Phil Mahler wrote:
>
> A colleague recently asked a group of math educators about using
> materials in a student's native language instead of in English. For
> example, using a text in Spanish for students for whom that is their
> first language. This in reaction to some non-native speakers of
> English who have a hard time with word problems in English.
>
> Does anyone out there have any experience with this, and therefore
> perhaps recommendations?
>
> Phil Mahler
> Middlesex CC
> Bedford, MA
Members of the list
please be apparaised that this will likely be a long post. Forewarned
is etc. :>)>
Phil,
FWIW, The community in which I'm living and teaching is a Yup'ik Eskimo
village on the banks of the Kuskokwim river in Western Alaska. The
Kuskokwim Yupiit (pl of Yup'ik-trans. "real people") are the only
indigenous people of Alaska whose language, according to the University
of Alaska Language Center research), is not endangered. In other words,
there are currently a large number of Yup'ik children who are first
language speakers of Yup'ik. Nonetheless, for a number of reasons, (the
introduction of television about 20 years ago and the corresponding
proliferation of videotapes and satellite dishes coupled with the
culturally traditional less verbal than western standards parenting
practices etc.), the percentage of first language Yup'ik speakers
entering kindergarten has dropped from 100% to about 50% over the
fifteen years I have lived and taught in this community. To respond to
this decline in the viability of Yup'ik in the communities served by the
Lower Kuskokwim School District, most schools, including ours, have
implemented a Yup'ik immersion program in which 90+ % of all curricular
instruction in grades K-2 is in Yup'ik. 50% of all curriculum in 3d
grade is in Yup'ik. Gradually, the current bilingual plan of service
for the district is to extend the Yup'ik immersion program through grade
6 and perhaps beyond.
Apologies for the length of the background info. As a parent of
bicultural children enrolled in the school, I take a couple of
perspectives regarding the teaching of mathematics in Yup'ik, regardless
of the childrens' first language. First notation-none. traditionally,
Yup'ik is a spoken not written language (although an orthography has
been established). Place value-counting system based on hands, feet and
numbers of peoples hands and feet. Arithmetic operators-difficult to
determine as a non-speaker. I can make a pretty strong case for
addition. Subtraction possibly. Multiplication, probably not, the
closest I can determine may be with the concept of four persons of
numeration is equivalent to 4*20=80. from what I am able to observe and
learn through questioning (a culturally inappropriate learning behavior
btw), no further extension of the concept of multiplication developed.
Division-Geometric combination with qualitative, quantitative, need,
status. A complex algorithm beside which the western concept of
division as an inverse operation of multiplication pales. Time-highly
fluid concept. Based seasonally which includes time of flowering,
fruiting, migration, molting, reproductive schedules, dates of freeze
and thaw, solar position etc, etc, etc. Quantity- starvation, hungry,
enough, full, some left over. (an over simplification, just one
example. apply to all survival needs). Linguistic simplicity of
numeration-To an outsider, very demanding. In order to say the number
93 requires the formation of as many as fifteen syllables. Logic-Yup'ik
does not include a term of negation. Nonetheless, I find that with
respect to task accomplishment, the people in this community are
predominantly linear thinkers. Still scratching my head over this one.
I wonder whether the teaching of early arithmetic concepts in Yup'ik is
an example of trying to turn a moose into a bear. I question what the
goals of the instruction are meant to be and whether the goals are
compatible. The district's mission and goals include what appear to be,
as a matter of pragmatism, diametrically opposed. On the one hand, we
have the goal of enrolling 80% of our graduating seniors in college as
freshmen performing successfully without remediation. On the other
hand, we are to prepare our students to live a traditional lifestyle
based on the local cultural heritage. I do not argue that there is no
traditional mathematics. To the contrary, I belive that there exists a
very high level of mathematical sophistication in the traditional
teaching. However, the approach the district has taken regarding math
instruction in Yup'ik is to translate english texts (Saxon) into
Yup'ik. The rationale for this is that "research shows" that children
who learn concepts in their first language are better prepared to make
the transition to their second language. I question whether this is
true for the teaching of mathematics. Much of the arcane language of
mathematics has been appropriated from the language in which the
concepts were originated or developed. Translating such concepts of
multiplication, division etc. through the invention of new vocabulary to
describe the concepts seems at best cumbersome, and at worst inaccurate
and confusing.
In short, it is very apparent that conceptual development requires
radical improvement locally. The vast majority of my high school
students do not readily conceptualize any operations beyond addition and
subtraction. Last year was the first year that 1st through 3d grade
math was taught in Yup'ik. It will take many years to assess the
relative effectiveness of this approach. My gut reaction is that unless
the pressure to churn out college graduates diminishes and that math
instruction in Yup'ik continues throughout k-12 with a corresponding
radical overhaul of scope and sequence which is more relevant to the
local cultural traditions and teachings, that the result will be greater
confusion rather than enlightenment.
I realize that the situation which I have described is likely remote
from the teaching of mathematics in Spanish, for which there is a strong
western tie which includes renowned contributors to the study of
mathematics. The questions you raised are precisely the issues with
which I am daily confronted in my teaching
Richard Kern
Napaskiak, Alaska
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************