LIPING MA
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She is of the opinion that the reason there is a
disparity between math test scores between USA (and by consequence Canada) and
China is the level of comfort with and knowledge of mathematics that the
teacher possesses
·
Teaching methods in China present more as
lecture style. This style means the
teacher must research, prepare, and practice in advance of the lecture. Meaning, teachers develop a higher level of
familiarity and comfort with the topic and strategies involved and the ability
to communicate them.
·
This is not the only pedagogical method that can
lead to increased knowledge, comfort, or communication, but is important when
comparing the two countries.
·
“Knowledge Packages - the teacher has an
idea in her mind about where this idea is situated in the field of mathematics.
There are “key pieces,” which are
certain related topics that are viewed as being more important to the
comprehension of the topic at hand. can contain both procedural and conceptual
elements With underdeveloped knowledge packages, it can be very difficult for a
teacher to plan and facilitate a course of study for their students.”
·
Learning Paths – a linear progression? - Knowledge
packages also contain implicit sequences of student learning, where a student
is expected to know and understand key related pieces before they can grasp the
topic at hand. topics in a knowledge package are interdependent, and do not
develop linearly, but in conjunction and association with other ideas
·
Profound Understanding of Fundamental Mathematics
(PUFM) – means understanding procedural and conceptual elements – not just
getting the right answer and following “the rules”
·
Connectedness –teacher makes
explicit connections among concepts and procedures that students are learning.
·
Multiple Perspectives –multiple
solutions are possible, but some solutions have advantages and disadvantages in
different situations
·
Basic Ideas –big ideas are important and
need to be explored
·
Longitudinal Coherence –awareness
of the entire elementary curriculum knowing where their students are coming
from and where they are headed in the mathematics curriculum.
·
We need to start including deeper understanding
of math concepts at the teacher training level.
·
Chinese teachers also have set times in their
teaching day to explore material and consult with other teachers – common planning
times
·
Language matters fundamentally
·
The language for math, numbers, and terminology
in Chinese differs significantly from English.
Some words derive from technology such as the abacus
·
It is important for students to discover their
own strategies – such as in multiplication – to foster a deeper conceptual
understanding of the mathematics
·
Chinese teacher’s feel the teacher’s guide is
virtually useless, preferring to interpret the student book with the students. Teacher guide does not include anticipated
responses or errors
Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States – Jan 25 2010 Liping Ma
Three approaches to one-place
addition and subtraction: Counting strategies, memorized facts, and thinking tools
·
Using counters and memorizing facts are of
limited use and do not help students with understanding or when numbers get
bigger
·
It is important to help student develop “thinking
tools” which helps them extrapolate as numbers increase
·
Composing numbers, equations and symbols,
commutative law, inverse operations, compensation
·
Use proper math terminology from the beginning
(e.g. addend, sum, equation,..)
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