along in math than
when other approaches were used.
Several special services pre
schoolers placed in mainstream
Union kindergarten classes are do
ing the work with success, and first
graders who have been referred to
Special mVms irttf ifg ibc yrsr "*vr
tested higher than usual on their
math assessments.
Tt. _ M ?S. .-*?** *
? ik i^cuuuu nynjin
gives students who didn't quite
grasp a concept when it was intro
duced more than ooe rhannr for
mastery.
There is lots of built-in repetition
and rfinfhfrfiwni hut dri!!j
work; it's scattered. It's not boring,"
said Wanda Phelps, kindergarten
chairperson. They may not get it at
first, but they will because the wort
sheets provide more chances for
them and review for the kids who
got it the first time."
There are some children who
might not be getting it all, but they
are thinking higher than they would
have been," said Watkins.
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