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Mathematically Gifted

"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, 'Mathematics for All' Must Include High-Ability and Highly Motivated Students

The 24 Game Recommended
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 difficulty
bulletAdd / Subtract Primer bulletIntegers
bulletMultiply / Divide Primer bulletFractions / Decimals
bulletFactors / Multiples Primer bulletFactors / Multiples
bulletSingle Digits bulletAlgebra / Exponents
bulletDouble Digits bulletVariables
Arthur Benjamin's formula for changing math education Recommended a TED Talk
Mathematician Art Benjamin offers a bold proposal on how to make math education relevant in the digital age...
Belin-Blank Ideal Solutions for Math Acceleration Recommended 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
The Calculus Trap Recommended 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...
Challenge Math Recommended 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...
bullet Challenge Math For the Elementary and Middle School Student for the upper elementary and middle school student Recommended  Also available from Amazon.co.uk and Amazon.ca
bullet Primary Grade Challenge Math Recommended for the younger elementary student  Also available from Amazon.co.uk and Amazon.ca
bullet Real World Algebra: Understanding the Power of Mathematics Recommended  Also available from Amazon.co.uk and Amazon.ca
bullet The Ten Things All Future Mathematicians and Scientists Must Know (But are Rarely Taught)  Also available from Amazon.co.uk and Amazon.ca
bulletBecoming a Problem Solving Genius: A Handbook of Math Strategies
bullet25 Real Life Math Investigations That Will Astound Teachers and Students
bullet Scammed by Statistics Recommended
Cogito.org Recommended
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...
Descartes' Cove Recommended by Johns Hopkins Center for Talented Youth (6 CD set for gifted grades 6 through 8)
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 Blending instructional design principles with computer game design: The development of Descartes' Cove.
Developing Math Talent: A Guide for Educating Gifted and Advanced Learners in Math Recommended by Susan Assouline and Ann Lupkowski-Shoplik
Educators (and parents) guide to educating the math-gifted child...  Also available from Amazon UK and Amazon Canada
Doctor Walt's CAD for Kids Recommended by CADKEY (ages 8 and up)
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...
Equate Recommended by Conceptual Math Media (or from Amazon or MindWare UK)
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!
Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Recommended 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 advanced study...
Math Curricula: How Do They Work for Gifted Kids? Recommended
The question is often asked: How does my district's math curriculum work for gifted kids?  Here are some of the answers...
Math is not linear and Playing to Learn Recommended Prezi presentations
Learn how we can make math more interesting for our students, and why it should be this way. A Prezi is a non-linear presentation...
A Mathematician’s Lament Recommended 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 is wrong...
Mathematics Recommended by Harold R. Jacobs
Arguably the best mathematics text books available...
bullet Mathematics: A Human Endeavor the quintessential pre-algebra text - makes math fun Recommended 
bullet Elementary Algebra Algebra I, in Jacobs tradition  or Amazon.co.uk
bullet Geometry: Seeing, Doing, Understanding  or Amazon.co.uk
The Opportunity Equation: Transforming Mathematics and Science Education for Citizenship and the Global Economy Recommended
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...
Stop Making Stupid Mistakes Recommended by Richard Rusczyk, Art of Problem Solving
You missed because you added wrong, bubbled the wrong answer on the answer sheet, misread the question, didn’t answer in the right units, didn’t…  You’ve been there. We all have. Maybe you’ve learned how to curb your errors, but if you’re reading this, you probably haven’t cut them down as much as you’d like.  Two keys to minimizing stupid mistakes are...
Why Memorize Math Facts? Recommended by Aimee
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...
Abstract Math Produces Tangible Learning, Study Finds in The Chronicle of Higher Education
Study Suggests Math Teachers Scrap Balls and Slices by Kenneth Chang, New York Times
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!
Activating 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)
Applying 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...
Arithmetic 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..."
The Art of Problem Solving, Volume 1: the Basics by Sandor Lehoczky and Richard Rusczyk
The Art of Problem Solving, Volume 2: and Beyond by Sandor Lehoczky and Richard Rusczyk
A problem-solving tutorial that can be used to prepare for mathematics competitions. Written at the high school level...
A 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)
Calculus 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 examples...
Can 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. schools...
Catering 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
Developing 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...
Developing 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 PAGE online professional development...
Discovering 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...
Education's 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 of problem...
The 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)
Foundations 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)
Good 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 programs...
Gender 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, long load)
Gifted 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...
How 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 improved “understanding”...
Immigrants' 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
Importance 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)
Individual Differences in Math Sense: "Give me the child at 7, and I will show you the man..." in the Eide Neurolearning Blog
"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 in school..."
Influences 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...
Is 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 Elementary Students
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
MASSIVE (Math and Science Song Information, Viewable Everywhere)
Database of over 2000 science and math songs...
Math Circles
Find 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 mathematics...
Math Education for Gifted Students edited by Susan K. Johnsen and James Kendrick
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...
The 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)
Mathematical 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...
Mathematical Reflections
Online journal of the AwesomeMath website...
Mathematical 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 mentoring.
Mathematically 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?
The Mathematics Calendar 2016 by Theoni Pappas
A problem a day, all year long!  Plus facts, curiosities, and challenging problems... 
bullet The Adventures of Penrose the Mathematical Cat: The Mathematical Cat
bullet Further Adventures of Penrose the Mathematical Cat
bullet Fractals, Googols and Other Mathematical Tales
bullet Math for Kids & Other People Too!
bullet The Joy of Mathematics
bullet More Joy of Mathematics: Exploring Mathematics All Around You
bullet Mathematics Appreciation
'Mathematics 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
Mathing 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...
Math Olympiad Contest Problems for Elementary and Middle Schools by George Lenchner
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)
Online Math League
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...
Parenting mathematically talented students in seventh grade and younger by Ann Lupkowski Shoplik
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?...
Parents' Observations of Kindergartners Who Are Advanced in Mathematical Reasoning by Michael D. Pletan, Nancy M. Robinson, Virginia W. Berninger, and Robert D. Abbott
What behaviors and abilities do young, mathematically precocious children display?  Are parents able to recognize such precocity?
Polydron by Polydron (ages 4+ and 7+ through middle and high school)
Polydron is the original manipulative, recognised in many countries as the world's leading resource for teaching Maths 2 and 3 dimensional geometry, design and technology. A major aid in developing spatial awareness. Polydron Classroom Pack and Polydron Frameworks Classroom Set or individual-size sets, Geometry Set, Frameworks Archimedean Solids Standard Set
Primed 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 up...
Sex 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 supporters
The 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...
Study 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)
Supplementing 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...
Teaching 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.
Teaching 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.” (requires Adobe Reader)
Tiered lessons: one way to differentiate mathematics instruction by Cheryll M. Adams
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...
United States of America Mathematical Olympiad and International Mathematical Olympiad
U.S. and International competition, held annually in over 80 countries...
USA Mathematical Talent Search NSA / CSS
Free (except for the cost of postage to mail student's solutions) mathematics competition open to all United States middle and high school students...
Virtual Math Club
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
What 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...
'Whole-group instruction' drags good math pupils down by Susan Goodkin and David G. Gold
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."
Why fewer women succeed in math by Nancy J. White,
Innate career leanings, not inferior ability, prompt calculating females to shun calculus, study finds.  The study also explains a glitch in the gender gap. Among those who score at the top of the heap in math, the girls also tend to excel verbally while the boys don't. Hence they have more choices, career-wise. Advantage: girls. "For the boys with high math ability, it's `This is my strength,'" explains the study's lead author, Stephen Ceci. "For the high-math girls, it's `This is one of my strengths.'"

Last updated December 01, 2020  

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