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Online Advanced Math Enrichment Courses
 One of our authors, Sandra Berger, recently pointed me toward a great Web site for parents of children needing extra math challenges beyond what’s offered in the classroom. Art of Problem Solving is a Web site geared to boost problem solving and other math skills through online courses, an interactive community, and textbooks for contest preparation.
The site’s newest focus is Math Jams, a series of online courses aimed at helping students in grades six and up who are planning to participate in MATHCOUNTS, a national mathematics contest. According to the site:
Math Jams are free online classes hosted by Art of Problem Solving for a variety of purposes. Some Math Jams are improvisational problem solving sessions, some are informational sessions about prominent programs, or college admissions, or other topics of interest to our students. Other Math Jams include reviews of major contests, such as the USAMTS or the AMC series of tests. Instructors employ the same Virtual Classroom for the Math Jams as used in our more structured online classes.
Upcoming courses include Introduction to Geometry (March 3–August 18, Mondays from 6:30 p.m. to 8 p.m. CST) and Introduction to Number Theory (February 28–May 15, Thursdays 6:30 p.m. to 8 p.m. CST). The Introduction to Geometry class includes a full course in geometry for students in grades 7–10 who have a strong background in the basics of algebra. The Introduction to Number Theory course covers fundamental principles in number theory, such as divisors and multiples, prime numbers, composite numbers, remainders, number bases, and modular arithmetic for grades 6–9.
To enroll, or for more information on the courses (including diagnostic tests), visit the Art of Problem Solving course information page.
In order to attend a Math Jam, you must first log on the Art of Problem Solving Forum, then click the Classroom button on the left panel of the site up to 15 minutes before the Math Jam begins. The Virtual Classroom should then open automatically. One of the biggest benefits I’ve found of this site is that the Math Jams courses and membership in the community forum are free—a great resource for parents!
Creative and Critical Thinking for Gifted Students through FPSPI
Saturday, January 12, 2008 - by CFertig - 439 Views - 0 Comments - Category: Math, Parents and Educators, Reading-Writing-L.A., Social Studies, General Education, Gifted and Talented Children, Gifted Education, Parenting Gifted Children, Teaching Gifted Children
We all have problems we’d like to solve. Some people aren’t very good at math. Some people have nosy neighbors. Some people go to bed hungry at night. No matter how small or how big the problems are, we’d like to solve them. It’s hard to solve a problem, though, unless we understand the problem very well. Who is involved in the problem? What is the problem? When and where does the problem occur? Why does the problem happen? How does it occur? The first step in successful problem solving is defining and describing the problem.
This is just one type of thinking fostered by FPSPI. The program (for students in grades 4–12) stimulates critical and creative thinking skills and encourages young people to develop visions for the future through both individual and team activities. It nurtures global awareness not only through choice of topics, but by knowing that the same problems are being studied by over 250,000 students annually, including those from Australia, Canada, Hong Kong, Korea, Malaysia, New Zealand, Russia, and the United States.
Curricular and co-curricular competitive activities, as well as non-competitive activities are offered.
Through FPSPI, students learn to
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formulate and attack complex, ambiguous problems
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analyze and better understand material
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improve in oral and written communication
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work together in a team.
You can get an idea of the scope of current and future topics by reading their descriptions at the program’s Web site.
2007-2008 Topics
Body Enhancement
Simulations Technology
Neurotechnology
Debt in Developing Countries
Child Labor
2008-2009 Topics
Olympic Games
Cyber Conflict
Space Junk
Counterfeit Economy
Pandemic
Even if your student never participates in the formal program, the organization’s website contains good instructional materials for creative and critical thinking. Materials include both written offerings available for purchase and also links to other Web sites.
Trends in Gifted Education
Friday, January 04, 2008 - by CFertig - 564 Views - 4 Comments - Category: Art, Label of Gifted, Math, Music, Parents and Educators, Reading-Writing-L.A., Science, Social Studies, Technology, General Education, Gifted and Talented Children, Gifted Education, Parenting Gifted Children, Teaching Gifted Children
The NAGC (National Association for Gifted Children) Convention was held in November. Each year, I like to read through the entire catalog of presentations so that I can form general impressions about categories that were considered important.
Disclaimer: I do not have access to information about presentation proposals that were submitted nor do I have information about how the presentations were chosen. I do not look at this information to make judgments; only to observe trends.
Like everything else in society, certain topics wax and wane. Someone else may interpret this very differently than I do. But, for the record, this is what I see.
Some of the topics that were considered top priorities in the past 10-30 years that I see no longer getting the same attention include
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Underachievement
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Multiple Intelligences
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Pullout/enrichment
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Advocacy
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GT resource teachers
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Affective issues
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Identification
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Learning Styles
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Differentiation
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Theory of giftedness
Topic trends that I do see increasing are
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The integration of technology into the curriculum rather than treatment as a separate subject
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Interest of programs on an international level (in fact, at the NAGC convention this year, a strand was added titled “International”)
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Special schools and programs
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Less talk about specifically meeting the needs of the gifted and more emphasis on the need for an increase in general academic rigor, including the need to let students advance at a faster speed
I would love to hear the ideas of others on these trends. You can always leave a comment at this blog entry or email me if you would prefer that others do not see your comments.
Science OCW Geared to AP Courses and Beyond
Friday, December 28, 2007 - by CFertig - 363 Views - 0 Comments - Category: Math, Parents and Educators, Science, Technology, Advanced Placement, Gifted and Talented Children, Gifted Education, Parenting Gifted Children, Teaching Gifted Children
Lately, we seem to be on a roll with more and more tools becoming available for advanced science students. (Click on the Science category in the column on the left of this Web page to see recent entries.) And now, yet another resource is available.
More and more very reputable universities are making available free video and audio clips, animations, lecture notes, and assignments online. Now MIT has taken that concept one step further and created Highlights for High Schools. This new site takes the information that MIT had already made available through what’s known as OpenCourseWare and has created a site that categorizes that information to match the Advanced Placement (AP) physics, biology, and calculus curricula.
The site also has just plain interesting, free courses appropriate for gifted high school students, including a class that teaches how to design sets for theater and one on designing toys (both under the heading of Knowledge in Action: Build Stuff).
There are also high school courses created by MIT students such as Guitar Building; a course exploring Gödel, Escher, and Bach; and Combinatorics, a fascinating branch of mathematics that applies to problems ranging from card games to quantum physics to the Internet.
You can also subscribe to an online newsletter that will keep you up-to-date on new courses and other information.
An estimated 10,000 U.S. high school teachers and 5,000 U.S. high school students already visit MIT OpenCourseWare each month, and MIT expects Highlights for High School to make MIT’s course materials even more useful to these audiences.
SAT Exam, Taken at Age 13, Can Predict Career Path of Gifted
Sunday, September 09, 2007 - by CFertig - 805 Views - 0 Comments - Category: Art, Math, Music, Parents and Educators, Reading-Writing-L.A., Science, Social Studies, Technology, Gifted and Talented Children, Gifted Education, Parenting Gifted Children, Teaching Gifted Children
A new study from Vanderbilt University finds that the future career path and creative direction of gifted youth can be predicted well by their performance on the SAT at age 13. The study offers insights into how best to identify the nation’s most talented youth, offering opportunities for educators and policymakers to develop programs to cultivate these individuals.
The current study looked at the educational and professional accomplishments of 2,409 adults who had been identified as being in the top 1% of ability 25 years earlier at age 13. Significant differences in the creative and career paths of individuals were found, with those showing more ability in math having greater accomplishments in science, technology, engineering, and mathematics, while those showing greatest ability on the verbal portion of the test going on to excel in art, history, literature, languages, drama, and related fields.
The key was to administer the SAT at a young age. When students take the test in high school, the most able students all score near the top, and individual differences are harder to see. Using the test with gifted students at a young age creates the potential to help shape that person’s education.
Overall, the creative potential of these participants was extraordinary, with individuals earning 817 patents and publishing 93 books.
With this knowledge, the policy question becomes: How best can we support these individuals, especially during their formative years?
For more information, see:
Girls and Science: What Are the Myths?
Since 1993, The National Science Foundation (NSF) has been working to broaden the participation of girls and women in science, technology, engineering, and mathematics (STEM). According to their Research on Gender in Science and Engineering program, there are five myths about girls and science.
- Myth: From the time they start school, most girls are less interested in science than boys are.
Reality: In elementary school there are about the same number of girls (66%) as boys (68%) who report liking science. But, by second grade, most students portray a scientist as a white male in a lab coat. Children often draw women scientists as severe and not very happy. There is a stereotype of the relationship between gender and careers in science. By eighth grade, boys are twice as interested in STEM careers as girls.
- Myth: Classroom interventions that work to increase girls' interest in STEM run the risk of turning off the boys.
Reality: Interventions that work to increase girl’s interest in STEM, such as showing images of women scientists, also increase such interest among the boys.
- Myth: Science and math teachers are no longer biased toward their male students.
Reality: Teachers, without realizing it, often treat boys differently than they do girls, explaining more to boys when asked for assistance, while just simplifying experiments for the girls.
Girls Creating Games was created as an afterschool and summer program designed to support the interest of middle school girls in computers and information technology. Its goal is to increase the number of females in the IT workforce.
- Myth: When girls just aren't interested in science, parents can't do much to motivate them.
Reality: Parental support has been shown to be crucial to a girl's interest in science, technology, engineering, and math. Parents can make girls aware of the range of science and engineering careers available, the relevance of these jobs in society, and the types of courses and grades necessary to put students on a path to a STEM career. A guide for parents can be found at Sally Ride Science.
- Myth: At the college level, changing the STEM curriculum runs the risk of watering down important "sink or swim" coursework.
Reality: Women often perceive "Bs" as inadequate grades and drop out, while men with "Cs" will persist with the class. Effective mentoring and "bridge programs" that prepare students for challenging coursework can counteract this. To help retain both women and men in engineering schools, programs should:
- have students work in pairs on programming in entry-level computer science and engineering courses, and
- provide coursework in spatial visualization.
One of the most effective interventions is mentoring. MentorNet, a virtual e-mentoring network and community offers award-winning, research-based, technology-leveraged mentoring programs that pair young people with professionals working in STEM careers in industry, government, and higher education.
Additional, helpful resources funded by the National Science Foundation are available online.
Many women have made significant contributions to the advancement of science. Go to Women in Science to hear some of their stories.
Incredible New Math, Science Web Site for the Gifted
Are you a precollege student who is passionate about math and science? The Center for Talented Youth (CTY) at Johns Hopkins University, along with eight partner organizations, recently launched a Web site that will feed your passion. The Web site, Cogito.org, means “I think.” Although most of the content at the site is available to the public, members have access to interactive features not available to everyone.
On Cogito.org, you can read news and features on topics ranging from global warming and biostatistics, to cold fusion and bioethics. You can explore the intersection of science and the arts, from computer animation, to science fiction. You can find great resources including book reviews, "Best of the Web" guides, and listings and reviews of summer and distance-education programs, internships, and academic competitions.
If you are a member, you can also participate in online interviews with experts in various fields and in discussion forums with other members. Membership also grants you access to the Cogito.org virtual library where you can find a wide variety of research materials and a librarian dedicated to helping you. Membership is currently offered by invitation only from Cogito Partners and Affiliates.
Cogito.org also publishes student-written work. Ideas must be submitted before sending actual drafts. Acceptable student submissions include full-length book and movie reviews, feature stories and articles, and essays. Also needed are Best of Web guides.
If you are a math and science buff, spend some time perusing the Cogito.org Web site. Just browsing the site will help you to become familiar with all that is available, but if you want to focus on a specific area, you can search using filters.
Study of Mathematically Precocious Youth After 35 Years
What does it take to create an intellectual leader like Albert Einstein or Stephen Hawking?
A report based on 35 years of research from the Study of Mathematically Precocious Youth was published on December 18 and reflects data collected from more than 5,000 participants. The report, from Vanderbilt University, reveals that a complex mix of factors is necessary to create these leaders: cognitive abilities, educational opportunities, investigative interests, and old-fashioned hard work. Both personal attributes and learning environments are required that are truly beyond the norm. While mathematical gifts and a variety of aptitudes have significant impact, special educational opportunities and commitment can dramatically increase this impact.
Researchers found that differences in ability exist even among the very top of this elite group. Researchers also found that the majority of the highest performers at age 33 were willing to work more than 65 hours a week.
Differences were revealed between men and women in types of abilities and interests. Female participants were more likely to prefer careers such as the social sciences, biology, and medicine, while men were more likely to prefer engineering and the physical sciences.
It will be interesting to follow the impact of this report and see if it has any influence on educational opportunities made available to students with top cognitive abilities who are also willing to work very hard.
Changes in Teaching Math—Implications for Gifted?
Friday, September 15, 2006 - by CFertig - 429 Views - 0 Comments - Category: Math
This week the National Council of Teachers of Mathematics (NCTM) announced a major shift in recommendations for teaching math. If its new recommendations have anywhere near the impact that the council’s 1989 report had, the teaching of math in American schools could witness a profound change. Although most states presently call for dozens of math topics to be addressed in each grade, the new NCTM report “Curriculum Focal Points” sets forth just three basic skills for each level. While the 1989 report downplayed memorization and emphasized children finding their own approaches to problems and writing about their reasoning, Dr. Chester E. Finn Jr., a Department of Education official in the Reagan administration, says the new report recommends a back-to-basics victory.
Math curricula in the United States today are often described as "a mile wide and an inch deep." We cover many topics, but we don’t study them in depth. Parents without a strong understanding of math often feel that children who understand how to add, subtract, multiply, and divide at an early age are extremely advanced in the subject and should be accelerated. This is actually what might be called “superficial math.” These children can often rattle off math facts or do problems quickly, but they do not have a deep understanding of mathematics. There is so much more to learn.
Because “Curriculum Focal Points” was just released, I have not yet seen any discussion of possible implications for students who are gifted in mathematics. We will all need to pay attention to how this will play out.
Math Competitions for Gifted Students
Sunday, February 05, 2006 - by CFertig - 485 Views - 0 Comments - Category: Math
One needs to plan well in advance to set up mathematics competitions. It is not too early to start planning for next year. Just choosing which competitions to participate in is a challenge. Many of the sites below list sample problems, so you can get a taste of what it’s like to participate. While most competitions are for high school students, there are a handful at the middle school/junior high level, and just a few at the elementary level. When a range of grade levels is listed, there are usually competitions set up for just one or two grades at a time (i.e., a test for each of grades 3-4, 5-6, and 7-8). Here are some competitions to consider.
High school students and some exceptional junior high students
High school students
High school students
High school students
High school students
Grades 4-12
Grades 4-8
Grades 6-12
Middle school
Grades 3-12
Middle and high school students
Children Gifted in Math
Sunday, April 17, 2005 - by CFertig - 521 Views - 1 Comments - Category: Math
Mary recently made the following comment in response to one of my postings:
My son, Michael, is a sixth grader and is really smart in math. Last summer he went to a summer program for kids interested in mathematics at the local university and loved getting to do the advanced math that he was exposed to there. But, there isn't a gifted program at his school.
While he's making good grades in his math class, he finds it too easy and boring. What do you think I should do? He's got such a talent for this, and I hate to see him so bored with something he loved so much last summer.
Mary, you are asking a very big question. Of course I can’t give specific advice for your son since I don’t know him, but I can give you some general information. Also, let’s ask our fellow bloggers. If anyone reading this posting has additional advice or comments, please post a response.
Assessment
First of all, it would be helpful to get a professional assessment of your son’s math abilities. Hopefully, you have already had a conversation with Michael’s math teacher. Talking to the teacher is always the first place to start. How does the teacher see Michael in relationship to other students in the classroom?
Second, if there is a gifted/talented resource teacher at the school or in the district I would talk with that person next to see what is available. You said that Michael's school doesn't have a gifted program, but there still may be a resource person who can help.
Standardized tests that have been given by your district will also help to shed some light on his abilities. You will find some good information on this by reading the ERIC Digest article, Discovering Mathematical Talent. Working with the School
Once you understand Michael’s mathematical abilities more clearly, you will want to educate yourself with current research on addressing the needs of high-ability, gifted, and highly motivated students in general and more specifically in math.
A Nation Deceived: How Schools Hold Back America’s Brightest Students is a recently released report that can be downloaded over the Internet. The report advances the merits of acceleration—not just grade-skipping, but the many ways available that schools can accommodate the needs of students who are more advanced. This includes advancing them within the regular classroom.
Once you have an understanding of some of the background research available, you will be better prepared to advocate for Michael at school. Another book that will help you with this is Developing Math Talent: A Guide for Educating Gifted and Advanced Learners in Math. This book is for both parents and teachers. The authors provide concrete suggestions for identifying mathematically talented students, tools for instructional planning, and specific programming approaches. It also provides concrete strategies for effectively advocating for gifted children with math talent.
One word of caution: In the U.S. we are often criticized for having a math curriculum that is "a mile wide and an inch deep." Rather that just accelerating students in math, it is highly recommended that students be given the opportunity to explore topics in depth. The article, High-Ability and Highly Motivated Students provides suggestions for students to think deeply in mathematics by investigating complex problems.
After-School Activities
Does Michael’s school have before and after school clubs? Are there any math clubs or competitions in which he might participate? If there are no such activities at his school, can you find these elsewhere in your community? You mentioned that last summer he attended a class at a local university. Are there similar classes that are held during the school year?
A number of well-respected universities offer multimedia, computer-based, distance-learning courses in math. You might explore one of these. Students who are most successful with these programs are those who are able to stay motivated while working independently. Information on the courses can be found at Stanford University, Johns Hopkins University, and Northwestern University.
I wish you the best with all of this. Please let us know what works for you. Being an advocate for your student can be a lot of work, but with a positive and understanding attitude, you will be successful.
Enrichment for Gifted Children in Math
Sunday, March 13, 2005 - by CFertig - 1080 Views - 8 Comments - Category: Math
Though a somewhat controversial theory, the teaching of mathematics in the United States is often criticized as being “a mile wide and an inch deep.”
Students who are gifted or have strengths in mathematics benefit greatly by exploring math concepts in-depth. Listed below are some of my favorite publishers of materials that offer great math enrichment. Included here are higher-level thinking opportunities that are challenging and exciting for these students. Your students will love these!
AIMS Education Foundation
This publisher produces K-10 activity resource books and a magazine/newsletter. I especially like the Historical Connections books. These are geared to grades 4-10 and come in three volumes that connect history and mathematics. Each of three volumes explores the lives of 30 mathematicians. Ready-to-use classroom activities are provided that help students “discover” the theories and work of each mathematician.
Continental Mathematics League, Inc.
This is actually a competition, but you don’t have to participate to benefit from this organization. Instead, you can buy books that contain some of the best math questions that are used in the competition. These books can be purchased for grades 2-3, 4-6, and 7-9. Each book contains individual problems that will really make your students think. It is extremely helpful for students to talk through the different strategies used in solving the problems, as there are often many different possible approaches.
Creative Publications
Once you arrive at this site, click on “Creative Publications.”
This publisher includes a wide variety of books that use manipulatives and contain critical thinking activities. Some of my favorites are Think About It!, which is a collection of daily and weekly math challenges for grades 4-8 and The Problem Solver Binders, which teaches specific strategies for solving problems in grades 1-8
The Critical Thinking Co.
You will find that the Mind Benders, designed for pre-K – 8+ is very challenging. While this logic-problem series is not strictly math, it involves many of the same skills used in math, such as determining what information is relevant in a problem and the logic of solving a problem.
ETA Cuisenaire
This K-12 math catalog is filled with all kinds of wonderful products from a variety of publishers. There are basic manipulative materials, games, books, and posters. I especially like their Mental Math books for primary, middle grades, and junior high. These books teach students strategies for doing amazing calculations in their heads. There are also many enrichment books that use common items like dominoes, dice, and playing cards. These books provide inexpensive activities that will extend the math curriculum in exciting ways. Books using tessellations and paper folding provide enrichment in geometry and the power of patterns.
Interact
Interact publishes fun-filled simulations using integrated theme units. There are math units for grades 1-12 where students take on a variety of “real-life” roles, acting out scenarios and solving problems. Every teacher I know who has used units from Interact has nothing but praise for them. Units cover all aspects of math, including basic facts, probability, geometry, algebra, problem solving, etc.
Mathematics Pentathlon Program
Pentathlon games are open-ended, higher-level thinking games that involve math and general problem-solving. The games are used in competitions, but may also be used by themselves as extensions in the classroom. Games are divided into divisions of grades K-1, 2-3, 4-5, and 6-7. Like chess or Scrabble, the games can be played at different levels from just making basic moves to incorporating complex strategies. The games are expensive, but excellent.
Prufrock Press Inc.
When arriving at this website, click on “Activity Books and Lessons for Teaching Gifted Children,” then “Mathematics.” You will find a wide variety of books for grades K-12 that are filled with enriching extensions to the math curriculum.
Sunshine Math Superstars
Published by the Panhandle Area Educational Consortium in Florida, this K-8 program is designed as enrichment for self-directed learners in mathematics. These weekly problem-solving activities can be managed by trained parents or by classroom teachers.
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