Gifted and Promising Mathematics
Students
The MCPS Policy on Gifted and Talented Education states
that, “In Grades Pre-kindergarten–8, accelerated
and enriched curricula will be provided to all students
who have the capability or motivation to accept the
challenge of such a program. This curriculum will be
rigorous and challenging and matched to the abilities,
achievement levels, and interests of high ability students.
There will be opportunities and expectations for students
to learn at an accelerated pace, to learn in depth,
and to learn integrated themes and connections between
disciplines…”
In order to discuss ways to identify and program for
gifted and promising mathematics students, mathematical
promise must be defined. The National Council of Teachers
of Mathematics (NCTM) Task Force on the Mathematically
Promising defined mathematical promise as a function
of--
- motivation,
- belief, and
- experience or opportunity.
These variables are not fixed and need to be developed
so that success for these promising students can be
maximized. This definition includes the students who
have been traditionally identified as gifted, talented,
precocious, and so on and it adds students who have
been traditionally identified as gifted, talented, precocious
and so on and it adds students who have been traditionally
excluded from previous definitions of gifted and talented
and therefore excluded from rich mathematical opportunities.
This definition acknowledges that students who are mathematically
promising have a large range of abilities and a continuum
of needs that should be met." (Richard Wertheimer)
There are many characteristics to consider when identifying
which students are mathematically gifted. The following
descriptors of characteristics of highly able mathematics
students should be viewed as examples of indicators
of potential. Few students will exhibit all characteristics
and these characteristics can emerge at different times
as the child develops cognitively, socio-emotionally,
and physically.
The highly able mathematics student should independently
demonstrate the ability to:
- display mathematical thinking and have a keen awareness
for quantitative information in the world around them.
- think logically and symbolically about quantitative,
spatial, and abstract relationships.
- perceive, visualize, and generalize numeric and
non-numeric patterns and relationships.
- reason analytically, deductively, and inductively.
- reverse reasoning processes and switch methods in
a flexible yet systematic manner.
- work, communicate, and justify matheatical concepts
in creative and intuitive ways, both verbally and
in writing.
- transfer learning to novel situations.
- formulate probing mathematical questions that extend
or apply concepts.
- persist in their search for solutions to complex,
"messy," or "ill-defined" tasks.
- organize information and data in a variety of ways
and to disregard irrelevant data.
- grasp mathematical concepts and strategies quickly,
with good retention, and to relate mathematical concepts
within and across content areas and real-life situations.
- solve problems with multiple and/or alternative
solutions.
- use mathematics with self-assurance.
- take risks with mathematical concepts and strategies.
- apply a more extensive and in-depth knowledge of
a variety of major mathematical topics.
- apply estimation and mental computation strategies.
It is important to realize that these variables are
not fixed and need to be continually developed.
There are many myths about gifted students. Some of
these are:
- Gifted students, because of their strengths, can
learn on their own and need no guidance.
- If students are not achieving academically, they
cannot possibly be in possession of any mathematical
talents.
- Equal opportunity in education means the same curriculum
at the same pace and employing the same pedagogy for
all students.
"These beliefs must be dispelled. we know that
gifted students who are not challenged and guided may
lose interest, perfom poorly, and even discontinue their
study of mathematics. we know that academic underachievement
can be reversed and talented students identified among
former underachievers. finally, equal opportunity is
not synonymous with having the same experiences. Every
child should be given maximum challenge, support, and
guidance in the larning process, but the nature of these
may be quite different from child to child." ("Empowering
Teachers to Discover, Challenge, and Support Students,"
Carol Greenes, Maggie Mode) Additionally, mathematical
promise cannot be equated either with school achievement
or with performance on computational algorithms.
In"Serving the Needs of the Mathematically Promising,"
Linda Jensen Sheffield presented a continuum of mathematical
understanding. All students fall on one place on the
continuum (but do not necessarily stay there), with
the more able students at the upper end.
Unfortunately, there is no single method for identifying
gifted and talented students nor for assessing their
performance. Ways of identifying mathematically promising
students include:
Observation—while the students are working, particularly
in problem solving situations of increasing difficulty
or those designed to elicit the characteristics listed
above.
Portfolios—students need access to exemplars
from other students and the scoring rubric should include:
- patterns noted and generalized
- predictions made and verified
- interesting related problems posed and investigated
- measures of creativity—
- fluency (number of different solutions)
- flexibility (variety of solutions)
- originality (uniqueness of solutions)
- elegance (clarity of expression)
Questioning—individually, in small group, or
whole class:
- Student interview
- Parent information
- Student interest/peer survey
- On-going assessment
- PADI diagnostic instruments, such as Rating Student
Potential Teacher Checklist
- Diagnostic Thinking Tasks
- Math logs or journals
When planning instruction for gifted and mathematically
promising students, there are questions that need to
be asked:
- Do the opportunities provide for the wide range
of abilities, beliefs, motivation, and experiences
of students who have mathematical promise regardless
of their socioeconomic and ethnic backgrounds, and
do the opportunities meet their continuum of needs?
- Are curriculum, instruction, and assessment qualitatively
different and designed to meet the differing needs
of promising students?
- Are there resources,m projects, problems, and means
of assessment that allow for differences in the level
of depth of understanding and engagement?
- Are there appropriate oportunities in mathematics
that have clearly defined, comprehensive, integrated
goals—that are not simply isolated activities?
- Are the opportunities available to all interested
students and in all schools?
As is stated in the Gifted and Talented Policy,
"Children with special abilities and talents
are part of the human mosaic in our schools and communities.
They typically learn at a pace and depth that set them
apart from the majority of their same-age peers. Because
they have the potential to perform at high levels of
accomplishment and have unique affective and learning
style need when compared to others of their age, they
require instructional and curricular adjustments that
can create a better match between their identified needs
and the educational services they typically receive."
Sections excerpted from Developing Mathematically
Promising Students, edited by Linda Jensen Sheffield,
National Council of Teachers of Mathematics, Reston,
Virginia.
