ERIC EJ750567: Mathematically Talented Children: How Can Parents Help?

2007·0.41 MB·English

by  ERIC

Mathematically
Talented Children:
How Can Parents
Help?
Jennifer V. Rotigel
and Michael J. Bossé
“My son used to love math. Now, I see him struggling and bored.”
“My daughter is so turned off from math in school that needs, including additional resources, experiences, and
I need to do something with her at home. But, I don’t opportunities, to continue his pursuit of advanced mathe-
know what.” matics. Every child should get what she needs to reach her
“I have always been very involved in my child’s educa- potential. We cannot measure one child by the rule of the
tion. But, his math is now going far beyond what I know. majority or by an equal distribution of resources. Rather,
It is now out of my league. I don’t know what to do.” we believe that the educational system should provide all
“I don’t know how to get the school system to challenge children with everything that they need to progress as far
my daughter in mathematics. I don’t want her to lose the as they can. Nothing less will do, even for children who are
edge she has.” truly gifted and advanced beyond their peers. We are not
encouraging parents, whether through school or home, to
These and many other comments come from parents
provide their child more than all other children get, but
throughout our nation. In this article, we will provide
rather that they provide experiences that are consistent
some recommendations for parents who want to facilitate
with, and appropriate for, the needs of their child.
the continuing mathematical development of their math-
Second, it is very important for parents to honestly and
ematically talented child. The objective of assisting parents
objectively assess the mathematical level of their child.
is central to the text, not mathematics per se. As authors
Despite best wishes, not every child is an Einstein, nor is
and professional educators, we are also parents who want
every child average. Parents must work with educational
to support other parents who are looking for ways to posi-
and psychological experts using numerous assessment
tively enhance their child’s mathematical learning and
strategies and examinations to clearly understand both the
experiences. This article considers various aspects that
ability and the learning style preferences of their child in
affect mathematically talented students and may have a
order to best ascertain how to help the child progress even
positive or negative impact on their continuing pursuits to
further. For the purposes of this article, we will not quibble
learn more mathematics.
over vocabulary. All too often, the terms gifted, advanced,
and talented are politically heated and carry agendas that
Five Foundational Issues
do not necessarily relate to a child’s ability. This article will
use the singular term mathematically talented to denote a
Before we provide recommendations regarding how student whose abilities are above the norm. We will refrain
parents can help their mathematically talented child, it is from differentiating how much or little above the norm
important for parents to understand a few philosophical is a mathematically talented student. It is up to parents,
beliefs we hold. First, your child deserves all the help he together with the child, the teacher, and the school sys-
gifted child today 17
Mathematically Talented Children: How Can Parents Help?
tem, to first determine if the child is own home and make the best choices port these students, some schools
talented before making educational accordingly. have implemented excellent instruc-
decisions for the child. Fifth, many cultural dynamics tional programs and competitions for
Notably, however, many means affect mathematically advanced chil- mathematically talents students. It
beyond scholastic assessments are dren. Parents must be aware of pres- is incumbent upon parents to inves-
available to lead to an intuitive belief sure that will be placed on the child tigate their local schools to ascertain
that a child is mathematically talented. to conform to lower standards by what is offered. Some schools will
Many parents recognize in their child peers, culture, and even the school have in place resources, teachers, and
unusual mathematical talent, preco- system. Additional factors inhibit experiences that fit well for the math-
ciousness, or an unusual level of inter- girls from pursuing advanced math- ematically talented child. These may
est in mathematics at a young age. ematics. Thus, parents must become include honors courses, gifted and
Some notice that mathematical skills advocates for, and allies with, their talented clubs and course work, and
and understandings usually associ- child in pursuing mathematical expe- association with mathematical com-
ated with significantly older children riences that will allow her to reaching petitions. We encourage parents to
are evidenced in their child. Parents her fullest potential in mathematics. speak with school personnel and find
should understand the mathemati- Additionally, parents must recognize the best placement for their child.
cal development of their child before the burden that meeting the needs When systems already exist, parents
attempting to significantly alter his or of a mathematically talented child will typically find that schools are
her world. may impose on the family. As with a willing to accept students into these
Third, ability is not synonymous star athlete who may need coaching, activities to maintain adequate enroll-
with interest. Not every child wishes special training, and numerous expe- ments so they may continue to offer
such experiences.
to continue to pursue his study of riences far beyond the needs of aver-
If, on the other hand, parents find
mathematics beyond that offered age students in order to meet their
that their local public schools do not
in the regular classroom. You must advanced potential, the needs of a
provide adequate programs for math-
know your child and determine with mathematically talented student also
ematically talented students, parents
may impact the time and resources
her input whether she wishes to con-
must be simultaneously firm and
of a family. Parents, and indeed the
tinue in her studies of mathematics.
sensitive toward schools, administra-
entire family, must be willing to sacri-
Although your child may be mathe-
tions, and teachers in order to procure
fice to meet the needs of such a child.
matically gifted, if he is disinterested,
additional assistance and resources for
With these preliminary consid-
too much parental encouragement
the mathematically talented student.
erations in place, we now provide
may be interpreted as additional and
Parents must strenuously advocate
parents with recommendations for
unwanted pressure. Thus, some stu-
for their child’s mathematical devel-
furthering their child’s mathemati-
dents who lack interest in mathemat-
opment while being sensitive to the
cal pursuits. These recommendations
ics may still be very advanced in the
constraints under which schools,
will be differentiated by whether or
subject. Just because mathematics
administrators, and teachers exist.
not they primarily occur in respect to
may be easy does not mean a child is
Whereas parents must sympathize
the school system or extracurricular
interested in the topic.
when the entire school system is over-
experiences. We begin by considering
Fourth, one size does not fit all. extended, they must also passionately
parental involvement with the child’s
Not every parent is competent to per- seek the resources and experiences that
school system.
sonally assist a child with the study their child both needs and deserves
of advanced mathematics. Parents in order to reach her mathematical
Navigating
should not place undo pressure and potential. Parents may be forced to
guilt on themselves. Rather, they the School System walk an emotional tightrope with the
should consider these recommenda- school system.
tions and find those that best meet the Parents are not always fully aware Some schools simply do not pro-
needs of their child and the family as of the numerous activities avail- vide adequate instructional resources
a whole. Every child and every home able to their mathematically gifted for mathematically talented students.
is different. Parents must be cognizant child through some public schools. Occasionally, inadequate program-
of the many dynamics within their In an effort to both attract and sup- ming is due to a school or admin-
18 winter 2007 • vol 30, no 1
Mathematically Talented Children: How Can Parents Help?
istrator taking the position that parents and schools and participate in ents must guard. First, many teachers
advanced children are already blessed the decision-making regarding their simply pile extra work on talented
and all additional resources should academic future. Parents should ask students. Although no malice may
be expended on the masses of stu- their child if she believes that there is be intended, the workload can easily
dents who need greater assistance. too much repetition and practice of be overwhelming. So, in an attempt
More often, failure to provide addi- basic skills. Does the teacher provide to make positive accommodations for
tional resources to advanced students too much time to complete a task? talented students, some schools bury
is simply a result of severely limited Are students allowed to read or work the desire to excel under a mountain
resources that require school person- on other tasks while waiting for other of meaningless and time-consuming
nel to make difficult choices regarding students to finish an assignment? homework. Second, well-meaning
school programs and program deliv- Understanding the child’s perspective teachers often use mathematically
ery. Teachers are already stretched to on the events of the school day may talented students as free teacher
their limit with multiple classes, large provide parents and school admin- aides and tutors for other students.
class sizes, inclusion of special needs istrators with better insight into the Although some may argue that learn-
students, documentation require- needs of the child.
ing is accentuated when one has the
ments, and endless meetings. Parents
• Create positive accommodations. opportunity to teach, this practice
must simultaneously be intolerant of
Through their attempts to provide removes from the mathematically
schools that refuse to provide services
mathematically talented students talented child the opportunity to
for advanced students for misguided
with more challenging and enriching encounter and learn additional math-
philosophical reasons and sensitive
learning experiences, some schools ematics commensurate with his or her
to schools that are attempting to do
may implement one or more objec- abilities. They may be learning the old
their very best with paltry resources at
tionable practices against which par- mathematics more fully, but they are
hand. To this latter scenario, we offer
the following recommendations.
• Form a team. Parents should get
to know their child’s school well. They College of William & Mary
should investigate what resources exist
Center for Gifted Education
and which teachers support the more
mathematically talented students. Williamsburg, Virginia
Parents should ensure that the rela-
tionship between them and the school
announces the 12th
is polite, respectful, and never adver-
sarial. If parents and school person-
nel can form a team in support of the National Curriculum Network Conference
child, success will be more assured.
Reflecting on Effective Practice
• Communicate with your child. In
March 14-16, 2007
seeking additional resources for their
child, parents should understand the
sometimes cryptic complaints of their Featuring
child. “I’m bored,” hardly adequately
explicates the needs of the student. Is
Joyce VanTassel-Baska, College of William and Mary, VA
he bored because he doesn’t like the
Michael Thompson,San Juan, PR
subject matter, the delivery methods,
Catherine Little, University of Connecticut, CT
the pacing, or the low level of the
content? Parents must communicate
Registration materials available at www.cfge.wm.edu/ncnc.php or contact the
effectively with their child in order to
Center at 757-221-2166 or [email protected]
best ascertain what she needs from the
school. Advanced students are usually
continued on page ??
more able to communicate with their
gifted child today 19
Mathematically Talented Children: How Can Parents Help?
not having the opportunity to see new understanding of mathematics rather the mathematics that is taught
materials and gain new knowledge. than mechanistic procedural knowl- and enhances students’ learn-
Various methods of accommoda- edge. To this end, teachers can lead ing. (p. 16)
tions and advancement are available students to continually ask why certain
for students who are academically mathematical concepts or procedures NCTM’s text also distinguishes two
advanced. Through careful consider- hold, investigate mathematical theo- types of standards and characterizes
ation and negotiation with the school, rems and definitions, develop alter- them as:
the parent may negotiate some strate- nate mathematical systems, and raise
gies to provide their child with what their own mathematical questions. It The Content Standards—Num-
he needs. Some of the strategies to is important for teachers to lead these ber and Operations, Algebra,
provide the student with involve- students to look more deeply into Geometry, Measurement, and
ment with more advanced math- common mathematics seen in regular Data Analysis and Probabil-
ematics include: early admission to classrooms. This can be accomplished ity—explicitly describe the con-
Kindergarten, middle school, high by connecting instruction and investi- tent that students should learn.
school, or college; placement into gations to the recommendations pro- The Process Standards—Prob-
more advanced classes or grades, by vided in the Principles and Standards lem Solving, Reasoning and
individual subject or in toto; grade for School Mathematics (NCTM, Proof, Communication, Connec-
skipping; compacting material within 2000). This volume of mathematics
tions, and Representation—high-
a grade level; continuous progress or education reform recommendations
light ways of acquiring and using
self-paced instruction; and mentoring defines its principles as:
content knowledge. (p. 30)
and extracurricular programs. Each
of these strategies carries its inherent Equity. Excellence in math-
Although parents may need to have
strengths and weaknesses. Parents, ematics education requires
this list with them as they discuss vari-
together with the child, the teachers, equity—high expectations and
ous curricular options with teachers,
and the administrators must deter- strong support for all students.
mathematics teachers should already
mine what is best for the student. Curriculum. A curriculum is
be well aware of NCTM’s recom-
Teachers have much control over more than a collection of activi-
mendations and how to apply them
what is taught in their class and what ties: it must be coherent, focused
in their instruction.
instructional practices they use in on important mathematics,
• Become aware of alternative experi-
their classes. Teachers can significantly and well articulated across the
ences. When parents find it impossible
affect the mathematics that students grades.
to procure the requisite resources and
encounter by making alterations in Teaching. Effective mathe-
experiences that their mathematically
the pace, breadth, and depth of the matics teaching requires under-
mathematics instruction. Each of standing what students know talented child needs from their local
these factors can revolutionize a stu- and need to learn and then chal- public schools, other alternatives exist.
dent’s experience and reinvigorate her lenging and supporting them to Charter schools for students more
pursuit of mathematics. Other tech- learn it well. interested and talented in the sciences
niques that are less dramatic include Learning. Students must and mathematics are continually
teachers selecting more appropri- learn mathematics with under- coming into existence. More univer-
ate sets of homework problems for standing, actively building new sities and high schools are providing
mathematically talented students knowledge from experience and students with opportunities to take
and teachers focusing on providing prior knowledge. classes via computers while off cam-
students with various experiences in Assessment. Assessment should pus. These distance education models
reading, analyzing, synthesizing, and support the learning of important take many forms; some are via video
evaluating mathematical books and mathematics and furnish useful conferencing, and others are provided
passages. information to both teachers and over the Internet and through numer-
Classroom teachers should focus students. ous types of interactive Web sites.
on developing within all students, Technology. Technology is Often, students are allowed to enter
and certainly within mathematically essential in teaching and learn- online courses that they would not be
talented students, deep conceptual ing mathematics; it influences able to attend in a traditional face-to-
20 winter 2007 • vol 30, no 1
Mathematically Talented Children: How Can Parents Help?
face style. Finally, and as a transition students the mathematics that the mathematics on their own can be
to providing mathematical experi- mentor encounters daily in his work. fulfilling for both the child and the
ences to advanced students through Thus, the materials covered may be parents. Both parents and the child
the home, many families have opted very different. In fact, processes of are often surprised to see all of the
for either single family homeschool- tutoring and mentoring may differ possibilities that surround them
ing or joining homeschool associa- significantly and proceed toward dif- daily. Unfortunately, many parents
tions. ferent ends. Although this brief article all too quickly dismiss opportunities
cannot fully explicate all of the dis- in which they find difficulty discov-
Providing Resources tinctions with respect to tutors and ering the mathematical connections.
mentors, it is nevertheless incumbent For instance, video games are unde-
Through the Home
upon the parent to carefully weigh niably programmed with sophisti-
the merits of both and to participate cated “logical engines” in which users
Many parents, for a number of
fully in the selection of one or both unconsciously use mathematics and
reasons, are seeking assistance to help
for their child. logic to conquer the playing environ-
their mathematically talented child to
Selecting either a tutor or a men- ment. Many other opportunities also
continue her mathematical pursuits
tor can prove to be daunting. Either abound and provide opportunities
through arenas outside of the class-
must be chosen to complement both to encounter mathematics in stimu-
room. Today, countless opportunities
the child’s temperament and the fam- lating ways. Every hobby or interest
are available to them, and generally,
ily’s concerns. College students often can be reinvestigated mathematically.
these will fall into three groups: com-
make some of the most convenient From the arts (e.g., music, singing,
munity resources and mentors, encour-
and cost effective tutors. However, dance, photography, painting, color,
aging children to discover mathematics
college student tutors may lack suf- perspective, texture), to hobbies (e.g.,
on their own, and technological tools
ficient mathematical understanding, model making, kite flying, cooking,
that are available to all.
knowledge of the interconnectedness collecting, crafts, puzzles, reading),
of mathematical topics, and skills with to sports (e.g., individual and team,
Community Resources
best instructional practices. Teachers statistics, strategies), to socializing
and Mentors
and professors also work well, but are (e.g., communicating, cell phones,
often quite busy and cannot devote the instant messaging), to technology,
Community resources include the
time needed by the child. Mentors are and so forth, all hobbies and interests
countless number of people in any generally found from more academic, can be mathematized. In so doing,
community who are particularly skill- scientific, and business fields by net- the mathematically talented child
ful in mathematics. These may include working within community groups can further his investigation of math-
mathematicians, scientists, engineers, and acquaintances. It is important ematics through a medium in which
accountants, professors, teachers, and for the student to understand that the he is already interested. While this
others who use mathematics regu- mentor has expertise in certain mathe- certainly enhances the interest level of
larly. Parents are encouraged to find matical fields and not in others. Thus, the mathematical investigation, it also
tutors and mentors who can help the mentor seeks to impart his or her solidifies the notion that mathematics
their mathematically talented child to knowledge to the student and does surrounds all that we do and is con-
continue his studies. Whereas tutors not seek to align that knowledge with nected to interests outside of those
usually charge regular fees, mentors any particular curriculum or course. seen in the traditional classroom.
generally assist young people free of Either the tutor or the mentor may Projects at Home. Projects around
charge. However, far more than costs work effectively for any student; how- the home also provide rich opportu-
should factor into the parents’ deci- ever, all involved must understand the nities for students to be involved in
sions regarding which option is best goals of the others. mathematics in real-world scenarios.
for their child. Tutors tend to look As parents entertain the thoughts of
specifically at the mathematics that Encouraging Children to Discover creating a sun room, installing a swim-
the student is investigating in their Mathematics on Their Own ming pool, creating new curtains for a
educational setting. So, a tutor will room, painting the house, installing a
help a student with his mathematics Using Hobbies and Interests. lawn or garden irrigation system, buy-
continued on page ??
work. A mentor, however, will show Encouraging children to discover ing a new car, or planning a family
gifted child today 21
Mathematically Talented Children: How Can Parents Help?
reunion, the mathematically talented Books. Many children love to read. which students can investigate math-
child can participate in the planning, Today, an ever increasing body of liter- ematical concepts. Parents should
designing, organizing, and purchas- ature is available to those who wish to ensure that their mathematically tal-
ing of necessary components. These meld mathematics with reading. For ented child has a graphing calculator
skills all employ mathematics. Bold every level, books are being published as early as the middle grades. Although
parents may wish to have their child that incorporate mathematics into the some educators argue that calcula-
participate in the annual tax prepara- story line in intriguing ways. Whether tor use has become a crutch to many
tion and see how various expenditures mystery novels, crime drama, or car- students and has hampered the math-
and charitable giving affect various tax toon stories for even younger chil- ematical development of many, this is
scenarios. Add to this a component dren, bookstores and Web sites are rarely so for the advanced child who is
of strategizing to minimize the next filled with books and magazines that more apt to use many of the features
year’s taxes, and the child can experi- promote mathematics in a friendly, of the calculator as investigatory tools
useful, and entertaining manner. This probing more deeply into mathemati-
ence a robust mathematical investiga-
mathematically enhanced literature cal concepts than as a replacement for
tion.
Investigations Outside the Home. provides students with opportuni- reasoning and learning.
ties to experience mathematics and Independent Research. Often, the
Many investigatory opportunities also
encourages them to continue in their mathematically talented child seeks
reside outside of the home. Parents
endeavors. to continue her mathematical inves-
and their children regularly see profes-
Field Trips. Field trips to facto- tigations independently. In these
sionals who use mathematics in their
ries and businesses can prove valu- cases, parents should ensure that a
occupations. Many of these profes-
able in allowing students to see the rich variety of technology is avail-
sionals would be elated to speak with
applications of mathematics around able to the child. The Internet is
a promising child regarding various
them. However, children are often replete with mathematical discus-
aspects of their careers. Architects,
especially interested in trips to sions and investigations. Parents
engineers, insurance agents, financial
mathematics and science museums. should allow (albeit monitored) a
planners, optometrists, dentists, law-
Although these museums do not child to dig deeply through vari-
yers, accountants, farmers, business
exist in all cities, parents should ous mathematical Web sites for
people, and countless others daily use
plan to visit as they pass through materials. Numerous inexpensive
mathematics and would be willing to
metropolitan areas in which these computer software packages allow
share their knowledge with an inter-
museums do exist. students to interactively investi-
ested child. Introducing a child to
Other Learning Materials. Parents gate mathematical concepts (e.g.,
these opportunities again validates the
of the mathematically advanced child Geometer’s Sketchpad, Fathom,
idea that mathematics is used widely
should search through used book- Derive, TI Interactive). Parents
and applied in almost every field.
stores and yard sales for used math- should speak with school districts
Puzzles and Games. It would be dif-
ematics textbooks and bring them to and teachers to see what software
ficult for a person to have missed the
the home. These are usually very inex- is being used in the schools. Those
new craze in this nation. The Sudoku
pensive and provide the child with packages and others should also
rage can be witnessed in countless
countless mathematical examples and be available to the child at home.
newspapers, on the Internet, and in explanations. The child can then read For families who cannot afford
bookstores. Adults and children alike and learn at his leisure. Most impor- mathematical software, many Web
enjoy the recreation of puzzles, chal- tantly, valuable resources will always sites provide learning activities for
lenges, and competitions. Because an be at his fingertips. spreadsheet software packages (like
inherent interest accompanies these Microsoft Excel and Corel Quatro
activities, they make natural fodder Technological Tools Pro) that are included on almost all
for the continued investigation of computers today.
mathematics. Parents should take the Technology and Calculators.
opportunity to investigate how to use Although calculators are ubiquitous Selected Resources
natural recreations as a medium for in mathematical learning today, many
their child to further her mathemati- improvements have lead to math- Parents are not always aware of
cal learning. ematically sophisticated tools through the countless resources available to
22 winter 2007 • vol 30, no 1
Mathematically Talented Children: How Can Parents Help?
them and their mathematically tal-
Table 1
ented child. The short list in Table 1
List of Mathematical
provides some valuable Web-based
and Gifted Education Resources
resources that parents and students
can access. Many of these resources
refer to games, puzzles, books, activ- Ask Dr. Math
ities, investigations, hobbies, com- http://www.mathforum.org/dr.math
petitions, ability testing, suggested
scholastic accommodations, parent Cool Math
and student support groups, tech- http://www.coolmath.com
nology and calculators, and many
other issues raised in this article in Funbrain
respect to mathematically talented http://www.funbrain.com
children.
Interactive Math Activities
Conclusion http://www.cut-the-knot.org/Curriculum
Math Forum Student Center
Parents of the mathematically tal-
ented child have many resources at http://www.mathforum.org/students
their disposal. Ideally, parents should
Math Games
collaborate with their child’s school
http://www.madras.fife.sch.uk/maths/activities.html
personnel to evaluate their child’s
ability, needs, and interest in math-
Mega-Math
ematics. Working with teachers and
http://wwwc3.lanl.gov/mega-math
administrators, parents may help to
craft a plan so that their child will
Set
be challenged in mathematics and
http://www.setgame.com
allowed to learn at his or her own pace
and level.
General Parent Resource
Schools cannot be expected to
http://www.hoagiesgifted.org/parents.htm
meet all children’s mathematical
needs if they are truly advanced and
Success Stories in Gifted Education
highly interested in math. Tutors
http://www.hoagiesgifted.org/success_stories.htm
and mentors, as well as enrichment
and accelerative options, may need
“Is it a Cheetah?” by Stephanie S. Tolan
to be investigated. The child should
http://www.stephanietolan.com/is_it_a_cheetah.htm
be included in decisions regarding
how much his mathematics program
should be modified, because this will socializing. Projects and family trips gestions useful as you engage in the
depend in part on his interest level
provide all sorts of ways to utilize exciting world of raising a child with
and time commitments.
mathematics. mathematical talent. GCT
Parents can help their child to dis-
This article offers a brief glimpse
cover mathematics by enriching the
of the myriad opportunities par- Reference
home environment so that ordinary
ents have for assisting their math-
activities become opportunities to use
ematically talented child to grow
mathematics. In one way or another, National Council of Teachers of Math-
almost everything has a mathematical and continue to develop his or her ematics (NCTM). (2000). Principles
component, whether it is a hobby, a mathematical interests and abilities. and standards for school mathematics.
continued on page ??
sport, the arts, technology, or even We hope that you will find our sug- Reston, VA: Author.
gifted child today 23