My Math Counts for so Much
Procedural and Conceptual Knowledge
Math is not the same the world over
especially in terms of the
procedural knowledge
of math
students are expected to learn. Conversely, the
conceptual knowledge of
math students have learned
will, most likely, be very similar to that they will learn in us classrooms. The most important aspect of teaching
math to students from other countries is being able to recognize and
identify places where differences in procedures or number systems may cause
students difficulties. When we recognize and understand these specific
differences we are in a better place to help students learn and progress in
their mathematical knowledge and understanding.
World Number Systems
Here is a collection of
World Number
Systems. When we know the number system a student has been using prior
to entering a US classroom we are in a better position to understand the
difficulties a student might face. For example, many languages do not have
the equivalent of eleven and twelve making it difficult for some
students to learn these two nonconforming number names. Some languages do
not have the n phoneme at the end of a word making the teen numbers
difficult to distinguish from the decade number names.
Using the
WIDA Standards
The WIDA
CANDO Descriptors
Sample
WIDA
ELP Language of Math video
Sheltered Instruction Observation Protocol
(SIOP)
The 8 components
of SIOP
All Students are Individuals First
It should be noted that
great variations exist in math education in other countries just as they do
in the US. When teaching math to a student from another country it is
recommended that the
Cultural Math Interview
(CMI)
be used when inconsistencies
are observed in the student's performance during math class. A copy of the
CMI can be obtained from Dr. Tim Whiteford at; twhiteford @smcvt.edu (remove
space).
Cultural Math Identities
The information contained in the pages below
was obtained from
individual interviews with people from these countries
using the
CMI
as well as independent research.
The information should therefore be treated
carefully as it may be unique to an individual, or possibly inaccurate or
out of date, if obtained from a web source.
This is just the beginning
Note: Some school districts block access to
YouTube. It might be possible to get the block lifted for specific
computers.
How to use this information
The information about the math students might
bring with them from other countries is provided here as a resource for
teachers who may have such a student in her/his classroom. It is recommended
that the information contained in the pages above be referred to by the
teacher a) briefly when the student first enters the class and b) more
extensively if the student appears to show particular difficulty learning a
math concept or skill. In situations where the student's difficulties appear
enigmatic it is recommended that the
CMI be administered as a means of
providing a more complete picture of the students mathematical knowledge,
skills, and understanding. 
My Math Counts Too
A resource for teaching mathematics to
students from other countries
My Math
Counts Too
When ELL Students enter US classrooms they
not only have to learn English they also will be required and expected to
learn all academic subjects including mathematics. To help them construct
meaningful understanding of mathematical concepts as well as the many
mathematical symbols and procedures used in American math it is important
for us to know and understand the math they bring with them, the math they
have already learned which will form the basis of their future learning.
Teaching from a
Constructivist Perspective
To understand the way ELL students think
mathematically it is important to know the nature of the math they might
have learned prior to entering the US classroom.
Mathematics differs internationally in
many ways. Many different countries have different numbering systems based on
different bases; the procedures used when doing arithmetic can differ
significantly from those taught in American schools and the math concepts
that form the basis of the school curriculum can be different from those
American students are expected to learn and understand. The language they
use when constructing mathematical meaning or completing computational
procedures my also be unique to the culture where they were learned. For
example, we know that students tend to do mental math in their first
language.
Just as in US classrooms, students may
have experienced a wide variety of math teaching techniques as well as math
concepts and procedures so care must be taken when making generalizations
about a particular students mathematical experiences. While such
generalizations and assumptions based on cultural norms or expectations are
a necessary part of the instructional process it is recommended that
students new to US classrooms be given the
Cultural Math Interview
(CMI) to ascertain the exact nature of their individual math
thinking. This is most effectively done with the student accompanied by
her/his family so that as complete a picture as possible is obtained about
the students mathematical knowledge, understanding and cultural math
background. The significant numbers in a culture, the
numbers that are important to individuals can also differ from culture to
culture. For example, 12 is an important number in western cultures while 50
is a significant number in the US culture. Such culturally derived numbers
can have a powerful influence on the way individuals construct a
quantitatively literate understanding of their lives.
Diversity of
Experience
Students
coming to the US are likely to have had a great variety of mathematicsrelated
educational experiences. Some students may have had no formal schooling or
education while others may have been subjected to a variety of educational
systems due to their moving from one country to another. Still others may
have stayed in one school.
Others variations in experience may
include the language of instruction. For example, some students were found
to have been taught in English even though this was not the primary language
of their country of origin. The effects of nineteenth century
colonialization are still felt through the the ubiquitous use of the words
"borrow" and "carry" in subtraction and addition algorithms. Many students may also speak more than one
language such as those from Bosnia who might speak Russian as well as
Bosnian and English.
Useful Resources;
For more
information contact Dr. Tim Whiteford at:
Last
updated April 3, 2011

