Support Hoagies' Page!
Shop Hoagies' Page before you visit your favorite on-line stores
Amazon, Prufrock Press
(Prufrock coupon code HOAGIES = 20% off) and many more.
Thanks for your support!
Your donations also help keep Hoagies' Gifted Education Page on-line.
"Our primary goal must be mathematical power for all students. We speak
often about providing rich opportunities for disadvantaged students. But among
the students we have in our mathematics programs are some that have either high
abilities or high interest, or both. Our programs must include opportunities for
these students as well. These students are likely to become significant users of
mathematics as our future scientists, mathematicians, statisticians, engineers,
technologists, and researchers. They deserve programmatic attention just as
students with other kinds of special needs do." Glenda Lappan, president NCTM,
for All' Must Include High-Ability and Highly Motivated Students
Benjamin's formula for changing math education
a TED Talk
Mathematician Art Benjamin offers a bold proposal on how to make math
education relevant in the digital age...
The 24 Game
Create the number 24 from the four numbers on a game card. You can add,
subtract, multiply and divide. Use all four numbers but use each number only
once. Available from simple addition and subtraction, right up to fractions,
decimals and algebra.
Click for 24 Challenge tournament schedule. Decks listed in order of
Ideal Solutions for Math Acceleration
by Susan Assouline and Nicholas Colangelo
Web-based evaluation of existing test scores (full scores from at least
one of ITBS, ACT, EXPLORE, or IAAT (Iowa Algebra Aptitude Test) required)
plus interview questions, provides student-centered feedback to inform
decisions about academic acceleration in math... Nurturing Potential
| Inspiring Excellence
Calculus Trap by Richard Rusczyk
The gifted, interested student should be exposed to mathematics outside
the core curriculum, because the standard curriculum is not designed for
the top students. Rather than learning more and more tools, avid
students are better off learning how to take tools they have and apply
them to complex problems. Then later, when they learn the more advanced
tools of curricular education, applying them to even more complicated
problems will come more easily...
by Edward Zaccaro
"Math is often taught as all scales and no music. This book contains the
music!" I couldn't have said it better myself - tons of fun problems...
Read news and features, explore the intersection of science and the arts,
from computer animation to science fiction. Find book reviews, "Best of the
Web" guides, and listings and reviews of summer and distance-education
programs, internships, and academic competitions. And if you are a member,
participate in online interviews with experts in various fields and in
discussion forums with other members, and access to the Cogito virtual
library where you can find a wide variety of research materials and a
librarian dedicated to helping you...
Johns Hopkins Center for Talented Youth (6 CD set for gifted grades 6 through
In a leaky lifeboat, students survive an ocean storm and become marooned
on a deserted island once inhabited by Rene Descartes. They discover his
parchment notebook, pick up a map and other gear, and begin their journey
through the island tunnels, volcanoes, underground rivers, jungles,
abandoned mines, sunken ships and many more surprises. At each step, they
solve increasingly difficult puzzles and math challenges, earn gold coins,
and make entries in their own journal. As they master each math concept,
they prepare to tackle the final quest... For more great details, read
design principles with computer game design: The development of
Math Talent: A Guide for Educating Gifted and Advanced Learners in Math
by Susan Assouline and Ann Lupkowski-Shoplik
Educators (and parents) guide to educating the math-gifted child...
Also available from Amazon
Doctor Walt's CAD for Kids
CADKEY (ages 8
Provides a dramatic introduction to both basic drafting and powerful
solid modeling. Create fancy cars, fascinating creatures, intricate robots,
and hundreds of other items with minimal effort...
by Conceptual Math Media
Strategic math thinking game, scrabble for mathematical expressions. Don't forget the junior tile set for
more integers, or the advanced tile set for negative numbers and exponents.
Classroom sets available, too!
and Understanding: Improving Advanced Study of Mathematics and Science in
U.S. High Schools
Center for Education
Results of a 2-year effort by a National Research Council (NRC) committee
to examine programs for advanced study of mathematics and science in U.S.
high schools. The committee focused on the two most widely recognized
programs in the United States, and the only two of national scope: Advanced
Placement (AP) and International Baccalaureate (IB). The committee also
identified alternatives to IB and AP and addressed specific questions about
Curricula: How Do They Work for Gifted Kids?
The question is often asked: How does my district's math curriculum work
for gifted kids? Here are some of the answers...
is not linear and
Playing to Learn
Prezi presentationsLearn how we can make math more interesting for our
students, and why it should be this way. A Prezi is a non-linear presentation...
by Paul Lockhart
If I had to design a mechanism for the express purpose of destroying a
child’s natural curiosity and love of pattern-making, I couldn’t possibly do
as good a job as is currently being done— I simply wouldn’t have the
imagination to come up with the kind of senseless, soulcrushing ideas that
constitute contemporary mathematics education. Everyone knows that something
by Harold R. Jacobs
Arguably the best mathematics text books available...
Opportunity Equation: Transforming Mathematics and Science Education for
Citizenship and the Global Economy
The U.S. must mobilize for excellence in mathematics and science education
so that all students — not just a select few, or those fortunate enough to
attend certain schools — achieve much higher levels of math and science
learning. Over the coming decades, today’s young people will depend on the
skills and knowledge developed from learning math and science to analyze
problems, imagine solutions, and bring productive new ideas into being. The
nation’s capacity to innovate for economic growth and the ability of
American workers to thrive in the global economy depend on a broad
foundation of math and science learning...
Why Memorize Math Facts?
Kids need to be independent enough that they can choose their brain over
the calculator as the most effective tool for the job, as it frequently is...
Math Produces Tangible Learning, Study Finds in The Chronicle of Higher
Suggests Math Teachers Scrap Balls and Slices by Kenneth Chang, New York
In a a randomized, controlled experiment (rare in education), researchers
found that teaching math in the abstract results in more understanding than
teaching math with real-life examples... uh, oh!
Your Young Child’s Potential in Mathematics by Marsha Landau
What clues should parents be watching for to identify a special aptitude
for mathematics in their young children?
American Mathematics Contests
Middle school (AMC 8 for grades 6 - 8) and high school tests (AMC 10), preliminary to the
United States of
America Mathematical Olympiad and International
Mathematical Olympiad (registration through October for November testing)
a mentor model for young mathematically talented students
Ann Lupkowski, Susan Assouline, and Julian Stanley
Diagnostic Testing Prescriptive
Instruction (DT→PI) is a beyond-level model developed for use with
talented junior high and high school students... The DT→PI method can be
adapted for effective use with elementary students who are extraordinarily
talented in mathematics, using a mentor...
Problem: New Report Urges Return to Basics In Teaching Math by John
Hechinger, Wall Street Journal
Critics of 'Fuzzy' Methods Cheer Educators' Findings; Drills Without
Calculators. National Council of Teachers of Mathematics will give
ammunition to traditionalists who believe schools should focus heavily and
early on teaching such fundamentals as multiplication tables and long
division. The council's advice is striking because in 1989 it touched
off the so-called math wars by promoting open-ended problem solving over
drilling. The council's 1989 report influenced textbooks and led to what are
commonly called "reform math" programs, which are used in school systems
across the country. Infuriated parents dubbed it "fuzzy math." The council's
new guidelines constitute "a remarkable reversal..."
Art of Problem Solving, Volume 1: the Basics by Sandor Lehoczky and
Art of Problem Solving, Volume 2: and Beyond by Sandor Lehoczky and
A problem-solving tutorial that can be used to prepare for mathematics
competitions. Written at the high school level...
Broadly Based Analysis of Mathematical Giftedness by David Lubinski
and Lloyd G. Humphries
Mathematically gifted students were found to be intellectually superior
across a wide range of cognitive abilities... (requires Adobe Reader)
of mediocrity by Cliff F. Mass,
The Seattle Times (free subscription required)
Why have math scores declined? One reason is surely the transition to
"Integrated Math" in middle and high schools during the 1980s. Instead of
teaching mathematical subjects such as algebra, geometry and trigonometry as
coherent subjects, "Integrated Math" combines them in a frenetic mix that
rapidly jumps between these subjects using lots of pictures and real-life
distance learning meet the needs of gifted elementary math students? by
Sylvia St. Cyr
The use of distance learning in an elementary setting has truly just begun.
Although data-specific to distance learning programs for gifted elementary
mathematics students was not available, the following statistics provide
considerations for further research regarding distance learning in U.S.
for Mathematically Gifted Elementary Students: Learning from Challenging Tasks by
Carmel M. Diezmann, James J. Watters, in
Gifted Child Today
All learners require challenging tasks to facilitate learning and develop
autonomy. To realize their potential, gifted students should engage in
challenging tasks for three reasons: cognition, metacognition, and motivation
Mathematical Talent: Advice to Parents by Ann Lupkowski-Shoplik,
director of the Carnegie Mellon Institute for Talented Elementary and
Secondary Students (C-MITES)
Although IQ testing is useful, it doesn’t provide enough specific
information to pinpoint students’ abilities in math. Grade-level tests are
not advanced enough and don’t accurately gauge these abilities. Students
need to take an above-level test, such as university talent searches offer,
to measure their mathematical reasoning. Based on the results of the
testing, a student’s abilities can be matched to the curriculum level...
Mathematical Talent: They Don't Have to Be Bored to Tears by Ann
Lupkowski-Shoplik, director of the Carnegie Mellon Institute for Talented
Elementary and Secondary Students (C-MITES)
Beginning with the common myths, and moving to identification and
programming, Lupkowski-Shoplik offers a comprehensive in-service for
teachers of math-gifted students K-12... (requires Adobe Reader)
Watch and listen
to Dr. Shoplik's entire presentation "live" via Illuminate Live! Visit
Mathematical Talent (ERIC Digest #482) by Richard C. Miller
Mathematical talent refers to an unusually high ability to understand
mathematical ideas and to reason mathematically, rather than just a high
ability to do arithmetic computations or get top grades in mathematics. Many
people place too much emphasis on computational skill or high ability in
replicating taught mathematical procedures. Unless mathematical talent is
correctly perceived, important clues can be overlooked and less important
clues can be given too much significance...
Rotten Apples by Alfie Kohn
From the world of math instruction. A few years back, a researcher named
Michelle Perry published a study in the journal Cognitive Development that
looked at different ways of teaching children the concept of equivalence, as
expressed in problems such as "4 + 6 + 9 = ___ + 9." Some were taught the
underlying principle, while others were given step-by-step instructions.
Consistent with other research, however, the principle-based approach was much
better at helping them transfer their knowledge to a slightly different kind
Effects of Grouping and Curricular Practices on Intermediate Students' Math
Achievement by Carol L. Tieso
Grade 4 and 5 students were exposed to curricular enhancement and
grouping, to compare both academic gains and qualitative benefits.
Both teachers and students enjoyed math more in appropriate groupings, and
students made significant gains when instruction was based on their academic
levels... (requires Adobe Reader)
for Success: Report of the National Mathematics Advisory Panel by the
National Mathematics Advisory Panel
As noteworthy for what it doesn't show, as well as what it does. Math
in K-8 should be streamlined and clarified. "Recommendation:
Mathematically gifted students with sufficient motivation appear to be able to
learn mathematics much faster than students proceeding through the curriculum at
a normal pace, with no harm to their learning, and should be allowed to do so."
p. 53 (requires Adobe Reader)
math, bad math: What is math? Finding the fun in good math, Squashing
bad math and the fools who promote it
"What is math, really? I hear people throwing around phrases like
"elegant" and "artistic" regarding math. I don't understand how this can be.
To me, math is add, subtract, etc. It is purely functional. Is there
something you can compare it to so that I can understand?" This hits
on one of my personal pet peeves. Math really is a beautiful thing, but the
way that math is taught turns it into something mechanistic, difficult, and
boring. The person who posted this question is a typical example of a victim
of lousy math education...
On EPGY... by Draper
Kauffman, Kit Finn and Trindel Maine
Four gifted children's experience with EPGY K-8 and Pre-Calc math
Differences in Abilities and Preferences Among the Gifted: Implications for
the Math / Science Pipeline by David Lubinski and Camilla P. Benbow
In normative samples, recent studies on gender differences in cognitive
functioning have reported that males and females are converging toward a
common mean on a variety of abilities... In mathematically gifted
samples, disparate male / female proportions are well known... The resulting
proportion of males to females at various cutting scores on the SAT-M was
approximately as follows: SAT-M >= 500, 2/1; SAT-M >= 600, 4/1; SAT-M >= 700.
The effect of these disparate ratios for the math / science pipeline is clear:
a greater number of males than females will qualify for advanced training in
disciplines that place a premium on mathematical reasoning... (requires Adobe,
students speak: mathematics problem-solving insights Editorial by Thomas
R. Tretter, in
Gifted Child Today
...perhaps the differentiated instruction received by students identified as
gifted was ineffective. ...mathematics instruction they received in their high
school courses may not be helping them reach their high academic potential.
...need to rethink how and why we provide instruction for our gifted high
school students in order to have the most powerful impact on their learning.
The congruence between recommendations of the national mathematics standards
and recommendations of these students for effective mathematics curricula
serves to emphasize the need to enact these reforms...
Did It Ever Come to This? by Ralph A. Raimi
The phenomenon is briefly described as a galloping anti-intellectualism, a
“dumbing-down” of the curriculum for all students – but in the name of
kids: Nation's brainy superstars by Scott Stephens, Plain Dealer Reporter
Give us your tired, your poor . . . your scientists and your
mathematicians. The children of immigrants are becoming the top math and
science students in the United States, dominating academic competitions and
representing the strongest hope the nation has of keeping an edge in high-tech
and biomedical fields, according to a study released Monday.
Read the full report:
The Multiplier Effect from National
Foundation for American Policy
of Assessing Spatial Ability in Intellectually Talented Young Adolescents: A
20-Year Longitudinal Study
by Daniel L Shea, David Lubinski and Camilla P. Benbow
...Spatial ability added incremental validity to the SAT-M and SAT-V
assessments in predicting educational - vocational outcomes over these
successive time frames [age 13, 18, 23, and 33]. It appears that spatial
ability can compliment contemporary talent search procedures... (requires Adobe Reader)
Differences in Math Sense: "Give me the child at 7, and I will show you the
man..." in the Eide
"Scientists have for the first time established a link
between a primitive, intuitive sense of numbers and performance in math
classes, a finding that could lead to new ways to help children struggling
of Gender on Academic Achievement by Miriam R. Linver, Pamela E. Davis-Kean
and Jacquelynne S. Eccles
For both boys and girls, math grades fall over the course of junior high
and high school. Young women achieve at comparable or higher levels in math as
males, but their interest especially for the high achieving females, is the
same or lower than males. Our results, also, suggest that for young men in
higher-level math tracks, math interest is much more strongly related to math
school grades than for young women in the same math courses...
Math a Young Man's Game? No. Not every mathematician is washed up at 30
by Jordan Ellenberg
Last month at MIT, mathematician Grigori Perelman delivered a series of
lectures with the innocuous title "Ricci Flow and Geometrization of
Three-Manifolds." If Perelman is correct—and many in the field would
bet his way—he's made a major and unexpected breakthrough, brilliantly using
the tools of one field to attack a problem in another. There's only
one problem with this story. Perelman is almost 40 years old...
Jane and Johnny Love Math: Recognizing and Encouraging Mathematical Talent in
A Guidebook for Educators and Parents of young math 'whizzes'
"I make pictures with candy and math. You get to look at them!" But it's
far more than that... check out Bhaskara’s classic first proof of the
Pythagorean Theorem, hexagonal cellular automaton, and more!
7th and 8th grade, schools only (registration by November (late: January) for competition in February (local), March (state) and May (national)).
There are lots of (free) interesting problems on the warm-ups, workouts, & stretches available on their problem-solving page
(Math and Science Song Information, Viewable Everywhere)
Database of over 2000 science and math songs...
CirclesFind a Math Circle near you! Math Circles are education
enrichment and outreach that bring mathematicians and mathematical scientists
into direct contact with pre-college students. These students, and sometimes
their teachers, meet with mathematical professionals in an informal setting,
after school or on weekends, to work on interesting problems or topics in
Math Education for Gifted Students edited by Susan K. Johnsen and James
How to differentiate for mathematically gifted students, as well as
tried-and-true instructional strategies to employ, including tiered lessons,
distance learning, and activities combining architecture and math...
math gap: MIT economists find a new reason to think that environment, not
innate ability, determines how well girls do in math class by Peter
Dizikes, MIT News Office
Not only that girls are a small minority of elite high school math
students, but also that the prevalence of high-achieving girls in math
varies from school to school. Indeed, in research Ellison found that the
best female math students across the U.S. come from a tiny number of
institutions. The majority of the girls who have been chosen to represent
the U.S. in international mathematics competitions come from a set of about
20 high schools with elite math teams. This extreme concentration of talent
strongly indicates the crucial role that environmental factors, not just
innate ability, play in shaping the accomplishments of students...
Math League Contests
4th grade to high school (registration varies by level)
Association of America (MAA)
MAA membership has provided a forum for educators, students,
professionals, and math enthusiasts to share ideas, keep abreast of
developments in the mathematical community, enhance their careers, and make
new friends. Membership benefits include one of sevearl math journals,
geared for math-enthusiast high school students and above. Look for
Math Horizons and Math Magazine...
Online journal of the AwesomeMath
Talent: Interview with Isaac Greenspan by Paula Olszewski-Kubilius
Issac recounts his experiences in education from elementary school
through university. In the course of his education, Issac and his parents
sought programs that would accommodate his accelerated academic pace while
sustaining his social growth. Now a math teacher at Evanston Township High
School, Issac illustrates the importance of parent advocacy and teacher
gifted students: how can we meet their needs? by Jennifer V. Rotigel and
Susan Fello, in
Gifted Child Today
Unfortunately, many programs for gifted children are inadequate and
poorly designed, leaving classroom teachers to struggle to meet the needs of
gifted children effectively. What resources are available for these students?
What assessment tools are appropriate? Do these children need acceleration or
enrichment? How can we meet their needs when there are so many other demands
on teachers' time?
Mathematics Calendar 2012 by Theoni
A problem a day, all year long! Plus facts, curiosities, and
for All' Must Include High-Ability and Highly Motivated Students by
Glenda Lappan, president NCTM
All too often, we cope with [gifted math] students by giving them more of
the same. If the less able students do 10 problems, the more able students
do 25. This does little to encourage deeper mathematical thinking and might
even turn capable students against mathematics
Off Yahoo mailing list
Mailing list about unschooling math, deschooling math, deprogramming math
anxiety, and just plain having fun with math! This list is dedicated to
exploring how math can be learned without "school", without canned
curricula, without lesson plans, without artifically dividing it up into
grade levels and testing and drilling it to death; and how math is naturally
all around us and how children (and adults too!) are doing math all the
time, whether they realize it or not!
The Mathman - Don Cohen
Publisher of Calculus For Young People and lots
of related math materials...
Olympiad Contest Problems for Elementary and Middle Schools by George
Four hundred challenging math problems provide kids with a book of
problems which introduces many different problem-solving strategies...
GNU Octave is a high-level language, primarily intended for numerical
computations... (free, and as good as MATLAB and others)
Math competition for students in grades 3-12. School teams, homeschool
teams, and individuals are all eligible to join. Awards are given to
high-scoring teams and individuals...
mathematically talented students in seventh grade and younger by Ann
Q & A, with great questions, including Should I be concerned if my child
prefers to play with conceptual ideas of mathematics, rather than working
computations?, What are some specific ideas for working with my school?, and
What is the Diagnostic Testing -> Prescriptive Instruction model?...
Observations of Kindergartners Who Are Advanced in Mathematical Reasoning by
Michael D. Pletan, Nancy M. Robinson, Virginia W. Berninger, and Robert D.
What behaviors and abilities do young, mathematically precocious children
display? Are parents able to recognize such precocity?
Polydron (ages 4+ and 7+ through middle school)
Polydron is the original and still superior manipulative, recognised in
many countries as the world's leading resource for teaching Maths 2 and 3
dimensional geometry, design and technology. This is a major aid in
developing spatial awareness.
Classroom Pack available from Amazon; other sets available directly from
for Numbers by Rich Monasterky, The Chronicles of Higher Education
Are boys born better at math? Experts try to divide the influences of
nature and nurture. Lawrence H. Summers, president of Harvard
University, had said that "intrinsic" differences in aptitude between the
sexes might be an important reason that men dominate the
science-and-engineering work force. Researchers who study gender
differences say Mr. Summers's emphasis on innate aptitude simply doesn't add
Differences in Mathematical Reasoning Ability at Age 13: Their Status 20
Years Later by Camilla Persson Benbow, David Lubinski, Daniel L. Shea,
and Hossain Eftekhari-Sanjani
Follow-up of mathematically gifted adolescents whose earlier assessments
revealed robust gender differences in mathematical reasoning ability.
Both genders became exceptional achievers. Earlier sex differences in
math ability did predict differential education and occupational outcomes.
Profile differences in abilities and preferences are longitudinally
stable... (requires Adobe Reader)
A gathering place for all things STEM, a blog for math-lovers and
Structure of Abilities in Math-Precocious Young Children: Gender Similarities
and Differences by Nancy M. Robinson
For this study of the organization of cognitive abilities and gender
differences in young children advanced in mathematical reasoning... Boys
scored higher on 8 of 11 quantitative measures, 0 of 3 verbal measures, and
1 of 3 spatial measures...
of Mathematically Precocious Youth After 35 Years: Uncovering Antecedents
for the Development of Math-Science Expertise by David Lubinski and
Camilla Persson Benbow, Vanderbilt University
An account of the Study of Mathematically Precocious
Youth (SMPY) after 35 years of longitudinal research. Along
with mathematical gifts, high levels of spatial ability, investigative
interests, and theoretical values form a particularly promising aptitude
complex indicative of potential for developing scientific expertise and of
sustained commitment to scientific pursuits. Special educational
opportunities, however, can markedly enhance the development of talent...
(requires Adobe Reader)
the Education of Children with Exceptional Mathematical or Verbal Reasoning
Ability by Julian C. Stanley
Upon what principles is this highly successful,
robustly persistent, widespread set of programs based? Our approach has,
to coin an oxymoron, been benignly insidious. In effect, we have burrowed up
somewhat subversively under the school system, not approaching school boards
but instead sending scores directly to the student...
Mathematics to Gifted Students in a Mixed-Ability Classroom ERIC Digest
#594, by Dana T. Johnson
Mathematically gifted students have needs that differ in nature from those
of other students. They require some differentiated instruction, defined by
Tomlinson (1995) as "consistently using a variety of instructional approaches
to modify content, process, and/or products in response to learning readiness
and interest of academically diverse students." Yet recent studies have found
few instructional or curricular modifications in regular elementary
classrooms. In grades 9-12, students may be able to select honors, advanced,
and AP courses; however, even in these more homogeneously grouped classes
there is a range of differences that need to be acknowledged.
Mathematics to Non-sequential Learners by Linda Kreger Silverman
...children who show superior grasp of mathematical relations, but
inferior abilities in mathematical computation. These children consistently
see themselves as poor in mathematics and most hate math. This situation is
terribly unfortunate, since their visual-spatial abilities and talent in
mathematical analysis would indicate that they are “born mathematicians.”
lessons: one way to differentiate mathematics instruction by Cheryll M.
A tiered lesson is a differentiation strategy that addresses a particular
standard, key concept, and generalization, but allows several pathways for
students to arrive at an understanding of these components based on their
interests, readiness, or learning profiles. Take a closer look at the anatomy
of a tiered lesson...
States of America Mathematical Olympiad and International
Mathematical OlympiadU.S. and International competition, held annually in over 80 countries...
Mathematical Talent Search NSA / CSSFree (except for the cost of postage
to mail student's solutions) mathematics competition open to all United States
high school students...
Blog of lessons,
problems sets and more, challenge your brain and prepare for the AMC 8, AMC 10,
MATHCOUNTS, or the middle school math olympiads
Math Gender Gap? by Laura Vanderkam
For all of the noise, young women are going into some sciences. Women earn
46% of biology Ph.D.s. They fill more than half of incoming medical school
classes. It's just that their proportion in pure physical sciences, while
rising, remains low. But physics isn't tougher than biophysics, which suggests
that these choices have little to do with aptitude or confidence. In fact,
studies suggest girls simply don't view pure math and physics as practical or
varied enough to justify the slog to professorship...
instruction' drags good math pupils down by Susan Goodkin and David G.
Research consistently shows, and common sense dictates, that the best way
to nurture high-ability math minds is to group these children together and
give them a curriculum geared to their abilities. Rather than implementing
such "ability grouping," however, most elementary schools nationwide take
exactly the opposite approach: "whole-group instruction."
fewer women succeed in math by Nancy J. White,
October 23, 2012